Managerial Economics
Amjad Toukan
Spring 2020
PROBLEM SET #2
Problem 1:
A firm uses two variable inputs, labor (L) and raw material (M), in producing its output. At its
current level of inputs:
CL = $10/unit, MPL = 25
CM = $2/unit, MPM = 4
1. Determine whether the firm is operating efficiently, given that its objective is to minimize the
cost of producing the given level of output.
2. Determine what changes (if any) in the relative proportions of a labor and raw materials need to
be made to operate efficiently.
Problem 2:
Suppose that a firm’s production function is given by the following relationship:
Q = 2.5 L 0.5 K0.5
Where Q = output, L = Labor input, and K = capital input.
1. Determine the percentage increase in output if labor input is increased by 10 percent (assuming
that capital input is held constant).
2. Determine the percentage increase in output if capital input is increased by 2.5 percent (assuming
that labor is held constant).
3. Determine the percentage increase in output if both labor and capital are increased by 20 percent.
Problem 3:
Do the following functions exhibit increasing, constant, or decreasing returns to scale? What
happens to the marginal product of each individual factor as that factor is increased, and the
other factor is held constant?
a.
q  2L  2K
b.
q  (2 L  2 K ) 2
c.
q  3LK 2
1
d.
e.
1
2
qL K
1
2
1
2
q  4L  4K
Problem 4:
During the last few days the Superior Company has been running into problems with its
computer system. The last run of the production cost schedule resulted in the incomplete listing
shown below. From your knowledge of cost theory, fill in the blanks.
1
Q
0
1
2
3
4
5
6
7
8
9
10
TC
40
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
TFC
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
TVC
_____
_____
20
_____
_____
40
_____
_____
96
_____
_____
ATC
X
52
_____
21.33
_____
_____
15.67
_____
_____
_____
_____
AFC
x
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
AVC
x
_____
_____
_____
_____
_____
_____
10
_____
15
_____
MC
x
_____
_____
_____
4
_____
_____
_____
_____
_____
45
Problem 5:
Howard Bowen is a large-scale cotton farmer. The land and machinery he owns has a current
market value of $4 million. Bowen owes his local bank $3 million. Last year Bowen sold $5
million worth of cotton. His variable operating costs were $4.5 million; accounting depreciation
was $40,000, although the actual decline in value of Bowen’s machinery was $60,000 last year.
Bowen paid himself a salary of $50,000, which is not considered part of his variable operating
costs. Interest on his bank loan was $400,000. If Bowen worked for another farmer or a local
manufacturer, his annual income would be about $30,000. Bowen can invest any funds that
would be derived, if the farm were sold, to earn 10 percent annually. (Ignore taxes.)
a. Compute Bowen’s accounting profits.
b. Compute Bowen’s economic profits.
Problem 6:
The Blair Company’s three assembly plants are located in California, Georgia, and New Jersey.
Previously, the company purchased a major subassembly, which becomes part of the final
product, from an outside firm. Blair has decided to manufacture the subassemblies within the
company and must now consider whether to rent one centrally located facility (e.g., in Missouri,
where all the subassemblies would be manufactured) or to rent three separate facilities, each
located near one of the assembly plants, where each facility would manufacture only the
subassemblies needed for the nearby assembly plant. A single, centrally located facility, with a
production capacity of 18,000 units per year, would have fixed costs of $900,000 per year and a
variable cost of $250 per unit. Three separate decentralized facilities, with production capacities
of 8,000, 6,000, and 4,000 units per year, would have fixed costs of $475,000, $425,000, and
$400,000, respectively, and variable costs per unit of only $225 per unit, owing primarily to the
reduction in shipping costs. The current production rates at the three assembly plants are 6,000,
4,500, and 3,000 units, respectively.
a. Assuming that the current production rates are maintained at the three assembly plants,
which alternative should management select?
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b. If demand for the final product were to increase to production capacity, which alternative
would be more attractive?
c. What additional information would be useful before making a decision?
Problem 7:
Consider the following table of long-run total cost for three different firms:
Quantity 1
2
3
4
5
6
60
70
80
90
100
110
Firm A
11
24
39
56
75
96
Firm B
21
34
49
66
85
106
Firm C
7
120
119
129
Does each of these firms experience economies of scale or diseconomies of scale?
Problem 8:
Fill in the type of cost that best completes each sentence:
a. What you give up for taking some action is called the _ _.
b. __
is falling when marginal cost is below it and rising when marginal cost is above it.
c. A cost that does not depend on the quantity produced is a __ _________
d. In the ice-cream industry in the short run, __
___includes the cost of cream and sugar but
not the cost of the factory.
e. Profits equal total revenue less _ ______________________.
f. The cost of producing and extra unit of output is the __ _____________.
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