ON THE USES OF CONSUPER'S SURPLUS MEASURES
by
I r e n e Malinda Gordon
B.A.,
Honours, Simon F r a s e r U n i v e r s i t y , 1976
A THESIS SUBMITTED I N PARTIAL mFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ARTS
i n t h e Department
0f
Economics and Commerce
0
IRENE MALINDA GORDON 19 76
SIMON FRASER UNIVERSITY
November, 19 76
A l l r i g h t s r e s e r v e d . T h i s t h e s i s may n o t b e r e p r o d u c e d i n whole o r
i n p a r t , by photocopy o r o t h e r means, w i t h o u t p e r m i s s i o n o f t h e a u t h o r .
APPROVAL
Name :
I r e n e Malinda Gordon
Degree :
Master o f A r t s
T i t l e of Thesis :
On t h e Uses o f consumer's S u r p l u s Measures
Examining Commit t e e :
Chairman:
Zane A. S p i n d l e r
.
~ a c kL ~
Senior sup
n
visdr
r
?
~
TAothaf E-. B o r c h e r d i n g
&
M&$
Barker
Department of Geography
Simon F r a s e r U n i v e r s i t y
Date Approved:
November 23, 1976
PARTIAL COPYRIGHT LICENSE
I h e r e b y g r a n t t o Simon F r a s e r U n i v e r s i t y t h e r i g h t t o lend
my t h e s i s o r d i s s e r t a t i o n ( t h e t i t l e o f which i s shown b e l o w ) t o u s e r s
of t h e Simon F r a s e r U n i v e r s i t y L i b r a r y , and t o make p a r t i a l o r s i n g l e
c o p i e s o n l y f o r s u c h u s e r s o r i n r e s p o n s e t o a r e q u e s t from t h e l i b r a r y
o f a n y o t h e r u n i v e r s i t y , o r o t h e r e d u c a t i o n a l i n s t i t u t i o n , on i t s own
b e h a l f o r f o r one of i t s u s e r s .
I f u r t h e r agree t h a t permission f o r
m u l t i p l e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d
b y me o r t h e Dean of Graduate S t u d i e s .
It i s u n d e r s t o o d t h a t c o p y i n g
o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d
w i t h o u t my w r i t t e n p e r m i s s i o n .
T i t l e of ~ h e s i /s X M ~ ! A X m x
On t h e U s e o f Consumer's S u r p l u s Measures
Author
;
(signature)
I r e n e M a l i n d a Gordon
(date)
Abstract
The c o n c e p t of consumer's s u r p l u s i s o f t e n used when e c o n o m i s t s
a r e d e c i d i n g how s c a r c e r e s o u r c e s s h o u l d b e employed.
This i s a
measure o f t h e b e n e f i t s which a c c r u e , above t h e c o s t s , t o t h e u s e r s o f
the resource i n question.
two t y p e s o f q u e s t i o n s .
Consumer's s u r p l u s i s measured b a s i c a l l y by
One i s "What w i l l you pay t o u s e x?" and t h e
o t h e r i s , "What compensation would you r e q u i r e t o f o r e g o X?"
The
answers t o t h e s e two q u e s t i o n s a r e c o n s i s t e n t l y d i f f e r e n t i n d o l l a r
value.
The c u r r e n t e x p l a n a t i o n of t h e d i f f e r e n c e r e v o l v e s around t h e f a c t
t h a t e m p i r i c a l l y w e c a n n o t h o l d t h e m a r g i n a l u t i l i t y of income c o n s t a n t .
Although t h i s e x p l a n a t i o n i s c o r r e c t from a t h e o r e t i c a l p o i n t of view,
i t was f e l t t h a t t h i s r e a s o n d i d n o t a c c o u n t f o r t h e t o t a l o b s e r v e d
d i f f e r e n c e between t h e two answers.
R e f e r e n c e i s made t o a n a r t i c l e by
Henderson (1941) where t h e c o n s t a n c y o f t h e m a r g i n a l u t i l i t y o f income
i s n o t assumed and where Henderson c l a i m s t h a t t h e measures of consumer's
surplus w i l l l i e close together.
I n t h e p r e s e n t e s s a y t h e a p p a r e n t i n c o n s i s t e n c y between t h e c u r r e n t
e x p l a n a t i o n and Henderson's view i s examined by d i s c u s s i n g t h r e e t o p i c s .
I n t h e f i r s t s e c t i o n t h e t h e o r y o f consumer's s u r p l u s i s d i s c u s s e d .
t h e second two e m p i r i c a l s t u d i e s were examined.
In
I n t h e t h i r d explan-
a t i o n s which c o u l d a i d i n p a r t i a l l y e x p l a i n i n g t h e l a r g e v a r i a n c e between
t h e two measures a r e examined.
From t h e s e d i s c u s s i o n s , i m p l i c a t i o n s were drawn f o r t h e usage o f
t h e two measures.
A major c o n c l u s i o n which r e s u l t e d was t h a t t h e u s u a l
e x p l a n a t i o n f o r t h e v a r i a t i o n i n b e n e f i t measures, t h e constancy o f t h e
m a r g i n a l u t i l i t y o f income, i s n o t a s u f f i c i e n t e x p l a n a t i o n a l o n e .
I would l i k e t o acknowledge t h e f i n a n c i a l s u p p o r t p r o v i d e d
by t h e B r i t i s h Columbia Hydro and Power A u t h o r i t y a s a p a r t o f a
r e s e a r c h g r a n t t o Simon F r a s e r U n i v e r s i t y .
Thanks a r e a l s o i n o r d e r
t o M r . W i l l i a m F. S i n c l a i r and M r . Rob Morley f o r t h e f i s h i n g s u r v e y
d a t a and f o r answering many q u e s t i o n s c o n c e r n i n g t h e d a t a .
I would l i k e t o thank M r . John Yu and M r . E r n i e Danow o f t h e
S .F.U.
Computing C e n t r e f o r t h e computer programming a s s i s t a n c e
t h e y p r o v i d e d and Mrs. Donna Popovic f o r h e r t y p i n g and e d i t o r i a l
assistance
.
T h i s t h e s i s h a s b e n e f i t t e d from t h e d i s c u s s i o n s and from t h e
e d i t o r i a l comments o f my s u p e r v i s o r y committee, J a c k L . Knetsch and
Thomas E. Borcherding.
Boland, M r .
A thank you i s a l s o i n o r d e r t o D r . L.A.
S . E a s t o n and D r . D.R.
Maki f o r d i s c u s s i n g s p e c i f i c
p o i n t s w i t h me i n t h e c o u r s e of w r i t i n g t h i s e s s a y .
I r e n e Malinda Gordon
Table of Contents
Page
CIIAPTER I :
CHAPTER 11:
Introduction
1
F o o t n o t e s t o Chapter I
4
Consumer's S u r p l u s
5
M a r s h a l l ' s D e f i n i t i o n of Consumer's
Surplus
6b
Comparison o f t h e M a r s h a l l i a n and
H i c k s i a n Consumer's S u r p l u s e s
Small v e r s u s Large V a r i a n c e i n
Consumer's S u r p l u s Measures
CHAPTER I11 :
F o o t n o t e s t o C h a p t e r I1
16
Two E m p i r i c a l S t u d i e s
20
E m p i r i c a l S t u d i e s and Consumer's S u r p l u s
20
Environment ~ a n a d a ' sS p o r t F i s h i n g Survey
25
R e g r e s s i o n s and R e s u l t s
F o o t n o t e s t o Chapter I11
CHAPTER I V :
E x p l a n a t i o n s o f V a r i a t i o n s i n Consumer's
S u r p l u s Measures
41
Income E l a s t i c i t y a s an E x p l a n a t i o n of
Variance
41
P r o p e r t y R i g h t s and N o n - I n t r i n s i c B e n e f i t s
42
I n t e r n a l R a t e s of Return a s an E x p l a n a t i o n
44
O p t i o n Demand a s a n E x p l a n a t i o n
47b
S t r a t e g i e s , Welfare Loss and D i s c o n t i n u o u s
Utility
49
A l l o r None Demand Curves
52b
Footnotes t o Chapter I V
- v -
Page
CfItlPTER V:
Conclus i o n
61
APPENDIX A:
S p o r t F i s h Survey
66
BIBLIOGRAPHY
95
L i s t of T a b l e s and C h a r t s
Page
TABLE I :
Condensed T a b l e s from Environment
Canada's T a b l e IV.l r e p r o d u c e d i n
Appendix A
26a
TABLE 11:
Variables Selected f o r Regression
2 7a
TABLE 111:
E x p l a n a t i o n o f Dummy V a r i a b l e s
28a
TABLE I V :
W i l l i n g n e s s t o Pay R e g r e s s i o n R e s u l t s
31a
TABLE V :
Compensation R e q u i r e d R e g r e s s i o n R e s u l t s
32 a
CHART I:
Compensation R e q u i r e d a n d Age
4 7a
-
vii -
L i s t o f Diagrams
Page
FIGURE I :
FIGURE 11:
FIGURE 111:
FIGURE I V :
FIGURE V:
Consumer's S u r p l u s as a n Area Under
t h e Demand Curve
6a
Consumer's S u r p l u s as a V e r t i c a l
D i s t a n c e Between I n d i f f e r e n c e Curves
(The M a r g i n a l U t i l i t y o f Income Held
Constant)
7a
Consumer's S u r p l u s as a V e r t i c a l
D i s t a n c e Between I n d i f f e r e n c e Curves
(The M a r g i n a l U t i l i t y o f Income Not
Held Constant)
lla
T h r e e Demand Curves a n d t h e A s s o c i a t e d
Prices
52a
Consumer's S u r p l u s as a V e r t i c a l
D i s t a n c e Between I n d i f f e r e n c e Curves
(The M a r g i n a l U t i l i t y o f Income Held
Constant)
53 a
-
viii
-
CHAF'TER I
Introduction
B e n e f i t - c o s t a n a l y s i s i s w i d e l y used i n d e t e r m i n i n g t h e d e s i r a b i l i t y o f contemplated i n v e s t m e n t s .
The i n t e n t of s u c h a n a n a l y s i s
i s t o g i v e an e x p l i c i t c a l c u l a t i o n of r e s o u r c e s r e q u i r e d f o r s u c h a n
u n d e r t a k i n g ( u s u a l l y i n monetary terms) and t h e e x p e c t e d g a i n s o r
b e n e f i t s , g i v e n i n commensurate terms.
In general, a benefit-cost
a n a l y s i s i s a comparison of t h e g a i n s and t h e c o s t s of i n v e s t i n g
resources i n available projects.
The u s e of b e n e f i t - c o s t
analysis
h a s been p a r t i c u l a r l y u s e f u l i n j u d g i n g t h e economic f e a s i b i l i t y of
public actions.
The a d v a n t a g e s of a b e n e f i t - c o s t
a n a l y s i s i s t h a t t h i s t y p e of
. s t u d y e n a b l e s economists t o examine problems which a r e d i f f i c u l t t o
evaluate.
Examples of d i f f i c u l t e v a l u a t i o n problems a r e e x t e r n a l i t i e s ,
non-market p r i c e d goods and p u b l i c goods.
S i n c e t h e s e goods a r e n o t
s o l d i n any m a r k e t , no p r i c e , and c o n s e q u e n t l y , no r e a d i l y a v a i l a b l e
monetary v a l u a t i o n , i s a s s o c i a t e d w i t h them.
The b e n e f i t - c o s t
analysis
p r o v i d e s a method which i s c a p a b l e of i n c l u d i n g t h e v a l u e of b o t h
p o s i t i v e and n e g a t i v e c h a r a c t e r i s t i c s of a good.
T h i s i s accomplished
by d e t e r m i n i n g how a good, s u c h a s a s p i l l o v e r , a f f e c t s s o c i e t y a s a
whole even though no market p r i c e e x i s t s (Mishan, 1 9 7 5 , x - x i ) .
I
U n f o r t u n a t e l y , t h e measurement of t h e b e n e f i t s and c o s t s of
r e s o u r c e s which do n o t have a market v a l u e i s more d i f f i c u l t t h a n i f a
w e l l f u n c t i o n i n g market e x i s t e d .
p l a c e d on i n d i r e c t t e c h n i q u e s .
Methods v a r y , and r e l i a n c e i s o f t e n
I n d i r e c t methods o f v a l u a t i o n a r e
r e q u i r e d where no o t h e r v a l u e such a s a market p r i c e e x i s t s .
Many o f t h e v a l u a t i o n t e c h n i q u e s a t t e m p t t o measure i n one way o r
a n o t h e r consumer's s u r p l u s .
Consumer's s u r p l u s i s o f t e n r e p r e s e n t e d
by two measures, t h e compensating and t h e e q u i v a l e n t v a r i a t i o n s .
These
two measurements may e s s e n t i a l l y be d e f i n e d by two q u e s t i o n s .
The f i r s t q u e s t i o n i s o f t h e type o f "What a r e you w i l l i n g t o pay
t o continue using a resource?"
This question represents the price-
compensating o r w i l l i n g n e s s t o pay measure o f consumer' s s u r p l u s .
11
What compensation would you r e q u i r e i n o r d e r t o s t o p u s i n g a re-
s o u r c e ? " i s r e p r e s e n t a t i v e o f t h e second type o f q u e s t i o n .
This question
i s u t i l i z e d to discern t h e price-equivalent o r willingness to s e l l
measure ( K r u t i l l a , e t . a l . ,
1972, 96-7; Hammack and Brown, 1974, 6 ) .
E m p i r i c a l s t u d i e s have shown t h e answers t o t h e two q u e s t i o n s c i t e d
t o be very d i f f e r e n t .
For example, one s t u d y (Hammack and Brown, 1974,
27) found t h a t t h e mean v a l u e t o t h e f i r s t q u e s t i o n was $247 w h i l e f o r
t h e second q u e s t i o n t h e mean v a l u e was $1,044.
When r e f e r r i n g t o t h e
v a l u e s a s s o c i a t e d w i t h t h e compensated v a r i a t i o n and t h e e q u i v a l e n t
v a r i a t i o n r e s p e c t i v e l y , s u c h d i f f e r e n c e s i n answers might, i n p r i n c i p l e ,
b e e x p e c t e d when t h e constancy o f t h e m a r g i n a l u t i l i t y o f income does
n o t hold1 ( K r u t i l l a and F i s h e r , 1975, 29; S t i g l e r , 1966, 78-81).
This
h a s been t h e u s u a l e x p l a n a t i o n o f f e r e d f o r t h e v a r i a t i o n e n c o u n t e r e d .
The commonly o b s e r v e d d i f f e r e n c e s , however, a r e n o t l i k e l y t o b e p r e d i c t e d t o b e a s l a r g e a s t h o s e found and e s p e c i a l l y n o t f o r t h e range o f r e a l
incomes b r o u g h t a b o u t by t h e contemplated change i n r e s o u r c e a l l o c a t i o n s .
One e x p l a n a t i o n o f t h e d i f f e r e n c e s n o t e d i n t h e s u r v e y r e s u l t s i s t h e
method o f i n f o r m a t i o n e x t r a c t i o n such a s d e f i c i e n c i e s i n t h e survey
itself.
However, w h i l e shortcomings may be common, t h e r e s u l t s a r e
c o n s i s t e n t o v e r a l l of t h e s t u d i e s o f t h e i s s u e and t h e r e seems f a r too
l a r g e a d i f f e r e n c e t o be a s c r i b e d t o t h i s s o u r c e .
T h i s remaining o b s e r v e d v a r i a t i o n be tween t h e two r e s p o n s e s c a u s e s
a problem o f u n d e r s t a n d i n g a s t h e r e i s no reason t o b e l i e v e on t h e b a s i s
o f t h e u s u a l e x p l a n a t i o n t h a t t h i s d i f f e r e n t i a l s h o u l d b e o f such a l a r g e
magnitude.
Economic e x p l a n a t i o n s o f t h e d i f f e r e n c e i n answers have
c e n t e r e d on t h e income c o n s t r a i n t and t h e income e f f e c t s ( K r u t i l l a and
F i s h e r , 1975, 29-30).
However, t h e s e e x p l a n a t i o n s o f t h e v a r i a n c e do
n o t seem s u f f i c i e n t i n e x p l a i n i n g a l l t h e o b s e r v e d d i f f e r e n c e .
w i t h t h e problem o f u n d e r s t a n d i n g ,
Along
t h e r e i s t h e p a r a l l e l o n e o f choosing
a n a p p r o p r i a t e measure i n p a r t i c u l a r i n s t a n c e s o f a l l o c a t i o n d e c i s i o n s .
T h i s e s s a y p r e s e n t s a n o t h e r s t u d y o f r e s o u r c e e v a l u a t i o n where
t h e r e i s a wide v a r i a t i o n i n t h e two o b s e r v e d measures.
Then an a t t e m p t
i s made t o s u g g e s t f u r t h e r r e a s o n s f o r t h e l a r g e d i f f e r e n c e s i n magnitude
between t h e answers.
T h i s w i l l b e accomplished by examining f o u r t o p i c s .
F i r s t , t h e t h e o r y o f consumer's s u r p l u s w i l l be d i s c u s s e d .
This
g e n e r a l d i s c u s s i o n w i l l p r i m a r i l y d e s c r i b e t h e way t h i s t h e o r y i s used
i n economics.
The second t o p i c w i l l b e an a t t e m p t t o p r e s e n t two s e t s
o f s u r v e y d a t a i n o r d e r t o show t h a t t h e l a r g e v a r i a n c e i n answers i s
n o t a c h a r a c t e r i s t i c o f j u s t one survey.
The t h i r d s e c t i o n d e s c r i b e s s e v e r a l p o s s i b l e e x p l a n a t i o n s f o r t h e
v a r i a n c e such a s p r o p e r t y r i g h t s
t e r n a l r a t e s of return.
, income
e f f e c t s , p s y c h i c b e n e f i t s and i n -
The i d e a t h a t t h e respondent may s e e h i m s e l f i n
two d i f f e r e n t r o l e s i s a l s o d e s c r i b e d i n t h e t h i r d c h a p t e r .
Finally, the
e s s a y draws c o n c l u s i o n s and i m p l i c a t i o n s from t h e p r e c e d i n g d i s c u s s i o n s .
FOOTNOTES
1
The c o n s t a n c y o f t h e m a r g i n a l u t i l i t y of money means t h a t
t h e income e l a s t i c i t y i s e q u a l t o one.
Another i n s t a n c e where
t h e two consumer's s u r p l u s measures would b e e q u i v a l e n t i s where
homo t h e t i c u t i l i t y c u r v e s a r e i n v o l v e d .
The concept of h o m o t h e t i c i t y
i n v o l v e s c h a r t i n g t h e p o i n t s a consumer r e v e a l s a s p r e f e r r e d when
h i s income i s changed.
I f t h e changes i n income r e v e a l b u n d l e s of
goods which can b e c h a r t e d on a s t r a i g h t l i n e o u t o f t h e o r i g i n ,
t h e n t h e s i t u a t i o n i s a h o m o t h e t i c one even i f t h e i n d i f f e r e n c e
c u r v e s become i n c r e a s i n g l y f u r t h e r a p a r t .
Samuelson r e f e r s t o t h 5 s
p r i n c i p l e as l i n e a r t r a n s f o r m a t i o n s o f u t i l i t y c u r v e s
(Samuelson,
1965, 1 7 5 ; H a r b e r g e r , 1971, 1 8 8 ) .
T h i s p r o p o s i t i o n then s a y s t h a t t h e two consumer's s u r p l u s
measures may b e e q u i v a l e n t even though t h e i n d i f f e r e n c e c u r v e s a r e
not vertically parallel.
Consequently, t h i s i l l u s t r a t e s t h a t t h e
l a c k o f t h e constancy o f t h e m a r g i n a l u t i l i t y o f money cannot c a u s e
t h e consumer's s u r p l u s measures t o be d i f f e r e n t
241).
(T. Rader, 1972,
-
5
-
CHAPTER I1
Consumer's S u r p l u s
P u b l i c i n v e s t m e n t p r o j e c t s must b e e v a l u a t e d i n o r d e r t o d e t e r mine w h e t h e r t h e y w i l l b e n e f i t t h e p u b l i c .
Evaluating public p r o j e c t s
i s a matter o f comparing t h e c o s t s o f t h e p r o j e c t t o t h e b e n e f i t s
which w i l l r e s u l t from t h e i n v e s t m e n t .
I n o r d e r t o e v a l u a t e an
i n v e s t m e n t i t i s n e c e s s a r y t o g a i n a measure o f t h e c o s t s and
benefits.
One method o f measuring t h e consequences i s t o a s k t h e benef i c i a r i e s how t h e y would v a l u e a p r o j e c t .
T h i s measurement i s
assumed t o be t h e a r e a b e n e a t h t h e market demand curve f o r t h e o u t p u t s of t h e u n d e r t a k i n g .
T h i s a r e a under t h e demand curve i s
commonly taken t o b e a measure o f t h e consumer's s u r p l u s .
I f the
v a l u e i d e n t i f i e d a s t h e consumer's s u r p l u s i s g r e a t e r t h a n t h e c o s t s
o f a p r o j e c t , t h e n t h e i n v e s t m e n t w i l l u s u a l l y b e undertaken.
1
Consumer's s u r p l u s , , 2 t h e n , i s used i n t h i s manner t o r e p r e s e n t t h e
a g g r e g a t e d 3 n e t w e l f a r e g a i n t o s o c i e t y when a p r o j e c t i s t o b e
initiated.
4
The two e c o n o m i s t s most o f t e n c r e d i t e d w i t h d e f i n i n g consumer's
c e r t a i n a s p e c t s o f Marshalls u r p l u s a r e M a r s h a l l and ~ i c k s . While
~
i a n and H i c k s i a n consumer's s u r p l u s a r e s i m i l a r , t h e major d i f f e r e n c e s a r e a l s o o f c o n s i d e r a b l e importance.
These d i f f e r e n c e s and
s i m i l a r i t i e s o f t h e M a r s h a l l i a n and H i c k s i a n consumer's s u r p l u s views
w i l l b e compared i n t h e f o l l o w i n g s e c t i o n s .
0
0
0
0
0
N
e
(It
(It
II
II
d
PI
rl
hl
PC
M a r s h a l l ' s D e f i n i t i o n of Consumer's S u r p l u s
The term consumer's s u r p l u s was e x p l a i n e d by M a r s h a l l a s t h e
g a i n s d e r i v e d by an i n d i v i d u a l o v e r and above t h e p r i c e he pays f o r
a good.
The e x c e s s b e n e f i t s a r e r e p r e s e n t e d by what an i n d i v i d u a l
would b e w i l l i n g t o pay, above t h a t which he does pay, r a t h e r t h a n
do w i t h o u t t h e good
( M a r s h a l l , 1920, 1 0 3 ) .
The example which M a r s h a l l employed t o i l l u s t r a t e consumer's
surplus deals with t e a
( l i a r s h a l l , 1920, 104-5).
In Marshall's
example t h e consumer i s f i r s t f a c e d w i t h a s i t u a t i o n where t e a
c o s t s $20.00 p e r pound.
one pound of t e a .
A t t h i s p r i c e , t h e i n d i v i d u a l purchases
I f t h e p r i c e of t e a were t o f a l l t o $14.00 a pound,
t h e consumer i n t h i s c a s e buys two pounds o f t e a a t $14.00 each.
S i n c e t h e consumer p a i d $20.00 f o r t h e f i r s t pound o f t e a and now
pays o n l y $14.00, he s a v e s $6.00.
T h i s $6.00 i s e q u a l t o o r g r e a t e r
t h a n t h e e x c e s s b e n e f i t s which t h e consumer d e r i v e s from t h e f i r s t
pound o f t e a .
M a r s h a l l ' s concept o f consumer's s u r p l u s can b e r e p r e s e n t e d i n
a diagram.
Using t h e f i g u r e s from M a r s h a l l ' s example, p r i c e i s on
t h e v e r t i c a l a x i s and t e a i s on t h e h o r i z o n t a l a x i s .
c u r v e as drawn i l l u s t r a t e s two assumptions.
The demand
F i r s t , t h e demand curve
i s drawn a s a s t r a i g h t l i n e which i m p l i e s t h a t t h e good is i n f i n i t e l y
divisible.
The second assumption i s t h a t t e a i s a normal good.
6
T h i s assumption e n s u r e s t h a t t h e demand curve i s downward s l o p i n g .
The consumer's s u r p l u s f o r a p r i c e o f $14.00 p e r pound i n F i g u r e
I i s t h e shaded t r i a n g l e BP2A.
T h i s shaded a r e a r e p r e s e n t s t h e e x c e s s
b e n e f i t s which t h e consumer d e r i v e s above t h e p r i c e p a i d a s d e s c r i b e d
by M a r s h a l l .
Comparison of t h e M a r s h a l l i a n and H i c k s i a n Consumer's S u r p l u s e s
A more s a t i s f a c t o r y method o f i l l u s t r a t i n g b o t h t h e M a r s h a l l i a n
and H i c k s i a n consumer's s u r p l u s measures i s through t h e u s e of i n d i f f e r ence curves.
By drawing i n d i f f e r e n c e c u r v e s , t h e d e p i c t i o n and t h e
d i s c u s s i o n of f o u r consumer's s u r p l u s measures, two M a r s h a l l i a n and
two H i c k s i a n , i s made c l e a r e r .
F i g u r e I1 r e p r e s e n t s t h e f o u r consumer's s u r p l u s e s .
Marshall's
consumer's s u r p l u s measures a r e based on " t h e e x c e s s of t h e p r i c e
which ( t h e consumer) would b e p r e p a r e d t o pay r a t h e r t h a n do w i t h o u t
( t h e g o o d ) , o v e r t h a t which h e a c t u a l l y d o e s pay''
,
( M a r s h a l l , 1920,
103).
