ECONOMICS OF UPLAND RESOURCE DEPLETION
SHIFTING CULTIVATION IN THE PHI LIPPINES
Morion S.delos
Angeles
WORKINGPAPER _ 88-02
February 1988
Philippine Institute for DevelopmentStudies
:
TABLE
OF CONTENTS.
Page
List
List
of
Tables
of
Figures
I.
Introduction
II;
A Normative
Model
of Optimum
Use of
Forest
Lands
for Agricultural
Production:
Resource
Optimization
Under
Complete
Markets
.... . ........
, .............
,..--
III.
IV.
........
_.,.... , .....
The Private
Individual's
Soil
Resources:
Resource
Under
Incomplete
Markets
..... ...
Implied
Policy
VI.
Bibliography
VII.
Mathematical
Tools
........
ii
,.,.-
..................
.. ...... .. .... ..... .....
Annex
4
Use of Upland
Optimization
• ....... ...- ....
Some
insights
fromZthe
Philippine
Experience
....... ... ...........
......
V.
1
24
,
....
.............
29
33
35
LIST' ,OF TABLES
Page
Table
Table
•Table
1
2
3
:
:
:
Labor
Use
•Farming
.
Examples
Systems
Allowable
Density
in Hanunoo
Swidden
........................
25
of Up!and
Agricultural
Evaluated
in Terms
of
Population
28
ooeo_aomeoeoeo'eoomoe.oooo
Average
Land
Productivity
Traditional
Kaingin
Farm
Puting-Lupa,
Mr; Makiling,
1978•1980
eooe.oooo_loooaooooomoo
In
in
a
30
LIST,
OF FIGURES'
Pa_e
Figure
i:
Determination
of Area
for Agri a
cultural
Production
by Various
Decisionmakers
....................
15
18
Figure
2
:
Time
Figure
3
:
Shifting
Lands
Figure
Figure
4
5
:
:
Paths
of
S,
O,
Agriculture
P,
in
and
u
........
Forest
.........................
.....
21
Theoretical
Relationship
Between
Length
of Fallow
and Soil
Productivity
....4.. .........
, ......
22
Relative
intensity
Graph
of Various
Subsistence
Activities
of the Batak
in one Agricultural
Year
... .......
27
ECONOMICSOF UPLAND RESOURCE DEPLETION:
SHIFTING CULTIVATION IN THE PHILIPPINESI'/
by
Morion S. delos Angeles2"J
I.
INTRODUCTION
The
developed
and
wood
prac%ice
two
principal
countries
gathering
o_
today
for
sn1£tlng
Based
mostly
Res0urcelConservation
Ph.D
(Economics)
1986.
causes
are
fuel
of
land
(Eckholm
cultlvation"
deforestation
clearing
_or
1976).
has
in
on
agriculture
However,
largely
Chapter
III of "Economic
by Upland
Farmers
in the
Thesis,
University
of
the
"
less
the
dominated
Analysis
o£
Philippines,"
Philippines,
-2_:
Researchl
Studies.
Fellow,
Philippine
Institute
for
Development
2
clearing
is
an
of
of
forested
land
agricultural
fields
•means
of
agricultural
generally
than • crops,
with
slash
In
system
rather
alternating
for
long
and
burn"
conduc£ed
by
fallow
short
(Pelzer,
such
system,
as
it
locally,
logging
activities.
inflicted
by
forests
note
fourteen
(M.C.Cruz,
such
et
_e
agricultural
with
a
The
effects
We
forested
land
represents
cannot
be
in
of
investigate
clearing
by
usually
succeeded
i
the
the
the
•damage
loggers
on
Perhaps
of
Some
uplands
in
land'use
30
the
more
eountry's_
individuals
1980
systems
percent
of
the
understated.
the
investigation
uplands
by
shifting
optimum
society's
relative
is
systematic
practiced
treatment
from
a
Cropping,
"kaingin"
the
it
1986).
provide
rotation
the
and
M)
systems
problem.
on
(14.0
to
formal
debate
million
therefore,
attempt
has
in
which
by
of
occupancy
al,
total,
practice
unresolved,
that
population,
national
and
agriculturists
remains
to
reached
by
upland
still
important
While
a
It
1968).
Philippines,
termed
"by
.
periods•of
periods,
the
is
production
starting
cultivation
rate
viewpoint
of
of
and
use
from
of
the
•"Shifting
cultivation",
shifting
field
agriculture",
"swidden
farming•",
"slash-and-burn
farming"
and
"kaingin"
are
terms
which•
have
been
used
by
va_iQus
•.authors
to ....
indicate,
generally,
similar
agricultura%
system.s
and
.are
used
interchangeably
in this• paper.
The
technologies
development
workinglpaper.
economics
by
upland
projects
of
adoption
communities
shall
be
of
who
presented
soil
are
in
conserving
participants
a
subsequent
of•
3
individual
between
uplander's
timber
slash
and
expiained
on
production
burn
termS
access
of
constraints
which
Sections
completeness
of
a standard
2
use
use
resulting
the
of
of
forest
Upland
agricultural
land
Soil
of
rules
varying
and
degree
determinant
prices
by
of
major
In
are
the
as
ot
upland
resulting
stocks,
followed
of
valuation
resources.
zero
use.
effects
the
resource
production
decision
is
and
as "_ well
products/effects
future
model
bias,
resource
dissimilar
and
timepaths
varying
the
Specifically,
environmental,
_ of
discuss
is
economic
involved,
upland
through
farming
discounting
to
for
choices
production
resource
the
specific
markets
use.
agricultural
rates
are
traditional
swidden
externalities
land
external,
Here,
of
the
given
agricultural
exploitation,
valuation
resource
or
farming.
. in
open
viewpoint,
the
from
of
addition,
the
scarcity
rent,
discussed
under
different
resource-
users.
section
3_ubsequently
hypothesizes
the
likely
, [
behavior
of
conditions
insights
country.
policy
forest
of
on
use
under
accessibilityand
shifting
This
tools
land
in
is
Section
tenure,
cultivation
followed
4.
specific
by
in
a
and
varlous
discussion
Philippine
presents
parts
of
the
some
of
the
implied
4
rX;
A NORMATIVE MODEL• OF OPTIMUM USE OF .FOREST _,AI_P_, •
-FOR AGRICULTURAL PRODUCTION : RESOUR<;E,OPTIMIZATION'
UNDER COMPLETE MARKETS
Consider
the
agricultural
basic
Howe
following
production
natural
,(i979,
on
resource
Ch.
forest
=
where
Q(t)
=
L(t)
=
composite
S(t)
=
stock
resources
=
time.
function
""
[ L(,t)
calls
"stock
"(a)
an
S(t)i
a natural
)
reduction
as
in
adopts
the
as
presented
by
of
as
future
use
p'91),
and
to
a
•and
the
to
he
proceeds;
what
to
as:
derived
and
limit
he
defines
_( for the
finite
soil
production
reflect
which
costs
depletion
due
land
an argument'to
commodity
in"forest
input;
forested
therein;
and
extraction
(resource)
pla_ted
labor-capital
(ibid,
of
, t]
crops
resource
effegts"
increase
co_odity
•
which
model,
. S(t)
agricultural,
land;
includes
for
depicting
5):
Q(t)
Howe
land
exploitation
(i)
t
relationshiips
(b)
the
a
total
i
quantity
of
inserted).
