Econ 301 – F07
ANSWERS TO PROBLEM SET 6 - due before you leave on Wednesday Nov 21 at Jiyoun’s office
Wissink
1. Critically evaluate the following statements and explain in what way or ways they are true, false, or
uncertain.
a. If an entrepreneur's firm is earning zero accounting profit, then it should really consider getting
out of the market.
[ANSWER] Yup, if accounting profit is zero, then economic profit is NEGATIVE and so the
firm should seriously consider whether or not it is worth staying open in the short run and also
whether or not it is worth staying in the market in the long run. Either it needs to expect price to
go up, costs to go down, or both.
b. If a perfectly competitive industry is an external constant cost industry, then the normal long run
equilibrium price will never change.
[ANSWER] Nope… The long run equilibrium can change if factor prices and/or technology
change due to exogenous events OTHER THAN a change in the number of firms in the market.
c. All fixed costs are avoidable in the short run if you choose to shut down.
[ANSWER] Nope… some fixed costs are sunk and even if you shut down they are not
recoverable or avoidable.
2. Assume that the U.S. sugar cane industry is: 1) perfectly competitive, 2) presently in long-run
equilibrium, 3) an external constant-cost industry, 4) such that each farm has a set of "typically"
shaped cost curves (in particular this means that short-run supply is typically shaped), 5) such that all
cane farms are the same, 6) such that sugar cane demand is typically shaped.
a. Graph the present long-run equilibrium situation for both a typical plant and the entire industry.
[ANSWER]
a.
<A typical plant>
<The entire industry>
$
$
SRS0mkt with N0
srmc
sratc
lratc
P0
a
mr0
LRS
P0
A
D0mkt
q0
q
Q0
Q
b. Let the demand for sugar cane decrease because of public concern about child obesity. Explain
and indicate on the graphs for the previous part, what happens in the short-run and what must
happen for the industry to be in long-run equilibrium once again.
[ANSWER]
D0 → D1 ⇒ In the short-run, You get P1, Q1, q1, N0, πfirm <0 ⇒ Thus, firms exit.
⇒ In the long-run, you get P0, Q2, q0 =q2, N1, πfirm =0 with N1<N0
At point A,
At point B,
At point C,
Q0=q0*N0
Q1=q1*N0
Q2=q2*N1=q0*N1
b.
<A typical plant>
<The entire industry>
$
$
negative profit
SRS1
mkt
with N1
SRS0mkt with N0
srmc
sratc
lratc
b
P0
mr0
a=c
P1
mr1
C
LRS
P0
P1
A
B
D0
D1
q1
q0=q2
Q2
q
Q1
mkt
mkt
Q0
Q
c. Suppose now that the government is persuaded by a sugar cane lobbyist to impose a price
support at the ORIGINAL price level. Using your graphs in part (a), explain what will happen
consequently, that is, explain what will happen in the U.S. cane industry in the short-run and in
the long-run if the support is imposed.
[ANSWER]
In the short-run, you get a surplus, Q0-Q2, that the government must buy. No one exits, so the
industry has a persistent long-run surplus and is prevented from getting back to a long run
equilibrium.
c.
<A typical plant>
<The entire industry>
$
$
SRS0mkt with N0
srmc
sratc
lratc
P0
a=c
mr0
C
LRS
P0
A
D0mkt
D1
q0=q2
q
Q2
mkt
Q0
Q
3. You are given the following information about the perfectly competitive widget industry:
all firms are identical; all firms have access to a technology with the production function x=L1/2
where L is measured in hours; all firms must get a permit to operate and the cost of the permit is
$16; the current market wage rate is $1/hour; market demand is XD = 100 – P.
a. Find and graph the lratc curve.
[ANSWER]
x = L1/2
L* = x2
lrtc(x) = wL*(x)+16 = L*(x)+16 = x2+16
lratc(x) = x+16/x
2
$
32
24
lratc
16
8
0
0
4
8
12
x
b. What is the value for the long run equilibrium x*? P*? X*? N*?
[ANSWER]
①Perfectly competitive price-taking firms  P = mr at all values of x
②Profit maximizing firms  mr = lrmc at x*
③Zero economic profit  P=lratc at x*
From ①, ②,&③, we know that lrmc=lratc at x*  lratc is at its min point
lrmc(x)=2x
lratc(x)=x+16/x
When lrmc=lratc at x*, 2x*=x*+16/x* => x*=4
From ③, P*=lratc(x*)=x*+16/x*=8
The market demand is XD=100-P. XD*=100-P*=100-8=92.