H i c k s ' two v e r s i o n s of consumer's s u r p l u s a r e drawn from t h e
following :
...
t h e b e s t way o f l o o k i n g a t consumer's s u r p l u s i s
t o r e g a r d i t a s a means of e x p r e s s i n g i n terms of
money income, t h e g a i n which a c c r u e s t o t h e consumer
as a r e s u l t i n t h e f a l l i n p r i c e . O r b e t t e r , i t i s
t h e compensating v a r i a t i o n i n income, whose l o s s
would j u s t o f f s e t t h e f a l l i n p r i c e and l e a v e t h e
consumer no b e t t e r o f f t h a n b e f o r e (Hicks, 1939, 40-41).
Although Hicks and M a r s h a l l d e s c r i b e consumer's s u r p l u s i n
terms of money, t h e s e sums a r e n o t t h e same u n l e s s a s p e c i a l cond i t i o n h o l d s (Henderson, 1941, 1 1 7 ; P a t i n k i n , 1963, 93-5).
This
s p e c i a l c o n d i t i o n which must h o l d i n o r d e r t o make t h e H i c k s i a n and
M a r s h a l l i a n s u r p l u s e s e q u a l i s t h e assumption t h a t t h e m a r g i n a l
u t i l i t y of income i s c o n s t a n t a t l e a s t o v e r a given range7 ( S t i g l e r ,
1966, 78-81).
S t a t i n g t h a t m a r g i n a l u t i l i t y of income i s c o n s t a n t o v e r
t h e range of from one t o two thousand d o l l a r s i s t o s a y t h a t a consumer
d e r i v e s t h e same u t i l i t y from h i s one thousandth d o l l a r o f income a s he
T h i s means t h a t income i s n o t sub-
d o e s from h i s two thousandth d o l l a r .
j e c t t o d i m i n i s h i n g m a r g i n a l u t i l i t y o r d i m i n i s h i n g marginal r a t e s o f
s u b s t i t u t i o n o v e r t h i s range.
F i g u r e I1 h a s been drawn assuming t h e constancy of t h e m a r g i n a l
u t i l i t y o f income and t h e independence of t h e m a r g i n a l u t i l i t i e s of
I n t h e diagram, income (Y) i s on t h e v e r t i c a l a x i s
t e a and income.
and tea (T) i n pounds i s on t h e h o r i z o n t a l a x i s .
The m a r g i n a l u t i l i t y o f income assumption i s i n d i c a t e d by t h e f a c t
t h a t t h e d i s t a n c e from p o i n t s C t o D a r e e q u a l t o t h e d i s t a n c e Y
Y1
i n F i g u r e 11.
0
to
The f a c t t h a t t h e d i s t a n c e between t h e two s e t s of
p o i n t s and any o t h e r set of p o i n t s i s t h e same i n d i c a t e s t h a t t h e i n d i f f e r e n c e c u r v e s p i c t u r e d a r e v e r t i c a l l y p a r a l l e l throughout.
This
l a s t statement implies t h a t v e r t i c a l distances i n the centre of the
diagram can always b e t r a n s l a t e d t o d i s t a n c e s on t h e v e r t i c a l a x i s .
Using F i g u r e 11, t h e f o u r consumer's s u r p l u s measures can b e p i c M a r s h a l l ' s consumer's s u r p l u s measures a r e C t o
torially illustrated.
D b y d e f i n i t i o n and Y
0
t o Y 2 by e x t r a p o l a t i o n . 8
The d i s t a n c e from C
t o D may b e e x p l a i n e d a s f o l l o w s .
The consumer s t a r t s o u t w i t h OY
ence c u r v e I1.
0
income and no t e a on i n d i f f e r -
I n o r d e r t o maximize h i s u t i l i t y t h e consumer t r a d e s
money f o r t e a u n t i l he r e a c h e s p o i n t C which i s t a n g e n t i a l t o i n d i f f e r e n c e curve 12. The consumer h a s s p e n t a sum of money e q u a l t o t h e
v e r t i c a l d i s t a n c e EC f o r t h e q u a n t i t y of t e a ,
.
T1
I f the individual
was now allowed t o keep T b u t he had t o pay more, h i s t o t a l w i l l i n g 1
n e s s t o pay would be e q u a l t o E t o D.
T h i s i s an i n c r e a s e of money
p a i d e q u a l t o t h e d i s t a n c e between C and D .
A t D , t h e consumer s t i l l
h a s T q u a n t i t y of t e a , and i s on i n d i f f e r e n c e c u r v e I1.
1
Being on i n d i f f e r e n c e c u r v e I
a s well-off
1
i n d i c a t e s t h a t t h i s person i s
h a v i n g p a i d a t o t a l of E t o D f o r T1 a s h e w a s when h e
The consumer would n o t be w i l l i n g t o
had OYo income and no t e a .
pay any more t h a n t h e t o t a l of E t o D.
I f t h e i n d i v i d u a l d i d pay
a sum g r e a t e r t h a n E t o D , t h i s would l e a v e t h e consumer on an
i n d i f f e r e n c e c u r v e below I1.
l e f t of I
on I1.
1
Any i n d i f f e r e n c e c u r v e l y i n g t o t h e
on t h e graph means t h a t t h e consumer h a s less u t i l i t y t h a n
I f t h e consumer i n s t e a d pays a sum g r e a t e r t h a n E t o C b u t
l e s s t h a n E t o D , he w i l l s t i l l b e b e t t e r o f f t h a n when h e was a t OYo
o n i n d i f f e r e n c e c u r v e I1.
The d i s t a n c e from C t o D t h e n r e p r e s e n t s
t h e maximum i n c r e a s e a consumer would pay o u t r a t h e r t h a n do w i t h o u t
t h e q u a n t i t y T1 of t e a . T h i s then i s one measure o f consumer's s u r p l u s .
Although M a r s h a l l d o e s n o t d i s c u s s a second consumer's s u r p l u s
measure d i r e c t l y , Henderson (1941, 119) d e r i v e s and e x p l a i n s a
second measure, Yo t o Y2.
I f t h e consumer was f a c e d w i t h a s i t u a t i o n
where he must g i v e up a l l r i g h t s t o p u r c h a s e t e a , h e would want t o
b e compensated t o f o r e g o t h i s consumption.
ence curve I
2
Following a l o n g i n d i f f e r -
where t h e consumer maximized u t i l i t y a t p o i n t C , a
p o i n t of OYo i s r e a c h e d .
T h i s p o i n t r e p r e s e n t s a s i t u a t i o n where
t h e i n d i v i d u a l no l o n g e r h a s any t e a b u t i s on t h e same i n d i f f e r e n c e
c u r v e where h i s u t i l i t y was h i g h e s t .
The compensation r e q u i r e d
t h e n i s e q u a l t o t h e d i s t a n c e between Yo and Y 2 .
then is asking f o r E to C plus Y Y
0 2'
s i t u a t i o n o n l y r e c e i v e E t o C.
I n f a c t t h e consumer
He w i l l i n t h e M a r s h a l l i a n
The Y Y s u r p l u s comes a b o u t by t h e
0 2
consumer s t i l l h a v i n g t h e commodity a v a i l a b l e f o r p u r c h a s e " a f t e r
d e d u c t i n g t h e sum h e could s e t f r e e by g i v i n g i t up"
(Henderson,
1 9 4 1 , p. 1 1 9 ) .
The d i s t a n c e s YOYl
consumer's s u r p l u s .
and YOY2 r e p r e s e n t H i c k s ' measures o f
Y Y r e p r e s e n t s t h e s u r p l u s where an i n d i v i d u a l
0 1
i s a l l o w e d t o c o n t i n u e p u r c h a s i n g a good i n whatever q u a n t i t i e s h e
c h o o s e s w h i l e g i v i n g up a p o r t i o n of h i s income.
In Marshall's
f i r s t measure o f consumer's s u r p l u s , t h e consumer i s f o r c e d t o
c o n t i n u e consuming T
1'
The i n d i v i d u a l i n t h e H i c k s i a n c a s e w i l l
n o t c o n t i n u e consuming t h e same q u a n t i t y a s he s t a r t e d o u t consuming
u n l e s s t h e i n d i f f e r e n c e curves a r e v e r t i c a l l y p a r a l l e l .
I n Hicks'
s i t u a t i o n t h e consumer a g a i n s t a r t s o u t on i n d i f f e r e n c e c u r v e I
w i t h OYo income and no t e a .
1
The i n d i v i d u a l moves t o p o i n t C on I2
i n o r d e r t o maximize h i s s a t i s f a c t i o n .
Now assume a law i s p a s s e d
which r e q u i r e s a l i c e n s e i n o r d e r t o consume t e a .
The government
w i l l r e c e i v e t h e money from t h e p u r c h a s e o f t h e l i c e n s e , r e p r e s e n t e d
by t h e d i s t a n c e Y Y
and t h e consumer may buy whatever q u a n t i t y o f
0 1'
t e a he prefers.
A s i n t h e M a r s h a l l i a n c a s e , assuming t h e constancy
o f t h e m a r g i n a l u t i l i t y o f income, t h e i n d i v i d u a l would choose t o
c o n t i n u e consuming T q u a n t i t y o f t e a and maximize h i s u t i l i t y by
1
b e i n g a t p o i n t D on I
1
(Figure 11).
-
lla
-
-
llb -
I f t h e m a r g i n a l u t i l i t y of income i s n o t c o n s t a n t , t h e n a
s i t u a t i o n a s d e p i c t e d i n F i g u r e I11 w i l l o c c u r .
i n d i v i d u a l begins a t p o i n t C having T
1
q u a n t i t y of t e a .
example t h e consumer must c o n t i n u e t o consume T
p r i c e f o r t e a (E t o D ) .
I n F i g u r e I11 t h e
1
I n Marshall's
b u t pays a h i g h e r
The consumer w i l l be a t p o i n t D on I
1
but
w i l l n o t b e maximizing h i s s a t i s f a c t i o n .
I n o r d e r t o maximize h i s u t i l i t y i n t h i s l a s t s i t u a t i o n , t h e
i s j u s t tan-
consumer would b e a t p o i n t F where t h e budget l i n e , Y1,
g e n t i a l t o I1.
P o i n t F r e p r e s e n t s t h e H i c k s i a n s o l u t i o n when t h e
consumer pays a l i c e n s e f e e b u t chooses a new l e v e l of consumption,
T2.
T h i s H i c k s i a n s o l u t i o n , c a l l e d t h e compensating v a r i a t i o n , where
t h e m a r g i n a l u t i l i t y of income i s n o t c o n s t a n t w i l l always l i e t o t h e
l e f t of t h e M a r s h a l l i a n p o i n t (D) a s l o n g a s t h e good i n q u e s t i o n i s
n o t a n i n f e r i o r good (Henderson, 1941, 118; Mishan, 1975, 417-8).
The f i n a l measure of consumer's s u r p l u s i s r e p r e s e n t e d by t h e
d i s t a n c e Y Y (Mishan, 1975, 418) and i s named t h e e q u i v a l e n t v a r 0 2
i a t i o n of consumer's s u r p l u s .
I n t h e Hicksian formulation t h i s is
compensation which must a c t u a l l y b e p a i d t o t h e consumer i n o r d e r t o
g e t him t o s t o p consuming t h e good.
The e q u i v a l e n t v a r i a t i o n r e p r e s e n t s t h e same d i s t a n c e a s t h e
second M a r s h a l l i a n s u r p l u s measure and h a s a s i m i l a r e x p l a n a t i o n .
,
.
A f t e r a r r i v i n g a t p o i n t C t h e consumer w i l l be i n d i f f e r e n t between
consuming T
1
q u a n t i t y of t e a and b e i n g a t p o i n t OY
are on i n d i f f e r e n c e c u r v e I 2 '
equally well off.
2
a s b o t h C and Y2
A t e i t h e r p o i n t t h e consumer i s
The d i f f e r e n c e i n t h i s measurement between t h e
H i c k s i a n c a s e and t h e M a r s h a l l i a n c a s e i s t h a t i n t h e I I i c k s i a n c a s e
Y Y i s a c t u a l l y p a i d t o t h e consumer w h i l e i n t h e M a r s h a l l i a n c a s e
0 2
t h i s sum i s n o t p a i d t o anyone.
I n s t e a d i n M a r s h a l l ' s example t h e
consumer i s all-owed t o keep a l l of h i s income and t h e o p p o r t u n i t y t o
buy t h e commodity.
I n t h i s f i n a l comparison i t s h o u l d b e n o t e d t h a t
t h e M a r s h a l l i a n and H i c k s i a n measures, Y 0Y2
,
a r e equal.
Only t h e way
i n d i v i d u a l s a r e compensated d i f f e r s (Henderson, 1941, p. 1 1 9 ) .
A r e l a t i o n s h i p between t h e f o u r measures o f consumer's s u r p l u s
e x i s t s when t h e m a r g i n a l u t i l i t y of income i s n o t assumed f i x e d .
If
t h e good b e i n g r e f e r r e d t o i s n o t a n i n f e r i o r good, t h e n t h e YOY2
measure w i l l b e g r e a t e r t h a n t h e YOY1.
t h a n t h e CD measure.'
AS n o t e d above YOYl
is greater
Y Y w i l l be t h e l a r g e s t measure because of t h e
0 2
way t h a t d i m i n i s h i n g m a r g i n a l u t i l i t y of income a f f e c t s t h e i n d i f f e r ence curves.
By examining t h e compensating, e q u i v a l e n t and M a r s h a l l i a n cons u m e r ' s s u r p l u s measures, i t can b e shown how t h e f o u r measures a r e r e l a t e d .
The r e l a t i o n s h i p s have been examined under c o n d i t i o n s of c o n s t a n t and
non-constant m a r g i n a l u t i l i t y of income.
The i s s u e now t o b e examined
i s what i s t h e magnitude of d i f f e r e n c e between t h e s e measures.
Small v e r s u s Large V a r i a n c e i n Consumer's S u r p l u s Measures
I n a p a p e r t i t l e d "Consumer's S u r p l u s and t h e Compensating
V a r i a t i o n " , Henderson (1941) s t a t e s t h e e x p e c t e d r e l a t i o n s h i p s
between t h e s u r p l u s a s f o l l o w s .
( U n d e r l i n i n g h a s been a d d e d ) .
The s o l u t i o n h e r e s u g g e s t e d i s t h a t t h e r e a r e f o u r
a l t e r n a t i v e e x p r e s s i o n s of t h e consumer's s u r p l u s
from which we have t o choose one i n each p a r t i c u l a r
c a s e a c c o r d i n g t o t h e problem w i t h which we a r e
d e a l i n g . The s o l u t i o n c e r t a i n l y h a s t h e d i s a d v a n t a g e
of i n t r o d u c i n g complexity i n t o a f i e l d where i t i s o f
s i n g u l a r l y l i t t l e p r a c t i c a l importance, s i n c e we s h a l l
normally e x p e c t t h e f o u r r e s u l t s t o l i e s o c l o s e
t o g e t h e r t h a t i t would n o t m a t t e r which we chose and,
i n any c a s e , when we u s e t h e concept w e do s o w i t h o u t
making any p r e t e n s i o n s of a c c u r a c y (Henderson, 1941,
121)
.
C l e a r l y , Henderson b e l i e v e s t h a t t h e f o u r measures w i l l b e c l o s e
t o g e t h e r and h e does s o even though h e does n o t assume t h e constancy
o f t h e m a r g i n a l u t i l i t y o f income.
Also, t h e changes Henderson makes
i n t h e i n d i v i d u a l ' s consumption a r e l a r g e and n o t t h e s m a l l s h i f t s
made i n M a r s h a l l ' s d i s c u s s i o n which more r e a l i s t i c a l l y allowed t h e
m a r g i n a l u t i l i t y o f income t o be assumed t o remain c o n s t a n t ( M a r s h a l l ,
1920, 103-4)
.
Before c o n t i n u i n g on t o a d i s c u s s i o n o f what t h e e m p i r i c a l e v i d e n c e
shows t h e r e l a t i o n s h i p t o b e between t h e f o u r consumer' s s u r p l u s e x p r e s -
s i o n s , Henderson's r e a s o n i n g s h o u l d b e f u r t h e r examined.
Given a consumer who h a s an income, Y , and who i s consuming many
goods, i t i s p o s s i b l e t o e s t a b l i s h and e q u a t e r a t i o s between t h e marg i n a l u t i l i t y o f t h e goods and t h e r e s p e c t i v e p r i c e s .
This gives:
The symbol A r e p r e s e n t s t h e number t o which a l l t h e r a t i o s must be
e q u a l i n c l u d i n g t h e r a t i o f o r money ( Y ) .
The above r e l a t i o n s h i p s
e x i s t f o r t h e i n d i v i d u a l u n l e s s something o c c u r s which u p s e t s t h e
balance.
One such d i s t u r b a n c e c o u l d be a p r i c e change.
I f t h e p r i c e o f A f a l l s by one-half
and i f B i s a c l o s e sub-
s t i t u t e f o r A , t h e consumer w i l l buy l e s s o f A and more o f B.
This
a l t e r i n g o f t h e money s p e n t on A and B w i l l change t h e r e l a t i o n s h i p s
MU^
*A
o f - and - s u c h t h a t t h e s e r a t i o s may n o t e q u a l A .
In t h i s case
P~
B
t h e n , a l l t h e r a t i o s c o u l d b e e x p e c t e d t o change, t h u s a l t e r i n g A .
H e n d e r s o n ' s p o i n t i s d i f f e r e n t from t h e above e x p l a n a t i o n .
In
e f f e c t Henderson i s s a y i n g t h a t t h e r e c o u l d b e at l e a s t two c a s e s
where A w i l l n o t change o r i f
X does a l t e r , t h e magnitude o f change
w i l l b e s o s m a l l as t o c a u s e o n l y a s l i g h t d i v e r g e n c e i n t h e two
c o n s u m e r ' s s u r p l u s measures.
The f i r s t c a s e i s t h a t o f few s u b s t i t u t e s .
I f an individual
i s f a c e d w i t h a p r i c e change f o r good A a n d h e i s b u y i n g n o , o r o n l y
a few, c l o s e s u b s t i t u t e s , t h e n t h e r e w i l l b e o n l y a d i s t r i b u t i o n a l
.effect.
The d i s t r i b u t i o n a l e f f e c t i m p l i e s t h a t t h e r a t i o s o f t h e
few c l o s e s u b s t i t u t e s w i l l a l t e r u n t i l e q u a l i t y i s a g a i n r e a c h e d w i t h
A.
I f t h e r e are n o c l o s e s u b s t i t u t e s , t h e n o n l y t h e r a t i o o f A w i l l
change and i t must e q u a l A .
The s e c o n d c a s e r e p r e s e n t s a s i t u a t i o n where many o r a l l o f t h e
goods a r e c l o s e s u b s t i t u t e s .
I n t h i s i n s t a n c e a t e n p e r c e n t change i n
t h e p r i c e of A w i l l cause a diffusion e f f e c t .
means t h a t i f P
A
f a l l s by t e n p e r c e n t a l l t h e r a t i o s w i l l change by
some s m a l l amount.
factor.
This d i f f u s i o n e f f e c t
T h i s means t h a t A w i l l a l s o change by a s m a l l
I f A changes by t h e magnitude o f s a y one one-hundredth o f a
p e r c e n t a f t e r a l l t h e r a t i o s have s t a b i l i z e d , t h e n t h i s d i s r u p t i o n
c o u l d n o t c a u s e a l a r g e d i f f e r e n c e i n consumer's s u r p l u s measures.
A s H e n d e r s o n ' s l o g i c a p p e a r s t o h o l d , t h e problem now becomes
o n e o f d e t e r m i n i n g why, when consumer's s u r p l u s i s u s e d e m p i r i c a l l y ,
t h e v a r i a n c e between t h e measures i s s o v a s t l y d i f f e r e n t .
This
d i f f e r e n c e i s p a r t i c u l a r l y e v i d e n c e d when comparing t h e compensating
and e q u i v a l e n t v a r i a t i o n s .
The n e x t c h a p t e r w i l l s e t o u t n o t o n l y
t h e r e s u l t s o f o l d e r s t u d i e s b u t a l s o t h o s e o b t a i n e d from a new
empirical study.
T h i s w i l l b e done i n o r d e r t o i l l u s t r a t e t h a t t h e
v a r i a n c e between t h e c o n s u m e r ' s s u r p l u s measures i s n o t a n i s a l a t e d
i n c i d e n t b u t r a t h e r a w i d e s p r e a d phenomena.
FOOTNOTES
1
I n r e a l i t y n o t a l l i n d i v i d u a l s have t o be b e t t e r o f f .
The con-
d i t i o n which must h o l d i s t h a t t h e g a i n e r s could compensate l o s e r s and
s t i l l b e b e t t e r o f f t h a n b e f o r e t h e s i t u a t i o n changed ( K r u t i l l a and
F i s h e r , 1975, 28-9).
2
The p r e s e n t l i t e r a t u r e u s e s a t least t h r e e d i f f e r e n t terms t o
mean approximately t h e same t h i n g .
The terms a r e consumer's s u r p l u s ,
consumers' s u r p l u s and consumer-surplus.
The f i r s t and second a r e
used ambiguously t o mean b o t h a n i n d i v i d u a l and a s o c i e k y a l t h o u g h
some w r i t e r s a t t e m p t t o s e p a r a t e t h e terms (Hammack and Brown, 1974,
26-9; Mishan, 1975, 25-54).
The t h i r d term, consumer-surplus,
is
used by Harberger (1971) i n a n a t t e m p t t o a v o i d ambiguity b u t i t i s
n o t c l e a r from t h e a r t i c l e whether t h i s purpose i s accomplished.
3
Aggregation does have i t s p i t f a l l s b u t as a measure of b e n e f i t s ,
consumer's s u r p l u s i s t h e b e s t economists o f t e n have t o o f f e r as
s u g g e s t e d by H a r b e r g e r (19 71).
4
Although t h i s e s s a y i s n o t d i r e c t l y concerned w i t h t h e problems
i n v o l v e d i n a t t e m p t i n g t o a g g r e g a t e consumer's s u r p l u s v a l u e s , i t
s h o u l d b e n o t e d t h a t s u c h a problem does e x i s t (Harberger, 1971,
787-9).
T h i s e s s a y i s a n a t t e m p t t o examine o n l y t h e way consumer's
s u r p l u s i s used i n a p a r t i c u l a r s e t t i n g and d o e s n o t concern i t s e l f
w i t h o t h e r t h e o r e t i c a l problems of t h i s concept (Samuelson, 1942,
75-8; W i l l i g , 1976).
5
Most economists a g r e e t h a t t h e f i r s t d i s c u s s i o n of consumer's
s u r p l u s appeared i n D u p u i t ' s Annales d e s P o n t s e t Chaussees (1844).
M a r s h a l l though i s c r e d i t e d w i t h e x p l a i n i n g and p o p u l a r i z i n g t h e
concept.
For a d e t a i l e d h i s t o r i c a l a c c o u n t of u t i l i t y t h e o r y , s e e
S t i g l e r (1950).
6
M a r s h a l l assumed d i m i n i s h i n g m a r g i n a l u t i l i t y which h e thought
e n s u r e d downward s l o p i n g demand c u r v e s .
This condition did not
p r o v e t o b e n e c e s s a r y and s u f f i c i e n t a s M a r s h a l l e x p e c t e d ( M a r s h a l l ,
1 9 2 0 , 78-85; H i c k s , 1939, 26-7).
Hicks, a l s o , t h o u g h t he had t h e
n e c e s s a r y and s u f f i c i e n t c o n d i t i o n t o e n s u r e downward s l o p i n g demand
c u r v e s by assuming d i m i n i s h i n g m a r g i n a l r a t e s of s u b s t i t u t i o n
( H i c k s , 1939, 32).
Hicks d i s c o v e r e d t h a t t h i s concept d i d n o t
e n s u r e downward s l o p i n g demand c u r v e s e i t h e r .
F i n a l l y , t h e one
. a s s u m p t i o n Hicks made which gave downward s l o p i n g demand c u r v e s i n
t h e a g g r e g a t e was t h a t t h e good r e p r e s e n t e d by t h e c u r v e was a
normal good (Hicks, 1939, 3 5 ) .
T h i s means, a c c o r d i n g t o H i c k s ,
t h a t a n e g a t i v e income e f f e c t w i l l n o t b e s o l a r g e a s t o outweigh
t h e s u b s t i t u t i o n e f f e c t and t h e r e b y c a u s i n g a p o s i t i v e l y s l o p e d
demand c u r v e .
7
Samuelson ( 1 9 4 7 , 9 9 ) u s e s t h e m a r g i n a l u t i l i t y o f m o n e y a n d
t h e m a r g i n a l u t i l i t y of income i n t e r c h a n g e a b l y .
Samuelson, though,
p r e f e r s t h e l a t t e r of t h e s e two terms b e c a u s e t h i s term a v o i d s t h e
n u m e r a i r e problems.
(For a f u r t h e r d i s c u s s i o n of problems w i t h
h o l d i n g t h e m a r g i n a l u t i l i t y of income c o n s t a n t , see Samuelson,
1942).
Mishan (1975, 417 f o o t n o t e ) makes a s t r o n g d i s t i n c t i o n
between t h e m a r g i n a l u t i l i t y of money and income s a y i n g t h a t h o l d i n g
t h e m a r g i n a l u t i l i t y of money c o n s t a n t i s n o t t h e same t h i n g a s
h o l d i n g r e a l income c o n s t a n t .
Real income, a c c o r d i n g t o Mishan's
i n t e r p r e t a t i o n of Hicks, i s what must b e h e l d c o n s t a n t .
Real income
i s h e l d c o n s t a n t i n Hicks' examples of compensating v a r i a t i o n s by
i n c r e a s i n g o r d e c r e a s i n g money income.
Consequently, i n t h i s e s s a y
t h e m a r g i n a l u t i l i t y of income w i l l b e used t o i n d i c a t e what i s
held constant.