the
An
effective
in
situ
example
logging
costs
resource',
of
such
for
(ibid,
stock
cutting
p.72;
effects
smaller
italics
include
sized
higher
trees.
i
We
model
forests
differ
for
the
andsoil
in
use
our
of
treatment
upland
resources.
of
S(t)
resources
Under
as _ We
which
theshifting
adapt
include
the
both
agriculture
k
system,
as
the
_ollows.
the
flow
•
services
cleared
provides
production.
burning
trees,
biomass;
vegetation
that
content
which
clearing
in
an
after
still
is
the
also
addition
burning
agricultural
enhanced
•. by
by
slightly
organic
(Sanchez,
•,
fores£
accompanied
of
the
felled
contains
are
increase•of
are
for _
resources
is,
uplahds•proceeds
forests
-fertility
the.soil
results
nitrogen
area,
•the
forested
standing
enough
••When
of
burnt
•from
Immediately•af•ter
resulting
litter,
of
the
burned
•matter
1976),
and-
Thus,
an •
...
immediate
• (i.e.,
(_Q/_S(t))
better
> 0;
.sites
•example;
land)
same
structure
topsoil
which
heavy
in
more
diffi_ul£
forest
the
burnt
uplands
stock
no
to
measures
'•
less,
.
forest
"extract"
the
forest
••
described
current
the
by
use
be
to
the
Howe
a
therefore
for
pasture
from
nutrient.s
are
no
feasible
it
longer
as
given
the
(usually
becomes
products
provided
r ,
due
of
rainfall
Thus,
earlier
howeve
erosion
" agricultural
vegetation
from
by
the
avaiiabie,,
• -•v•
or
, .
•
subsequent
negative
of
not
•
for
or
compared
taken,
l_tter,
cropping
z
manner,
are
ire
and,
•
are
may
10ngerprotected
because
of
results
(e.g•_-, •grassland,
pr0d_ction
tropics)by
land
forested
production,
deterioratioh.,
is
effect
slope.
agriculturai
soil
stock
are
agricultural,
soilconservation
continued
tO
which
non-forested•
the
Unless
•positive
uplands
for
with
of
current)
stock
a
cost
Inthis
.
_ffects
hold.
experienced
resource
cycle.
stock.
These
in
the
effects
future
due
are
to
6
2
We
expect (_O/_L(t))
> 0,
and
(2
2
Q/_L
(t))
< 0
from
i
the
usual
returns)
behavior
(2)
agricultural
of
(2)
production
•
(law
of
diminishing
•.
Equation•
price
of
p(t)
=
D
the
value
inverse
of
,
demand
given
function_
p(t_
as
the
for
composite
products:
next
•include
an
crops/c0mmodities
such
The
is
[ Q(t)
, t]
relationship
use
of
•shows•• sooial
agricultural
environmental
. benefits,
products,:
services
of
as
untilled
which
well
as
forest
the
land,
s(t):
Q(t)
(3)
SB(t)
Here,
the
we
area
=
_
D[q(t),
integrate
over
under
demand
the
Q(t)
t]
to
d n
+
E_S(t)]
indicate
cur.ve,
that
we
are
•and•estimating
valuing
consumers'
surplus.
The
by
a
soil
environmental
stock
of
erosion
ecological
present
study
as
>
lands
0.
the
and
largely
off-site
lead
E[S(t)]
may•pertain
well•as
focuses
among
forest
(dE/dS)
forests
diversity,
concern
_f
services
to
more
to
others
the
on
forest
which
the
such
provision
soil
erosion
servicesl.
environmentali
are
provided
minimization
as
of
windbreaks,
of
oxygen.
as
The
the
primary
Larger
stocks
services,
thus
7
Subsequently,
agricultural
costs
_bss
area•.
in
crops
such
of
we
as
the
to
costs
soil
as
opportunity
•
production
involves
cost
of
labor-capital,•
due
to
a•reduced
those
harvest
imposed
from
of • raising
direct
and
forest
on
the
agricultural
crops
due
problem
the
social
cost
of
for
• discount
rate
and
the • labor-capital
agricultural
_
input,
•production
as
the
on
forest
becomes:
Max.
L(t)
_[
subject
to
:
Equation
control
I
0
-rt
D( n,t)d_
+ E
(4.1)
S(t)
=
(4.2)
S(t)
>
(4),
problem
the
state
net
•production
cost,
iperiod,
product,
• (4.1)••
where
maxlmizing
time
land
forests,
[S(t)]
- wL(t)]
e
dt
Q(T)
dT,
t
s(t)
the
future,
secondary
Q(t)
(4)
of
fertility.
_
optimization
land
foregone
the
landswhich
include
difficulty
Setting
unit
forest
• services
the
decreasing
•investigate
opportunity
Indirect
increasing
the
on
environmental
particular,•
and
now
benefits,
wL(t),
from
•under
environmental
the
services
{
decision
(4)
_ or
equation
complete
a
describes
••Equation
social
Thus,
is
-
0.
and• (4.2)
L(t)
variable.
•S(0)
•
(3)
future
optimal
variable
says
that
subtracting
• markets,
and
an
over
the
we
and
are
current
a perpetual
agricultural
effects
of
using
8
part
of
forested
Considered.•
are
Presumably,
based
on
of
forested
of
upland
Equation
rate
the
S(O)
(4.2)•
of
is
agricultural
while
change
crop
occurs
pro_iuction"
when
t_e
are
decisions
all
made
concerns.
(•4.1)
land;
for
•this
societal
Equation
land,
uplands
an
accounting
constant
a
production
denotes•
is
the
of
S(t)
the
equation
(>0)
on
initial
the • stock
reiflects
the
effect
reduction
of
forest
forested
land.
stock•bf
non-negative
,• is
the
for
conditioh
of
S(t).
The
•inc°rp°rate
the
therefore:
•e
(5)
s(t)
For
-a . Q(t)
purposes
constraint
equation
:
of
• equation
rt
by
_e
manageability,
(5)
dt
into•
or
we
(4 )
and
equiva_entiy,
mulitiply
rlt
e _ ,
:
to
whole
form
the
the
rake
i
current
of
the
net
value
social
Hamiltonian
benefits
function
at
instant
which'
depicts
%:•
Q(t)
(6)
H
=
_
D(_,
t)
-
dq
+
wL(t)
E
-
[S(tl)]
a
. u!(t) Q(t)
.• •
Here,
u(t)
is • equal
first
of
sacrifices
the
to l.e
two•
benefit
cost
is
,
terms
rates;
current
Lagrange
corresponding
of
the
labor-capital
imposed
value
on
to
(6)show
third
the
term
constraint
direct
pertains
• inputs,
while
future
periods.
multiplier,
the
add
tol
which
(5).
•The
environmental
the
opportunity
last••term
represents
9
Differentiating
7)
H
_H
_L(t)
=
.