Since each firm is doing x* = 4, N* must equal 92/4 = 23.
From ①&②, we get P=lrmc => P=2x => xS =1/2P
Since XS=NxS, the market supply curve is XS=23(1/2P) OR PS = (2/23)X
Thus, x*=4, P*=8, X*=92, N*=23 and profit for each firm equals zero.
c. Find and graph the typical firm’s short run supply curve.
[ANSWER]
There is only one input, L, in this industry.
srfc(x)=16
srvc(x)= x2
srtc(x)= x2+16
srafc(x)=16/x
sravc(x)=x
sratc(x)=x+16/x
srmc(x)=2x
See graph below: Left is firm, right is market.
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$
$
d. Graph the side-by-side picture of the long run equilibrium in this market. Show where the
following are in your graphs (P*, x*, X*, N* and profit*).
[ANSWER]
32
100
32
srs=srmc
24
C
24
NSS=CS+PS
Profit*=0
16
lratc
SRSmkt with N*=23
16
CS
sravc
B
P*= 8
P*=8
A
PS
Dmkt
0
0
0
x*= 4
8
12
x
70
X*= 92
114
x
e. What is the value of Net Social Surplus at the long run equilibrium and show it in the appropriate
graph?
[ANSWER] See graphs at part (d)
Net Social Surplus: the area, AOC, is 100*92*1/2=4,600
f. What are the values of Consumers’ and Producers’ Surplus and show them in the appropriate
graph?
[ANSWER] See graphs at part (d).
Consumers’ Surplus: the area, ABC, is 92*(100-8)*1/2=4,232
Producers’ Surplus: the area, ABO, is 92*8*1/2=368
4. Recall from prelim 2… Ackles Apples of Cortland which is a perfectly competitive apple orchard.
Suppose Ackles Apples has typical “text book curvy” short run cost curves. Also suppose that the
market demand for apples is typically shaped. Assume that the apple market is currently in a long
run equilibrium. Now suppose that Governor Spitzer and the New York State legislature pass a bill
requiring that each apple farm in New York State immediately pay the state $L for a license to sell
apples. How do the long run market and firm equilibiria change? Answer just using graphs.
[ANSWER]
4
<A farm>
Before
<Ackles Apples of Cortland Market>
$
$
SRS0
srmc
mkt
with N0=100
sratc
lratc0
P0=6
mr0
a
LRS0
P0=6
A
D0mkt
q0=100
After
$
Q0=10,000
q
negative profit
Q
SRS1mkt with N1=60
$
SRS0mkt
lratc1
P1=7
P0=6
b
a
B
mr1
lratc0
P1=7
mr0
P0=8
LRS1
LRS0
A
D0mkt
q0=100 q1=150
q
Farms exit because of negative profit until the point b.
At point b, the profit is zero.
Q1=9,000 Q0=10,000
Q
LRS shifts up since lratc increases.
SRS shifts left since firms exit.
The new equilbirum is the point, B.
5. Ima Baker runs her own bakery specializing in cheese cakes. Every month she pays $5,000/month in
rent for a store-front bakery shop. She also rents a special oven for $200 month. Ima has also
borrowed money to buy a fax/printer/copier. The machine does not depreciate. Ima took out a month
long loan from the bank to buy the super-duper printer at an interest rate of 5%. The machine cost
$1,000 to purchase. Ima also uses her garage to store cream cheese. Her garage is nice and could
easily be rented out for $200 a month in the real estate market. Ima uses cream cheese and Ima's
labor to make her cheese cakes. The table below shows the relationship between number of hours
Ima works on baking cheese cakes and how many she can bake. It also shows the number of pounds
of cream cheese Ima must use as a function of how many cheese cakes she bakes. Cream cheese
sells for $2/pound. The maximum number of cheese cakes she can make a month is 1100.
Ima also happens to be a financial wizard and knows a lot about corporate financial statements.
CitiBank is interested in Ima's expertise and offers to pay her $100/hour to review their books and do
consults for their legal battles. She can do the consulting work at her convenience for as many hours
as she wants each month. She would get $100 per hour for each hour of consulting for CitiBank.