8
M a r s h a l l d i d n o t s p e c i f i c a l l y d i s c u s s a consumer's s u r p l u s
measure of Y
0
t o Y2 b u t Henderson (1941, 119) i l l u s t r a t e s how t h i s
measure can b e deduced from M a r s h a l l ' s w r i t i n g .
words, one can s u g g e s t t h e YO-Y2
I n Henderson's
consumer's s u r p l u s measure as
follows :
M a r s h a l l , h i m s e l f , d i d n o t need t o t a k e t h i s
c o n s i d e r a t i o n i n t o account s i n c e h e was opera t i n g w i t h t h e assumption of t h e constancy
of t h e m a r g i n a l u t i l i t y of money which i s
s u f f i c i e n t t o e n s u r e t h a t t h e two r e s u l t s a r e
t h e same, b u t when we abandon t h i s assumption
the dual solution is a s relevant t o the
M a r s h a l l i a n consumer's s u r p l u s a s i t i s t o t h e
compensatory s o l u t i o n .
9
I t s h o u l d be n o t e d t h a t t h i s e x p l a n a t i o n of which measure i s
t h e l a r g e s t r e l i e s h e a v i l y on d i m i n i s h i n g m a r g i n a l u t i l i t y .
This
e x p l a n a t i o n of Y -Y
> Y -Y > CD comes from t h e s t a n d a r d v i e w p o i n t s
0 2 - 0
1a s e x p r e s s e d by Henderson and P a t i n k i n .
A c r i t i c i s m of t h i s e x p l a n a t i o n d e a l s w i t h n e g a t i v e c r o s s
effects.
For example :
+
2PxPyMUXy
+
2
PxMLJyy < 0
where P
Y
i s t h e p r i c e o f good Y , PX i s t h e p r i c e o f good X ,
MUXX i s
t h e r a t e of change o f t h e m a r g i n a l u t i l i t y o f X w i t h r e s p e c t t o X,
MUW
i s t h e r a t e o f change o f t h e m a r g i n a l u t i l i t y o f Y w i t h r e s p e c t
t o Y and MUXy i s t h e r a t e of change o f X w i t h r e s p e c t t o Y .
MUXy i s e q u a l t o MU
YX'
MUXX and MUyy
> 0 and MXy < 0.
Also
I f MUXy i s
e x t r e m e l y n e g a t i v e , t h i s c r o s s - e f f e c t can c a n c e l o u t t h e p o s i t i v e
MUXX and MUyy.
I n o r d e r f o r t h i s MU
XY
t o be. s u f f i c i e n t l y n e g a t i v e
t o c a n c e l t h e o t h e r two t e r m s o u t i m p l i e s t h a t t h e X and Y goods b e
e i t h e r extreme s u b s t i t u t e s o r extreme compliments.
Extreme s u b s t i t u t e s
would mean t h a t t h e goods a r e s o c l o s e i n n a t u r e a s a c t u a l l y t o be
t h e same composite good.
I f t h e two goods were extreme compliments
s u c h as l e f t and r i g h t s h o e s and o n l y t h e l e f t shoe i s s o l d , a g a i n
5 c o u l d be
. and MUyy.
s u f f i c i e n t l y n e g a t i v e t o c a n c e l o u t t h e p o s i t i v e MU
XX
Otherwise t h e MUXy w i l l n o t b e s u f f i c i e n t l y n e g a t i v e t o
c a u s e t h i s overwhelming o f MU
XX
and MUyy
(Henderson and Quandt, 1971,
31-9).
Also, a s mentioned b e f o r e t h e d i s c u s s i o n o f which consumer's
s u r p l u s measures a r e l a r g e s t i s b a s e d on t h e u s u a l view found i n t h e
presently accepted l i t e r a t u r e .
CHAF'TER I11
Two E m p i r i c a l S t u d i e s
I n t h e l a s t c h a p t e r t h e n o t i o n o f c o n s u m e r ' s s u r p l u s and i t s u s e
a s a measure of w e l f a r e change was e x p l a i n e d i n g e n e r a l t e r m s .
The
e x p l a n a t i o n was d i s c u s s e d w i t h t h e i n t e n t i o n of examining how c o n s u m e r ' s
s u r p l u s i s a p p l i e d i n economics.
The n e x t p o i n t t o c o n s i d e r w i l l b e
how c o n s u m e r ' s s u r p l u s i s u s e d i n e m p i r i c a l s t u d i e s .
These s t u d i e s
o f f e r a springboard f o r contrasting t h e t h e o r e t i c a l relationships
between c o n s u m e r ' s s u r p l u s m e a s u r e s a n d t h e r e l a t i o n s h i p s uncovered
empirically.
I
1
Using t h e H i c k s i a n compensating and e q u i v a l e n t v a r i a t i o n s , t h e d i s -
I
c u s s i o n w i l l f i r s t o u t l i n e a p r e v i o u s l y r e p o r t e d s t u d y (Hamrnack and Brown,
1 9 74) which i n d i c a t e s t h a t t h e s e two consumer's s u r p l u s measures have an
unpredicted relationship.
I n o r d e r t o v e r i f y Hammack and Brown's
r e s u l t s , a second more r e c e n t s t u d y i s a l s o r e p o r t e d .
The v e r i f i c a t i o n
o f t h e Hammack and Brown f i n d i n g s w i l l s e r v e a s t h e l a u n c h i n g p o i n t
f o r c a u s a l e x p l a n a t i o n s of t h e d i v e r g e n c e between t h e t h e o r e t i c a l and
t h e e m p i r i c a l consumer's s u r p l u s r e l a t i o n s h i p s .
E m p i r i c a l S t u d i e s and Consumer's S u r p l u s
I n 1969 a s t u d y o f w a t e r f o w l h u n t e r s was u n d e r t a k e n i n o r d e r t o
p r o d u c e a v a l u a t i o n o f w a t e r f o w l and w e t l a n d s (Hammack and Brown,
1 9 7 4 , 1). The v a l u a t i o n was t o b e u s e d i n d e c i s i o n s r e l a t i n g t o t h e
c r e a t i o n of new w e t l a n d s o r t h e d r a i n i n g o f e x i s t i n g w e t l a n d s .
These
,
d e c i s i o n s were t o b e made b a s e d on t h e v a l u a t i o n o f w a t e r f o w l a s r e p r e s e n t e d by t h e demand f o r t h e u s e o f t h e r e s o u r c e and on a n e s t i m a t e d
b i o l o g i c a l supply function.
The v a l u a t i o n o r demand p r e s e n t a t i o n was
t h e s i d e o f t h e model which d e a l t w i t h consumer's s u r p l u s and, t h e r e f o r e ,
i s t h e s i d e examined h e r e .
The v a l u a t i o n o f w a t e r f o w l was b a s e d on a s u r v e y t e c h n i q u e which
a s k e d many q u e s t i o n s about t h e r e s p o n d e n t ' s socio-economic c h a r a c t e r i s t i c s and h u n t i n g h a b i t s .
The q u e s t i o n s on t h e s u r v e y which were
i n t e n d e d t o b e used i n measuring b e n e f i t s were:
Q u e s t i o n 6: "What i s t h e s m a l l e s t amount you t h i n k you
would t a k e t o g i v e up your r i g h t t o h u n t w a t e r f o w l f o r
a season?"
Q u e s t i o n 8: "About how much g r e a t e r do you t h i n k y o u r
c o s t s would have had t o have been b e f o r e you would have
d e c i d e d n o t t o have gone h u n t i n g a t a l l d u r i n g t h a t
s e a s o n ? " (Hammack and Brown, (19 74) , 91-2)
.
I n t h e . i r d i s c u s s i o n , Hammack and Brown c a l l Q u e s t i o n 6 t h e
" w i l l i n g n e s s t o s e l l " and Q u e s t i o n 8 t h e " w i l l i n g n e s s t o pay" (Hammack
and Brown, 1974, 6-7).
The answers g i v e n t o t h e s e two q u e s t i o n s were
t h e n t a k e n t o b e t h e two H i c k s i a n measures o f consumer's s u r p l u s .
I
The w i l l i n g n e s s t o s e l l (Question 6) i s assumed t o b e t h e e q u i v a l e n t v a r i a t i o n i n d i c a t e d a s YOY2 on F i g u r e s I1 and I11 i n Chapter 11.
T h i s e q u i v a l e n t v a r i a t i o n r e p r e sen ts t h e compensation r e q u i r e d t o
remove a r e s o u r c e o r a good from t h e market and t h u s , from an i n d i v i d u a l ' s consump t i o n bundle.
The compensating v a r i a t i o n (Hicks, 1939, 40) i s taken t o b e t h e
e q u i v a l e n t o f t h e w i l l i n g n e s s t o pay v a l u e .
T h i s measure of consumer's
s u r p l u s i s t h e e x t r a amount a n i n d i v i d u a l would pay i n o r d e r t o cont i n u e consuming a good r a t h e r t h a n do w i t h o u t i t .
I n F i g u r e s I1 and
I11 i n C h a p t e r I1 t h e compensating v a r i a t i o n i s i n d i c a t e d by t h e
distance Y Y
0 1'
A l t h o u g h Henderson d i s c u s s e s f o u r consumer's s u r p l u s e s , Hammack
and Brown a r e t a l k i n g a b o u t o n l y two o f t h e s e e x p r e s s i o n s .
(1941, 1 2 1 ) e x p e c t s a l l f o u r m e a s u r e s t o l i e c l o s e t o g e t h e r .
Henderson
If this
comment i s t r u e f o r f o u r measurements, t h e n one c a n e x p e c t t h a t any
two o f t h e m e a s u r e s w i l l a l s o b e c l o s e t o g e t h e r .
Consequently, t h e r e
s h o u l d b e no r e a s o n why Hammack and Brown's u s e o f o n l y two of t h e
m e a s u r e s s h o u l d c a u s e any d i s t r e s s .
Knowing t h a t ~ e n d e r s o n ' s (1941, 21) t h e o r e t i c a l d i s c u s s i o n p r e d i c t s
o n l y a s m a l l d i f f e r e n c e between c o n s u m e r ' s s u r p l u s m e a s u r e s , Hammack
,
and Brown's r e s u l t s need c l o s e e x a m i n a t i o n .
A f t e r dropping extremely
h i g h v a l u e s and "not w i l l i n g t o s e l l " r e s p o n s e s from t h e i r s u r v e y d a t a ,
t h e s a m p l e s i z e o f 1 , 5 1 1 y i e l d e d a mean v a l u e f o r t h e w i l l i n g n e s s t o s e l l
( e q u i v a l e n t v a r i a t i o n ) o f $ 1 , 0 4 4 (Hammack and Brown, 1 9 7 4 , 2 6 ) .
t h e mean v a l u e o f t h e w i l l i n g n e s s t o pay q u e s t i o n was $247.
In contrast
This
means t h a t t h e e q u i v a l e n t v a r i a t i o n was j u s t o v e r f o u r t i m e s a s l a r g e
as t h e c o m p e n s a t i n g measure.
Such a v a r i a n c e between a n s w e r s c a n n o t
b e d e s c r i b e d i n any way a s " c l o s e " .
Hammack and Brown do n o t p u r s u e a v i g o r o u s e x p l a n a t i o n o f t h e
d i f f e r e n c e between t h e two consumer's s u r p l u s m e a s u r e s .
Instead,
Hammack and Brown, by c l a i m i n g t h a t t h e p r o p e r t y r i g h t s w e r e most
r e a l i s t i c a l l y a s s i g n e d by t h e w i l l i n g n e s s t o pay q u e s t i o n and t h a t
t h e r e s p o n s e s t o t h e w i l l i n g n e s s t o s e l l query were " t o o emotionally'
biased",
d e c i d e d t o use o n l y t h e compensating v a r i a t i o n a s a consumer's
s u r p l u s measure (Hammack and Brown, 19 74, 26-7)
\
.
A f t e r d e t e r m i n i n g which measure o f consumer's s u r p l u s t o employ,
Hammack and Brown s e t up t h e model f o r w a t e r f o w l e v a l u a t i o n .
Such a
model would p o i n t o u t t h e d e t e r m i n a n t s and importance o f t h e f a c t o r s
r e s p o n s i b l e f o r v a r i a t i o n s i n t h e w i l l i n g n e s s t o pay among d i f f e r e n t
individuals.
T h i s model was V = V(Y, U, D / Z ,
s u r p l u s measure i s r e p r e s e n t e d by V .
income measure ( Y ) ,
Z) where t h e consumer's
The exogenous v a r i a b l e s a r e an
a measure o f t a s t e (U), one h u n t e r ' s d a i l y bagged
w a t e r f o w l (D/Z) and t h e number o f days t h e r e s p o n d e n t h u n t e d i n one
s e a s o n (Z) (Hammack and Brown, 1974, 2 3 )
.
The q u e s t i o n s on t h e s u r v e y were d e s i g n e d t o g a t h e r some measure
of each of these variables.
A s p o i n t e d o u t e a r l i e r t h e consumer's s u r -
p l u s measure, (V) , was w i l l i n g n e s s t o pay.
The o b s e r v a t i o n s o f Y , D
and Z came d i r e c t l y from answers t o s u r v e y q u e s t i o n s asked.
measure o f t a s t e , (U), was r e p l a c e d by (E).
The g e n e r a l
(E) was t a k e n t o b e t h e
responses t o a q u e s t i o n regarding t h e i n d i v i d u a l ' s average c o s t f o r
hunting i n c u r r e d p e r season.
T h i s replacement was made on t h e assumption
t h a t t h e more a r d e n t t h e h u n t e r , t h e more h e w i l l spend.
The model was r u n i n t h r e e forms, t o t a l l o g a r i t h m i c , r e c i p r o c a l and
s e m i - l o g a r i thmic t r a n s f o r m a t i o n s .
The b e s t r e s u l t s 2 were o b t a i n e d u s i n g
t h e t o t a l l o g a r i t h m i c t r a n s f o r m a t i o n w h i l e t h e p o o r e s t f i t came from t h e
reciprocal function.
The b e s t e q u a t i o n form and f i t a r e reproduced h e r e :
1nV = 1 . 4 4 -I-0.466 1nY
(t-values)
(8.7)
+
0.168 I n s
(4.5)
+
0 . 1 4 1 1nE
(5.3)
+
0.308 l n D / ~
(7.0)
-2
K
= 0.222,
S
2
= 1 . 7 0 , n = 1511 (Hammack and Brown, 1974,
28).
An i n d e p e n d e n t v a r i a b l e (S) was added t o t h e model. T h i s v a r i a b l e r e p r e s e n t e d t h e t o t a l number o f s e a s o n s an i n d i v i d u a l had h u n t e d which was
e x p e c t e d t o e x e r t a p o s i t i v e e f f e c t on w i l l i n g n e s s t o pay because o f t h e
g r e a t e r a p p r e c i a t i o n and awareness o f t h e v a l u e o f f e r e d by t h e o p p o r t u n i t y .
The a u t h o r s a l s o n o t e t h a t o t h e r independent v a r i a b l e s were
tested.
These v a r i a b l e s , t e s t e d i n dummy v a r i a b l e form, were l e v e l
o f e d u c a t i o n , w h e t h e r o r n o t t h e h u n t e r s p a i d t o h u n t on p r i v a t e
l a n d , s t a t e o f r e s i d e n c e and r e s p o n s e t o f i r s t m a i l i n g .
v a r i a b l e s were r e j e c t e d because o f i n s i g n i f i c a n t t - v a l u e s
and Brown, 1974, 30)
A l l these
(Hammack
.
Those v a r i a b l e s used by Hammack and Brown i n t h e b e s t r e g r e s s i o n ,
reproduced above, a l l had p o s i t i v e c o e f f i c i e n t s .
This is a reasonable
r e s u l t when t h e r e l a t i o n s h i p o f w i l l i n g n e s s t o pay t o each o f t h e
i n d e p e n d e n t v a r i a b l e s i s examined s e p a r a t e l y .
I f income i n c r e a s e s , i t i s r e a s o n a b l e f o r t h e i n d i v i d u a l t o be
w i l l i n g t o pay more f o r t h e r i g h t t o h u n t .
This reasoning c a r r i e s
o v e r t o t h e r e l a t i o n s h i p between w i l l i n g n e s s t o pay and t h e average
cost.
The p o s i t i v e c o e f f i c i e n t s a s s o c i a t e d w i t h t h e number o f s e a s o n s
h u n t e d , t h e number o f days h u n t e d p e r s e a s o n and t h e number of bagged
waterfowl per season a r e explained a s follows.
Individuals usually
do n o t spend t h e i r l e i s u r e time i n a c t i v i t i e s such a s h u n t i n g i f they
a r e n o t w i l l i n g t o pay f o r t h e a c t i v i t y .
always imply a monetary f e e .
Payment, however, does n o t
Here, p a r t of t h e payment f o r h u n t i n g
i s t h e o p p o r t u n i t y c o s t of p a r t i c i p a t i n g evidenced i n t h e days hunted
p e r s e a s o n and t h e t o t a l s e a s o n s hunted.
F i n a l l y , i f t h e h u n t e r i s good a t bagging waterfowl o r t h e r e i s a
p l e n t i f u l s u p p l y o f game t o a s s u r e g r e a t e r s u c c e s s , then t h e h u n t e r
s h o u l d r e a s o n a b l y be w i l l i n g t o pay more f o r t h e o p p o r t u n i t y t o c o n t i n u e
hunting.
For l e i s u r e a c t i v i t i e s t h i s r e l a t i o n s h i p can b e e x p e c t e d t o
b e p o s i t i v e a s l o n g a s t h e a c t i v i t y i s n o t a n i n f e r i o r good.
Hammack and Brown a s n o t e d chose t o i g n o r e t h e w i l l i n g n e s s t o s e l l
consumer's s u r p l u s e x p r e s s i o n b e c a u s e i t s v a l u e was " b i a s e d by t h e
emotions o f t h o s e surveyedu (19 74, 26-7).
Although i g n o r i n g t h e w i l l i n g -
n e s s t o s e l l v a l u e s because o f a s s i g n i n g e x p l i c i t p r o p e r t y r i g h t s i s
v a l i d , t h e i d e a o f i g n o r i n g t h i s measure on t h e b a s i s t h a t i t i s answered
t o o e m o t i o n a l l y seems t o b e a m i s t a k e .
.
When viewed a s a v a l i d measure
o f consumer's s u r p l u s , one wonders how Hammack and Brown know t h a t i t
i s answered o n l y e m o t i o n a l l y .
By n o t r u n n i n g r e g r e s s i o n s and tests on
t h i s measure, no knowledge o f what can ( o r could) c a u s e t h e extreme
answers i s found.
Having new d a t a a v a i l a b l e n o t o n l y o f f e r e d t h e o p p o r t u n i t y t o
v e r i f y t h e Hammack and Brown r e s u l t s b u t a l s o o f f e r e d t h e o p p o r t u n i t y
t o examine t h e e q u i v a l e n t consumer's s u r p l u s v a r i a t i o n ( w i l l i n g n e s s
to sell).
The f o l l o w i n g s e c t i o n o u t l i n e s t h e new s t u d y and p r o c e d u r e s
used.
Environment Canada's S ~ o r tF i s h i n g Survev
I n 1975 Environment Canada, F i s h e r i e s and Marine S e r v i c e ,
u n d e r t h e d i r e c t i o n o f W i l l i a m F. S i n c l a i r conducted a s u r v e y on
Note:
-
Number
950
P e r c e n t of
Sample Drawn
79.7
Percent of
Fishing
Licenses
3.7
Completed Telephone Survey
Interviews
Telephone Survey
Percentage
8.4
Number
2140
Number
3192
Percentage
12.5
Number o f Usable
Completed Responses
Number Drawn f o r
Sample
The r e s p o n s e t o t h e m a i l s u r v e y w a s 67% which was accomplished by f i v e m a i l i n g s ,
one f o r t h e o r i g i n a l s u r v e y and then f o u r m a i l i n g s of follow-up l e t t e r s .
P e r c e n t of
Number Mail R e t u r n s
1192
55.7
Percent of
Fishing
Licenses
4.7
T o t a l Mail Survey R e t u r n s Drawn
f o r Telephone Survey
T o t a l Number o f F i s h i n g
L i c e n s e Holders
Mail Survey
[Condensed from t h e Environment Canada's Table I V . l reproduced i n Appendix A ]
TABLE I
s p o r t f i s h i n g i n n o r t h e r n B r i t i s h Columbia.
The survey was conducted i n
o r d e r t o measure t h e economic importance of f i s h i n g t o t h e p o p u l a t i o n of
t h e Yellowhead, B.C.
,
r e g i o n -- an a r e a of B . C. from P r i n c e Rupert t o
P r i n c e George.
The s u r v e y was o r i g i n a l l y mailed i n A p r i l , 1975, t o a sample of
v a l i d 1974 f i s h i n g l i c e n s e h o l d e r s .
The s u r v e y s , follow-up l e t t e r s ,
Environment Canada d a t a codes and two t a b l e s i l l u s t r a t i n g t h e usage of
t h e d a t a by t h e government agency a r e reproduced i n Appendix A.
When
t h e m a i l s u r v e y s were r e t u r n e d , a l l t h o s e c o n t a i n i n g a telephone number
were c o n t a c t e d by phone.
The m a i l s u r v e y produced 2,140 u s a b l e r e s p o n s e s .
9 5 0 w e r e c o n t a c t e d a second time.
Of t h e 2,140,
T a b l e I , a c o n d e n s a t i o n o f t h e two
government t a b l e s found i n Appendix A, i l l u s t r a t e s t h e t o t a l s u r v e y s
i n terms o f p e r c e n t a g e s of (1) t o t a l l i c e n s e h o l d e r s and (2) s u r v e y s
completed and r e turned.
3
Before p r o c e e d i n g t o a d i s c u s s i o n o f t h e r e g r e s s i o n model, one
s i m p l e s t a t i s t i c a l comparison s h o u l d be made between t h e Hammack and
Brown d a t a and t h e f i s h i n g s u r v e y d a t a .
I n t h e Hammack and Brown survey
t h e mean v a l u e s f o r t h e compensating and e q u i v a l e n t v a r i a t i o n s were $247
and $1,044 r e s p e c t i v e l y (Hammack and Brown, 1974, 2 6 ) .
The mean v a l u e s
f o r t h e s e two consumer's s u r p l u s measures c a l c u l a t e d from t h e f i s h i n g
d a t a a r e $55 f o r t h e compensating v a r i a t i o n and $24,382 f o r t h e equivalen t v a r i a t i o n .
Although t h e f i s h i n g d a t a h a s v a l u e s which have a l a r g e r v a r i a n c e ,
t h e e q u i v a l e n t v a r i a t i o n i n t h e h u n t i n g d a t a was a d j u s t e d t o e x c l u d e
e x t r e m e l y l a r g e answers w h i l e t h e f i s h i n g d a t a was n o t s o a d j u s t e d .
TABLE I1
Variables Selected f o r Regressions
Name o f V a r i a b l e
Region (D)
*
Model Name
RD1 t h r u RD5
I d e n t i f i c a t i o n Number
IDNBR'
T o t a l A n g l e r s i n Family
TOTANG
Age o f Household Head (D)
DAGEl t h r u DAGE8
Sex o f Household Head (D)
DSEX
Number o f Days F i s h e d by Household
Members i n 1974
O c c u p a t i o n o f Household Head (D)
O C C l t h r u OCC9
Gross Annual Income o f Household
INCOME
Years Resided i n Yellowhead
Days Normally F i s h e d p e r Year i n
Yellowhead
DNrn
Days F i s h e d i n 1974 i n Yellowhead
DF 74Y
P r e f e r r e d Type o f F i s h i n g (D)
PTYFl t h r u PTYF4
Days F i s h e d a t F i r s t F a v o r i t e
Location
DFI ST
M a i l i n g Responded t o by Household (D)
MAIL1 t h r u MAIL9
Compensation Require t o Forego Usage
of F i r s t Favorite Fishing Location
COW R
Average Cost p e r Day f o r F i r s t F a v o r i t e
Fishing Location
AVCPD
W i l l i n g n e s s t o Pay f o r F i r s t F a v o r i t e
Fishing Location
WILLPA
A c t u a l L o c a t i o n of Residence
REGID'
*
(D) d e n o t e s dummy v a r i a b l e
1
Used o n l y f o r i d e n t i f i c a t i o n p u r p o s e s
S i n c e t h e two s e t s o f d a t a were n o t handled i n t h e same manner, i t i s
i n t e r e s t i n g t o n o t e t h e medians and t h e modes from t h e f i s h i n g s u r v e y .
T h e median and mode f o r t h e w i l l i n g n e s s t o pay, t h e compensating v a l u e ,
w e r e $35 and $50.
mode o f $1,000.
The w i l l i n g n e s s t o s e l l had a median o f $700 and a
C l e a r l y , what i s i l l u s t r a t e d by t h e s e v a l u e s i s t h a t
t h e d i f f e r e n t i a l between answers i s v e r y l a r g e no m a t t e r which s t a t i s t i c i s chosen a s a n e v a l u a t o r .
S i n c e t h e model used i n t h i s p a p e r was t o be a rough approximation
o f t h e Harnmack and Brown f o r m u l a t i o n , v a r i a b l e s had t o b e s i n g l e d o u t
as u s e f u l .
The v a r i a b l e l i s t and t h e computer v a r i a b l e code names a r e
r e p r o d u c e d i n Table 11.
V a r i a b l e s which were determined t o b e c l o s e a p p r o x i m a t i o n s t o t h e
v a r i a b l e s i n t h e Hammack and Brown work were: (1) number o f days f i s h e d
b y household members i n 1 9 74, (2) g r o s s a n n u a l income o f household,
( 3 ) days n o r m a l l y f i s h e d p e r y e a r i n t h e Yellowhead r e g i o n , (4) days
f i s h e d i n 1974 i n Yellowhead, (5) compensation r e q u i r e d , (6) a v e r a g e
f i s h i n g r e l a t e d e x p e n d i t u r e s p e r day o f f i s h i n g and (7) w i l l i n g n e s s t o
Pay
A second s e t o f v a r i a b l e s was chosen and t e s t e d even though
Hammack and Brown had found them t o b e i n s i g n i f i c a n t .
are:
(1) t h e m a i l i n g responded t b and (2)'
These v a r i a b l e s
t h e a r e a of r e s i d e n c e .