D
with
respect
[Q(t),
t]
. •
to
_(t)
_L(t)
dS(t)
dQ(t)
-a.
L(t)
+
.•
gives
us:
dE[S(t)]
dS(t)
_•Q(t)
_L(t)
-
w
u(t) _O(t)
_L(t)
Obtaining
(_H/_L(t))
•
'=
••
Condition
on
(8),• p(t)
price,
=
-
O, we•derive•the
•••
cost/
dE
and
following
basic
5/
ren£:-
[S(t)]
, dS(t)
dS(t)
+
w
_O]q7
_Q(t)
3L(t)
+ a
That
••is,
products
three
the
derived
since
loss
dS/dQ
marginal
from
components.
marginal
. u(t)
foreBt
The
of
social
land
firs_
<• O.
The
two
at
term
environmental
value
any
on
of
time
the
must
right
Services.
other
agricultural
covers
This
components
include
are
the
is
positive.
the
marginal
m
_production
cost
up
cost
(or
second
scarcityrent)
which
wiped
(the
are
•out
(third
agricultural
society•.'s
not
on
replenished
term).
_roduction
and
the
and_
on-site
from•
mlrgina!
resources
marginal
forest
therefore
inter_temporal
the
being
because•secondary•forests
The
• commodities
viewpoint,
term),
cost
•
land}
includes
Of
user
used
are
producing
according
to
environmental,•
costs.
5/
matical
-- The
•appendix
derivations.
presents
the
details
of
the
mathe-
I0
Once
no
the
longer
pays
agricultural
better
hand • side
for
of
society
eq.
obtaining
_sour_es
as
exceeds
the
lands.
additional
_such
(8)
toproduce
commodity•on•forest
off
other
right
lowlands
Hence,
or
it
unit
of
society
is
next
agricultural
the
p(t),
products
the
from
international
market.
The
movement
may
be seen
(9)
Basic
from•the
+
From
in
of
2
[p(t),
(9)
size
benefits
> 0,
is
of
u(t)]
i_n_n
_itu
+
[p(t)
and
•resources
Here
is
enjoyed
u(_)]
> 0,
we
carried
by
dE
dS (t)
- a
(dE/dS)
positive.
f0restland
are
on
8Q(t)
_S(t)
(8),
(_Q/_S)
equation
rents
now
:
a.
equation
that
optimum
scarcity
following:
condition
u(t)
given
of
=
> 0
then
can,see
u(tl
;
thus,
(u(t)/u(t))
that
forward,
[
society
r.
whenthe
three
(left-hand
types
side
of
f,
(9):
(a)
increase
production
value
of
italics
costs
in
of
additional
its
value;
(b)
•
..agrgc_.ZCura z
enylronmental
inserted).
The
sum
reduction
I
commodities;
services
9f
of
these
future
and
(Howe
ben4fits
(c)
the
1979,
p.93;
should
yield
i
the
u(t),
socially
the
required
of
return
r
on
the
value,
of
scarcityrent.
Hence,
the
rate
optimal
the
rate
first
of
basic
producing
condition
agricultural
(eq.
8),
crops
tells
on
us
forest
11
land
of
While
basic
forest
III.
2
(eq. 9)
shows
the
optimai
stock
lands.
THE PRIVATE INDIVIDUAL'S USE OF UPLAND SOIL RESOURCES"
RESOURCE OPTIMIZATION UNDER INCOMPLETE MARKETS
After
having
discuss
land
of private
tenure;
those
case
Private
A
potential
ignore
of
his
would
without
With
for
tackle
with
secure
rights
Secure
agricul£ural
environmental
;
Land
in
and
the
objective
function,
with
Tenure
a
products
services
The
would
provided
Corresponding
the
perfectly
likely
by
Q(t)
[ /
Maxlmize
formulation
omission
of
E
[S(t)],
D (_,
t) d_
wL(t)]
-rt
e
-a
Q(t)
-
o
t
subject
to:
(i0.i)
(i0.2)
(ii)
corresponding
p(t)
the
in:
L_t)
The
now
"We
those
cultivator
resources.
(i0)
:
we
Cultivators.
upland
off-site
rules,
criteria.
users
in situ
result
decision
property
Resource-User
setting
the
resource
shifting
The
Competitive
stock
of
societal
decision-making
cases
special
3.1
derived
individual
three
of
condition
=
basic
conditions
w
Qi't)
L(t)
+
a
"
S(t)
S(t)
>
would
be:
. u(t)
0
.
dt
12
I%
(12)
"
'_(t)
+
[_(t)
Equation
(ii)
- a.
implies
agricultural
crops
raised
the
cost
p(t)
social
because
off'site
the
value
the
factor
the
same
both
more
of
demand
area
society
would
for
equations
incomplete
through
larger
the
forested
swidden
areas
tend
to
be
than
tha6
as
are
of
not
deforested
(8)
that
is,
(8)
_by
eq.
would
ailarger
in
area
that
given
for
u
iconditions,
o_
the
whenl
the
agricultural
included
produce
rent
is, i golving
by
, f0rested
the
situ
basic
given
faced
environmental
to
than
Therefore,
against
Hence,
off-site
lower
products
difference
< u.
of
eguation
individual
second
p(t)
Ignored;
> 0.
That
uplands
farming
are
result,
the
a
Q
because
a
be
in
i
convert
faster.
for
implies
Converting
would
use,
respectively,
> 0
less
an
As
rise
would
agricultural
or
consider.
two
(12)
for
cost"
earlier
(dS/dQ)]
agriculture
u
(dE/dS)
is
.r . .u(t)
"private
costs
.
crops,
(12)woul_
and
(ii)
=
uplands
_ecisi0n-makers,
equation
the
the
indicated
curve
agricultural
upland
in
in
the
eDvironmental
equation
of
Q(t)
S(t)
that
[-- (dE(S)/dS)
types
_(t)]
.
in
and
(9)
magnitude
market
is
effects
of
croplands
in the
and
scarhity
decision'making
a_so
exchange,
rent
rises
faster.
Furthermore?
public
individual
choice
private
in
normally
terms
uses
of
a
the
rate
time
higher
preference
than
what
differs
from
rate:
a
an
public
13
planner
would
comparing
equations
(dE/dS)
3.2
apply,
> 0, we
The
Individual
(9)
and
the
resources
the
_or
a
right s
effects
U(t)
=
0.
would
be:
(13)
p
In
this
=
Land
area
be
u.
from
may
rights.
use
more
a decreasing
of
soil
responsive
stock
of
soil
rights.
land
are
decreasing
forests)
case,
corresponding
the
u and
property
would
r&s,
that
production
secure
public
mind
land-use
exclusive,
of
the
Tenure
changing
tovarying
effects
use
in
between
Secure
without•pr0perty
to
(of
has
for
bearing
gap
of
thus
agricultural
upland
future
th'an one
When,
stock
who
given
on-site,
resources
Without
according
cultivator
and
wider
to
differ
Solving
(12),
effects
production
An/upland
> r."
evena
User
to
additionally
to
r
obtain
Reaction
timber
or
may
not
secure,
be
excluded,
basic
the
or
conditions
w
_(t)
8L(t)
(.14)
u(t)
•=
r.
u(t),
or
u(t)
=
u(t)
The
price
thatthe
tilled,
to
his
public,
valuation
production,
That
reflected
as
is,
by
cultivator
(erstwhile)
Of
depicted
the
attaches
forest
effort
by
eq.
that
to
his.produc
land
is
went
into
equivalent
e
only
agr'icultural
(13).
assuming
the
time preference
r, for purposes
of. asimpler
rate
is properly
exposition.
