Managerial Economics
Tutorial Problems - Week 3
Hirschey 15th Edition: Chapter 2: Problems P2.6, P2.10 and Chapter 3: Problems P3.3 and P3.4
P2.6: Profit Maximization: Equations. 21st Century Insurance offers mail-order automobile insurance to
preferred-risk drivers in the Los Angeles area. The company is the low-cost provider of insurance in this
market but doesn't believe its annual premium of $1,500 can be raised for competitive reasons. Rates are
expected to remain stable during coming periods; hence, P = MR = $1,500. Total cost for the company is
as follows:
TC = $41,000,000 + $500Q + $0.005Q2
MC = $500 + $0.01Q
A. Calculate the profit-maximizing activity level.
MR = MC
$15000 = $500 + $0.01Q
0.01Q = $1000
Q = 100,000
B. Calculate the company's optimal profit, and optimal profit as a percentage of sales revenue (profit
margin).
TOTAL REVENUE FUNCTION:
TR = P x Q = $1500Q
TOTAL PROFIT =
Π = TR – TC
= 1500Q – 41000000 – 500Q – 0.005Q²
= 9000000
TR = 1500(100000)
= $150,000,000
PROFIT MARGIN = π/TR
= 9000000/150000000
= 0.06 = 6%
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P2.10: Average Cost Minimization. Giant Screen TV, Inc., is a Miami-based importer and distributor of
60-inch screen HDTVs for residential and commercial customers. Revenue and cost relations are as
follows:
TR = $1,800Q - $0.006Q2
TC = $12,100,000 + $800Q + $0.004Q2
A. Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing
activity level.
B. Calculate these values at the profit-maximizing activity level.
C. Compare and discuss your answers to parts A and B.
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P3.3 Supply Curve Determination. Cornell Pharmaceutical, Inc., and Penn Medical, Ltd., supply generic
drugs to treat a wide variety of illnesses. A major product for each company is a generic equivalent of
an antibiotic used to treat postoperative infections. Proprietary cost and output information for each
company reveal the following relations between marginal cost and output:
MCC
= $10 + $0.004QC.
(Cornell)
MCP
= $8 + $0.008QP.
(Penn)
The wholesale market for generic drugs is vigorously price competitive, and neither firm is able to
charge a premium for its products. Thus, P = MR in this market.
A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a
function of price. (Hint: Set P = MR = MC to find each firm’s supply curve.)
B. Calculate the quantity supplied by each firm at prices of $8, $10, and $12. What is the minimum
price necessary for each individual firm to supply output?
C.
Assuming these two firms make up the entire industry, determine the industry supply curve when P
< $10.
D. Determine the industry supply curve when P > $10. To check your answer, calculate quantity at an
industry price of $12 and compare your answer with part B.
P3.4 Demand Function. The Creative Publishing Company (CPC) is a coupon book publisher with markets
in several southeastern states. CPC coupon books are sold directly to the public, sold through religious
and other charitable organizations, or given away as promotional items. Operating experience during
the past year suggests the following demand function for CPC’s coupon books:
Q = 5,000 - 4,000P + 0.02Pop + 0.25I + 1.5A,
where Q is quantity, P is price ($), Pop is population, I is disposable income per household ($), and A is
advertising expenditures ($).
A. Determine the demand faced by CPC in a typical market in which P = $10, Pop = 1,000,000 persons,
I = $60,000, and A = $10,000.
B. Calculate the level of demand if CPC increases annual advertising expenditures from $10,000 to
$15,000.
C. Calculate the demand curves faced by CPC in parts A and B.
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