F i n a l l y , a t h i r d t y p e of v a r i a b l e was s e l e c t e d .
T h i s t h i r d type
w a s n o t used by Hammack and Brown b u t was s u s p e c t e d t o have an e f f e c t
on t h e r e s p o n d e n t s
'
consumer's s u r p l u s measures.
These v a r i a b l e s were :
(1) t o t a l a n g l e r s p e r f a m i l y , (2) age o f household head, ( 3 ) s e x o f
household head, (4) o c c u p a t i o n o f household head, (5) y e a r s r e s i d e d i n
Yellowhead, ( 6 ) p r e f e r r e d t y p e o f f i s h i n g and ( 7 ) days f i s h e d a t f i r s t
-
RD5)
Sex of Household Head (DSEX)
DSEX
Age of Household Head (DAGEI-DAGE~)
DAGEl
DAGE2
DAGE3
DAGE4
DAGE5
DAGE 6
DAGE 7
DAGE 8
Region (RDl
RD1
RD2
RD3
RD4
RD5
Name of V a r i a b l e
1 i f a Male head o f f a m i l y
0 i f a Female head of f a m i l y
0 t o 9 years
10 t o 19 years
20 t o 29 y e a r s
30 t o 39 y e a r s
40 t o 49 y e a r s
50 t o 59 y e a r s
60 t o 69 y e a r s
70 and o v e r
P r i n c e George
K i t i m a t , T e r r a c e , P r i n c e Rupert
S m i t h e r s , H a z e l t o n , Telkwa, Kitiwanga, Houston
Bums Lake, G r a n i s l e , Takysie Lake, Southbank
Vanderhoof, F r a s e r Lake, F o r t F r a s e r , Endaka,
F o r t S t . James, Engen
Variable Specifications
E x p l a n a t i o n of Dummy V a r i a b l e s
TABLE I11
I
P,
N
CO
Mailing Responded t o (MAIL1
MAIL1
MAIL2
MAIL 3
MAIL4
MAIL5
MAIL6
MAIL 7
MAIL 8
MAIL 9
-
-
0CC9)
PTYF4)
-
MAIL9)
P r e f e r r e d Type o f F i s h i n g (PTYF1
PTYFl
PTYF2
PTY F3
PTYF4
Occupation of Household Head (OCC1
OCCl
OCC2
OCC3
OCC4
OCC5
OCC6
OCC7
OCC8
OCC9
F i r s t m a i l completed
Second o r t h i r d m a i l completed
F o u r t h o r f i f t h m a i l completed
F i r s t m a i l incompleted
Second o r t h i r d m a i l incompleted
F o u r t h o r f i f t h m a i l incompleted
F i r s t m a i l recompleted
Second o r t h i r d m a i l recompleted
Fourth o r f i f t h m a i l recompleted
Lake
River ( o r stream)
No p r e f e r e n c e
S a l t water
Labourer
Tradesman o r T e c h n i c a l
Professional
Sales
Clerical
Management and E x e c u t i v e
S e l •’-employed
Retired
Other
f a v o r i t e l o c a t ion.
These v a r i a b l e s were chosen because they may char-
a c t e r i z e o r r e f l e c t on t h e r e s p o n d e n t ' s l i f e s t y l e and m i r r o r d i f f e r e n c e s
i n t h e values associated with fishing opportunities.
Therefore, although
s u c h v a r i a b l e s a r e n o t commonly found i n r e g r e s s i o n models, i t i s p l a u s i b l e t h a t t h e y may i n f l u e n c e a n i n d i v i d u a l ' s answers t o t h e w i l l i n g n e s s
t o pay a n d / o r compensation r e q u i r e d q u e s t i o n s .
A f t e r matching t h e t e l e p h o n e and m a i l s u r v e y s , 944 s u r v e y s were
a v a i l a b l e f o r s o r t i n g on m i s s i n g d a t a .
This s o r t i n g procedure l e f t a
sample s i z e o f 785 f o r t h e r e g r e s s i o n s .
Most o f t h e v a r i a b l e s l i s t e d i n T a b l e I1 have s e l f - e x p l a n a t o r y names.
The v a r i a b l e s though which were u s e d i n dummy v a r i a b l e form need f u r t h e r
clarification.
T h i s c l a r i f i c a t i o n and s p e c i f i c a t i o n a p p e a r s i n Table 111.
The dummy v a r i a b l e s a r e d i s c r e t e r a t h e r t h a n c o n t i n u o u s l y q u a n t i f i a b l e , b u t
n e v e r t h e l e s s may have a b e a r i n g upon e x p l a i n i n g t h e dependent v a r i a b l e .
I n o r d e r t o u n d e r s t a n d t h e r e l a t i o n s h i p of independent t o dependent
v a r i a b l e s , i t i s n e c e s s a r y t o s u g g e s t how t h e two t y p e s o f v a r i a b l e s a r e
related.
The two dependent v a r i a b l e s were compensation r e q u i r e d and
w i l l i n g n e s s t o pay.
The w i l l i n g n e s s t o pay r e l a t i o n s h i p s were p r i m a r i l y
p o s t u l a t e d on t h e b a s i s o f Hammack and Brown's r e g r e s s i o n s .
A s no o t h e r s t u d y was l o c a t e d which a t t e m p t e d t o u s e t h e e q u i v a l e n t
variation i n regressions,
a matter of s p e c u l a t i o n .
i t s r e l a t i o n s h i p t o t h e dependent v a r i a b l e s was
T h e r e f o r e , i t was assumed t h a t most v a r i a b l e s
would r e l a t e t o compensation r e q u i r e d i n t h e same way they r e l a t e d t o
w i l l i n g n e s s t o pay.
I n t h e Hammack and Brown e q u a t i o n , reproduced e a r l i e r , t h e i n d e p e n d e n t
v a r i a b l e s had p o s i t i v e r e l a t i o n s h i p s w i t h w i l l i n g n e s s t o pay.
Variables
i n t h e f i s h i n g s t u d y which a r e c l o s e a p p r o x i m a t i o n s t o t h e Hammack and
Brown v a r i a b l e s a r e income, t h e a v e r a g e c o s t p e r day, and t h e number o f
days f i s h e d i n Yellowhead i n 1974.
There were no c l o s e s u b s t i t u t e s i n
t h e f i s h i n g s u r v e y d a t a f o r t h e h u n t i n g s u r v e y v a r i a b l e o f t h e bagged
w a t e r f o w l p e r day and t h e number o f s e a s o n s h u n t e d .
The e x p e c t e d r e l a t i o n s h i p s between t h e independent v a r i a b l e s and t h e
dependent v a r i a b l e were a s f o l l o w s .
The age v a r i a b l e was e x p e c t e d t o
have b o t h n e g a t i v e and p o s i t i v e s i g n s depending on t h e age c a t e g o r y .
The
o l d e r c a t e g o r i e s such a s 40-49 y e a r s t o 70 y e a r s and o v e r were s u s p e c t e d
t o have p o s i t i v e s i g n s .
The o t h e r c a t e g o r i e s c o u l d have e i t h e r s i g n and
t h e r e was no i n d i c a t i o n b e f o r e r u n n i n g t h e r e g r e s s i o n s a s t o what t h e
s i g n s would b e .
The c o n t i n u o u s , i n d e p e n d e n t v a r i a b l e s were e x p e c t e d t o have p o s i t i v e
c o e f f i c i e n t s e s p e c i a l l y a s t h e numbers became l a r g e r .
These v a r i a b l e s
were t h e t o t a l number o f a n g l e r s p e r household and t h e number o f days
f i s h e d by t h e household.
Only s p e c u l a t i o n s c o u l d b e made c o n c e r n i n g the s i g n s of t h e coe f f i c i e n t of t h e mail variable.
T h i s v a r i a b l e was added b a s i c a l l y i n
o r d e r t o t e s t w h e t h e r t h o s e who responded f i r s t gave h i g h e r o r l o w e r
answers t o t h e w i l l i n g n e s s t o pay and compensation r e q u i r e d q u e s t i o n s .
Having d e c i d e d upon t h e v a r i a b l e s t o b e used i n t h e r e g r e s s i o n s and
t h e h y p o t h e s i z e d s i g n s o f t h e c o e f f i c i e n t s , t h e remainder of t h e f i s h i n g
s t u d y i n v o l v e d a t t e m p t i n g t o reproduce t h e Hamack and Brown model and
regression results.
The f o l l o w i n g s e c t i o n d e s c r i b e s t h e d i f f e r e n t
r e g r e s s i o n s run and t h e r e s u l t s .
R e g r e s s i o n s and R e s u l t s
A s d e s c r i b e d above t h e Hammack and Brown model was t o be used a s
t h e s t a r t i n g p o i n t f o r r e g r e s s i o n s on t h e f i s h i n g s u r v e y d a t a .
The
RD1
0.14
RD3
-0.02
OCC6
0.01
RD2
-0.12
OCC5
-0.03
AVCPD
1.84
21.65*
REGRESSION 4 (Form of LN W i l l p a = A+BX)
INTERCEPT INCOME AVCP
Coefficient
2.95
0.01
0.02
t-values
--2.11* 23.44*
REGRESSION 3 (Form o f LN W i l l p a = A+BX)
INTERCEPT
RD1
RD2
Coefficient
2.85
0.20
0.01
--t-values
1.49
0.07
-2
R
0.42
D.F.
778
S td. E r r o r
0.69
REGRESSION 2 (Form of W i l l p a = a+bX)
INTERCEPT
INCOME
Coefficient
0.50
0.72
---t-values
2.23*
-2
R
0.38
D. F.
782
S t d . E r r o r 63.07
RD3
0.10
0.61
REGRESSION 1 (Form o f W i l l p a = a+bX)
INTERCEPT
OCCl
OCC2
0CC3
Coefficient
23.92
-28.98
-27.50
-22.34
t-values
--- 2.01* - 2.07* - 1 . 5 0
3
0.38
INCOME
D. F.
7 74
(Coefficient)
0.79
S t d . E r r o r 62.77
(t-values)
2.35*
C o r r e l a t i o n of
Independent
Variables
with
Dependent
RD4
0.05
0.24
0CC4
-30.06
- 1.85*
AVCPD
1.83
21.30*
OCC7
0.12
RD4
-0.02
0.01
2.00*
INCOME
OCC5
-30.16
- 1.58
OCC8
-0. 04
OCCl
-0.09
w i l l i n g n e s s t o Pay R e g r e s s i o n R e s u l t s
TABLE I V
-
-
AVCPD
0.02
21.88*
OCC7
-5.94
-0.42
AVCPD
0.61
OCC3
-0.02
OCC8
-26.52
- 1.25
OCC4
0.04
SIMPLE CORRELATIONS**
RD~/RD~
=-0.75
OCC6
-31.10
- 2.16*
-
0.09
INCOME
OCC2
-0.04
= LN X
LTOTA
-2.89
-0.60
Z)
*
**
***
LAVCP
42.93
15.88*
LYRSR
0.53
0.20
LYRSR
0.03
1.55
LDFIS
10.18
3.54*
LDNFY
0.11
2.57*
LDF74
-0.02
-0.35
LAVCP
43.13
15.70"
LAVCP
0.75
33.52*
SIMPLE CORRELATION***
LHD741LDNFY = 0.81
L H D ~ ~ / L D =F ~0.93
~
LHD741LDFIS = 0.63
LDNFY /LDF74 = 0 . 8 3
LDNFY~LDFIS = 0.70
LDF74lLDFIS = 0.65
LDFIS
0.02
0.61
S t u d e n t s t - v a l u e one t a i l e d t e s t : s i g n i f i c a n t a t 5%.
Simple c o r r e l a t i o n s between independent v a r i a b l e s > . 4 , h e r e r e p o r t e d f o r nontransformed v a r i a b l e s .
Simple c o r r e l a t i o n s f o r transformed i n d e p e n d e n t v a r i a b l e s > . 4 .
LAVCP
0.75
33.94*
l = LN X + LN Z)
LTOTA
LHD74
LINCO
-0.04
-0.01
0.12
-0.97
-0.13
2.21*
LDFIS
10.11
3.54*
+ LN
Z)
LINCO
11.52
1.72*
+ LN
REGRESSION 8 (Form o f LN W i l l = LN X + LN Z)
INTERCEPT LINCO
LDFIS
Coefficient
1.03
0.12
0.80
--2.31*
3.43"
t-values
-2
R
0.61
D. F.
781
Std.Error
0.57
REGRESSION 7 (Form o f LN W i l
INTERCEPT
Coefficient
0.89
--t-values
-2
R
0.61
D. F.
776
Std.Error
0.57
REGRESSION 6 (Form o f W i l l p a = LN X
INTERCEPT LINCO
Coefficient
-112.65
10.78
--1.64
t-values
-2
R
0.25
D. F.
78 1
S t d . E r r o r 69.43
REGRESSION 5 (Form o f W i l l p a
INTERCEPT
Coefficient
-114.10
--t-values
-2
R
0.25
D. F.
779
S t d . E r r o r 69.50
D. F.
0.42
782
Std. E r r o r
0.69
-2
R
I
RD1
0.14
RD3
-0.02
OCC6
0.01
RD2
-0.12
OCC5
-0.03
OCC7
0.12
RD4
-0.02
0CC8
-0.04
OCCl
-0.09
INCOME
0.09
OCC2
-0.04
DFIST
-0.91
OCC3
-0.02
AVCPD
0.61
OCC4
0.04
REGRESSION 3 (Form o f Compr = LN X + LN Z)
INTERCEPT LINCO
LDFIS
LAVCP
Coefficient
-56235.22
-1036.97 24347.54 11264.66
--- - 0 . 0 8
4.45*
2.186;
t-values
-2
R
0.02
REGRESSION 2 (Form o f LN Compr = A + BX)
INTERCEPT
RD1
RD2
RD3
RD4
OCCl
Coefficient
5.84
0.66
1.08
0.53
0.77
-1.51
t-values
--1.36
2.17*
0.93
1.13
-2.65*
-2
R
0.04
0CC5
0CC6
0CC7
0CC8
D. F.
769
( C o e f f i c i e n t ) - 0.95 - 1 . 0 3 - 0.98 - 0.59
S t d . E r r o r 2.45
(t-values)
-1.28 -1.82*-1.75*-0.70
0.02
1.86*
INCOME
OCC2
-0.75
-1.44
OCC3
-0.90
-1.53
DFIST
0.01
3.39*
OCC4
-1.20
-1.88*
AVCPD
0.91
3.56*
BEST LINEAR RESULTS PARTIALLY REPRODUCED: (Form o f Compr = a + bX)
Compr = •’(Region, Age, Sex, Occupation, Years Resided i n Yellowhead,
P r e f e r r e d Type o f F i s h i n g )
-2
The
o
n
l
y
s
i
g
n
i
f
i
c
a
n t t - y a l u e s were f o r PTYF1-PTYF3 and were r e s p e c t i v e l y :
R
0.02
D. F.
760
-5.28, -5.15, and -5.14.
S t d . E r r o r 133,093.68
C o r r e l a t i o n of
independent
variables
with
Dependent V a r i a b l e
Compensation Required R e g r e s s i o n R e s u l t s
TABLE V
I
I
PJ
h)
W
H . . .
B
OOOddd
4
\I 1
I II
h
.
.
b o d
a
z
In&
JU
oe
0
. .
II Z O N
W
\I II II
dependent v a r i a b l e s i n t h e e q u a t i o n s were w i l l i n g n e s s t o pay and compensation required.
The r e g r e s s i o n forms used were t h e simple l i n e a r
form, t h e t o t a l l o g a r i t h m i c form, and t h e semi-log forms.
The r e g r e s s i o n r e s u l t s a r e o f i n t e r e s t i n comparing t h e two s e t s
of answers.
The r e s u l t s from o n l y t h e b e s t r e g r e s s i o n runs a r e pro-
duced i n T a b l e s I V and V.
Not a l l t h e v a r i a b l e s d e s c r i b e d i n t h e
p r e v i o u s s e c t i o n a r e l i s t e d i n t h e two t a b l e s .
The v a r i a b l e s excluded
had l i t t l e o r no s i g n i f i c a n c e i n e x p l a i n i n g t h e v a r i a t i o n s i n t h e dependent variables.
-2
Where v a r i a b l e s added l i t t l e t o t h e R
f i c a n t t-values
( l e s s than 1 . 6 5 ) , t h e s e were dropped.5
and had
insigni-
The r e s u l t s i n
T a b l e s I V and V show t h a t t h e t o t a l l o g a r i t h m i c f u n c t i o n s and t h e
p o s i t i v e v a r i a b l e s i g n s of Hammack and Brown's r e g r e s s i o n s were v e r i f i e d
i n t h e f i s h i n g equations.
I n t h e f i s h i n g r e g r e s s i o n s t h e average c o s t f i g u r e was based on a
p e r day b a s i s w h i l e t h e h u n t i n g r e g r e s s i o n s were based on a s e a s o n a l
basis.
This f a c t should not t h e o r e t i c a l l y a f f e c t the r e s u l t s .
The
major d i f f e r e n c e s between t h e b e s t Hammack and Brown e q u a t i o n and t h e
b e s t w i l l i n g n e s s t o pay e q u a t i o n (8) a r e , f i r s t , d i f f e r e n t v a r i a b l e s .
There a r e fewer v a r i a b l e s i n t h e f i s h i n g r e g r e s s i o n .
-2
The second d i f f e r e n c e i s t h e h i g h e r R
i n the fishing equation.
I n p a r t t h i s i s due t o a s m a l l e r sample s i z e f o r t h e f i s h i n g s u r v e y ,
n = 785 a s opposed t o n = 1511 f o r t h e h u n t i n g survey.
A smaller
sample s i z e c a u s e s l e s s random v a r i a t i o n t h a n a l a r g e r s i z e .
The t h i r d d i f f e r e n c e i s i n t h e t - v a l u e s .
The f i s h i n g s u r v e y h a s
a more s i g n i f i c a n t t - v a l u e f o r a v e r a g e c o s t b u t a l e s s s i g n i f i c a n t
t-value
f o r income.
A f i n a l difference t o note i s i n the standard error.
The s t a n d a r d
e r r o r i s s m a l l e r i n t h e f i s h i n g r e g r e s s i o n s than i n t h e waterfowl valu-
a t i o n equations.
T a b l e s I V and V l i s t t h e simple c o r r e l a t i o n between n o t o n l y independent and dependent v a r i a b l e s , b u t a l s o t h e c o r r e l a t i o n s g r e a t e r t h a n
+ .4000 between independent v a r i a b l e s .
-
T h i s i s done w i t h t h e purpose of
examining how i n t e r d e p e n d e n t t h e independent v a r i a b l e s a c t u a l l y a r e .
The Hammack and Brown work does n o t n o t e t h e c o r r e l a t i o n between v a r i ables.
It would b e of p a r t i c u l a r i n t e r e s t t o s e e i f i n t h e waterfowl
e q u a t i o n s whether t h e w i l l i n g n e s s t o pay measure i s a s h i g h l y c o r r e l a t e d
t o t h e average c o s t f i g u r e as i t i s i n t h e f i s h i n g r e s u l t s .
The compensation r e q u i r e d e q u a t i o n s tempt one t o i g n o r e them.
I g n o r i n g t h e r e s u l t s , however, would b e a mistake.
These r e g r e s s i o n s
show t h a t compensation r e q u i r e d does n o t a p p e a r t o b e h i g h l y c o r r e l a t e d
t o any o f t h e independent v a r i a b l e s
.
The i m p l i c a t i o n can b e made t h a t t h e r e must b e o t h e r e x p l a n a t i o n s
f o r t h e w i l l i n g n e s s t o s e l l answers.
This i s e s p e c i a l l y applicable
when i t i s n o t i c e d t h a t changing t h e r e g r e s s i o n form adds l i t t l e t o t h e
-2
R
.
The l a r g e s t
X* w i t h
s i g n i f i c a n t t - v a l u e s i s 0.12.
-2
i n c r e a s e of 0.10 from t h e f i r s t e q u a t i o n ' s R
-2
seem s i z e a b l e e x c e p t when compared t o an R
of 0.02.
T h i s i s an
T h i s change may
i n c r e a s e from 0.38 t o 0 . 6 1
f o r t h e w i l l i n g n e s s t o pay e q u a t i o n s when t h e form i s changed from
l i n e a r t o a t o t a l logarithmic function.
A f i n a l s e t of e q u a t i o n s w a s attempted.
T h i s s e t of r e g r e s s i o n s
w a s b a s e d on a s u g g e s t i o n 6 t h a t consumer's s u r p l u s r e p r e s e n t s n e t benef i t s d e r i v e d by t h e consumer.
Harking back t o M a r s h a l l ' s e x p l a n a t i o n
o f consumer's s u r p l u s , t h e measure s h o u l d be t h e a r e a below t h e demand
c u r v e l e s s t h e t o t a l p r i c e p a i d ( s e e F i g u r e I i n Chapter 1 1 ) .
N o t only i s t h i s regression t h e o r e t i c a l l y appealing, i t i s a l s o
i n t u i t i v e l y appealing.
The i n d i v i d u a l s answering t h e s u r v e y may have
i n t e r p r e t e d t h e q u e s t i o n on w i l l i n g n e s s t o pay a s t h e t o t a l sum o f
A s t h e s u r v e y q u e s t i o n ( s e e Appendix A) does
money t h e y would pay o u t .
n o t s p e c i f i c a l l y a s k f o r a v a l u e n e t of c o s t s , t h e r e g r e s s i o n a s . o u t l i n e d t h e r e f o r e was r e a s o n a b l e .
The c l o s e s t r e p r e s e n t a t i o n of t h e p r i c e w a s t h e average c o s t per
day.
I f w i l l i n g n e s s t o pay was n o t n e t o f c o s t s , t h e n w i l l i n g n e s s t o
pay c o u l d b e used a s a s u b s t i t u t e f o r t h e t o t a l a r e a below t h e demand
curve.
T h i s would l e a d t o a n e q u a t i o n w i t h w i l l i n g n e s s t o pay less
a v e r a g e c o s t p e r day (WILAV) a s t h e dependent v a r i a b l e .
Two forms were run and t h e s i n g l e b e s t r e s u l t s o f t h e s e e q u a t i o n s
are r e p r o d u c e d below.
WILAV = 29.08
(t-values)
-2
R
= 0.02,
+
20.06 (RD1)
(1.53)
33.13 (OCC8)
(-1.47)
+
+ 12.91
(0.96)
( R D ~+
) 15.00 (RD3)
(0.97)
0.83 (INCOME)
(2.33)
S t a n d a r d e r r o r = 66.41, n = 785
The above r e s u l t s a r e i n t e r e s t i n g a l t h o u g h somewhat d i s a p p o i n t i n g .
-2
The m a j o r i n d i c a t i o n o f what o c c u r r e d i s t h e R
.
The a d j u s t e d co-
-2
e f f i c i e n t o f d e t e r m i n a t i o n i s low and i s much l e s s than R ' s f o r t h e
w i l l i n g n e s s t o pay e q u a t i o n s .
The t - v a l u e s a r e n o t very s i g n i f i c a n t
e x c e p t f o r o c c u p a t i o n s 1, 2, 3 , 5 and 6 and income.
There may b e s e v e r a l r e a s o n s why t h e w i l l i n g n e s s t o pay l e s s
a v e r a g e c o s t p e r day r e g r e s s i o n s a r e i n s i g n i f i c a n t .
F i r s t , t h e r e may
Second,
b e c o s t s such a s queueing which a r e n o t taken i n t o a c ~ o u n t . ~
t h e w i l l i n g n e s s t o pay may a c t u a l l y b e n e t o f c o s t s .
This i s suggested
by t h e coding s h e e t i n Appendix A b u t o n l y 180 r e s p o n d e n t s a c t u a l l y
stated this.
Given t h a t 605 r e s p o n d e n t s d i d n o t s a y t h a t t h e w i l l i n g n e s s
t o pay was n e t o f c o s t s , i t may b e concluded t h a t t h e i n d i v i d u a l s i n t h e
t o t a l sample d i d n o t u n d e r s t a n d t h e q u e s t i o n .
I f t h i s i s t h e c a s e , then
t h i s sample i n c l u d i n g t h e 180 r e s p o n s e s o r e x c l u d i n g t h o s e same responses
may n o t b e v a l i d .
S e v e r a l c o n c l u s i o n s can b e d e r i v e d from t h i s c h a p t e r .
Willingness
t o pay i s v e r y w e l l e x p l a i n e d by t h e v a r i a b l e s t h a t Hammack and Brown
suggest.
Also, t h e f u n c t i o n a l form o f t o t a l l o g a r i t h m s p r o v i d e s t h e
b e s t f i t f o r w i l l i n g n e s s t o pay e q u a t i o n s .
The compensation r e q u i r e d ,
e q u i v a l e n t v a r i a t i o n , i s n o t e x p l a i n e d by any o f t h e v a r i a b l e s t o any
s i g n i f i c a n t degree.
The b e s t f i t f o r t h e e q u i v a l e n t v a r i a t i o n was a l s o
t h e t o t a l l o g form b u t even t h i s r e g r e s s i o n had l i t t l e e x p l a n a t o r y
ability
.
One c o n c l u s i o n which cannot b e made i s t h a t t h e two measures l i e
close together.
A s p o i n t e d o u t above, t h e means, medians and modes
between t h e compensating and e q u i v a l e n t v a r i a t i o n s of t h e f i s h i n g d a t a
a r e very l a r g e .
These d i f f e r e n c e s f o r t h e means a r e l a r g e r t h a n t h e
Hammack and Brown r e s u l t due t o t h e f a c t t h a t no o b s e r v a t i o n s were
dropped.
T h i s , however, does n o t e x p l a i n t h e l a r g e d i f f e r e n c e s
between t h e medians and t h e modes.