14
Public
farming;
cost
land
a
"smaller
rises
at
u(t)/u(t)
.in
the
following
with
the
the
>
used
stock
a
at
of
faster
a
faster
forests
rate.
equations
(9),
differences-being
>
(12)
and
(u/u)
>
0,
for-swidden
,.results
accounted
[_Q(t)/_S(t).]
rate
Thafi
relationships:
terms
a.u(t)
is. hence
and-
is,
solving
. (14)
(u/u)
>
forby
[dE[S(t)
.user
for
would
yield
(u/u)
> _ 0,
exclusion
of
/dS(t)]
>
'0,
and
rights
for
tilling
the
forests
0.
Indeed,
with
the
absence
of
property
1
"I "
the
are
Uplands,
even
the
upland
depleted
at
a
resources
faster
'
whichinclude
rate
because
the
stock
effects
[
are
excluded
tenure
indecision-making.
leads
comparing
_to
an
even
equations
marginal
user
faster
rate.--
arrived
at
Moreover,
higher
(14)
cost
and
rises
byvarious
discount
(12),
and
because
Figure
of
the
forest
of
rate.
_
land
.i .shows
users
insecurity
> r,
_s
Thus,
the
faster
depleted
results
Of
land•
at
.a
decisions
Theforest
area
1
used
for
agricultural
production
by
socilety
(aQ)
-
than
by
that
the
largest
In
we
shall
aQ.
is
thereby
U/U
determined
by
individual
area
the
aQ
special
!/
Scarcity_rent
.'=
_
•
<aQ
case
more
furthermore
resulting
individuals
withoutproperty
(i.e.,
discuss
private
of_the
fully
faster
being
rights
less
A
and
who.
•
aQ),
and
uses-
the
< aQ).
cultivated
in
(aQ
is
Shifting
in
section
cultivator-,
2._
frequently
depletio
equal
n of
below,
by
soil
to zeroS"
in
which
the
Several
area
users,
_es0urces.
fact,
implies
is
p(t )
_
.MC(t)
= (dE[S]
'dS)(dS(t)/dQ(t))
+-
w(aQ/_L):+ .a.u(t)
-_C(t).
p(t )
%
i_( t )
\
= w(aQ/aL)+
a a
"_ t) = w(_0/as)..
• i
:
[_(t)
• I
•l
I
I
-
|
ap,
FIGURE.
I
I
. i.
I.
I
I
I
I
I
.
L
""
t •
I •
!
•
I
[
I
.I
I
<_
D(t )
I.
I •
-_
_a_4
_(t)
,- -.
I : ..DETERMINATIONOF AREAFOR ,.AGRICULTURALPRODUCTION
.BYVARIOUS DECISION 'MAKERS
L
E G.E.N
D :
Decision-maker
Marginal Cost
Area
for Agricultural
production
society
MC
aO
individual .with property rights
_
a_
individual,w/o property rights
MC
a_
16
3.3
Behavior
Given.•
•paths
of
_•, •2,
these,
we
forest
production
and
of
in
scarcity
focus
on
rent
in
products•
and
soil)
for
proceed
of
three
cases
factors_
for
hot5
time
to
determine
stock,
time
agricultural
discussed
above.
products,
assume
th@t
services,
We
abstracting•from
agricultural
and
the
agricultural•commodities
therefore
We
products
over
price
amenities.
resource,based
•_
resource
the
supply
demand
and
now
uplands,
resource
changes
may
(and
the
R
forest
for
relative
varying•
prices
will
hold.
We
the
compare
market
is
decision
maker
resource
stock,
property
(ii)
forest
soil
complete,
with
butwho
_rights
would
We
0.
attribute
a
produce
would
initially
at
lower
a higher
decrease
Further,
since
the
from
a
faster
social
and
[p(t)
individual's
- a
discount
u(t)
and , he
of•the
> u(t)
in
als0
[-dE[S(t)]/dS(t))
sector
resource
commod{ty
the
ra_e
rate,
private•
< or
user
r
is
{
society;
and
price
resource
stock
is•
lower
than
i
discount
u(t)]
(8)•
rate.
F
the
from
equations
private
,
individual
effectsbecause
•agricultural
Q
an
where
amenities
since
•the
level
at
by
stock
> p(t),
Thus,
society,
off-site
obtain
p(t)
>
p(t),
the
by
use
internalizes
exist.
(dS(t)/dQ(t))]
use
resource
•who disregards
the • relationship,
user
resource
excludes
equations
the
leiss than
initial
that
for
°1
(dE/dS).
(9)
> _•
and
H_n_e,
(12). •
the
terms
•scarcity
rent
17
thus
increases
resource
faster
stock,
-.After
resource
more
a
for
individual
..has
.elapsed,
longer
time
stockswould
result,
in
,
extracting
who
uses.
the
rapidly.
. ,
in
the
the
however,
higher
lower
incremental
costs
.
resource'based
- product.
In
addition,
1
rents
rise
p(t)
at
> p(t)
In
case
or
rates,
Q(.t)<Q(t)
when
the
uplands,
,faster
of
the
u
(Figure
a resource
shifting
or
user
> u.
Eventually,
2).
who
cultivator,
has
the
no
tenure
in
situation
is
the
even
J
worse:
the
initially
decrease-rapidly
increase
time,..
who.
has
Q
no
production.."
>
lower
rapidly.
in
u
to
u.
,
higher
This
> Q
levels,
means
and
tenure
disregards
Scarcity
rent
Thus.,
and
that
.<.p
virtually
production...
agricultural
a
scarcity
during
because
even.
'rent
would
earlier
point
resource
user
an
the
the
wouldrise
affecting
during
production.would
stock,
ata
effects
higher
agricultural
latter-point
in
rate,
of
or
commodity
time..,, p
> p
A
when
3.4
Q
< Q
The
Shifting
For
public
..
Cultivator
upland..farmers
forests,
several-
the
.cultivators
land
occupying
.may be
in . a
inadequately
tilled
similar
many
secured
timesover
fashion,".thus
by
crowding
}'.
occurs,
specially
alternatives,
in
the
exploitation
under,
in
condit_bns,
the
economy
of
open
of"high
(clark.
access
fishery
unemployment,
1973),.
and
resources,
orlack
high-man-land
of
18
FIGURE 2"
,..
TT_MEPATHS OF S,
. . ,. ,
Q, p
AND u.
............
_
•"
•
_._---'_"_-"
-
,,
Social optimum
' ' "
I*
I_%
-_'- -__
-- S
_"
•_
7-:
private
-- S
w/o property
,,,,i
,
i
I,
rr
I
J
.
