Part 3C. Profit Maximization & Supply
6
6.
Producer Surplus
生產者剩餘


Measuring Producer Surplus Using a Supply
Curve
Using
g Producer Surplus
p
Perloff (2014, 3e, GE), Section 9.2.
2015.3.12
1
Measuring Producer Surplus
Using a Supply Curve

Producer Welfare
A supplier’s
supplier s gain from participating in the market is
measured by its producer surplus (PS).
(PS)
2

Producer Surplus
 the difference b/w the amount for which a good
sells & the minimum amount necessary for the seller
to be willing to produce the good.
q*
PS   [ p  MC (q )]dq
0
 pq*  VC (q* )  TR  VC
 F
   TR  (VC  F )
PS is
i total
t t l revenue, TR,
TR minus
i
variable
i bl cost,
t VC.
VC
PS is equal to current profits, , plus SR fixed
costs, F.
3

Figure:
g
Producer Surplus
p
Perloff (2014, 3e, GE), Figure 9.2, p. 316.
4

Another interpretation
p
of producer
p
surplus is as a gain to trade.
trade.
 PS equals the profit from trade minus the profit
(loss) from not trading.
PS    ( F )
 TR  (VC  F )  ( F )
 TR  VC
5

SR Producer Surplus
p
Let p1 be the market price and p0 be the firm’s
shutdown price.
The firm’s SR profit function is  ( p, w, v, K 0 ).
B th
By
the Hotelling
H t lli Lemma,
L
the
th SR producer
d
surplus
l
will be
p1
p1  ( p, w, v, K )
0
PS   q ( p )dp  
dp
p0
p0
p
  ( p1 , w, v, K 0 )   ( p0 , w, v, K 0 )
  ( p1 , w, v, K 0 )  (vK 0 )
P0 = minAVC
  ( p1 , w, v, K 0 )  vK 0    F
6

LR Producer Surplus
p
Let p1 be the market price and p0 be the price that
firm earns zero profit.
The firm’s LR profit function is  ( p, w, v).
B the
By
th Hotelling
H t lli Lemma,
L
the
th LR producer
d
surplus
l
will be
PS 

p1
p0
q ( p )dp  
p1
p0
 ( p, w, v)
dp
p
  ( p1 , w, v)   ( p0 , w, v)
=0
  ( p1 , w, v)  
7
Using Producer Surplus

A Major Advantage of PS
 to measure the effect of a shock on all the firms in
a market without having to measure the profit of each
firm in the market separately
separately.
8

Solved Problem: Producer Plus
Green et al. (2005) estimate the inverse supply curve
for California processed tomatoes as p = 0.693q1.82,
where q is the quantity of processing tomatoes in
millions of tons per year and p is the price in dollars
per ton.
If the price falls from $60 (where the quantity
supplied is about 11.6) to $50 (where the quantity
supplied is approximately 10.5),
10 5) how does producer
surplus change?
Sh th
Show
thatt you can obtain
bt i a good
d approximation
i ti using
i
rectangles and triangles. (Round results the nearest
t th )
tenth.)
Perloff (2014, 3e, GE), Solved Problem 9.1, pp 317-318.
9
Answer:
1. Using calculus
PS1  
11.6
0
PS 2  
10.5
0
(60  0.693q
1.82
(50  0.693q
1.82
0.693 2.82
q
)dq  60q 
2.82
11.6
0
 449.3
0.693 2.82
q
)dq  50q 
2 82
2.82
10.5
0
 338.7
PS  PS 2  PS1  110.6
2. Approximate
pp
area B
1


PS   (10  10.5)   (60  50)  (11.6  10.5)   110.5
2


10