S i n c e no r e a s o n h a s been l o c a t e d
which e x p l a i n s a l l t h e v a r i a t i o n between t h e two measures, t h e n e x t
c h a p t e r w i l l a t t e m p t t o o f f e r v i a b l e e x p l a n a t i o n s f o r t h e observed
differences.
FOOTNOTES
1
A s P a t i n k i n (1963, 88) p o i n t s o u t , t h e M a r s h a l l i a n consumer's
s u r p l u s cannot b e measured.
2
-2
"Best r e s u l t s " h e r e mean t h e h i g h e s t R
a s s o c i a t e d w i t h c o e f f i c i e n t s and
3
t h e l a r g e s t t-values
the smallest standard error.
Table I i s an i l l u s t r a t i o n o f t h e way Environment Canada used
t h e data.
1976)
,
.
The government h a s r e c e n t l y p u b l i s h e d i t s s t u d y ( S i n c l a i r ,
T h i s p u b l i c a t i o n does n o t d i s c u s s t h e l a r g e v a r i a n c e between
t h e two consumer's s u r p l u s measures.
4
That i s n o t t o s a y t h a t t h e use o f t h e e q u i v a l e n t v a r i a t i o n i s
n e v e r recommended i n t h e l i t e r a t u r e .
I n f a c t , the "willingness to
sell" i s c o n s i d e r e d a v e r y l e g i t i m a t e measure ( K r u t i l l a , e t . a l . ,
19 72 ; Mishan, 1976)
.
What was n o t found a s i n d i c a t e d was an a c t u a l s t u d y which used
t h e e q u i v a l e n t measure i n a s e t of r e g r e s s i o n s .
5
C e r t a i n v a r i a b l e s were given an e x t r a s t a t i s t i c a l t e s t b e f o r e
t h e y were d i s c a r d e d .
These v a r i a b l e s were o c c u p a t i o n , age and r e g i o n .
The s t a t i s t i c a l t e s t i s one o u t l i n e d by Maki (1971)
.
The t e s t i s a
p a r t i a l F-test defined as:
T h i s p a r t i a l F - t e s t was a t t e m p t e d by t a k i n g t h e b e s t r e g r e s s i o n s
f o r b o t h t h e w i l l i n g n e s s t o pay and compensation r e q u i r e d e q u a t i o n s
a n d t h e n a d d i n g o n e o f t h e t h r e e v a r i a b l e s , o c c u p a t i o n , a g e and
region.
None o f t h e s e v a r i a b l e s , even g i v e n t h i s s p e c i a l t e s t ,
p r o v e d s t a t i s t i c a l l y s i g n i f i c a n t a t a 5% l e v e l of s i g n i f i c a n c e .
The r e s u l t s o f t h e tests are o u t l i n e d i n t h e f o l l o w i n g c h a r t .
1. LCOMP = f(OCC1 - OCC8, LINCO, LDFlS, LAVCP)*
P a r t i a l F = ( . I 3 1 3 8 - . l 2 3 4 6 ) (785-8-3-1)
( 1 - .13138)8
1 0.88102
C r i t i c a l F i s 1 . 7 7 , t h e r e f o r e 0.88102 < 1 . 7 7
2.
LCOMP = f(RD1
-
RD4, LINCO, LDFIS, LAVCP) *
P a r t i a l F = (.12669 - . l 2 3 4 6 ) (785-4-3-1)
( 1 - .12669)4
C r i t i c a l F i s 2.385,
3.
-
LCOMP = f(DAGE2
1 0.71845
t h e r e f o r e 0.71845 < 2.385
DAGE8, LINCO, LDFIS, LAVCP)*
P a r t i a l F = (.I2959 - . l 2 3 4 6 ) (785-7-3-1)
( 1 - .l2959) 7
A
0.77872
C r i t i c a l F i s 1.805, t h e r e f o r e 0.77872 < 1.805
4.
LWILL = f(OCC1
-
OCC8, LINCO, LDFIS, LAVCP)**
P a r t i a l F (.61272
(1
Critical F i s 1.77,
5.
LWIL'L
=
f (RD1
-
.6O696) (785-8-3-1)
- .61272)8
A
1.4371
t h e r e f o r e 1.4371 < 1.77
RD4, LINCO, LDFIS, LAVCP)**
P a r t i a l F = (.60976 - .6O696) (785-4-3-1)
( 1 - .60976)4
A
1.39376
C r i t i c a l F i s 2.385, t h e r e f o r e 1.39376 < 2.385
6.
LWILL = f(DAGE2
-
DAGE8, LINCO, LDFIS, LAVCP)**
P a r t i a l F = (.60800
(1
-
-
.60696)(785-7-3-1)
.60800) (7)
0.29335
C r i t i c a l F i s 1.805, t h e r e f o r e 0.29335 < 1.805
*
These e q u a t i o n s compared w i t h LCOMP = f(LINC0, LDFIS, LAVCP)
from Table V.
**
These e q u a t i o n s compared w i t h LWILL =, f(LINC0, LDFIS, LAVCP)
from Table I V .
6
D.R.
7
B a r z e l s t a t e s t h a t f r e e goods a r e u s u a l l y n o t f r e e .
Maki i n a c o n v e r s a t i o n , 1976.
That i s a
z e r o money p r i c e may e x i s t b u t w a i t i n g time, e t c . w i l l be t h e r a t i o n i n g d e v i c e which r e p l a c e s t h e d o l l a r p r i c e ( B a r z e l , 1974, 73).
CHAPTER I V
E x p l a n a t i o n s of V a r i a t i o n s i n ~ o n s u m e r ' s S u r p l u s Measures
Having p r e s e n t e d t h e t h e o r y of consumer's s u r p l u s and having
r e p o r t e d a n a c t u a l s e t of s u r v e y r e s u l t s u s i n g consumer's s u r p l u s
m e a s u r e s , t h e q u e s t i o n s t i l l remains t o b e answered:
"What e x p l a i n s
t h e v e r y l a r g e d i f f e r e n c e s between t h e two consumer's s u r p l u s e x p r e s s i o n s ? " '
T h i s c h a p t e r i s an a t t e m p t t o e x p l a i n how t h e p r e s c r i p t i o n o f p r o p e r t y
r i g h t s may a f f e c t t h e r e s p o n s e s of i n d i v i d u a l s surveyed.
Secondly,
t h i s c h a p t e r w i l l a t t e m p t t o e x p l a i n how t h e c o n c e p t s of c o m p e t i t i o n
and monopoly may h o l d c l u e s t o t h e v a r i a n c e between t h e compensating
and e q u i v a l e n t measurements.
Income E l a s t i c i t y a s a n E x p l a n a t i o n of V a r i a n c e
B e f o r e e x p l a i n i n g how p r o p e r t y r i g h t s may a f f e c t t h e consumer's
s u r p l u s measurements, i t i s n e c e s s a r y t o u n d e r s t a n d t h e d i f f e r e n c e
between e x p l i c i t and i m p l i c i t p r o p e r t y r i g h t s .
Explicit property
r i g h t s a r e t h o s e r i g h t s s e t o u t by law a s s i g n i n g t h e u s e of a r e s o u r c e
t o a c e r t a i n i n d i v i d u a l o r group of i n d i v i d u a l s . 2
On t h e o t h e r hand,
i m p l i c i t r i g h t s a r e n o t s e t o u t by law b u t r a t h e r are p r o p e r t y r i g h t s
a t t a i n e d through usage.
3
When d i s c u s s i n g t h e u s e s of consumer's s u r p l u s i n economics, t h e
p r i n c i p l e measurements a r e of i m p l i c i t p r o p e r t y r i g h t s .
F o r example
t h e h u n t i n g and f i s h i n g s u r v e y s measured i n d i v i d u a l s ' r i g h t s t o u s e a
r e s o u r c e which t h e y do n o t own.
According t o Hammack and Brown, however,
t h e two measurements of consumer's s u r p l u s can b e used t o e x p l a i n
why t h e r e i s a v a r i a n c e between t h e two answers of an i n d i v i d u a l
(1974, 6-7)
.
Given an income e l a s t i c i t y g r e a t e r than zero means t h a t t h e
w i l l i n g n e s s t o s e l l measure w i l l b e l a r g e r than t h e w i l l i n g n e s s t o
pay measure.
I n t h i s s i t u a t i o n income changes cause corresponding
changes i n t h e demand f o r t h e good.
The p o s i t i v e income e f f e c t f e e d s
i n t o a r e s p o n d e n t ' s answers t o t h e two q u e s t i o n s i n t h e f o l l o w i n g
manner.
When t h e i n d i v i d u a l i s asked t o s e l l h i s p r o p e r t y r i g h t ,
h i s answer r e f l e c t s t h e c o n s t r a i n t he f e e l s due t o h i s income.
The
w i l l i n g n e s s t o s e l l answer i s n o t , however, c o n s t r a i n e d by t h e i n d i v i d u a l ' s income.
The s i t u a t i o n a s d e s c r i b e d h o l d s a s l o n g as t h e
good i n q u e s t i o n i s n o t an i n f e r i o r good.
5
The above e x p l a n a t i o n o n l y shows t h a t one consumer's s u r p l u s
v a r i a t i o n w i l l b e g r e a t e r than t h e o t h e r .
What i s n o t i l l u s t r a t e d
i s why t h e e q u i v a l e n t v a r i a t i o n i s s o very much l a r g e r than t h e
compensating v a r i a t i o n , e s p e c i a l l y o v e r a r e l a t i v e l y s m a l l range o f
a p e r s o n ' s r e a l income.
Consequently, t h i s e x p l a n a t i o n a l o n e a p p e a r s
t o b e l e s s t h a n a d e q u a t e and f u r t h e r e x p l a n a t i o n s s h o u l d be examined.
P r o p e r t y R i g h t s and Non-In t r i n s i c B e n e f i t s
Chapter I11 c i t e d a c o r r e l a t i o n between t h e w i l l i n g n e s s t o pay
r e s p o n s e s and t h e a v e r a g e c o s t p e r day of an a c t i v i t y .
This c o r r e l a t i o n
i n d i c a t e s t h a t t h e i n d i v i d u a l i s d e r i v i n g b e n e f i t s from f i s h i n g above
h i s c o s t s and i f n e c e s s a r y , would pay o u t t h a t s u r p l u s i n o r d e r t o
continue p a r t i c i p a t i o n i n t h i s a c t i v i t y .
The w i l l i n g n e s s t o pay f i g u r e was u s u a l l y a s m a l l d o l l a r amount
and was always l e s s than t h e i n d i v i d u a l ' s a n n u a l income.
This
i l l u s t r a t e s how t h e income c o n s t r a i n t o f t h e i n d i v i d u a l bounds h i s
answer t o t h e w i l l i n g n e s s t o pay q u e s t i o n .
A l t e r n a t i v e l y , compensation r e q u i r e d was n o t h i g h l y c o r r e l a t e d
w i t h any exogenous v a r i a b l e s i n c l u d i n g average c o s t and income.
The
i m p l i c a t i o n i s t h a t t h e compensation r e q u i r e d i s n o t bounded by an
income c o n s t r a i n t .
I n support of t h i s statement is t h e f a c t t h a t
most i n d i v i d u a l s surveyed i n t h e B. C. s p o r t f i s h i n g survey c i t e d a
compensation r e q u i r e d which was much l a r g e r t h a n t h e i r annual income.
W i l l i n g n e s s t o s e l l , t h e r e f o r e , must b e b a s e d on t h i n g s i n t e r n a l t o
t h e respondents.
There a r e many i n t e r n a l p r o c e s s e s which may i n f l u e n c e t h e w i l l i n g n e s s t o s e l l answers.
Some of t h e s e i n t e r n a l f a c t o r s t h a t a r e r e l a t e d
t o t h e p r o p e r t y r i g h t s a s s i g n e d may b e n o n - i n t r i n s i c b e n e f i t s , i n t e r n a l
r a t e s o f r e t u r n , o p t i o n demand and s t r a t e g i e s used t o answer
questionnaires.
N o n - i n t r i n s i c b e n e f i t s r e f e r t o b e n e f i t s which a r e n o t c a p t u r e d
by t h e market p r i c e b u t which a r e d e r i v e d by t h e p r o p e r t y r i g h t owner.
An example of a n o n - i n t r i n s i c b e n e f i t would b e t h e memories an
i n d i v i d u a l h a s s u r r o u n d i n g h i s a n c e s t r a l home.
T h i s b e n e f i t would
n o t a c c r u e t o someone e l s e buying t h e home and t h e r e f o r e , would n o t
b e i n c l u d e d i n t h e market p r i c e .
Although n o n - i n t r i n s i c b e n e f i t s e x i s t when t h e respondent answers
b o t h t h e w i l l i n g n e s s t o pay and w i l l i n g n e s s t o s e l l q u e s t i o n s , t h e
e x i s t e n c e of t h e s e b e n e f i t s w i l l b e t o i n f l u e n c e t h e answers d i f f e r e n t l y .
Even when t h e i n d i v i d u a l d e r i v e s non-in t r i n s i c b e n e f i t s from a
p r o p e r t y r i g h t , h e w i l l s t i l l answer t h e w i l l i n g n e s s t o pay q u e s t i o n
a c c o r d i n g t o h i s income c o n s t r a i n t .
Therefore, non-intrinsic b e n e f i t s
may cause an i n f l a t i o n o f t h e w i l l i n g n e s s t o pay answer b u t t h i s
answer w i l l b e s m a l l e r than t h e compensation r e q u i r e d response.
The w i l l i n g n e s s t o s e l l answer may b e i n f l a t e d b y t h e i n d i v i d u a l
r e s p o n d i n g f o r two r e a s o n s .
F i r s t , t h e i n d i v i d u a l would a t t e m p t t o
e n s u r e t h a t i f h i s p r o p e r t y were t a k e n away, h e would b e compensated
f o r t h e l o s s of h i s n o n - i n t r i n s i c b e n e f i t s .
Second, t h e i n d i v i d u a l
would i n c r e a s e h i s r e s p o n s e t o t h e w i l l i n g n e s s t o s e l l q u e s t i o n i n
order t o s t o p the expropriation of h i s property r i g h t .
The f i s h i n g s u r v e y d e a l t w i t h a r e g i o n where s u b s t i t u t e f i s h i n g
l o c a t i o n s abound i n l a r g e numbers.
With s o many s u b s t i t u t e s a v a i l -
a b l e t h e i n d i v i d u a l r e s p o n d e n t s may n o t have a s t r o n g p r e f e r e n c e
between a l t e r n a t i v e f i s h i n g a r e a s e s p e c i a l l y when n o t i n g t h a t some
o f t h e fishermen had been f i s h i n g f o r o n l y a few s e a s o n s .
The
i m p l i c a t i o n i s t h a t t h e fishermen i n q u e s t i o n p r o b a b l y had n o t formed
s t r o n g e m o t i o n a l f e e l i n g s t o any one p a r t i c u l a r l a k e o r stream.
Since
673 o u t o f t h e 785 r e s p o n d e n t s t o t h e f i s h i n g survey gave answers
g r e a t e r than t h e w i l l i n g n e s s t o pay mean, i t can b e assumed t h a t t h e
n o n - i n t r i n s i c b e n e f i t s do n o t e x p l a i n a l l of t h e d i f f e r e n c e between t h e
w i l l i n g n e s s t o pay and w i l l i n g n e s s t o s e l l r e s p o n s e s .
I n t e r n a l R a t e s of Return a s an E x p l a n a t i o n
A second r e a s o n f o r t h e l a r g e v a r i a n c e between an i n d i v i d u a l ' s
r e p o n s e s may b e due t o h i s i n t e r n a l r a t e s of r e t u r n .
Internal rates
o f r e t u r n a r e numbers which when used t o d i s c o u n t r e t u r n s from a s s e t s ,
h y p o t h e t i c a l l y make t h e p r e s e n t v a l u e o f r e t u r n s e q u a l t o z e r o (Herf i n d a h l and Kneese, 19 74, 198-9)
.
D i f f e r e n t views o f i n t e r n a l r a t e s of r e t u r n would o n l y b e an i n f l u ence i n t h e q u e s t i o n r e g a r d i n g w i l l i n g n e s s t o s e l l .
When an i n d i v i d u a l
i s f a c e d w i t h l o s i n g an a s s e t , h e w i l l a t t e m p t t o e x t r a c t a p r i c e l a r g e r
t h a n what he would b e w i l l i n g t o pay.
T h i s l a r g e r response t o t h e
w i l l i n g n e s s t o s e l l q u e s t i o n i s an a t t e m p t on t h e i n d i v i d u a l ' s p a r t t o
r e c o v e r t h e f u t u r e b e n e f i t s he h a s l o s t by having t o s e l l h i s p r o p e r t y .
The concept o f i n t e r n a l r a t e s of r e t u r n may a l s o b e used t o e x p l a i n
t h e v a r i a n c e i n t h e answers of d i f f e r e n t i n d i v i d u a l s .
A t age 20 an
i n d i v i d u a l e x p e c t s t o d e r i v e b e n e f i t s from h i s p r o p e r t y f o r approximately
45 more y e a r s .
T h i s i m p l i e s t h a t h i s answer t o t h e w i l l i n g n e s s t o s e l l
response w i l l be very l a r g e .
On t h e o t h e r hand, an i n d i v i d u a l who i s
m i d d l e aged h a s a s h o r t e r time h o r i z o n due t o h i s p r e s e n t age.
Conse-
q u e n t l y , t h e middle aged p e r s o n would have a lower i n t e r n a l r a t e o f
r e t u r n and w i l l g i v e a s m a l l e r answer t o t h e q u e s t i o n r e g a r d i n g t h e
equivalent variation.
Two c o m p l i c a t i o n s a r i s e when d i s c u s s i n g i n d i v i d u a l s approaching
r e t i r e m e n t age.
The f i r s t complexity i s due t o h i g h e r investment i n
equipment made by i n d i v i d u a l s .
T h i s h i g h e r investment may cause t h e
o l d e r i n d i v i d u a l s t o e x p e c t n o t o n l y a r e t u r n from t h e p r o p e r t y b u t
a l s o a r e t u r n from t h e i r equipment.
Second, t h e r e i s t h e f a c t t h a t i n d i v i d u a l s o f r e t i r e m e n t age may
p l a c e a v e r y l a r g e v a l u e on t h e i r p r o p e r t y r i g h t s .
T h i s second compli-
c a t i o n may b e e x p l a i n e d by t h e i d e a t h a t r e t i r e e s have more t i m e t o
e n j o y t h e i r a c t i v i t i e s e s p e c i a l l y r e c r e a t i o n a l p u r s u i t s and t h i s group
may b e l e s s t r a n s i e n t i n n a t u r e than younger i n d i v i d u a l s .
Therefore,
t h e s e i n d i v i d u a l s p l a c e a h i g h e r v a l u e on p r o p e r t y a s s o c i a t e d w i t h a
s p e c i f i c u s e , such a s a f a v o r i t e f i s h i n g s p o t .
Two g r a p h s have been drawn t o i l l u s t r a t e how p e r c e i v e d i n t e r n a l
r a t e s o f r e t u r n may b e d e p i c t e d .
I.
The two g r a p h s a r e d i s p l a y e d i n C h a r t
Graph A r e p r e s e n t s i n d i v i d u a l s from t h e f i s h i n g s u r v e y who r e c e i v e d
a $13,000 income p e r annum w h i l e Graph B d e p i c t s t h o s e i n d i v i d u a l s who
e a r n e d a $20,000 a n n u a l income.
The g r a p h i n g o f b o t h graphs i s o f t h e
means o f t h e compensation r e q u i r e d f o r t h o s e i n d i v i d u a l s i n one age
group.
S i n c e s p e c i f i c knowledge o f t h e i n d i v i d u a l ' s age was unknown,
t h e mid-points o f e a c h age c l a s s were u s e d i n t h e graphing.
Graph A a s drawn h a s t h e b e g i n n i n g o f a U-shaped
function.
This
f u n c t i o n a l s h a p e f i t s t h e e x p l a n a t i o n o f e x p e c t e d i n t e r n a l rates o f
r e t u r n as d i s c u s s e d above.
The younger i n d i v i d u a l s p l a c e h i g h v a l u a t i o n s
on p r o p e r t y r i g h t s because o f t h e i r e x p e c t e d span o f l i f e .
aged v a l u e i s l o w e r t h a n t h e young a n d / o r o l d e r i n d i v i d u a l s .
The middle
This is
due t o t h e i r h a v i n g a s h o r t e r s p a n than t h e 2 4 . 5 y e a r o l d s and a l o w e r
i n v e s t m e n t i n equipment than t h e 5 4 . 5 y e a r o l d s .
The second graph (B) does n o t have a U-shape.
It is not d i f f i c u l t ,
t o e x p l a i n away t h e p o i n t f o r t h e 20-29 age group which c a u s e s t h e shape
problem.
An income o f $20,000 p e r y e a r i s a r e l a t i v e l y l a r g e income
b e i n g e a r n e d by such a young group o f p e o p l e .
I t may be h y p o t h e s i z e d
t h a t t h e s e i n d i v i d u a l s spend s o much of t h e i r t i m e working t h a t they do
n o t f u l l y a p p r e c i a t e t h e i r r i g h t s t o t h e use of p r e s e n t l y a v a i l a b l e
fishing resources.
I n both graphs t h e r e i s a s i g n i f i c a n t l a c k of information.
The inform-
a t i o n m i s s i n g i s t h e s p e c i f i c a g e s o f i n d i v i d u a l s and t h e number o f y e a r s
-
47a
-
CHART I
Compensation R e q u i r e d and Age
Graph A
0
4.5
14.5
24.5
34.5
Graph B
44.5
54.5
64.5
r e s i d e n t i n the region.
This l a c k i s p a r t i c u l a r l y apparent i n attempting
t o e x p l a i n t h e 24.5 p o i n t on Graph B.
I t may b e t h a t a l l t h e i n d i v i d u a l s
e a r n i n g $20,000 p e r y e a r a r e c l o s e r i n age t o 29 t h a n t o 20.
b e t h a t t h i s income b r a c k e t i s very t r a n s i e n t i n n a t u r e .
Also, i t may
I f those with a
low compensation r e q u i r e d were 20 y e a r s v e r s u s h i g h e r e q u i v a l e n t v a r i a t i o n s
d e n o t e d by 20 y e a r o l d s , o r i f t h i s income b r a c k e t i s very t r a n s i e n t , then
t h e U-shaped
f u n c t i o n might s t i l l e x i s t i n Graph B.
7
Option Demand a s an E x p l a n a t i o n
Option demand h a s been s u g g e s t e d a s an e x p l a n a t i o n of t h e d i f f e r e n c e
between t h e two consumer's s u r p l u s measures.
One w i d e l y a c c e p t e d d e f i n -
i t i o n o f o p t i o n demand i s " a w i l l i n g n e s s t o pay f o r r e t a i n i n g a n o p t i o n
t o u s e an a r e a o r f a c i l i t y t h a t would be d i f f i c u l t o r i m p o s s i b l e t o r e p l a c e and f o r which no c l o s e s u b s t i t u t e i s a v a i l a b l e " ( R r u t i l l a ,
\
1967, 780).
The key t o u n d e r s t a n d i n g o p t i o n demand and i t s i n f l u e n c e on t h e cons u m e r ' s s u r p l u s measures i s u n c e r t a i n t y .
The u n c e r t a i n t y comes from t h e
f a c t t h a t an i n d i v i d u a l i s b e i n g r e q u e s t e d t o pay f o r a r e s o u r c e which he
may n e v e r u s e ( B y e r l e e , 1971, 523; C i c c h e t t i and Freeman, 1971, 528).
T h i s u n c e r t a i n t y f a c t o r may i n f l u e n c e an i n d i v i d u a l ' s w i l l i n g n e s s t o pay
answer b y c a u s i n g t h e r e s p o n s e t o b e lower than i f t h e i n d i v i d u a l was
c e r t a i n of consuming t h e good.
T h i s i n combination w i t h t h e consumer's
income c o n s t r a i n t c o u l d cause a v e r y low w i l l i n g n e s s t o pay.
O p t i o n demand would p l a y a r o l e even i n a f i s h i n g s u r v e y where t h e
r e s p o n d e n t s were known fishermen.
One f a c t n o t e d concerned t h e number
of t i m e s p e r y e a r an i n d i v i d u a l f i s h e d .
Many i n d i v i d u a l s r a r e l y went
f i s h i n g more t h a n once o r t w i c e a y e a r .
I n f r e q u e n t u s e r s may b e much
l e s s w i l l i n g t o pay a l a r g e p o r t i o n o f t h e i r incomes f o r an a c t i v i t y
t h e y may n o t pursue n e x t y e a r .
The l o g i c o f t h e s i t u a t i o n i s t h a t once
a n i n d i v i d u a l pays o u t h i s money, i t i s l o s t r e g a r d l e s s of w h e t h e r o r
n o t h e u s e s h i s o p t i o n t o consume o r n o t .
By analogy t h e u n c e r t a i n t y a s s o c i a t e d w i t h o p t i o n demand may a l s o
a f f e c t t h e answers t o t h e w i l l i n g n e s s t o s e l l 'query i n two ways.
Since
t h e consumer does n o t have p e r f e c t knowledge, h e cannot be c e r t a i n t h a t
t h e property r i g h t he i s s e l l i n g i s replaceable.
I f the property right
i s s u f f i c i e n t l y unique i n t h e r e s p o n d e n t ' s mind, he may name a v e r y
l a r g e amount of money.
A second u n c e r t a i n t y a s s o c i a t e d w i t h t h e w i l l i n g n e s s t o s e l l q u e s t i o n
i s t h e money.
The consumer does n o t know i f h e w i l l r e c e i v e any money o r
when h e w i l l r e c e i v e
ty
sum.
extremely l a r g e willingn&s
T h e r e f o r e , t h e consumer may b e naming an
t o s e l l sum f o r two reasons.
