Econ 22060 Principles of Microeconomics
Spring, 2005
Dr. Kathryn Wilson
Due: Tuesday, March 8
Homework #3 – Answer Key
1. The cost data of a firm has been partially entered in the table below. Please fill in the remaining
entries in the table.
Quantity
0
1
2
3
4
5
6
FC
24
24
24
24
24
24
24
VC
0
30
54
84
136
196
258
TC
24
54
78
108
160
220
282
MC
30
24
30
52
60
62
AFC
24
12
8
6
4.8
4
AVC
30
27
28
34
39.2
43
ATC
54
39
36
40
45
47
2. The following is a partially completed cost table for company. Complete the table.
Quantity
0
1
2
3
4
5
6
7
FC
40
40
40
40
40
40
40
40
VC
0
10
18
30
44
60
90
140
TC
40
50
58
70
84
100
130
180
MC
10
8
12
14
16
30
50
AFC
40
20
13.3
10
8
6.7
5.7
AVC
10
9
10
11
12
15
20
ATC
50
29
23.3
21
20
21.7
25.7
3. Melissa averages 20 points per game in basketball. In the last game she only scored 10 points. What
happens to Melissa’s average points per game? Explain how this relates to the relationship between
marginal cost and average total cost.
Her points per game falls. Since she scored fewer points than her average, she is bringing her
average down. This is similar to the relationship between marginal cost and average total cost. If
marginal cost (the extra cost of making the last one) is less than average total cost, then average
total cost will be falling. Similarly, if marginal cost is greater than average total cost, then average
total cost will be rising. This is the reason why marginal cost crosses average total cost at the
minimum of the average total cost curve.
4. Suppose Farmer Sam gives sleigh rides and the sleigh ride market is perfectly competitive. Farmer
Sam can sell each sleigh ride for $110 and has marginal costs indicated in the table below. (Hint for this
problem: Remember what firms have to do to maximize profit and think about how you can calculate
different costs with the information you are given, similar to how you answered questions 1 and 2.)
Quantity
1
2
3
4
5
6
7
8
Total Cost
Marginal Cost (fixed = $150)
90
150+90=240
70
240+70=310
60
310+60=370
80
370+80=450
95
450+95=545
105
545+105=650
115
650+155=805
125
805+125=930
Total Cost
(fixed = $200)
200+90=290
360
420
500
595
700
855
980
a) Suppose Farmer Sam’s total fixed cost is $150 for the sleigh and tractor. How many sleigh rides does
Farmer Sam produce in the short run? What are Farmer Sam’s profits in the short run? Does Farmer
Sam stay in business in the long run? Why? (Assume that sleigh rides are not just seasonal – he can sell
them for $110 all year round.) He wants to sell where marginal revenue equals marginal cost. Since
the market is perfectly competitive, marginal revenue is the same as price; for each additional
sleigh ride he gets and additional $110. There is no place on the table where marginal revenue
exactly equals marginal cost, but the logic still holds. He wants to sell the first 6 because his
marginal revenue ($110) is greater than marginal cost. However, he doesn’t want to sell the 7 th or
8th because it would cost him more to make the good than what he would be paid. Thus he wants to
sell 6. To find profit we take Total Revenue – Total Cost. We can calculate total cost using the
information that fixed cost is $150. This means if he produces zero, his total cost will be $150.
Marginal cost tells us how much extra it costs to make each of the additional units. I have filled in
the rest of the total costs on the table above. Profit = $110*6 – 650 = 660 – 650 = $10. The firm will
stay in business in the short run and in the long run because it is earning a positive profit. It is
earning $10 more than it could in its next best alternative.
b) Suppose Farmer Sam’s total fixed cost is $200. How many sleigh rides does Farmer Sam produce in
the short run? What are Farmer Sam’s profits in the short run? Does Farmer Sam stay in business in the
long run? Why? (Assume that sleigh rides are not just seasonal – he can sell them for $110 all year
round.)