I
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i
,
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I
,
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,...,-" '
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!
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I
•
rW
,, ,-JJf
,
,
I
I
p, U
I
i
tim_ pa,ths of agricultural prOduction
and lstocks of
forest lands
i
...........
rights
.
I
I
a.
optimum.
w/property
private
opt_It_,rights
__
I
II
J,,
/
_
"
..
"
time •paths of agricultural
and scarcity rent
•prOduct price
19
ratios.
In
stringent
time
seasonal
few
because
are
are
uplands
to
that
slash-and-burn
of
If
time
portion
of
of
is
a
average
is
only
the
first
the
Fast
rains
Mostshifting
1-3
cultivation
more
come,
after
too
a
which
farmer
the
is
is
highest.
till
invasion
of
shifting
the
has
agricultural
follows
yields.
field
weeds
to
it
negative
subsequent
the
is,
In figure
resources
lower
therefore
that
burning
for
soil
type
Indeed,
and
curves
in
relevant
_
declines.
top
and
feasible
technique,
section,
illustrate
product
laborious,
low
available
the
af£erfelling
the
is
slash-and-burn
sloping
resulting
by
arenot
input I,
for
depletionof
imposed
kaingin-making.
lines
cultivators
years,
or
a
not
preparation
production
total
is
season),
productivity
Solid
the
labor
land
downward
is
where
availability
labor
curv6
harvest
with
of
hiring
variable
agricultural
curves
labor
planting
product
the
conditions
preparation
surplus
only
agricultural
production.
after
or
the
the
is
when
portions
low
and
farming,
total
the
occurred
used
a time-saving
agriculture
when
3,
adopt
land
effeCtive
during
induced
£ropical
for
and
tools
incomes
tMe
under
constraint
patterns,
(e.g.,
in
addition,
for
makes
another
0nly
further
field
is
desirable.
The
effects
shifting
by
cultivator
either
use
technology,
the
availability
developing
or
of
udjusting
produce
Who
has
better,
his
from
tenure
stock
land-conserving,
consumption
the
avoids
land,
soil-
pattern
andor
to
seek
suit
other
20•
•sources
of
during
livelihood.
the
fallow
replenish
system
by
• of
other
of
w. crul,
1982
for
the
e_amples
country's
•.
is
soil
is
Indeed,
on
to
from
under
a given
evolution
of
by • a
!documented
case
minority
of
able
eMploitatiQn
been
practice
that
protected
Philippine•f•isheries'!
The
is
_he
resource
cultural
implies
feasible
usershas
• of
••up!an_s)
the
land
this
rules
for
Of
rights.
resource
choi.ce
which
piece
users;
determined
community
1984
the
property
•commonly
latter
period • during
itself,
•encroachment
The
(e.g.
and
Lynch,
groups
shifting
in
to
the
another
r
field
is
cost
thus
(and
natural
allowing
process
The
upland
choice
of
Ithe rules
for
man'land
the
•
presented
opposite
(Figure
by
Figure
3b).
Sanchez
a
technique
the
the•use
,stable"
long
of
(1976,
p.
land
of
area
land.
of
periods
• such
384)
the
land
among
the
availability••and
For
areas
shifting
are
with
followed
with
the
diagrams
which
we
low •
a_riculture
areas
{
4.
the
preparing
eventualshorteningof
Similar
through
of ; declining
characterizes
and
user
reiatiOnship
system
fallow
marginal
•
degrees
on
case
density,
[
as
a
higher
conservation
cultivators,
governing
where
population
period
as
varioUs
upland
result,
3a);
in
ratios,
soil
burning
depending
population
avoiding
regeneration).
of
results
of
on-site
of
productivity,
may
a process
(Figure
high
fallow
• have
been
reproduce
here
21
FI-GURE
3 ;i SHL_r-'_EAG_CUL_mE
IN.I__3_T
J
......
Total
product
,
'
'
•
•
•
•
"
_
.-f_
:
• • .
,,
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t,3 ,.. t_
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s_a.hleshifting agriculture replacing
aforest managedfor timber production
II
I
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,
.,
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I I'II
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21 _.,_
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-_'_, -
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,
.
.
2 _3.t4
an unstable shifting cultivation syst_n
..
"
Time
..
22
-- _ -
-
L--Y ._;
CLIIlivallon
_
y_t_
,
_
. I
_
Maintenance
u°,,e_es_,V
Retlenefal.ion
years
,.
o_o<._a,y
_ F dlJ_w
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1
1
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.5
FIGURE 4:
Source:
_
year'.,--
\/.
--
I
I0.
q
I
I
__v._. __ =
I
,....,141. .:.<.20_".. 25 _' 30' :
Years
Theoretical
failowand
t
I
35""
relationship betw__n
soil productivity.
t
1 :
40 :'
.45
"
length of
Guiliemen, R. _956.
Evolution de l'agriculture
autochtone dans l_ savarun__sde i'Oubangui,
Agron, Tropica]e
(France)
ll: 143-176;
reproduced
p. 384
in Sanchez
(197.,6),Figure
i0.17,
23
The
the
F-labelled
forest
lands.
which
The
production.
signify
•.
is
have
and
the
Q
is
•_irst
of
to
tlme
t
forest
agricultural
•F
at
the
the
when
C0nducted
by
from
curves
to•
output.
at
indicated
use
the
harvested.
•thus
production
pertain
below
of
the
been
timber
traditional
located
values
is
• to
'Q'
production
by
timber,
,
are
3a • depicts
shall
signified
been
current
agricultural
refer
labelled
They
iower
trees
has
curves
Figure
for
curves
forest
the
is
stand •
used
of
Production
of•crops,
the
of
expense
segment
Of
curve
future
F
that
4
covered
du_ing
the
time
interval
(t
, t
1
The
dashed
portion
of
curve
Q
).
4
shows
production
of
2
biomass
by
the
cultivation
untilled
again
fallowed
in year
t
land
.
which
Figure
3a
is
used
there£ore
for
shows
a
2
shifting
piece
equal
of
of
and
equal.
land
gives
the
variagt
of
in
such
a way
is used '•only
at
same
other
•of
yield,
this
intervals
periods
and
piece
of
land
when
at
shorter
which
increasing
a
given
which
things
diagram
fallow
that
are
remaining
depicts
yields
is
a
not
here.
The
agriculture,
result
patterned
forest
A
lengthening
shown
fields
in
same
which
productivity
occurs
declines
in
subjected
time
the
to
shifting
intervals,
long-run.
The • determination
of
t •is
the subject
area
of study/ and is treated
as a •given here.
may
see Samuelson
(1976)
for this.
shall
This
of
The
is
another
reader
24
depicted•in
• Figure
•3.1b
(t ' < t
,
t ' .<
•2
2
3
production
dedlines.
This
figure
effects
of
off-site
where
the
fallo_
periods
t
,.
t. '
<
t ) , ! and
3 "
.4
'4
(Q ' <.Q. , Q
' < Q
' and
2
2
3
3
shows
both
depletion
user
.but
enviEonmental.
it
•effects
c0st.a:nd,
-does •
of
decrease,
agricultural
Q
'.<
4
Q
"
on-site
not.
