CHAPTER 12:
The Partial Equilibrium Competitive Model
The problems in this chapter focus on competitive supply behavior in both the short and long
runs. For short-run analysis, students are usually asked to construct the industry supply curve (by
summing firms’ marginal cost curves) and then to describe the resulting market equilibrium. The
long-run problems (12.4–12.7), on the other hand, make extensive use of the equilibrium
condition P = MC = AC to derive results. In most cases, students are asked to graph their
solutions because such graphs provide considerable intuition about what is going on. The
analytical problems here mainly involve taxation. Problem 12.9 shows that many of the results
for per-unit taxes introduced in the chapter carry over for ad valorem taxes. Problem 12.10
introduces the Ramsey formula for optimal taxation.
Comments on Problems
12.2 This problem illustrates “interaction effects.” As industry output expands, the wage for
diamond cutters rises, thereby raising costs for all firms.
12.3 This problem shows that, with simple linear demand and supply curves, equilibrium
solutions can be found either through substitution or through the comparative statics
procedures illustrated in the chapter.
12.4 This is a simple problem in the interaction between short-run and long-run analysis. The
long-run equilibrium price is always $10. But the price may diverge from this in the short
run.
12.5 This problem introduces the concept of increasing input costs into long-run analysis by
assuming that entrepreneurial wages are bid up as the industry expands. Solving part (b)
can be a bit tricky; perhaps an educated guess is the best way to proceed.
12.6 This is a problem in (short-run) tax incidence. The final part of the problem concerns the
share of any tax is ultimately borne by that input that is in inelastic supply. Here, it is the
film studio that incurs all of the producer’s share of the tax burden.
12.8 This is a simple partial equilibrium problem in trade theory.
12.10 Ad valorem taxes . This problem shows that the comparative statics results for ad
valorem taxes are very similar to the results for per-unit taxes shown in Chapter 12. The
optimal rates of ad valorem taxation that minimize the excess burden of these taxes
subject to a total revenue constraint.
12.12 The Cobweb model . This is a simple algebraic model where a lagged supply response
leads to fluctuating prices.
12.14 The Le Chatelier principle . This introduces Samuelson’s Le Chatelier principle, which
in the supply–demand context simply, shows that any effect of a shift in demand on
12.1 Given the cost function
32
1
( ) 0.2 4 10.
300
C q + + q
qq
Differentiating,
2
( ) 0.01 0.4 4.MC q = q
q
a. Setting
P MC
yields:
2
0.01 0.4 4.P q q
Solving,
2
2
100 40 400
20 100
20 10
10 20.
P q q
qP
q = P
q = P
b.
100 1,000 2,000.Q = q P
12.2 Given the cost function
2.C q wq
If
20,P
5,000.Q
If
21,P
5,250.Q
Supply is more steeply sloped in the
case where expanded output bids up wages.
12.3
Demand: or 0 ( 0),
Supply: or 0 ( 0).
Q a bP cI a bP cI Q b
Q d gP d gP Q g
would also increase by 0.5. Hence, the new equilibrium is
**
15.5, 5.5PQ
as
would have been predicted by the multipliers from parts (b) and (c).
*10.P MC AC
0.25 ,
SD
Q w Q n
or
4.wn
Hence,
2
( , ) 0.5 10 4 .C q w q q n
2,000 50 8
2,000 50 8 8
( 50) 8 2,000.
S
n = Q
n = n n
n n =
50,n
*
*24,
Q
qn
**
10 14,Pq
*4 288.wn
c.
This curve is upward sloping because as new firms enter the industry, the cost
curves shift up:
4
0.5 10 .
n
AC q q
b. Equilibrium where
100 1,000 1,100 50 .PP
So,
*14,P
*400.Q
0
Q
10, P
producer surplus 0.5 14 10 400 =800.
Commented [CE1]: COMP: Set 1000 and 1728 as 1,000 and
1,728.
5 1,500 0.5(2,250 1,500) 15 10 9,375.