F i r s t , the
i n d i v i d u a l may b e a t t e m p t i n g t o h a l t t h e c o n f i s c a t i o n of t h e p r o p e r t y
right.
Second, t h e consumer may b e d i s c o u n t i n g t h e l a r g e sum named o v e r
an i n d e f i n i t e time p e r i o d s i n c e h e does n o t know when he w i l l r e c e i v e
t h e payment.
O p t i o n v a l u e , l i k e t h e i n t e r n a l r a t e o f r e t u r n , i s based on t h e
f u t u r e consumption of a good.
I n case of surveys dealing with individuals
who a c t u a l l y a r e u s i n g a r e s o u r c e , t h e p r e s e n c e of an o p t i o n demand may
b e a n o t h e r p a r t i a l e x p l a n a t i o n o f t h e d i v e r g e n t answers.
This i s
e s p e c i a l l y t r u e i n t h e c a s e of w i l l i n g n e s s t o pay responses.
However,
i t i s i m p o s s i b l e t o know w i t h c e r t a i n t y whether o p t i o n demand accounted
f o r a l l the difference.
A s e r i o u s problem a r i s e s i n c o n n e c t i o n w i t h e x p l a i n i n g t h e d i f f e r e n c e s when t h e r e s o u l L e s i n q u e s t i o n a r e consumed o f t e n .
This f a c t would
d e f i n i t e l y a f f e c t t h e w i l l i n g n e s s t o s e l l q u e s t i o n a s u n c e r t a i n t y would
n o t b e such a p r i n c i p l e i n f l u e n c e .
I n t h e c a s e o f a f r e q u e n t fisherman,
h e i s l i k e l y t o know o f many s u b s t i t u t e s i f he were t o l o s e h i s f a v o r i t e
fishing location.
He knows how e a s y i t i s t o r e p l a c e a f i s h i n g s p o t .
T h e r e f o r e , t h i s fisherman i s n o t a s l i k e l y t o name a v e r y l a r g e sum a s
under circumstances of u n c e r t a i n t y .
O p t i o n v a l u e might b e measured by a p p r o x i m a t e l y t h e same s u r v e y
q u e s t i o n s a s t h e o t h e r measures o f consumer's s u r p l u s .
This implies
t h a t t h e i n d i v i d u a l s a r e g i v e n t h e same i m p l i c i t p r o p e r t y r i g h t s as
p o i n t e d o u t above.
Consequently, w h a t e v e r i s c a u s i n g t h e v a r i a n c e
between t h e consumer's s u r p l u s measures may a l s o b e t h e c a u s e o f t h e
differences i n option value stqveys.
S t r a t e g i e s , Welfare Loss and D i s c o n t i n u o u s U t i l i t y
S t r a t e g y i n answering s u r v e y q u e s t i o n s h a s a l s o been s u g g e s t e d a s
a n e x p l a n a t i o n o f t h e v a r i a n c e between a n i n d i v i d u a l ' s r e s p o n s e s (T.E.
Borcherding, 1976).
The s t r a e e g y i s b a s e d on t h e i d e a t h a t i n d i v i d u a l s
might r a t i o n a l l y o v e r s t a t e t h e i r compensations r e q u i r e d .
The o v e r s t a t e m e n t would o c c u r i n o r d e r t o s t o p t h e e x p r o p r i a t i o n
o f a r e s o u r c e f o r u s e s o t h e r t h a n t h e one t h e i n d i v i d u a l p a r t i c i p a t e s
in.
The primary r e a s o n f o r s u c h a s t r a t e g y i s a f e a r of n o t b e i n g
compensated and y e t h a v i n g l o s t t h e r e s o u r c e by n o t keeping h i s p r i c e
high.
Rather than allow t h i s t o occur, t h e i n d i v i d u a l w i l l o v e r s t a t e
h i s b e n e f i t s from t h e p r e s e n t u s e of t h e r e s o u r c e .
This s t r a t e g y i s
more l i k e l y t o b e f o l l o w e d , t h e h i g h e r t h e s u b j e c t i v e p r o b a b i l i t y o f
such an e x p r o p r i a t i o n .
T h i s would cause a b e n e f i t - c o s t r a t i o
based
on s u c h answers t o f a v o r n o t a l t e r i n g t h e employment of t h e r e s o u r c e .
A s i n t h e c a s e o f n o n - i n t r i n s i c b e n e f i t s , t h e s t r a t e g y of answering
s u r v e y q u e s t i o n s may s e r v e t o e x p l a i n some of t h e r e s p o n d e n t s ' answers.
The o n e problem which t h i s e x p l a n a t i o n does n o t t a k e i n t o a c c o u n t i s t h e
l a r g e number o f s u b s t i t u t e s .
A s above, some i n d i v i d u a l s i n t h e f i s h i n g
s u r v e y might f i n d t h e i r f i r s t f a v o r i t e f i s h i n g l o c a t i o n v e r y i m p o r t a n t .
For o t h e r s , however, t h e r e i s p r o b a b l y l i t t l e d i f f e r e n c e between t h e
f i r s t and second and t h e f i r s t and t h i r d f a v o r i t e l o c a t i o n s .
Mishan (19 76) o f f e r s a n o t h e r e x p l a n a t i o n f o r t h e magnitudes of d i f f e r e n c e b a s e d upon t h e i d e a o f a w e l f a r e l o s s .
T h i s e x p l a n a t i o n i s de-
r i v e d from t h e s i t u a t i o n where one could use b o t h t h e compensating and
e q u i v a l e n t v a r i a t i o n s i n d e c i d i n g whether t o proceed w i t h a p r o j e c t o r
not
.
The problem a r i s e s when one measure, f o r example b h e compensating
v a r i a t i o n , l e a d s one t o t h i n k t h a t a p r o j e c t s h o u l d b e s t a r t e d .
The
e q u i v a l e n t v a r i a t i o n i n t h i s example would s u g g e s t t h a t t h e p r o j e c t
s h o u l d n e v e r b e begun.
Mishan (1976, 195) s t a t e s t h a t t h i s s i t u a t i o n
i s a r e s u l t o f t h e w e l f a r e l o s s f e l t by t h e i n d i v i d u a l s .
Although t h e magnitude o f d i f f e r e n c e may be due t o a w e l f a r e l o s s ,
Mishan does n o t e x p l a i n why t h e i n d i v i d u a l s always f e e l t h i s l o s s .
In
o t h e r words when an i n d i v i d u a l i s f a c e d w i t h t h e l o s s of one o f many
f i s h i n g l o c a t i o n s , o r one o f many s m a l l c i t y p a r k s , t h e w e l f a r e l o s s
e x p l a n a t i o n seems t o b e l a c k i n g .
I n o r d e r t o have a t o t a l e x p l a n a t i o n
o f t h e magnitude o f d i f f e r e n c e s , i t a p p e a r s t h a t i n d i v i d u a l s ' p e r c e p t i o n
o f f a c t s , and n o t j u s t t h e f a c t s , s h o u l d b e examined.
Another a l t e r n a t i v e e x p l a n a t i o n o f t h e v a r i a t i o n between t h e answers
may b e due t o t h e i d e a t h a t t h e two q u e s t i o n s a r e an a t t e m p t t o compare
a s i t u a t i o n which i s d i s c o n t i n u o u s .
That i s , t h e i n d i v i d u a l i s b e i n g
a s k e d t o compare two d i f f e r e n t b u n d l e s o f goods which a r e n o t i n t h e
same commodity s p a c e .
... , Xn,
X2,
g i v e n by U1 = f(X1.
t h e U2 s i t u a t i o n X
For e a s e o f e x p o s i t i o n t h e two b u n d l e s would b e
1
Y) and U 2 = f(X2,
. . .. Xn,
Y).
In
h a s been e n t i r e l y d e l e t e d from t h e i n d i v i d u a l ' s
consump t i o n .
The w i l l i n g n e s s t o pay q u e s t i o n i s a n a t t e m p t t o g e t t h e respondent
t o determine how much more he would pay f o r t h e commodity bundle U1 t h a t
h e already possesses.
The w i l l i n g n e s s t o s e l l q u e s t i o n uses s i t u a t i o n
U2 where X1 h a s been taken away by g i v i n g t h e i n d i v i d u a l h i s r e q u e s t e d
---
increase i n Y.
-- .
1
.
T h i s method i s a means f o r t h e s u r v e y o r t o a t t e m p t t o
f o r c e t h e consumer t o s u b s t i t u t e (X
2'
. .., Xn,
Y) f o r XI.
The i n d i v i d u a l f e e l i n g an income c o n s t r a i n t i n s i t u a t i o n U
1
and
a l r e a d y h a v i n g X1 w i l l o n l y pay a s m a l l sum of money t o c o n t i n u e consumi n g XI.
I n t h e second s i t u a t i o n t h e i n d i v i d u a l does n o t want t o s u b s t i -
t u t e and i s s o f a m i l i a r w i t h t h e c h a r a c t e r i s t i c s of X1
v e r y l a r g e sum o f money.
h i s l o s s of X
1
t h a t h e names a
This sum of money i s a r e f l e c t i o n n o t o n l y of
b u t i s compensation f o r t h e consumer's time which w i l l b e
s p e n t s e e k i n g o u t t h e c h a r a c t e r i s t i c s o f a l l o t h e r goods.
This character-
i s t i c s s e a r c h w i l l b e t h e o n l y means t h e consumer h a s of r e p l a c i n g X
1
adequately.
T h i s a l t e r n a t i v e cannot be d i s c u s s e d u s i n g a two dimensional diagram.
I n f a c t , t h e problem may b e such a s t o make i t more of a L a n c a s t e r chara c t e r i s t i c s diagram w i t h v e c t o r s f o r a t l e a s t 3 goods, Y , X1 and X2 and
two c h a r a c t e r i s t i c s , C1
and C2.
I f t h i s i s t h e e x p l a n a t i o n we r e q u i r e t o understand t h e compensating
and e q u i v a l e n t v a r i a t i o n s , i t makes t h e use o f b o t h measures s u s p i c i o u s .
T h i s i s one l i n e o f argument which s h o u l d be pursued f u r t h e r i n o r d e r t o
d e t e r m i n e i f t h i s c r i t i c i s m o f t h e use o f consumer's s u r p l u s i s powerful
enough t o make i t s usage q u e s t i o n a b l e .
One f i n a l e x p l a n a t i o n w i l l b e o f f e r e d i n t h e n e x t s e c t i o n .
The
e x p l a n a t i o n w i l l s u g g e s t t h a t t h e i n d i f f e r e n c e c u r v e s o f a n all-or-none
n a t u r e o f f e r a f u r t h e r means o f examining t h e d i f f e r e n c e s between t h e two
consumer's s u r p l u s measures.
One p o i n t which makes s u c h a n argument
p a r t i c u l a r l y i n t e r e s t i n g i s t h a t t h e m a r g i n a l u t i l i t y o f income may be
assumed c o n s t a n t and t h e s o u r c e o f d i f f e r e n c e might s t i l l b e e x h i b i t e d .
A l l o r None Demand Curves
\'\
Under a n o r d i n a r y s i t u a t i o n , a conscmer i; given a p r i c e 8 and then
h e i s a b l e t o s a y what amount o f X ( a composite good) he w i l l consume.
F o r t h e l a s t u n i t consumed, t h e i n d i v i d u a l w i l l have h i s m a r g i n a l u t i l i t y
o f X set equal t o t h e p r i c e of X.
I n t h e o r y t h e consumer i s assumed t o
have shown t h a t he i s a u t i l i t y maximizer.
I n t h e all-or-none
case, the i n d i v i d u a l i s confronted with a p r i c e
which i s e q u a l t o t h e t o t a l a r e a b e n e a t h h i s ( o r d i n a r y ) demand c u r v e f o r
a given q u a n t i t y of X.
The purpose o f s u c h a p r i c e i s t o e x t r a c t from
t h e i n d i v i d u a l concerned a l l o f h i s consumer's s u r p l u s .
The r e l a t i o n s h i p o f t h e o r d i n a r y t o t h e all-or-none
b e s t i l l u s t r a t e d i n a graph ( F i g u r e V)
sumer i s allowed t o buy o n l y X
X
0
0
.
demand curve i s
I n t h i s i l l u s t r a t i o n t h e con-
q u a n t i t y o f t h e commodity.
i s d i f f e r e n t f o r t h e two demand c u r v e s .
The all-or-none
The p r i c e o f
demand curve
p r e s e n t s a p r i c e which i s t h e a v e r a g e o f a l l t h e p r i c e s t h e consumer
would have t o pay i f he bought each u n i t of X from a d i s c r i m i n a t i n g
monopolist.
The consumer then i s n o t paying t h e s i n g l e p r i c e of t h e
m a r g i n a l u n i t f o r a l l t h e u n i t s of X.
I n s t e a d t h e i n d i v i d u a l i s paying
t h e h i g h e s t p r i c e he would b e w i l l i n g t o pay i f t h a t u n i t of X were t h e
o n l y u n i t h e c o u l d buy.
P
n XiPi
.
C - This p r i c e
i=ln
w i l l n e c e s s a r i l y b e h i g h e r than t h e m a r g i n a l p r i c e given by t h e o r d i n a r y
The all-or-none
demand p r i c e i s given by
demand curve ( F i g u r e IV) ( P a t i n k i n , 1963, 86-7;
=
B a r z e l , 1974, 82-4).
Using a f i g u r e s i m i l a r t o F i g u r e I1 i n Chapter 11, t h e all-or-none
p o i n t may b e i l l u s t r a t e d .
income.
I n F i g u r e V t h e consumer b e g i n s a t p o i n t OA
T h i s p o i n t i s on i n d i f f e ~ n c ecurve I1.
The consumer i n t h e
/
all-or-none
income.
s i t u a t i o n i s kept/on
11, w i t h o u t changing t h e i n d i v i d u a l ' s
T h i s i s t h e d i f f e r e n c e between t h e all-or-none
H i c k s i a n compensating s i t u a t i o n .
example and t h e
It w i l l b e r e c a l l e d t h a t i n t h e compen-
s a t i n g s i t u a t i o n t h e consumer i s k e p t on I
1 by t a k i n g away income e q u a l
t o t h e d i s t a n c e AA2.
I n t h e all-or-none
s i t u a t i o n then t h e consumer r e c e i v e s OB u n i t s of
X b u t pays t h e p r i c e o f OE u n i t s .
AA2,
t o t h e all-or-none
Comparing t h e compensating v a r i a t i o n ,
v a r i a t i o n , AC, i l l u s t r a t e s t h a t t h e all-or-none
measure w i l l normally b e l a r g e r .
T h i s d i f f e r e n c e i n v a r i a t i o n h o l d s even
when t h e c o n s t a n c y o f t h e m a r g i n a l u t i l i t y o f income i s assumed a s i n
F i g u r e V.
The all-or-none
v a r i a t i o n may b e used t o e x p l a i n t h e d i f f e r e n c e s
i n t h e answers t o w i l l i n g n e s s t o pay and w i l l i n g n e s s t o s e l l q u e s t i o n s
a s follows.
When an i n d i v i d u a l i s answering t h e w i l l i n g n e s s t o pay
q u e s t i o n , h e s e e s h i m s e l f a t p o i n t D.
He then would be w i l l i n g t o give
up D t o F i n o r d e r t o c o n t i n u e t o consume t h e OB u n i t s r a t h e r than do
w i t h o u t X.
The d i s t a n c e DF (=&I2)
i s an income l o s s which t h e i n d i v i d u a l .
f e e l s p e r s o n a l l y (Mohring, 1971, 362-3).
The w i l l i n g n e s s t o s e l l q u e s t i o n i l l i c i t s a s e t of d i s t i n c t p e r s o n a l
feelings.
The consumer may f e e l powerful i n h i s p o s i t i o n o f b e i n g a b l e
t o name t h e p r i c e .
R e f e r r i n g t o h i s own i n t e r n a l " i n d i f f e r e n c e curve", 1 0
t h e r e s p o n d e n t a t t e m p t s t o f o r c e t h o s e paying him t o p o i n t C.
I n o r d e r t o u n d e r s t a n d why t h e consumer f e e l s h e can f o r c e t h o s e
o f f e r i n g t o buy t h e p r o p e r t y t o pay a v e r y l a r g e sum, i t i s n e c e s s a r y
t o examine t h e concept of a d i s c r i m i n a t i n g m o n o p o l i s t .
I n t h i s case
t h e i n d i v i d u a l s e e s h i m s e l f ag t h e o n l y s e l l e r o f t h e good, o r i f n o t
i
t h e o n l y s e l l e r , t h e i n d i v i d d a l a t l e a s t f e e l s he h a s t h e power o f
I
holding out.
I f t h e i n d i v i d o a l i s a monopolist o r i s a hold-out,
he
e f f e c t i v e l y h a s a power p o s i t i o n where he might b e a b l e t o g a i n .
Asking f o r t h e l a r g e w i l l i n g n e s s t o s e l l sum does n o t i n d i c a t e
t h a t t h e consumer a c t u a l l y t h i n k s h e w i l l f o r c e t h e b u y e r t o p o i n t C .
The i m p l i c a t i o n i s t h a t even i f t h e i n d i v i d u a l r e c e i v e s o n l y one d o l l a r
more t h a n t h e g o i n g market p r i c e , h e h a s made a g a i n .
I n t h e c a s e o f t h e w i l l i n g n e s s t o p a y , n o t o n l y i s t h e consumer
c o n s t r a i n e d by h i s income and f e e l i n g s o f p e r s o n a l l o s s , he a l s o s e e s
himself a s a p e r f e c t competitor.
A s a p e r f e c t competitor the individual
knows he w i l l n o t have t o pay more t h a n t h e g o i n g market p r i c e f o r a
good.
T h e r e f o r e , t h e r e must b e something i n h e r e n t l y d i f f e r e n t between
t h e two s i t u a t i o n s which makes t h e i n d i v i d u a l s e e t h i s o p p o r t u n i t y t o
e x t r a c t such a s u r p l u s i n the f i r s t case.
I f a l a r g e e n t r e p r e n e u r o r t h e government wanted t o remove a
p u b l i c p r o p e r t y , suc-h a s a p a r k o r a l a k e from f i s h i n g , from i n d i v i d u a l s ' consumption, t h e y might have t o compensate t h e consumers.
When d e a l i n g w i t h a l a r g e f i r m o r w i t h t h e s t a t e , t h e consumers might
t h i n k o f t h e w e a l t h such groups p o s s e s s .
The consumers by e x t r a c t i n g
v e r y l a r g e sums would b e e f f e c t i n g a r e d i s t r i b u t i o n of income.
Given
t h a t t h e consumers were r e l a t i v e l y p o o r e r t h a n t h e f i r m o r s t a t e , t h e
i n d i v i d u a l s might see t h e l a r g e sum a s "only f a i r " .
Even i n t h e c a s e
of t h e s t a t e where t h e consumers a r e a p a r t of t h e t a x p a y e r s and are
i n o n e s e n s e paying t h e m s e l v e s , t h e i n d i v i d u a l may t h i n k he i s t h e o n l y
7
p e r s o n who w i l l r e c e i v e s u c h a 1 r g e payment.
I f he i s t h e o n l y p e r s o n ,
h e w i l l n o t b e paying h i m s e l f b u t a l l t h e o t h e r t a x p a y e r s w i l l compens a t e him f o r h i s l o s s .
Given g r e e d i n t h e above s i t u a t i o n coupled w i t h f e e l i n g s of power,
t h e i d e a set f o r t h i s p e r h a p s n o t a b s u r d .
Instead it is a rational
e x p l a n a t i o n based on how i n d i v i d u a l s a c t .
The all-or-none
curve
s e r v e s a s a t h e o r e t i c a l and g r a p h i c a l v e h i c l e which i l l u s t r a t e s
t h e p o i n t s on a n i n d i f f e r e n c e mapping t h a t a n i n d i v i d u a l consumer s e e s
as p e r t i n e n t i n w i l l i n g n e s s t o s e l l and w i l l i n g n e s s t o pay c a s e s .
The major c r i t i c i s m of t h e all-or-none
measure i s due t o t h e f a c t
t h a t t h i s measure p e r t a i n s t o a h y p o t h e t i c a l s i t u a t i o n ( P a t i n k i n , 1963,
88) .I1 When asked f o r a n all-or-none
p r i c e , t h e r e s p o n d e n t s may g i v e
a n answer l e s s t h a n t h e a c t u a l p r i c e t h e y would pay r a t h e r t h a n do
w i t h o u t X.
The c o u n t e r p a r t of t h e above f o r compensation r e q u i r e d d e a l s
w i t h how a n i n d i v i d u a l may a t t e m p t t o e x t r a c t a h i g h e r p r i c e t h a n i s
r e a l i s t i c a l l y a v a i l a b l e i n t h e market.
all-or-none
T h i s c r i t i c i s m i s n o t of t h e
e x p l a n a t i o n g i v e n b u t of t h e s u r v e y q u e s t i o n used t o
measure compensation r e q u i r e d .
The all-or-none
e x p l a n a t i o n does n o t p r e c l u d e o t h e r e x p l a n a t i o n s
of t h e o b s e r v e d d i f f e r e n c e s i n t h e a l t e r n a t i v e measures of consumer's
surplus.
F a c t o r s s u c h a s a n a s y m e t r y i n t h e importance o f n o n - i n t r i n s i c
b e n e f i t s , p r o p e r t y r i g h t s , i n t e r n a l r a t e s o f , r e t u r n , o p t i o n v a l u e and
s t r a t e g i e s f o r answering s u r v e y q u e s t i o n s can s t i l l b e t h e c a u s e s o f
v a r i a t i o n s between t h e two answers.
c a u s e s of t h e a l l - o r - n o n e
I t i s , however, i m p o s s i b l e t o know t h e
consumer's s u r p l u s d i r e c t l y .
which c o n t r i b u t e t o t h e
If the factors
c o u l d b e measured, t h e n
t h i s measure c o u l d be used t o e x p l a i n why t h e answers t o t h e w i l l i n g n e s s t o pay and w i l l i n g n e s s t o s e l l q u e s t i o n s v a r y w h i l e assuming t h e
c o n s t a n c y of t h e m a r g i n a l u t i l i t y of income.
One method of e f f e c t i v e l y u t i l i z i n g t h e a l l - o r - n o n e
formulation
would b e t o e s t a b l i s h a d i f f e r e n t i a l between t h e compensating p r i c e
and t h e e q u i v a l e n t p r i c e .
I n F i g u r e V t h e d i f f e r e n t i a l would b e c a l -
and PC.
c u l a t e d between P
A-N
T h i s d i f f e r e n t i a l could then be used a s
a dependent v a r i a b l e i n r e g r e s s i o n s .
The problem w i t h a t t e m p t i n g
t o u s e t h i s p r i c e d i f f e r e n t i a l approach h a s t o do w i t h knowing t h e
a p p r o p r i a t e p r i c e s t o use.
Such a n i n d i v i d u a l ' s i n d i f f e r e n c e map i s
n o t known, t h e p r i c e s w i l l o n l y b e approximate e s t i m a t e s of t h e r e a l
prices.
A second problem i s a t t e m p t i n g t o f i n d o u t e x a c t l y what
causes t h e all-or-none
questions.
answers t o be g i v e n t o t h e compensation r e q u i r e d
I f a s p e c i f i c l i n k c a n n o t b e e s t a b l i s h e d between t h e r e s p o n s e s
t o an all-or-none
t h e all-or-none
q u e s t i o n and p o s s i b l e independent v a r i a b l e s , t h e n
approach becomes e m p i r i c a l l y ambiguous.
Without a
l i n k , no d e f i n i t e c o n c l u s i o n s can b e drawn from a s p e c i f i c r e s p o n s e .
The i m p l i c a t i o n i s t h a t one cannot i n f e r from an observed compensation
r e q u i r e d r e s p o n s e any u s a b l e i n f o r m a t i o n .
T h i s means t h a t measure-
ments o f consumer's s u r p l u s w i l l o n l y b e re1,evant i n p r a c t i c e where
/
t h e w i l l i n g n e s s t o pay q u e s t i o n i s t h
a p p r o p r i a t e query.
Unfortun-
a t e l y , t h e v a l u a t i o n o f r e s o u r c e s w i l l b e d i f f i c u l t t o make where t h e
w i l l i n g n e s s t o s e l l i s t h e t h e o r e t i c a l measure r e q u i r e d .
12
FOOTNOTES
1
Note t h a t t h e e x p l a n a t i o n i s between t h e two consumer's s u r p l u s
m e a s u r e s of one p e r s o n and i s n o t a n a t t e m p t t o e x p l a i n t h e v a r i a n c e
between d i f f e r e n t i n d i v i d u a l s ' r e s p o n s e s t o t h e two q u e s t i o n s .
This
t h e n r u l e s o u t a s a n e x p l a n a t i o n t h e i d e a of t h e i n f r a m a r g i n a l r e s p o n s e s
v e r s u s t h e m a r g i n a l answers.
2
/
May n o t o n l y a s s i g n t h e u s e of t h e p r o p e r t y b u t t h e r i g h t t o
convey t h e p r o p e r t y t o o t h e r s a n d t h e r i g h t t o t h e " f r u i t s " from
the property.
3
I n t h e c a s e of i m p l i c i t p r o p e r t y r i g h t s , t h e i n d i v i d u a l may n o t be
a b l e t o s e l l t h e p r o p e r t y o r r e a p t h e f r u i t s of t h e p r o p e r t y .
example of s u c h a p r o p e r t y i s a p u b l i c p a r k .
An
The i n d i v i d u a l s may u s e
and e n j o y a p a r k b u t n o t s e l l t h e p a r t n o r any p a r t s of i t .
4
Given t h a t t h e income e l a s t i c i t y i s e q u a l t o z e r o , n o t o n l y a r e
t h e compensating and e q u i v a l e n t v a r i a t i o n s p i c t u r e d by t h e consumer's
s u r p l u s t r i a n g l e ( F i g u r e I i n Chapter 1 1 ) b u t s o a r e t h e M a r s h a l l i a n
consumer's s u r p l u s e s .