)..
4
Stock
present
slash-_nd-burn
the
farming_
[
Thus,
only
the
concerns
of:the
individuail
•
(timber
IV.
manager
and
theshifting
.SOME INS!GHTS
We
now
points
we
FROM THE
.presen
raised
cultivator)
evidence
gathered
We.
focus
not
always,
firit
t
some
• in
the
i,
data
and.
has
of
several
discussion
on
.agricultural
the
hastens
severalyears.
use
except
compared
of
at
for
as
on
felling
climax
alternative
j
are
usually,
labor,use,
by
was
the
eleven
years.
and
3),
We
• ofdecay,
note
protection,
This
forests
biomass
in
relative"to
•
activity
gathered
"Hanunuo
is
(woody
which
.(old-@rowth)
• of
but
minorities.
labor-u6!ng,.
of•secondary
the
by-.citing
kaingin-maki.ng.
interplanting,
more
•thick
the
Cultural
least
theconversion
to
whichi
(stages:2
.. such
for.. the
trees,
data
climax•forests
and"harvesting,.are
for
Of
vargous
•
oh
swidden.farming
weeding,
intensive
systems
members
.cycle
activities,I
bamboo•type•),,
researchers
presents
•presented.
the
,
by
a
are
whichsupport,
preceding
"stable"
(.19.57)
that• felling
other
on
which
Conklin
:Mi.ndoro,
by
evolved
Table
Burning
makers
PHILIP, PINE I_XIPERIENCE
•
by
decision
,.,,,
from
which
is
true
or
more
forests.
the
could
felled
take
'25
TABLE
LABOR-USE
IN HANUO0
I
SWIDDEN
of
FARMIN_
Ma_,.--day s
Swid_e_
i_ Secor, d Growth
New
=
C lima
Sta_es
i
Site
Act ivity
" Forest
Selecting
.8
•2
SlashirmD
•3
Fel i ir,g
4
5
•6
Piar, tino Maize
Plargting
Rice
lr,terol ant inq.
Repiar_t iTi'._
Fencing
Protect
i_g
Guardir, c!
First
Weedir_o
Secorld Weedino_
ThirJr_irw_0& Last
"
Wee diri0
Harvestir__q
Maize
•H-arvestirt_
Rice
Storir,
o' Rice
Cleahirtg
Norr--ora in -Cuit i vat ior,
arwd Harvestir_g
'
• .
Total
SOURCE:
43. 8
18. _
i..2
.5
.21.9
5. •
.2
_2. 5;
1.2
18.8
37.5
6
18.8
18.8
50.0
1_.5
.
;_5.0
Cor, klir,
(1957).
4
18.8
5.0
..
1.2
16._
37.5
.6 :
18.8
9.4
_5.0
18.8
25". 0
31.2
.
5.0
.2
6.21.2
lb.2
3 t. 5
.3
18_ 8.
9.4
25.0
18.8
25.0
3!.2
-'i0.0
37.5
3.8
25.0
10.0
37'5
3.8
25.0
10.0
37.5
3.8
25.0
62.5
b2.5
6_.5
,
. -.
,
..
Bainboo
12.5:
, 358. I
371.9
,
Cor,klir,'s
original
figures
whic_
we_'e
cor_verted
to rnar,-days.-usirig
pe_?..mar_-clay..
Woo c_y
.4
397.5
,
N.B. :
hours
"
.8
Fire •breaking
Burriirlg
Rebu_r_i'rJ_o
--8
x
(
were
exoresseo
a facto_
of..8.,
:tr, mar,r_ari-hours
26
The
highly
seasonal
rainfed
uplands
•Palawan
•Island.
differing
some
collection
labor
to
allowable
that
of
is
the
practice
such
years,
system's
trusive"
with
by
this
include
in
numbers
Of
depicted
where
the•
a
system.
a
small
seventy-five
a
that
very
terms
of
system,
agricultural
is
!ow
as
notes
to
Rice's
potential
for
that
lowlanders
•
assumed
far
•Rice
at_:empt
predominantly
an•
(as
the
this
living
•in
80).
• pattern
Rice •,
•by
an
in
to
in
people.
practiced
•
a system
has
on
••The first
l•iveli•hood
it
similar
depends
systems
refers
As
with
2 presents
resulting
of
cultivation
to
Table
density.
concerned),
p.
second
people
three
lengthy.
normally
(1981,
support
evaluate
source
large
shifting
According
of
andlpa_ticipation
uplands
used.
upland,
quite
are
is
The
the
Batac
undertaken
other
population
the
major
supporting
clusters
the
of•livelihood
fishing,
to
"s ingle-crop-i•a
use
system
for
from
activities
are
sources
of
being
(1981)
computations
(18)
capacity
system
labelled
be
food
products,
conditions
Rice
cycle
5,
crops
supplementary
non-farm
forest
the
agricultural
pasture
Figure
produce
the
producing
market.
•geoclimatic
maximum
of
by
Various
of
of
Indeed,
by
depicted
abilities•to
group,
the
is
• pattern
a
Ikalahans
The
years.
Table
single
of
crop
Nueva
agricultural
fraction
(75)
in
compared
The
2 • is
is
Vizcaya
cycle
to
third
•that
Of
planted.
typically
is
eighteen
the
previous
system,
which
27
28
TABLE
EXAMPLES
OF
•
a
"
UPLAND
AGRICULTURAL'SYSTEMS
OF ALLOWABLE
POPULATqON
.
EVALUATED
DENSI?Y
IN
TERMS
_ca.di t i9r,a_
No r,-T_md i_tior,a i Systems:
Single
Crop
Intrusive
Single
C_c',p
Ind i _er,o_s
.
Usual
period
cultivation
m
2
,,
"
of
.
•
,
Ir,diqer, ous
Ir,t er-Croppin9
.
,,
5 years
4
year:_
5 years
,L
b.
Subsequent
use
_
40 •yea_?_
pasture
-
-
i
c.
Required
faliow
.per:_orJ
d_
Total
agricultu_a%
•cycle
( a+b+c)
e.
Utilizatior,
(a/d)
f.
rate
..
"Sr_ years
14
yea_s
1 I yea_s
. " _"
75 Yea_s
18
yea_s
16
7%
•Cultivated
larfd
r,eecled pe_ _ami ly
as observed
.
1.4
2.2.%
h_.
_1.0
'J
_.
"
h.
A_i.cult
ural
neeclecl per
: (c/e)
31%
h_.
0.7
ha.
2. 3
ha.
,25. 3
ha,
i
la_,d
_?arhily
20
ha.
4.5
ha_.
Agricult
ural ar,d
• watershed
lan_ •
riemclecl
i.
years
Maximum
per
family
_9.5
ha.
al iowem
populatic, r, der,s_ty
per
1000
-,bern'tares
SOUrCe:
420,: ha_
Rice
a. 4
(198[L')_ 'TaDle
2,
20_
fmrnD
p.
80.
.
_-_ "_arn.
