Homework 4: Cost of Production (to be handed in on Thursday 26th February)
1. Gertrude, a second year MBA student, takes three hours off one evening, and uses her car to go to a
movie with a friend. A ticket to the movie costs Gertrude $10, gas for the trip costs $5, and she
passed up tutoring a student that night at $8 an hour. What is her opportunity cost of going to the
movie? (1 point)
Opportunity cost = $8 * 3 = $24.
Total economic cost = $24 + $10 + $5 = $39.
2. If the marginal cost of production is greater than the average cost, do you know whether the
average cost is increasing or decreasing? Explain. (1 point)
Note that MC can be increasing while AC is either increasing or decreasing (MC crosses AC at the
minimum of the AC curve). However, if MC > AC, then this is telling us that the cost of an additional
unit is greater than the average cost of all the units produced to date, which will cause the AC to rise.
3. Suppose you have the following information: complete the Table. (2 points)
Q
1
2
3
4
5
TFC
100
100
100
100
100
TVC
50
80
120
170
250
TC
150
180
220
270
350
MC
50
30
40
50
80
AFC
100
50
33.33
25
20
AVC
50
40
40
42.5
50
ATC
150
90
73.33
67.5
70
4. Suppose a firm must pay an annual franchise fee or tax, which is a fixed sum, independent of
whether it produces any output or not. How does this tax affect the firm’s fixed, marginal and
average costs? (1 point)
TC = FC + VC, where fixed costs are constant. As the franchise fee is fixed, then the firm’s fixed costs
will increase by the amount of the franchise fee. Given that average cost = AFC + AVC, then the
firm’s average costs will increase by the average franchise fee. Because the marginal cost equals the
change in total costs as output increases by one additional unit, then the franchise fee will not affect the
firm’s marginal cost.
5. A chair manufacturer hires its labor for $22 per hour, and calculates that the rental cost of its
capital is $110 per hour. Suppose a chair can be produced using 4 hours of labor or machinery in
any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it
minimizing its costs of production? If not, why not and how can it improve the situation? (1 point)
If a firm can produce a chair in 4 hours with any combination of L or K, then L and K are perfect
substitutes, and the isoquant is a straight line, with a slope of -1, and intercepts at K=4; L=4.
Given the information above, TC = 22L + 110K. The isocost line therefore has a slope of -22/110 = 0.2. If the firm is currently using 3L to produce a chair, then it must be using 1K. This is not
minimizing its costs of production (TC = $176). To minimize costs, the firm should use 4L, 0K =
corner solution. TC = $88.
6. If a firm enjoys increasing returns to scale up to a certain output level, and then constant returns to
scale, what can you say about the shape of its long-run average cost curve? (1 point)
If a firm is enjoying increasing returns to scale, then the LRAC is downward sloping. With constant
returns to scale, the LRAC is horizontal (constant). Thus, this LRAC will be L-shaped.
7. In the United States, more than 50 firms produce textiles but only 3 produce automobiles. This
statistic shows that government antimonopoly policy has been more harshly applied to the textile
industry than to the automobile industry”. Can you give an alternative explanation for the
difference in the number of firms in the two industries? (1 point)
A lower bound on the number of firms in the industry is given by the degree of economies of scale in
the industry. The higher the degree of economies of scale, the fewer the number of firms that can
profitably survive (N = f(S/MES). Given that MES is much higher in the automobile industry than in
textiles, we would predict fewer firms ex ante.
8. Suppose that a firm’s total cost is best described by the following quadratic cost function: TC =
100 + 6q + q2, and MC = 6 + 2q. Write down the expressions for the firm’s TFC, TVC, AFC, AVC
and ATC. (2 points)
TC = TFC + TVC. Thus, TFC = 100; TVC = 6q + q2
AFC = TFC/Q = 100/Q
AVC = AVC/Q = 6 + q
ATC = AFC + AVC = 100/q + 6 + q