Farmer Sam still compares marginal revenue ($110) to marginal cost, and will choose to sell 6. His
profits = $110*6 – 700 = -40. He has negative profits. However, even though he is losing money he
will still want to stay in business in the short run because his total revenue is greater than his
variable costs (if total costs are $700 and fixed costs are $200 then variable costs must be $500,
which is less than his total revenue of $660). Basically, he can either stay open in the short run and
lose $40 or he can shut down in the short run and lose $200 (since he still has to pay his fixed costs
even if he shuts down); he would rather stay open and lose $40. In the long run, though, he will go
out of business because there he has some other opportunity where he could be earning $40 more
than he is in the current business (-40 profits means he is doing 40 worse than his next best
alternative).
5. Suppose Dress-O-Rama is a perfectly competitive dress maker. They can sell each dress for $80, have
total fixed costs of $200 and total variable costs below. (Hint for this problem: Remember what firms
have to do to maximize profit and think about how you can calculate different costs with the information
you are given, similar to how you answered questions 1 and 2.)
Quantity
0
1
2
3
4
5
6
7
8
Total Variable Cost
0
20
40
90
160
260
360
480
620
Total Cost
$200
$220
$240
$290
$360
$460
$560
$680
$820
Marginal Cost
20
20
50
70
100
100
120
140
a) How many dresses does Dress-O-Rama produce in the short run? What are their profits or losses in
the short run? This problem is just like problem 4, but with different costs given. Since you are told
fixed costs and variable costs, you can figure out total cost and use that to figure out marginal cost.
See the table above. The logic for the rest of the question follows question 4 so I will give the
numbers but not the long explanation. She wants to sell 4 dresses. Her profits are 4*80 – 360=-40.
She is doing $40 worse than her next best alternative
b) Will Dress-O-Rama stay in business in the short run? in the long run? Explain.
She will stay in business in the short run because her total revenue is more than her variable costs.
She would rather stay open and lose $40 than shut down and lose $200. In the long run, though,
she will shut down because she is losing money.
6. There are 100 firms in a competitive industry currently and all of them have identical cost curves,
which are shown on the graph below.
Firm
Industry
110
110
100
100
90
MC
80
80
S
ATC
70
Price
90
ATC
70
AVC
60
60
50
50
AVC
40
30
30
20
20
10
10
0
0
0
5
D0
40
MC
10
15
20
25
30
35
40
45
50
55
60
D1
0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6500
quantity
a) Suppose the market demand for this good is given by D0. What is the price and what quantity does the
firm produce in the short run? How much are the profits or losses in the short run? Will the firm exit the
industry in the short run? What is the price and what quantity does the firm produce in the long run?
Will the firm exit the industry in the long run? Explain.
Price is determined by where the supply curve crosses the demand curve for the industry, $65. We
then look at the firm’s curves to determine where marginal cost equals this price of $65, which is a
quantity of 40. Profit = (Price – ATC) * quantity = ($65 - $60) * 40 = $200. Since there are positive
profits, new firms will enter the industry. This shifts out the industry supply curve driving down
price. Firms will keep entering until price is pushed low enough that there are zero profits – once
he get to zero profit there is not longer an incentive for firms to enter. This happens at the price
where marginal cost crosses ATC for the firm, $50. (Any price higher than $50 the firm would be
earning a positive profit; any price lower than $50 the firm would be earning a negative profit; $50
is the only price that gives zero profit.) Thus the long run price is $50, the firm chooses to sell 25,
and the industry sells 5500 (the quantity people want to buy on D0 for a price of $50).
b) Suppose the market demand for this good is given by D1. What quantity does the firm produce in the
short run? How much are the profits or losses in the short run? Will the firm exit the industry in the
short run? What is the price and what quantity does the firm produce in the long run? Will the firm exit
the industry in the long run? Explain.
Using the same process as in part a but with D1 we see Price = $45, quantity = 20. Profits = ($45$52)*20 = -140. (It isn’t clear that ATC is exactly 52; as long as you were close to that you will be
fine.) Since firms are losing money, as they can get out of their fixed input obligations firms will
start leaving the industry. This will shift the supply curve in, driving up prices and profits. Once
price gets high enough that profits are zero, there is no longer a reason to leave. As in part a, this
happens at price = $50; quantity = 25; the industry sells 1500.