Summary 267marginal cost per truck? If West Coast demand is similar to demand in
Michigan, could the West Coast factory profit by changing its output
from 40,000 units?- a. Firm K is a leading maker of water-proof outerwear. During the winter
months, demand for its main line of water-proof coats is given by:
where P denotes price in dollars and Q is quantity of units sold per
month. The firm produces coats in a single plant (which it leases by the
year). The total monthly cost of producing these coats is estimated to be:(Leasing the plant accounts for almost all of the $175,000 fixed cost.)
Find the firm’s profit-maximizing output and price. If the firm’s other
outerwear products generate $50,000 in contribution, what is the firm’s
total monthly profit?
b. From time to time corporate customers place “special” orders for
customized versions of Firm K’s coat. Because they command
premium prices, corporate orders generate an average contribution
of $200 per coat. Firm K tends to receive these orders at short notice
usually during the winter when its factory is operating with little
unused capacity. Firm K has just received an unexpected corporate
order for 200 coats but has unused capacity to produce only 100.
What would you recommend? In general, can you suggest ways to free
up capacity in the winter?
c. Because of rival firms’ successes in developing and selling comparable
(sometimes superior) coats and outerwear, Firm K’s winter demand
permanently falls to P 600 .2Q. What is the firm’s optimal
operating policy during the next three winter months? When its plant
lease expires in June?- A manufacturing firm produces output using a single plant. The relevant
cost function is C 500 5Q^2. The firm’s demand curve is P 600 5Q.
a. Find the level of output at which average cost is minimized. Hint: Set
AC equal to MC. What is the minimum level of average cost?
b. Find the firm’s profit-maximizing output and price. Find its profit.
c. Suppose the firm has in place a second plant identical to the first. Argue
that the firm should divide production equally between the plants.
Check that the firm maximizes profit at total output Q* such that
MR(Q*)MC 1 (Q*/2)MC 2 (Q*/2).C175,000300Q.1Q^2.
P 800 .15Q,
*Starred problems are more challenging.*
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