5
I f t h e good i n q u e s t i o n i s a n i n f e r i o r good, t h e n n o t h i n g a b o u t
t h e consumer's b e h a v i o r can b e g u a r a n t e e d .
For example a n i n c r e a s e i n
t h e consumer's income may o r may n o t i n c r e a s e t h e amount of an i n f e r i o r good consumed.
6
T h i s argument i s a l s o t h e one p r e s e n t e d by K r u t i l l a and F i s h e r
(1975, 3 1 ) .
7
It was hoped t h a t i n t e r n a l r a t e s of r e t u r n c o u l d be c a l c u l a t e d
f o r a l l 785 i n d i v i d u a l s i n t h e s p o r t f i s h i n g s u r v e y .
A t l e a s t two
problems e x i s t .
The f i r s t i s no v a r i a t i o n i n a g e e x c e p t f o r e i g h t
grouped c a t e g o r i e s .
duals.
The second i s s i n g l i n g o u t incomes f o r i n d i v i -
A person who e a r n s $3,000 cannot b e expected t o have t h e
same i n t e r n a l r a t e of r e t u r n a s one who e a r n s $50,000 even i f t h e
two a r e t h e same a g e .
D.R.
Maki i n a d i s c u s s i o n s u g g e s t e d t h a t t h e
dummy v a r i a b l e s used f o r a g e would b e s u f f i c i e n t t o measure t h e shape
of t h e i n t e r n a l r a t e of r e t u r n curve.
The p r o b l ~ a r i s e st h a t age
,/'
a l o n e appeared t o have l i t t l e c o r r e l a t i o n w i t h compensation r e q u i r e d .
T h i s d o e s n o t , however, make t h e concept of i n t e r n a l r a t e s of
return useless.
The f i s h i n g s u r v e y was n o t designed t o g a i n t h e
b e s t e s t i m a t e s of age a s n o t e d above.
r a t e s o f r e t u r n was dropped.
Hence, a t t e m p t i n g t o c a l c u l a t e
It s h o u l d , however, be pursued i n some
l a t e r s t u d y w i t h more p r e c i s e i n f o r m a t i o n on r e s p o n d e n t s ' a g e s .
8
T h i s i s o r d i n a r y i n a Walrasian s e n s e ( P a t i n k i n , 1963, 86) a s t h e
consumer i s c o n f r o n t e d w i t h a p r i c e and t h e n asked what he would consume.
A M a r s h a l l i a n c a s e would b e where t h e i n d i v i d u a l was c o n f r o n t e d
w i t h t h e q u a n t i t y and asked what h e would pay.
9
Not o n l y i s t h e consumer n o t allowed t o b e a u t i l i t y maximizer,
h e must a l s o n o t b e allowed t o e q u a t e h i s m a r g i n a l r a t e of s u b s t i t u t i o n (MRS) t o t h e p r i c e of t h e good ( P a t i n k i n , 1963, 8 6 ) .
e s s e n t i a l t o notice i s that t h i s decision is
10
What i s
not a m a r g i n a l one.
The i n d i f f e r e n c e c u r v e s cannot i n a c t u a l i t y b e measured.
However,
what i n d i f f e r e n c e c u r v e s r e p r e s e n t can b e t r u e w i t h i n each i n d i v i d u a l .
11
T h i s c r i t i c i s m i s one which a p p l i e s t o a l l s u r v e y s .
12
Henderson (1941, 119) p o i n t s o u t t h a t t h e r e e x i s t s i t u a t i o n s
where o n l y t h e w i l l i n g n e s s t o s e l l ( e q u i v a l e n t v a r i a t i o n ) i s t h e
measure t o u s e .
There h a s been some argument, though, o v e r t h e
usefulness of t h e equivalent v a r i a t i o n .
Mishan i n h i s 1 s t e d i t i o n
of C o s t - B e n e f i t A n a l y s i s (19 71) regarded t h e e q u i v a l e n t v a r i a t i o n
a s n o t a s u s e f u l a s t h e compensating v a r i a t i o n .
However, Mishan
(1976) r e f u t e s h i s p o s i t i o n and e l e c t s t o u s e t h e e q u i v a l e n t vari a t i o n a s w e l l a s t h e compensating v a r i a t i o n .
B u m s (1973, 338-34*
a l s o s u g g e s t s t h a t compensating and e q u i v a l e n t v a r i a t i o n s have t h e i r
p l a c e i n d e s c r i b i n g t h e d i f f e r e n c e between s m a l l m u l t i p l e p r i c e and
income changes and l a r g e m u l t i p l e p r i c e and income changes
respectively.
Although t h e s e l e a r n e d gentlemen s e e a p l a c e f o r t h e e q u i v a l e n t
v a r i a t i o n , t h e a r t i c l e s mentioned do n o t g u a r a n t e e t h a t t h e w i l l i n g n e s s t o s e l l f u n c t i o n i s measurable.
For p r o o f , one must f a l l back
on t h e r e g r e s s i o n a n a l y s i s o f t h e l i n k s between t h e e q u i v a l e n t
v a r i a t i o n and t h e exogenous v a r i a b l e s .
Before d i s m i s s i n g t h i s
measure, however, i t would r e q u i r e f u r t h e r a n a l y s i s t h a n t h a t
presented here.
CHAPTER V
Conclusion
Attempts t o a p p l y a measure of consumer's s u r p l u s t o a p r a c t i c a l
c a s e o f r e s o u r c e e v a l u a t i o n a r e c o n f r o n t e d w i t h a problem of measurement.
T h i s i s e s p e c i a l l y t h e c a s e f o r r e s o u r c e s f o r which market
prices are not available.
One problem i n p a r t i c u l a r i s t h a t o f which
o f t h e a l t e r n a t i v e measures of consumer's s u r p l u s i s most a p p r o p r i a t e
t o e a c h i n d i v i d u a l case.
I n t h e main, t h e r e l e v a n t a l t e r n a t i v e s a r e
t h o s e g i v e n by answers t o two q u e s t i o n s on t h e v a l u e o f one r e s o u r c e :
"What would you b e w i l l i n g t o pay f o r t h e continued u s e o f X?"
II
and
What compensation would you r e q u i r e t o f o r e g o t h e use of X f o r e v e r ? "
The answers t o t h e two q u e s t i o n s , when asked i n s u r v e y s , v a r y
c o n s i s t e n t l y by l a r g e amounts i n d o l l a r terms.
T r a d i t i o n a l theory o r
consumer's s u r p l u s s u g g e s t s t h a t such a l a r g e d i f f e r e n c e s h o u l d n o t
exist.
The u s u a l reason given f o r any v a r i a t i o n between them i s t h a t
t h e r e i s a s i g n i f i c a n t income e f f e c t t h a t b r i n g s t h i s about.
This
income e f f e c t e x i s t s e s s e n t i a l l y because t h e marginal u t i l i t y o f income
i s n o t c o n s t a n t o v e r t h e range of r e a l income o f t h e r e s o u r c e u s e r s ,
w i t h and w i t h o u t t h i s use.
T h i s means t h a t a s a t r a d e - o f f
i s made
between a good and income, t h e more of t h e good t a k e n away t h e l a r g e r
t h e sum o f income w i l l have t o b e t o r e p l a c e t h e good.
Along w i t h t h i s income e f f e c t , t h e r e may a l s o b e an income
c o n s t r a i n t t h a t would e x p l a i n d i f f e r e n c e s i n answers t o t h e two
questions.
This c o n s t r a i n t i s s a i d t o r e s t r a i n t h e w i l l i n g n e s s t o
pay r e s o u r c e s b u t n o t t h e compensation r e q u i r e d answers (Hammack and
Brown, 19 74, 26 ; K r u t i l l a and F i s h e r , 1975, 30)
.
Although t h e income e f f e c t and income c o n s t r a i n t e x p l a n a t i o n s
may i n p a r t e x p l a i n t h e d i f f e r e n c e between t h e two answers, t h e r e
seems f a r too l a r g e a v a r i a n c e between t h e means of t h e survey r e s p o n s e s
t o b e a t t r i b u t e d t o j u s t these.
s tudy (1974, 26-7)
For example i n t h e Hammack and Brown
a f t e r d i s c a r d i n g e x t r e m e .v a l u e s , t h e mean answers
w e r e $247 f o r t h e w i l l i n g n e s s t o pay q u e s t i o n and $1,044 f o r t h e compensation required.
I n t h e B.C.
s p o r t f i s h i n g survey p r e s e n t e d h e r e
i n d e t a i l , t h e mean and median were r e s p e c t i v e l y $55 and $35 f o r t h e
w i l l i n g n e s s t o pay and $24,382 and $700 f o r t h e compensation r e q u i r e d .
With such e x t r e m e l y l a r g e d i f f e r e n c c s i n e v i d e n c e , i t i s d i f f i c u l t t o
a s c r i b e a l l t h e v a r i a n c e t o j u s t t h e income e f f e c t .
The B.C.
s p o r t f i s h i n g s u r v e y was s u b j e c t e d t o a s e r i e s of
regresscLons which were an a t t e m p t t o e x p l a i n t h e two s e t s o f answers.
Although t h e w i l l i n g n e s s t o pay (compensated v a r i a t i o n ) answers were
e x p l a i n e d r e a s o n a b l y w e l l by t h e exogenous v a r i a b l e s , t h e compensation
r e q u i r e d ( e q u i v a l e n t v a r i a t i o n ) r e s p o n s e s were n o t s u c c e s s f u l l y
e x p l a i n a b l e by t h e c o l l e c t e d d a t a .
Consequently, r e a s o n s were examined
which might f u r t h e r e x p l a i n t h e two s e t s of answers and a l s o , might
e x p l a i n t h e d i f f e r e n c e s between t h e r e s p o n s e s .
The s u g g e s t e d r e a s o n s ranged from t h e concept o f e x p e c t e d i n t e r n a l
r a t e s o f r e t u r n t o t h e a l t e r i n g of t h e p e r c e i v e d u t i l i t y l e v e l and t h e
p e r c e i v e d power p o s i t i o n .
These r e a s o n s a s o u t l i n e d were n o t a n t i c i p a t e d
t o e x p l a i n a l l o f t h e v a r i a n c e between t h e two r e s p o n s e s , b u t were p u t
f o r w a r d i n an a t t e m p t t o i l l u s t r a t e how o t h e r r e a s o n s might be i n c l u d e d
i n explaining the difference.
T h i s examination o f t h e d i f f e r e n c e and t h e r e a s o n s o u t l i n e d may
have i m p l i c a t i o n s f o r f u r t h e r s t u d y .
I t may, f o r example, be v e r y
u s e f u l t o a t t e m p t t o c o n s t r u c t a s u r v e y which a v o i d s some o f t h e p i t f a l l s o f a p e r c e i v e d power p o s i t i o n on t h e p a r t o f t h e r e s p o n d e n t s .
T h i s m i g h t b e accomplished, f o r example, by . a s k i n g t h e i n d i v i d u a l what
compensation h e e x p e c t e d o t h e r s t o r e c e i v e f o r t h e l o s s o f a r e s o u r c e .
A s e c o n d s u g g e s t i o n might b e t o d e s i g n a s u r v e y i n which t h e c h a r a c t e r i s t i c s o f t h e r e s o u r c e i n q u e s t i o n were v a l u e d and n o t t h e v a l u e o f
t h e p a r t i c u l a r resource i t s e l f .
T h i s p r o c e d u r e might a v o i d t h e problems
o f t h e i n c l u s i o n o f n o n - i n t r i n s i c b e n e f i t s and t h e i n c l u s i o n o f
e x p e c t e d r a t e s o f r e t u r n o f t h e i n d i v i d u a l surveyed.
,
Non-intrinsic
b e n e f i t s r e f e r t o such t h i n g s a s memories and e m o t i o n a l f e e l i n g s
attached t o a p a r t i c u l a r property.
An i n t e r n a l r a t e o f r e t u r n i s an
i n f l u e n c e which might cause t h e compensation r e q u i r e d answer t o b e v e r y
large.
I f a r e s o u r c e was b e i n g f o r e v e r removed from an i n d i v i d u a l ' s
u s e , t h e p e r s o n might a t t e m p t t o s e c u r e a l a r g e enough sum of money
i n o r d e r t o compensate him f o r t h e l o s s of many f u t u r e y e a r s ' b e n e f i t s .
I n o r d e r t o a v o i d t h i s from i n f l u e n c i n g t h e s u r v e y r e s u l t s , t h e s u r v e y
could attempt t o ask questions about c h a r a c t e r i s t i c s of a resource,
f o r example t h e view a s s o c i a t e d w i t h a p a r k , i n s t e a d o f t h e r e s o u r c e
itself.
The e x i s t e n c e o f l a r g e d i f f e r e n c e s i n a l t e r n a t i v e measures o f
consumer's s u r p l u s g i v e s rise t o s p e c u l a t i o n on which measure t o u s e
and when.
When an e s t a b l i s h e d use of a r e s o u r c e i s t o b e d i s -
r u p t e d , then t h e compensation r e q u i r e d measure might w e l l be
s u g g e s t e d a s b e i n g most a p p r o p r i a t e .
I f a resource is t o be
developed o r made a v a i l a b l e f o r t h e f i r s t time, then t h o s e who
would g a i n from t h i s p r o j e c t s h o u l d b e surveyed f o r t h e i r w i l l i n g n e s s t o pay and t h i s measure of v a l u e used i n a l l o c a t i o n
decisions.
N e i t h e r t h e compensated n o r t h e e q u i v a l e n t v a r i a t i o n
seems t o b e a r e l i a b l e measure o f a p p r o p r i a t e v a l u e i n e v e r y
i n s t a n c e ; with t h i s being e s p e c i a l l y t h e case with t h e present
d e s i g n of s u r v e y s .
Another i m p l i c a t i o n may b e t h a t t h e e q u i v a l e n t
(compensation r e q u i r e d ) v a r i a t i o n i s n o t used of t e n enough.
The
answers b e i n g " t o o l a r g e " o r " e m o t i o n a l l y b i a s e d " (Harnmack and
Brown, 1974, 26-7)
would n o t seem enough j u s t i f i c a t i o n f o r i g n o r -
i n g t h i s me a s u r e of v a l u e .
F i n a l l y , i n choosing which measure t o u s e , a t h i r d i m p l i c a t i o n
may b e t h a t t h e income c o n s t r a i n t on t h e compensated ( w i l l i n g n e s s
t o pay) v a r i a t i o n may induce i n d i v i d u a l s t o p r e s c r i b e too low a
value t o t h e resource i n question.
I f t h e income c o n s t r a i - n t can
b e a s s o c i a t e d w i t h making t h e compensated v a r i a t i o n " r e a l i s t i c " ,
t h e income c o n s t r a i n t may a l s o cause an under-valuation
of a
resource.
T h i s e s s a y h a s been an a t t e m p t t o i l l u s t r a t e t h a t f u r t h e r
though s h o u l d b e given t o t h e e x p l a n a t i o n o f t h e d i f f e r e n c e s
between t h e e m p i r i c a l l y observed compensated and e q u i v a l e n t variations.
Although new e m p i r i c a l d a t a have been d i s c u s s e d a l o n g
w i t h n e w e x p l a n a t i o n s , no one r e a s o n can b e g i v e n precedence o v e r
all o t h e r s i n e x p l a i n i n g t h e d i f f e r e n c e .
f u r t h e r , more d e t a i l e d r e s e a r c h and s t u d y .
T h i s must b e l e f t f o r
APPENDIX A
SPORT FISH SURVEY
I n 1975, Environment Canada completed a s u r v e y which d e a l t
w i t h v a l i d h o l d e r s of f i s h i n g l i c e n s e s i n Yellowhead.
As the
f i r s t follow-up l e t t e r m a i l e d t o t h e s e fishermen s t a t e s , t h e
p u r p o s e o f t h e s u r v e y was t o measure t h e "socio-economic
import-
ance of fishing" t o those i n d i v i d u a l s r e s i d i n g i n n o r t h e r n B r i t i s h
Columbia.
From t h e m a i l s u r v e y e v o l v e d a t e l e p h o n e s u r v e y which
re-surveyed many o f t h e i n d i v i d u a l s who had responded t o t h e m a i l
survey.
Reproduced i n t h i s appendix a r e t h e two q u e s t i o n n a i r e s , m a i l
and t e l e p h o n e , t h e follow-up l e t t e r s f o r t h e m a i l s u r v e y , t h e
.instructions
t o t h e t e l e p h o n e s u r v e y p e r s o n n e l , t h e coding s h e e t s
u s e d by t h e Department o f F i s h e r i e s f o r t h e p r o d u c t i o n o f t h e i r
computer c a r d s and t h e d e p a r t m e n t ' s t h r e e t a b l e s .
Two t a b l e s a r e
f o r t h e m a i l and t e l e p h o n e o v e r a l l r e s u l t s and t h e t h i r d t a b l e i s
a breakdown by s t r e a m and r e s i d e n c e of t h e compensating consumer
surplus p r i c e values.
T h i s appendix w i l l b e o f i n t e r e s t i n o r d e r t o u n d e r s t a n d t h e
p r o c e d u r e s o f t h e department and t o i l l u s t r a t e t h e t y p e o f usage t h e
d a t a was b e i n g p u t t o by Environment Canada, F i s h e r i e s and Marine
Department.
A l l o f t h e l e t t e r s , d a t a and computer c a r d s were
r e c e i v e d from M r . William F. S i n c l a i r and M r . Rob Morley.
SPORT FISH MAIL QUESTIONNAIRE
S ec tion A
Ti
;
f i r s t s e c t i o n a s k s s e v e r a l q u e s t i o n s a b o u t members o f
y o u r hr c;ehold i n an e f f o r t t o e n s u r e t h a t t h e o p i n i o n s e x p r e s s e d
survey a r e t r u l y r e p r e s e n t a t i v e of a l l the sport fisher-
i n th:
i n g i n n o r t h e r n B r i t i s h Columbia and n o t j u s t i s o l a t e d
men
segments o f t h e s p o r t f i s h i n g p o p u l a t i o n .
1. P l e a s e i n d i c a t e i n t h e a p p r o p r i a t e s p a c e t h e t o t a l number of
males and females and t h e number of male and female s p o r t
f i s h e r m e n (who s p o r t f i s h a t l e a s t once a y e a r ) who permane n t l y r e s i d e i n your household a c c o r d i n g t o age.
Fishermen
Age
Male
0 - 9
10
-
19
20
-
29
30
-
39
40
-
49
50
-
59
60
-
69
7 0 and Over
Female
T o t a l Household R e s i d e n t s
Male
Female
2.
How many days d u r i n g 1974 d i d members of y o u r h o u s e h o l d s p o r t
f i s h i n t h e a r e a between P r i n c e George and P r i n c e R u p e r t ( s e e
Map showing a r e a o f c o n c e r n ) ?
(no. o f days d u r i n g 1974)
3.
P l e a s e i n d i c a t e (,/)
which c a t e g o r y b e s t d e s c r i b e s t h e o c c u p a t i o n
of t h e h e a d o f t h e household.
Labourer
I
Tradesman o r T e c h n i c a l
Professional
Sales
-
Clerical
Management and E x e c u t i v e
Self-Employed
Retired
Other ( p l e a s e s p e c i f y )
4.
What i s t h e g r o s s ( b e f o r e t a x e s ) t o t a l income of y o u r household per year?
$
Section B
I n S e c t i o n B we wish t o d e t e r m i n e t h e importance of s p o r t
f i s h i n g and t h e amount o f a n g l i n g e f f o r t on p a r t i c u l a r waterways
l o c a t e d i n t h e c e n t r a l n o r t h w e s t e r n a r e a s of B r i t i s h Columbia.
We
a r e i n t e r e s t e d i n y o u r (you a s an i n d i v i d u a l ) f i s h i n g a c t i v i t y i n
t h e g e n e r a l a r e a between P r i n c e George and P r i n c e Rupert.
We
r e a l i z e t h a t few p e o p l e keep e x a c t r e c o r d s of t h e i r f i s h i n g
e x p e r i e n c e , b u t we would a p p r e c i a t e i t i f you would answer a l l
q u e s t i o n s a c c o r d i n g t o your b e s t e s t i m a t e .
5.
P l e a s e i n d i c a t e how many y e a r s you have l i v e d i n P r i n c e George
o r i n t h e a r e a s n o r t h of P r i n c e George i n B r i t i s h Columbia ( a r e a
o f concern a s shown on Map).
(no. o f Years)
6.
How many days e a c h y e a r do you n o r m a l l y f i s h i n t h e a r e a between
P r i n c e George and P r i n c e R u p e r t ?
(no. of days p e r y e a r )
7.
How many days d i d you f i s h i n t h e a r e a between P r i n c e George and
P r i n c e R u p e r t d u r i n g 1974?
(no. o f days d u r i n g 1974)
8.
P l e a s e i n d i c a t e ( 4 )what t y p e o f f i s h i n g you p r e f e r .
Lake
9.
o r River (stream)
What s p e c i e s o f f i s h do you p r e f e r t o c a t c h ?
Please list i n
o r d e r of p r e f e r e n c e ( y o u r p r e f e r r e d s p e c i e s f i r s t ) .
10.
What i s y o u r f a v o u r i t e f i s h i n g r i v e r o r l a k e and how many
.
days do you n o r m a l l y f i s h t h e r e e a c h y e a r ?
(1st favourite location)
11.
(days f i s h e d p e r y e a r )
What would b e t h e minimum a n n u a l c a s h payment t h a t you would
a c c e p t t o forego f o r e v e r your r i g h t t o f i s h a t your f a v o u r i t e
r i v e r o r lake?
P l e a s e n o t e t h a t you o n l y g i v e up y o u r r i g h t
t o f i s h on y o u r f a v o u r i t e r i v e r of l a k e ( f o r a l l t i m e ) , b u t
t h a t you s t i l l c o u l d f i s h on any o t h e r r i v e r o r l a k e .
$
12.
per year.
What i s y o u r second f a v o u r i t e f i s h i n g r i v e r o r l a k e and how
many days do you n o r m a l l y f i s h t h e r e e a c h y e a r ?
(2nd f a v o u r i t e l o c a t i o n )
13.
(days f i s h e d p e r y e a r )
We would l i k e you t o e s t i m a t e t h e a v e r a g e c o s t of a d a y ' s
To t h i s end, w e
f i s h i n g on your f a v o u r i t e r i v e r s o r l a k e s .
a s k t h a t you i n c l u d e any c o s t s t h a t you f e e l a r e d i r e c t l y
r e l a t e d t o your f i s h i n g t r i p .
These c o s t s may i n c l u d e t r a v e l
and equipment c o s t s b u t w i l l n o t i n c l u d e any c o s t s t h a t would
have been i n c u r r e d i f no f i s h i n g t r i p had taken p l a c e .
What i s t h e a v e r a g e c o s t of a d a y ' s f i s h i n g :
(i) On your f a v o u r i t e r i v e r o r l a k e ?
( i i ) On your 2nd f a v o u r i t e r i v e r o r l a k e ?
$-
p e r day.
$
p e r day.
Section C
T h i s i s a h y p o t h e t i c a l q u e s t i o n which, i f answered c o r r e c t l y ,
w i l l h e l p us t o d e t e r m i n e t h e v a l u e of t h e s p o r t f i s h e r y t o r e s i d e n t s o f c e n t r a l n o r t h w e s t e r n B r i t i s h Columbia.
Please consider
i t c a r e f u l l y and answer a c c o r d i n g t o y o u r b e s t e s t i m a t e .
Please
n o t e t h a t Q u e s t i o n 1 4 a s k s f o r a maximum " p e r day" e s t i m a t e .
14.
Suppose t h e c o s t s of a d a y ' s f i s h i n g a t your f a v o u r i t e r i v e r
o r l a k e were t o rise.
What would be t h e maximum amount t h a t
you would pay b e f o r e you would s t o p f i s h i n g a t your f a v o u r i t e
river o r lake altogether?
$
p e r day.
15.
P l e a s e f e e l f r e e t o make any comments you wish e i t h e r a b o u t
t h i s q u e s t i o n n a i r e o r a b o u t any i d e a s you may have r e g a r d i n g t h e
improvement o f s p o r t f i s h i n g i n t h e c e n t r a l n o r t h w e s t e r n a r e a
o f B r i t i s h Columbia.
P l e a s e n o t e your t e l e p h o n e number i n t h e s p a c e p r o v i d e d s o t h a t
w e w i l l b e a b l e t o d i s c u s s your comments w i t h you o r answer any
q u e s t i o n s which might a r i s e .
Telephone Number
THANK YOU!
SPORT FISH MAIL QUESTIONNAIRE 1975
COMPUTER CLASSIFICATION AND CODING
Codes
Classification
P l a c e of Residence
B -
A
C
-
E
-
F
-
D
Kitimat
P r i n c e George
Terrace
P r i n c e Rupert
Smithers
Vanderhoof
J
- B u m s Lake
- F r a s e r Lake
- Hazelton
- Granisle
K
-
G
H
I
Telkwa
N
-
@
-
P
- Fort
L
M
Q
R
S
V
Fort Fraser
Houston
Kitwanga
Endako
S t . James
- T a k y s i e Lake
- Southbank
- Engen
- P r i n c e George
Column
2,394
5
Classification
Codes
I d e n t i f i c a t i o n Number
Number (range 000-999)
Male A n g l e r s , 0-9 y e a r s o l d
Number ( r a n g e 0-9)
X
-
No Response
Female A n g l e r s , 0-9 y e a r s o l d
Same a s Column 5
Males, 0-9 y e a r s o l d
Same a s Column 5
Females, 0-9 y e a r s o l d
. Same a s Column 5
Male A n g l e r s , 10-19 y e a r s o l d
Same a s Column 5
Female Anglers, 10-19 y e a r s o l d
Same a s Column 5
Males, 10-19 y e a r s o l d
Same a s Column 5
Females, 10-19 y e a r s o l d
Same a s Column 5
Male A n g l e r s , 20-29 y e a r s o l d
Same a s Column 5
Female A n g l e r s , 20-29 y e a r s o l d
Same a s Column 5
Males, 20-29 y e a r s o l d
Same a s Column 5
Females, 20-29 y e a r s o l d
Same a s Column 5
Male Anglers. 30-39 v e a r s o l d
Same a s Column 5
Female Anglers., 30-39 y e a r s o l d
Same a s Column 5
Males, 30-39 y e a r s o l d
Same a s Column 5
Females.