Please do this problem with the discrete information in the table below. Best to set up an Excel
spreadsheet.
a. Suppose that the "cheese cake" market is perfectly competitive and that the going price for a
cake is P=$50. How many cakes each month should Ima bake if she tries to maximize her
economic profit? (Note: assume Ima makes her cakes in multiples of 100) What are her
economic profits at this solution? Note: Figure out fixed costs, variable costs, total costs and
marginal costs before trying to figure out the profit maximizing position.
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b. What are Ima's accounting profits at this solution?
c. Where are Ima's accounting profits in her cheese cake operation maximized?
d. In the short run, should Ima be baking cakes? Or should she spend all her working hours as a
consultant for CitiBank?
e. How would your answers change if the market price of cheese cakes fell to P=$20/cake?
Ima's monthly short-run cheese cake production function:
# of Ima's pounds of number of
baking
cream
cheese
hours
cheese
cakes
0
0
0
5
2
100
20
4
200
45
6
300
80
8
400
125
10
500
180
12
600
245
14
700
320
16
800
405
18
900
500
20
1000
605
22
1100
[ANSWER] See charts below for lots of data and information.
a. Ima's ECONOMIC profits are maximized 500 cakes. Her economic profit is $7,030.
b. ACCOUNTING profits at 500 cakes = $19,730
c. Accounting profits are maximized at 1100 cakes. (Note economic profit is much lower there.)
d. In the short run Ima should run her cheese cake bakery, since she has a nice healthy economic profit.
The economic profit took into consideration her opportunity cost, so if econ profit is positive, then it
makes sense for her to do 500 cakes at the bakery each month.
Note: Instead of looking at profit, you could look at marginal revenue and marginal cost to get the point
where economic profit is maximized: as long as MR>MC do that group of 100 cakes. Do not do the
next 100 if for that next 100 cakes MR<MC. Still get 500 cakes as the answer.
e. If the price falls to P=$20 Ima should reduce cake supplied to 200 cakes. In the short run she will
have economic losses, that is to say profit = -3458. She is better off doing 200 cakes in the short run
than shutting down. If she shuts down her profit = -5450. So for the month, she should continue to
operate. Whether or not she continues to operate month after month will be determined by what
happens to the market price for cheese cakes and/or the costs of making cheese cakes. Either the price
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better get higher, or Ima's costs better get lower (via better technology or lower factor prices) or both, or
Ima will go out of business eventually.
120
100
mr0
srmc
sratc
sravc
mr1
$
80
60
40
20
0
0
500
1000
1500
cakes
Ima's short run costs (using production function and all info above)
fixed
variable
cheese fixed acct.
cream
variable
implicit
implicit total acct.
hours
cheese
costs acct. costs
costs
costs
costs
cakes
0
0
0
5,250
0
200
0
5,250
5
2
100
5,250
4
200
500
5,254
20
4
200
5,250
8
200
2000
5,258
45
6
300
5,250
12
200
4500
5,262
80
8
400
5,250
16
200
8000
5,266
125
10
500
5,250
20
200
12500
5,270
180
12
600
5,250
24
200
18000
5,274
245
14
700
5,250
28
200
24500
5,278
320
16
800
5,250
32
200
32000
5,282
405
18
900
5,250
36
200
40500
5,286
500
20
1000
5,250
40
200
50000
5,290
605
22
1100
5,250
44
200
60500
5,294
Ima's revenues and profits when P=$50/cake
total accounting economic
cakes
revenue
profit
profit
0
0
-5,250
-5,450
100
5000
-254
-954
200
10000
4,742
2,542
300
15000
9,738
5,038
400
20000
14,734
6,534
500
25000
19,730
7,030
600
30000
24,726
6,526
700
35000
29,722
5,022
800
40000
34,718
2,518
900
45000
39,714
-986
1000
50000
44,710
-5,490
1100
55000
49,706
-10,994
marginal
revenue
x
50
50
50
50
50
50
50
50
50
50
50
total
total implicit economic
costs
costs
200
5,450
700
5,954
2200
7,458
4700
9,962
8200
13,466
12700
17,970
18200
23,474
24700
29,978
32200
37,482
40700
45,986
50200
55,490
60700
65,994
marginal
cost
x
5.04
15.04
25.04
35.04
45.04
55.04
65.04
75.04
85.04
95.04
105.04
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