-,
3"9. 5] Tam,
29
•is
swidden
•therefore
farming
• able
with
multiple
tosuppor
t a
iarger
system"is.usua!lyobservedof,
Kalingas
of./Northern
An
the
.aspect..
of
.Tiboli
of
more
and
people.
is
This
Mindanao
and
the
by-Rice
which
.:is.
not
" '
usually
.tackled
terms,
.is..tl_e
by
other
researchers,
.at. least
watershedarea.implied
(item.
the
group
presented
W.
of
yields
Luzon.
important
systems
crops,•
h
of. Table
environmental
by
2). ' " This
service
the.
empirical
three,
implies
provided
in
.a
upland
recognition
byforests
in
the
uplands.
Table..
for
a
3
presents
grQup.
of
data."on
erstwhile
!owlanders
:
porti0n-of
yields...
a major
Over
time
characterized
View,.
and
degradation
as
minoritiesare
V.
.urgency
now
[
productivity
cultivating
a
[
Luzon.
It
whose
shows
decreasing
conditi0n
has.
theenvironmental
for
been
point
solving
.cultivation..Problems
the
.where"
"
of
upland
non-culturall
concerned.
derive
the
.decision
conditi0n.s.for
has
•
rice
IMPLIED POLICY TOOLS
•To
public
•
a watershed
.critical.from
.-implies
and
•
watershedin
for
upland
property
respectively,
various
maker,
we
opti_izationl.by
.rights;
as
and..the
follows:
pol•icy
tools
rewrite
the
society;
,squa£ter"
available
set
the
of
first
private
on
forest
to
the
basic
user
who
lands
30
TABLE
AVERAGE
FARM
"_=¢ _"
"_" _ _ _'_"_'_-
LAND
IN
_-- _---_ :_ _
::_.
:_
PRODUCTIVITY
PUTING
_,_-_-_-
LUPA_
_- _==
3
IN
MT.
A TRADITIONAL
MAKILING,i
_-_-_-_-_-_-_-_-
_=¢_
w_.D_._.
_-',,_
1978-1980
=s _ -,i. _ .-,:._•
Producti_,r,. Per
(ca_an)
Year
197e
26.74
1979
13.89
19_o
_---__--.-_---_-__=,___
Source:
KAINGIN
_.68
_:______
Corpuz
Hectare
(1984),
___
Table
28,
p,88
_.,_
_
_ _. _==
31
(8)
p(t)
= w/[
•
(11)
^ (t)=
p
(13)
p(t)
We
Q(t)/
= w/[
Q(t)/
the
restricts
access
encourage
the
•
.
L(t)]
+ a
. u(t)-(dE[S(t)]/dS(t)])
+
.
(dS(t)/dQ(t))•
W/[
note
marginal
Q(t)/
L(t)]
a
L(t)]
assignment
to
the
Upland
user• cost,
of•
property
uplands
by
cultivator
or•a
. u(t)
•rights,
which
users,
would
other
to
consider
(i.e.,
(3.11)
at
least
the
( 3.•!3).
versus
.'
Furthermore,
a comparison
between
Shows
that
•the additional•policytool
user
to
take
environmental
cost
equations
account
would
charges.
would
be
curves,
as
optimal
of
to
him
tax
.
in
indicated
agricultural
use
of
of
•Figure
of
the
at
the
the
forest
land
such
off-site
a
rate
which
or
impose
•policy
relevant
i. '• These
(•3.11)
allow
[dS(t)/dO(t)],
rotation
in
and
would
some
Application
result
(3.8)
that
[ - dE[S{t)]/dS(t)]
environmental
discussed
into
effects
approximates
an
u(t)
tools
marginal"
would
lead
to
fromthepublic
standpoint.
A
problem
feasibility
of
farmers
whose
policy
tool
subsidies
•may
arise,
imposing
minimal
however,
environmental
cash
income,
unimplementable.
It
may
be
soilconservation
a more
at
effective
•least
in
the
if
may
with
respect
charges
on
any,
would
even
incentive
be
to
SUbsistence
make
argued,
for
the
such
that
encouraging
short-run.
9_/
versus
•See Baumol
subsidies
and Oatas
(1975)
for a discussion
as environmental
policy
tools.
of
taxes
32
•More
of
•importantly,
•fields
••still
rotations,
provide
when-
implies
an
source
large
•area•of•
that
• For
of
end
up.landarea
subsistence.
major
the
of
there
are
T
is
.those
livelihood,
land.to
result
a
stable
shifting
periods
under.fallow
during
.and
cannot
who
relyion
the
uplands
this.
implies
the
need
be.worked.out,
I/n£h
of
an
as
a
for
area
a
at
a
' l
time•
for
a
•rotation
Moreover,
.w_thin
there
.an
• is
requirements,
given
year
to
.be
met,
through
food
that
like•.
That
detrimental
land-extensive,
population
on
sources
is,. given
effects
the
is
'is cropped,
when
.through
food •
surplus
a .large
tract
such
..hunting,
as
of
••, ••
the
has
years.
months)
•
.fishing,and
land
either
working
other
n
whi_ch
(dry
(implying.again,or
.of
during
off, farmingseason
need •
production
land) •,
a
period
on
potential
severely
land-use•
technology
soil.conservation,.and
for
limited.
a
supporting
Therefore,
is.
.a
there
growing.
is
a
case
F
for
developing
a more
•efficient,
erosive.type_of.technology
the
for
-land-saving,
producing
•less
soil-
non-timber
croPs•in
need•
securing
up•lands.
The
r@ghts
dis•cuss•ion
to•use
•encouragement
Conserving.
conserving
up•land
• of.
" .The
alternative
Case
out
the
resources"for
for
uplandfarmers,
and..well,defined
overemphasized.
t_us. points
.rights
agricultural
technologies
agro-forestry,
control'
for•such
for
.use.,
and
which
are
soil-
Subsidies
for
soil -•
of•upland
use'cannot
resource
therefore
use
be
33
- BIB.LIOGRAPHY
Aguilar,
_FI., Jr. "Social
Forestry
for upland
Development
Lessons
from
•Four Case
Studies."
Final
Report
submitted
to
the
Bureau
of Forest
DeveloPment
by the Institute
of
Philippine
Culture,
Ateneo
de Manila
University,
Quezon
City,
1982.
•
Baumol,
w.
J.
Poiicy.
and
.
W. E.
:- Oates.
Englewogd_Cliffs,
New
. Th e Theory
Jersey,
.
',,5
of _Env!ronment@l
Prentice_Hall,
1975.
Cadelina,
R. V.
•"•Food • Management
Under
Scarce
Resources
by
Philippine
Marginal
Agriculturists:
Techn01og_ical
Pluralism
Towards
National
Building."
Philippine
Economic
Journal,
20
(1),
1981.,
_
•Clark,
.• C.
W.
181:630_634,
Conklin,
" H.
Orqanization
1957.
Corpuz,_
E.
"A
Modified
Makiling."
Philippines
"The
Economics
August
197_.
of
Overexploitation_"
"Hanunoo
Agriculture.
(_AO)
Forestry
Development
science,
Foo_i
and
Paper•No.
igriculture
12.