Same a s Column 5
30-39 v e a r s o l d
Male A n g l e r s , 40-49 y e a r s o l d
Same a s Column 5
Female A n g l e r s , 40-49 y e a r s o l d
Same a s Column 5
Males, 40-49 y e a r s o l d
Same a s Column 5
Females, 40-49 y e a r s o l d
Same a s Column 5
Male A n g l e r s , 50-59 y e a r s o l d
Same a s Column 5
Female A n g l e r s , 50-59 y e a r s o l d
Same a s Column 5
Column
Classification
Codes
27
Males, 50-59 y e a r s o l d
Same a s Column 5
28
Females. 50-59 v e a r s o l d
Same a s Column 5
29
Male A n g l e r s , 60-69 y e a r s o l d
Same a s Column 5
30
Female A n g l e r s , 60-69 y e a r s o l d
Same a s Column 5
31
Males. 60-69 v e a r s o l d
Same a s Column 5
32
Females, 60-69 y e a r s o l d
Same a s Column 5
33
Male A n g l e r s , 70 o r more y e a r s
o
ld
-
Same a s Column 5
Female Anglers. 70 o r more
years o l d
Same a s Column 5
Males. 70 o r more v e a r s
Same a s Column 5
Females, 70 o r more y e a r s o l d
Same a s Column 5
Household days f i s h e d i n
Yellowhead i n 1974
Number ( r a n g e 000-365)
No Response
Occupation o f household head
0
-
-
XXX
No r e s p o n s e
1 - Labourer
2
-
Tradesman o r T e c h n i c i a n
3
-
Professional
4
5
-
6
-
7
8
-
Retired
9
-
Other
Sales
Clerical
Management and E x e c u t i v e
Self-employed
Column
4 1 - 42
Classification
Gross
household a n n u a l income
Codes
Number ( r a n g e 00-99) i n
thousands
XX
43
-
44
Years of r e s i d e n c e i n Yellowhead
-
47
Days n o r m a l l y f i s h e d p e r y e a r
i n Yellowhead
No r e s p o n s e
Number ( r a n g e 00-99)
XX
45
-
No r e s p o n s e
Number ( r a n g e 000-365)
XXX - No r e s p o n s e
AAA
48
-
50
Days f i s h e d i n 1974 i n
Yellowhead
P r e f e r r e d type o f f i s h i n g
-
Not a fisherman
Number ( r a n g e 000-365)
XXX
-
No r e s p o n s e
AAA
-
Not a fisherman
0
-
No r e s p o n s e
1 - Lake
F i r s t preferred species
2
-
River (stream)
3
-
No p r e f e r e n c e
4
-
S a l t Water
0
-
No r e s p o n s e
1 - Salmon
2
-
3
-
Steelhead
4
-
Dolly Varden
5
-
Lake T r o u t (Char)
6
-
Other
7
- No
T r o u t (Rainbow,
Cutthroat)
preference
Co 1umn
Codes
Classification
Second p r e f e r r e d s p e c i e s
Same a s Column 52
Third preferred species
Same a s Column 52
Fourth p r e f e r r e d s p e c i e s
Same a s Column 5 2
F i r s t favourite fishing location
0
'
- No r e s p o n s e
1 - No f a v o u r i t e
2 - Copper R i v e r (Zymoetz)
3 - Kitimat River
4 - Lakelse River
5 - Skeena R i v e r
6
-
8 7
Douglas Channel
Telkwa R i v e r
Babine Lake
9
-
A
- Kitwanga
B
-
Wedeene R i v e r
River
Dala R i v e r
E
- Kildala River
- Uncha Lake
- P o p l a r Lake
F
-
McBride Lake
G
-
Nadina R i v e r
H
-
O t h e r Lakes
I
-
L a k e l s e Lake
J
-
Kalum R i v e r
K
-
T c h e s i n k u t Lake
C
D
Codes
Classification
F i r s t f avouri t e f i s h i n g
l o c a t i o n continued
L
-
Kasids River
M
-
Owen Lake
N
-
Kitwanga Lake
(8
-
Nass R i v e r
P
-
Kalum Lake
Q
-
Other Rivers
R
-
F r a n c o i s Lake
S
-
K i s p i o x River
T
- Mezeadin
U
-
S t u a r t Lake
V
-
Nechako R i v e r
W
-
F r a s e r Lake
Lake
Y
-
Maxan Lake
Z
-
Bulkley R i v e r
X
c -
Babine R i v e r
P i n k u t Lake
. - Takysie Lake
*
Morice R i v e r
(
-
Burns Lake
)
-
Ootsa Lake
$
-
P a r r o t t Lakes
?
-
Augier Lake
=
-
S t e l l a k o River
:
-
Exchamsiks River
Column
C l a s s i f i--c ation
F i r s t favourite fishing
l o c a t i o n continued
56
Codes
#
-
C l u c u l z Lake
;
-
N u l k i Lake (Tachick)
,-
B e d n e s t i Lake
+ - Morice Lake
% - Dean R i v e r
B - Grassham Lake
- Norman
57
-
59
Days f i s h e d p e r y e a r a f i r s t
favourite location
<
-
!
- McLure
/
-
60
-
65
Compensation r e q u i r e d f o r l o s s
of f i r s t f a v o u r i t e l o c a t i o n
Oona and Ormand Lakes
Fulton River
- No
response
Number ( r a n g e 000000-999999)
XXXXXX
66
Lake
Number ( r a n g e 000-365)
XXX
'
Lake
-
No r e s p o n s e
Second f a v o u r i t e f i s h i n g
locat ion
See Column 56
67
-
69
Days f i s h e d p e r y e a r a t second
favourite location
See Columns 57-59
70
-
72
Average c o s t p e r day a t f i r s t
favourite location
Number ( r a n g e 000-999)
XXX
-
No r e s p o n s e
73
-
75
Average c o s t p e r day a t
second f a v o u r i t e l o c a t i o n
Number ( r a n g e 000-999)
76
-
79
Maximum w i l l i n g n e s s - t o - p a y
Number ( r a n g e 0000-9999)
XXXX
M a i l i n g responded t o
A
-
-
No r e s p o n s e
F i r s t Mail Completed
Co 1u r n
80
Classification
Mailing responded t o continued
Codes
B
-
Second Mail Completed
C
-
T h i r d Mail Completed
D
-
F o u r t h Mail Completed
E
-
F i f t h M a i l Completed
F
G
H
I
J
K
L
M
N
@
-
F i r s t M a i l Incompleted
Second Mail I n c o m p l e t e d
T h i r d Mail I n c o m p l e t e d
F o u r t h Mail I n c o m p l e t e d
F i f t h Mail I n c o m p l e t e d
F i r s t M a i l Recompleted
Second M a i l Recompleted
T h i r d Mail Recompleted
F o u r t h M a i l Recompleted
F i f t h M a i l Recompleted
TELEPHONE ENUPERATOR INSTRUCTIONS
SUMMER SURVEY. 1 9 75
It i s i n t e n d e d t h a t a l l telephone enumeration w i l l t a k e p l a c e
r o u g h l y between 6:00 and 7:30 PM on weekdays i n T e r r a c e , Smithers
and P r i n c e George.
PM p r i n c i p l e .
Enumerators a r e t o a d h e r e t o t h e 6:00 t o 7:30
However, i t i s e x p e c t e d t h a t they w i l l a d j u s t t h e i r
h o u r s around t h a t time i n a manner which i s c o n s i s t e n t w i t h t h e i r
success experience.
Telephone t r y - a g a i n s
o r c a l l - b a c k s may be
c a r r i e d o u t any t i m e a f t e r t h e i n i t i a l t r y .
I n o t h e r words, i t
i s r e a s o n a b l e t o e x p e c t t h a t f o r one r e a s o n o r a n o t h e r c e r t a i n
i n d i v i d u a l s a r e n e v e r i n e a r l y i n t h e evening.
c a l l s may b e made a t noon o r on weekends.
I n t h a t case,
It i s n o t expected t h a t
t h e enumerator w i l l e v e r have t o make c a l l s i n t h e morning p r i o r
t o noon any day of t h e week.
Telephone format i s a s f o l l o w s :
.
H e l l o , my name i s
I am an economist w i t h
t h e F i s h e r i e s and Marine S e r v i c e , Department of t h e Environment.
I a m c a l l i n g i n c o n n e c t i o n w i t h t h e m a i l q u e s t i o n n a i r e which we
s e n t t o you i n J a n u a r y t h i s y e a r .
out the questionnaire?
May I speak w i t h whoever f i l l e d
(Might b e some e x p l a n a t i o n r e q u i r e d h e r e ) .
I f t h e p e r s o n i d e n t i f i e s h i m s e l f ( o r h e r s e l f ) a s t h e person who
f i l l e d o u t t h e q u e s t i o n n a i r e o r once t h e p e r s o n who f i l l e d o u t t h e
q u e s t i o n n a i r e comes t o t h e t e l e p h o n e , then you a r e t o s a y :
I would l i k e t o t a k e a few moments o f your time t o go o v e r some
o f t h e answers you f i l l e d o u t on y o u r q u e s t i o n n a i r e t h i s s p r i n g .
(Might t a k e some e x p l a n a t i o n h e r e ) .
You m i g h t want t o c l a r i f y some p o i n t s o f m i s u n d e r s t a n d i n g about why
you a r e c a l l i n g and what t h e purpose o f t h e s u r v e y was.
However,
p r o c e e d from h e r e i n t h e f o l l o w i n g manner:
One o f t h e t h r e e q u e s t i o n s I want t o d e a l w i t h i s t h e q u e s t i o n
which a s k s :
What would b e t h e minimum a n n u a l cash payment t h a t you
would a c c e p t t o f o r e g o f o r e v e r y o u r r i g h t t o f i s h a t y o u r f a v o u r i t e
r i v e r o r lake?
Interpret
-
Your answer was $
I n o t h e r words, you i n d i c a t e d by your answer t h a t you
were w i l l i n g t o g i v e up f i s h i n g a t
i t e l o c a t i o n ) f o r a cash payment of $
(favourp e r year.
Are you s a t i s f i e d t h a t t h i s answer g i v e s a f a i r
i n d i c a t i o n of what v a l u e you p l a c e on y o u r f a v o u r i t e
fishing location?
He ( o r s h e ) w i l l e i t h e r s a y y e s o r no.
I f he s a y s yes t h e n d r o p i t
and c a r r y on w i t h t h e n e x t q u e s t i o n .
I f he s a y s no a s k him whether
h e t h i n k s t h e answer i s low o r h i g h .
I f he s a y s low s t a r t b i d d i n g .
( T h i s may need some e x p l a n a t i o n a b o u t r a r e p a i n t i n g s , etc. and a b o u t
how you i n t e r p r e t t h e answer b u t you s h o u l d r e a c h a f i g u r e t h a t he
w i l l f i n d s a t i s f a c t o r y w i t h e x p l a n a t i o n and c o n t i n u a l b i d d i n g ) .
One of t h e q u e s t i o n s asked was t o e s t i m a t e t h e a v e r a g e c o s t
o f a d a y ' s f i s h i n g a t your f a v o u r i t e and second f a v o u r i t e f i s h i n g
location.
Your answer was t h a t on a v e r a g e i t c o s t you $
per d a y t o f i s h a t your f a v o u r i t e l o c a t i o n .
Are you s a t i s f i e d w i t h
t h a t answer?
Do you t h i n k t h a t i s h i g h o r low?
i f h e answers
low.
Then s t a r t b i d d i n g
Your answer t o t h e second p a r t of t h a t q u e s t i o n was t h a t i t was
worth $
location.
p e r day t o f i s h a t your second f a v o u r i t e f i s h i n g
Once a g a i n , a r e you s a t i s f i e d w i t h t h a t answer?
Do
y o u t h i n k t h a t i t i s h i g h o r low?
The f i n a l q u e s t i o n which I would l i k e t o review w i t h you i s
t h e q u e s t i o n t h a t asked you:
Suppose t h e c o s t of a d a y ' s f i s h i n g
a t y o u r f a v o u r i t e r i v e r o r l a k e were t o rise.
What would be t h e
maximum amount t h a t you would pay b e f o r e you would s t o p f i s h i n g a t
your favourite r i v e r o r lake?
up t o a maximum o f $
Your answer was t h a t you wou
. pay
p e r day b e f o r e you would s t o p f i s h i n g
a t your favourite f i s h i n g location.
Do you t h i n k t h a t t h a t answer
i s a f a i r i n d i c a t i o n o f what i t would have t o c o s t you p e r day b e f o r e
y o u would q u i t f i s h i n g a t y o u r f a v o u r i t e l o c a t i o n ?
H e w i l l say
y e s o r no, t h e n a s k him i f i t i s h i g h o r low, and then s t a r t your
bidding.
Is y o u r answer t o t h i s q u e s t i o n o v e r and above what i t c o s t s
y o u t o f i s h each day?
(Pause)
I f he ( o r s h e ) does n o t a p p e a r t o
That i s , t h e maximum amount you would pay i s
u n d e r s t a n d go on:
(13(i)
+
(14))
$
o r ( j u s t 14) $
?
I n c l o s i n g you a r e t o thank t h e p e r s o n f o r t h e i r c o o p e r a t i o n .
Say t h a t t h e i r i n f o r m a t i o n w i l l b e t r e a t e d s t r i c t l y c o n f i d e n t i a l
and t h a t i t w i l l be o f t h e utmost v a l u e when p r e p a r i n g environmental
i m p a c t s t a t e m e n t s o r a s s e s s i n g t h e e n v i r o n m e n t a l consequences o f
p a r t i c u l a r development p r o j e c t s .
The f o u r b a s i c r u l e s f o r t e l e p h o n e s u r v e y s a r e :
1. P o l i t e n e s s
2.
Speak i n a c l e a r c o n c i s e v o i c e
-
i t is absolutely
n e c e s s a r y t h a t t h i s be done because a person who i s
i n t e r r u p t e d by a t e l e p h o n e c o n v e r s a t i o n which i s n o t
p e r s o n a l l y d i r e c t e d t o them and by what i s e s s e n t i a l l y
an i n v a s i o n of p r i v a c y by t e l e p h o n e w i l l t e r m i n a t e
t h e c o n v e r s a t i o n immediately i f t h e y do n o t unders t a n d what t h e c o n v e r s a t i o n i s a b o u t .
3.
I t i s a b s o l u t e l y e s s e n t i a l t h a t when t h e r e i s no
answer t h a t a l l "no answers'' b e t r i e d a g a i n s e v e r a l
times.
"Try a g a i n s t ' s h o u l d be t r i e d a t l e a s t t w i c e
i n t h e e v e n i n g and then p e r h a p s t r i e d t h e n e x t day
during the afternoon.
4.
Bidding must be r e a l i s t i c a l l y c a r r i e d o u t i n a c a s u a l
manner and t h e enumerator must t h o r o u g h l y u n d e r s t a n d
t h e b a s i c argument a b o u t why t h e economic e v a l u a t i o n
o f nonpriced resources i s important.
PHONE SURVEY
Co 1umn
1
-
1 9 7 5 COMPUTER CODES
Codes
C l a s s i f i c a t ion
P l a c e o f Residence
A
-
Kitimat
B
-
P r i n c e George
C
-
Terrace
E
-
F
-
Vanderhood
G
-
B u m s Lake
H
I
-
Hazelton
J
-
Granisle
D
F r a s e r Lake
L
M
-
Houston
N
-
Kitwanga
-
Endako
P
-
F o r t S t . James
Q
-
T a k y s i e Lake
Telkwa
Fort Fraser
S
-
V
- Prince
R
I d e n t i f i c a t i o n Number
Smithers
-
K
2,3,4
P r i n c e Rupert
Southbank
Engen
George
Number ( r a n g e 000-999)
Column
-
5
Classification
F i r s t favourite fishing location
Codes
0
- No
response
1 - No f a v o u r i t e
3
-
K i t i m a t River
4
-
Lakelse River
5
-
Skeena River
6
-
Douglas Channel
7
-
Telkwa River
8
-
Babine Lake
9
-
Wedeene River
A
-
Kitwanga River
B
-
Dala River
C
-
K i l d a l a River
D
-
Uncha Lake
E
-
P o p l a r Lake
F
-
McBri.de Lake
G
-
Nadina River
H
I
-
J
-
Kalum River
K
-
Tchesinkut Lake
2
L
M
N
Copper River ( ~ y m o e t z )
0 t h e r Lakes
Lakelse Lake
- Kasiks River
- Owen Lake
- Kitwanga Lake
Column
5
Classification
Codes
F i r s t favourite fishing location
continued
'
@
-
Nass River
P
-
Kalum Lake
Q
-
Other Rivers
R
-
Francois Lake
S
-
Kispiox River
T
-
Meziadin Lake
U
-
S t u a r t Lake
V
-
Nechako River
W
-
F r a s e r Lake
X
-
Babine River
Y
-
Maxan Lake
Z
-
Bulkley River
C
-
Pinkut Lake
. - Takysie Lake
*-
Morice River
(
-
Burns Lake
)
-
Ootsa Lake
$
-
P a r r o t t Lakes
?
-
Augier Lake
- -
S t e l l a k o River
:
-
Exchamsiks River
#
-
Cluculz Lake
;
-
Nulki Lake ( ~ a c h i c k )
,-
Bednesti Lake
Column
F i r s t favourite fishing location
continued
5
Codes
Classification
+%
-
Dean R i v e r
B
-
Grassham Lake
It
-
Norman Lake
<
-
Oona and Ormand Lakes
!
-
/
6
7
-
12
Morice Lake
McLure Lake
Fulton River
Second f a v o u r i t e f i s h i n g l o c a t i o n
See Column 5
Compensation r e q u i r e d f o r l o s s of
f i r s t favourite location Original
response
Number ( r a n g e 000000-999999)
XXXXXX
-
No r e s p o n s e
13
-
18
Compensation r e q u i r e d f o r l o s s o f
f i r s t f a v o u r i t e l o c a t i o n New
response
See column 7-12
19
-
20
Reason f o r d i v e r g e n c e i n compens a t i o n required
00
21
24
-
-
23
26
Average c o s t p e r day a t f i r s t
favourite location Original
response
Average c o s t p e r day a t f i r s t
f a v o u r i t e l o c a t i o n New r e s p o n s e
- No r e s p o n s e
0 1 - Misunderstood
02
-
Indifferent
03
-
owns p r o p e r t y
04
- wouldn't
05
-
06
-
discuss
cannot p l a c e
monetary v a l u e
rising costs
Number ( r a n g e 000-999)
XXX
-
No r e s p o n s e
See column 2 1
-
23
Column
27
-
29
Classification
Codes
Average c o s t p e r day a t second
f avouri t e location Original
response
Number ( r a n g e 000-999)
XXX
-
No r e s p o n s e
30
-
32
Average c o s t p e r day a t second
f a v o u r i t e l o c a t i o n New r e s p o n s e
See column 27-29
33
-
34
Reason f o r d i v e r g e n t c o s t s
00
-
No r e s p o n s e
01
-
Misunderstood
02
-
New a c c e s s o r i e s a c q u i r e d
03
-
Rising costs ( i n f l a t i o n )
35
-
38
Maximum w i l l i n g n e s s - t o - p a y
O r i g i n a l resDonse
Number ( r a n g e 0000-9999)
XXXX
39
-
42
Maximum w i l l i n m e s s - t o - ~ a v
New r e s p o n s e
43
-
44
Reason f o r d i v e r g e n t w i l l i n g e s s t o pay
-
No r e s p o n s e
See column 35-38
- No r e s p o n s e
0 1 - Misunderstood
00
-
02
Net o f c o s t s
- Rising costs
- No r e s p o n s e
03
W i l l i n g n e s s - to-pay N e t of c o s t s
0
1 - yes
8.3
9 .O
7.6
11.6
151
130
99
105
31
32
26
26
18
10
11
P r i n c e Rupert
Smithers
Vanderhoof
Bums Lake
F r a s e r Lake
Hazel ton
Granisle
Telkwa
Fort Fraser
Houston
Kitwanga
12.5
---
5
4
---
Southbank
Engen
TOTAL
Cluculz Lake
F r a n c o i s Lake
10.0
4
Takysie Lake
12.5
10.9
7
F o r t S t . James
7.8
5
Endako
11.5
9.6
9.4
8.7
7.0
9.4
8.3
9.4
8.2
8.1
212
1,012
Number of Usable
Completed Responses
No.
% of L i c e n s e s
-
Kitimat
Number Drawn For Sample
% of L i c e n s e s
No.
-
262
T o t a l Number of Fishi n g L i c e n s e Holders
MAIL SURVEY 1975 RESULTS BY RESIDENCE CATEGORY
Terrace
P r i n c e George
P l a c e of Residence
TABLE I V . l :
2,264
1,824
1,376
1,192
1,168
2,024
Kitimat
P r i n c e Rupert
Smithers
Vanderhoof
B u m s Lake
Other P l a c e s of
Residence
TOTAL
3,184
12,504
Terrace
P r i n c e George
P l a c e of Residence
-
50
52
89
84
143
152
622
No.
-
-
47.6
52.5
68.5
55.6
67.5
58.0
61.5
-
4.3
4.4
6.5
4.6
6.3
4.8
5.0
T o t a l Mail Survey
R e t u r n s Drawn
f o r Telephone Survey
P e r c e n t of
P e r c e n t of
Fishing
Mail R e t u r n s
Licenses
-
28
-
5.6
-
2.4
Completed Telephone
Survey I n t e r v i e w s
Percent of
Percent of
Fishing
No.
Sample
Drawn
L
icenses
-
TELEPHONE SURVEY 1975 RESULTS BY PLACE OF RESIDENCE
T o t a l Number of
Fishing License
Holders
TABLE V . l :
SUMMARY OF RESIDENT ANGLER DAYS BY STREAM AND PLACE OF RESIDENCE
-
SHOWING PRICE COMPENSATING CONSUMER SURPLUS VALUES
T o t a l Angler
~ a y/s~ r .
Norman Lake
B e d n e s t i Lake
C l u c u l z Lake
N u l k i Lake
Nechako R i v e r
S t u a r t Lake
Oona & Ormond Lakes
Grassham Lake
F r a s e r Lake
S t e l l a k o River
F r a n c o i s Lake
Burns Lake
P i n k u t Lake
T c h e s i n k u t Lake
T a k y s i e Lake
Uncha Lake
Ootsa Lake
Maxan Lake
Augier Lake
Babine Lake
Fulton River
Owen Lake
P o p l a r Lake
P a r r o t t Lakes
Morice R i v e r
Morice Lake
McBride Lake
Nadina R i v e r and Lake
Babine R i v e r
Telkwa R i v e r
Bulkley R i v e r
MacLure Lake
Kispiox River
Kitwanga R i v e r and Lake
Copper R i v e r
Skeena R i v e r
Kalum R i v e r
Kalum Lake
L a k e l s e Lake
Lakelse River
Mean Value
P e r Day ($)
Annual T o t a l
($) Value Q.9
79,200
105,042
2,086,004
453,388
626,208
630,300
39,046
210,455
5 75,952
22,246
889,204
18,369
15,240
101,167
44,418
112,464
239,209
9,800
l,38O*
1,403,534
13,140*
'
-
14,098
52,340
1,125,912
-
43,921
20
4,220
50,800
61,290
25,382
983,100
9,720*
1,274,982
142,775
2,042,226
3,377,780
430,103
2,605
169,660
878,420
T o t a l Angler
Days /Y r
.
Mean Value
P e r Day ($)
K i t i m a t River
Wedeene River
K i l d a l a River
Exchamsiks River
Kas i k s Rivers
Dala River
-
no mean v a l u e s a v a i l a b l e
*
Q. 7 mean v a l u e s used
( ) w i t h o u t extreme v a l u e
Annual T o t a l
($) Value Q.9
P R I C E COMPENSATING CONSUMER S U R P L U S VALUES BY STREAM
T o t a l Annual ValuesIStream
= t o t a l number o f Yellowhead a n g l e r s
who f i s h l e a c h s t r e a m
X mean y e a r l y p . c .
surplus
consumer
Mean y e a r l y p r i c e compensating consumer s u r p l u s
= mean v a l u e [ ( d a i l y w i l l i n g n e s s - t o -
pay - d a i l y c o s t s of f i s h i n g ) X
(days f i s h e d p e r / y e a r / s tream) ]
= mean v a l u e [ ( t e l e p h o n e s u r v e y ' 7 5
Q.3(a)(ii) - Q.Z(b)(ii)) X
( m a i l s u r v e y Q.10)]
T o t a l number of Yellowhead Anglers who f i s h each s t r e a m
+ mean
number a n g l e r days a t s t r e a m p e r
angler
= t o t a l angler dayslstream
Mean # Angler days a t Stream p e r a n g l e r by p l a c e o f r e s i d e n c e
= mean ( m a i l s u r v e y Q.10 and 4.12)
T o t a l Angler dayslstream
= t o t a l r e s i d e n c e a n g l e r s by p l a c e
o f r e s i d e n c e ( ' 74 phone s u r v e y
a n g l e r s a s % o f pop.)
X mean days f i s h l y r . i n Yellowhead by p l a c e of r e s i d e n c e ( ' 7 5
m a i l s u r v e y Q. 6)
X d i s t r i b u t i o n of a c t i v i t y
o c c u r r e n c e a t e a c h s t r e a m by
p l a c e of r e s i d e n c e (mail s u r v e y
Q.10 and 4.12)
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