Rome,
Comparative
Economic
Study
of Traditlmnal
Kaingin,
Cropping
Patterns
and
•Tree
Farming
in
Mt.
Unpublished,
M.
S.
Thesis,
University•of
the
at Los Banos/
Co!lege,
Laguna,
1984.
Cr_uz,
M.
/C.
"Popuiation
Pressure,
Migration
and
Implications
for Upland
Development."
Philippine
for Development
Studies • Working
Paper
84-05.
Cruz,
W. D.
"Technical
and Institutional
charge
in
Renewable
Resource
Development
(withApplication
for
Traditional
Fisheries,"
Unpublished_
Ph.D,
Dissertation,
.Univeristy
of
Wisconsin-Madison,
1982,
Delos
Angeles,•
M. S. "Economic
Analysis
of Resource
Conservation
by
Upland
Parmersin
the
•Philippines."
Ph.D.
(Econ.)
Thesis,
School
of Economics
University
of the
Philippines,
1986.
Eckholm,
E.
P.
Losing
PrroS.pects/.
New
York:
•
Howe,
C.
W,
• Policy.
•
.
•Ground•:
Environmental
Stress
W.W.
Norton
& Co.
1976.
.
.
.
Natural
Resource
Economics,
Issues,
John
wiley
and Sons,
Inc.,
19_9.
Markets:
Institute
and
Food
v
Analysis,
and
34
Kamien,
M.
I.
and N. L. Schwartz.',Dynamic !Optimization:
The
Calculus
of Variations
and Optimal
ControZ,
in Economics
and
Management."
Series
Volume
4 in
Dynamic
Economics:
Theory
and
Application,
Edited
by
Maurice
Wilkinson,
North
Holland,-198i.
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Pelzer,
K.
Asia,"
Rice,
J. "Man's
Role
The Journal
of
in changing
the Landscape
of
Asian
Studies,
27 (2), 1968.
Southeast
D.
"Upland
Agricultural
Development
in £he Philippines:
An
Analysis
and
a Report
on the Kalahan
PrOgrams."
Adaptive
Strateqies
and Change
in Philippine
Swidd_n,based
Societies.
Edited
b_H.
Olofson,
Forest
Research
Institute,
College,
Laguna,.
1981.
Samuelson,
P.A.
"Economics
of Forestry
Economic
Inquiry_
14
(4): 466-492,
Sanchez,
P..A"
JohnWiley
and
Lynch,
O.J.,
Fuijisaka,
Agriculture
Institu£e
1986.
Properties
of
Sons,
1976.
Soil
in an; Evolving
December
1976.
Management
in
Society."
the
Tropics.
Jr .
"Philippine
Law
and
Upland .
Tenure,
"
in
S.,
P.
Sajise,
and
R.
A.
del Castillo,
Man_____,
.and the Tropical
Forest_
WiDrock
International
for Agricultural
Development.
Bangkok,
Thailand,
APPENDIX
•MATHEMATICAL
ANNEX
Optimum
Agr-icultur,al
Useof
Forest
Lands:
Soil
Conserving
Technology
(Agrof0restry)
Unknown
Given
the
agricultural
function•
and
(i)
following
firstthree
production,
(2),
and
social
environmental
O(t)
function
(I),
benefits
services
•equations
from
from
agricultural
agricultural
resource
•_Q
_L (t)
•
_Q
,
_S (t)
_2Q
and
'
stocks:
p(t)
=
[O(t_,
(3)
SB(t)
= _0 (t) D[_(t),
Net
benefits
(4)
Max
from
_
/0
L(t)
s.t.
[
dQ
> 0
d2Q
%S _(t)
(2)
'--d_
< 0
t]
resource
t]d_
+ E
use
[S(t)],
is
maximized
IQ (t)O
,
0
[_(t) t] dD + E
S(t)
S(0) - a • f0
dE
dS > 0
as
[S(t) _- wL(t)]
follows:
e'rtdt
Q(T)dT
S(t) > O
the
(5)
S(t)
products
dt
_2Q
_L 2(t)
D
,
first
=
constraint
~a•.
Q(t)
of
equation
(4),
we
obtain:
the
demand.
= _ [L(t), s(t),t]
where
From
for
35
Using
(4 )
Hamilt0nian
(6)
_
may
be
=_N(t)D(_,t)
where
u(t)
equation
(7)
and
the
following
current
value
formed:
d_ + E IS(t)'
•is• the
(5),
(5 )
•and
current
is
value
equal
DO(t)
_
= D[Q(t),tJ
BL (t)
wL(t)]
_L (t)
_t"
multiplier
rt
•to•l e
+
i U'_'Q
- a
_
associated
with
:.
dE[S (t)]
"
dS (t)
dS(t)
_Q(t)
"
dQ (t) •
8L (t)
_Q (t)
-w-a
. u(£)
Or, substituting
(2)
_
=
gives-
_
. _L(t)
p(t)
-w
-
BL(t)
+
dE[S (t)I
- dS(t)
a_. u(t)
dS(t)
• dQ(t)
_O(t)
•
_Q(t)
_Q (t)
Setting
obtain
_
_L(t)
dividing
by
_
we
) 0
:
(8)
•
ds
aL(t) = _(ti
Thus,
and
0
we
have
(9)
p(.t) =
The
second
•
differentiating
basic
+
dE[S(t)]••
dS(t)
condition.
- cIE[S tt-_h]
_(t)
basic
as
follows:
_ t,) S 0
1 as:
dS_
" •dO(t)
condition
dQ(t)
(t,)- w - a
+
•_'w
aL(t)
may
be
•
s_
•. u(t)
obtained
by
•
(I0)
u(t)
-- r
. u(t)
-
_H
._s
(t)
=
r.
[D [O(ti,
u(t)-
-a
•using
+
dE [S (t)]
dS(t)
'r
•j
_Q
8s(t)
. u(t) .
Again,
_Q
8S(t)
t]
(2)
and
rearranging:
'
J
(t) = r ..u(t) -
+
_Q
_S(t)
p(t)
dS (t).
dE[S(t)]
I
= r . u(t)
Thus,
the
(ii)
u(t)
-
..
' - •
•_
[p(t) - a . u(t)]
second
basic
_Q
3S(t)
a . u(t)
dE[s (t) ]
3S(-_
condition
-
dS(t)
is:
•
_Q
+
For ' the
[p(t)-
private
omitted
as
conditions
a
, u(t)]
decision'maker's
an
argument
in
dE[S(t)] r.u(t)
-_SqE]-.+
dSqt)'
case
(4) ,.
where
t_he
E[S(t)]
resulting
is
basic
•would • be :
w
(9)'
_
(ii)'
(t)=.
6(t)
Further,
private
••
_Q(t) + a . _(t)
+
.pit) - a
when
the
individual
corresponding
•
b_sic
S(t)
who
"W
_(t)
- 9
is excluded
has
conditions
_L (t)
(ii)"
• _(t)] _s(t):9
. _(t)
not
• Q(t)
as
a co,stralnt
property
as
follc_ws_
rig_tl
_
by
have
• ,
the
-
.• the