Answer to Question #76006 in Microeconomics for MED

Question

8. The Public Service Company of the Southwest is regulated by an elected state
utility commission. The firm has total assets of $500,000. The demand function
for its services has been estimated as
P = $250 − $0.15Q
The firm faces the following total cost function:
TC = $25,000 + $10Q
(The total cost function does not include the firm’s cost of capital.)
a. In an unregulated environment, what price would this firm charge, what
output would be produced, what would total profits be, and what rate of
return would the firm earn on its asset base?
b. The firm has proposed charging a price of $100 for each unit of output. If
this price is charged, what will be the total profits and the rate of return
earned on the firm’s asset base?
c. The commission has ordered the firm to charge a price that will provide the
firm with no more than a 10 percent return on its assets. What price should
the firm charge, what output will be produced, and what dollar level of
profits will be earned?

Answer 1

The firm has total assets of $500,000. Demand: P = $250 − $0.15Q, TC = $25,000 + $10Q.
a. In an unregulated environment the monopolistic or monopolistically competitive firm would produce output at MR = MC, so:
MR = TR' = (P*Q)' = 250 - 0.3Q,
MC = TC' = 10, so 250 - 0.3Q = 10,
0.3Q = 240,
Q = 800 units,
P = 250 - 0.15*800 = $130.
Total profits TP = TR - TC = 130*800 - (25,000 + 10*800) = $71,000.
ROA = $71,000/500,000 = 0.142 or 14.2%.
b. If the firm has proposed charging a price of $100 for each unit of output, then:
100 = 250 - 0.15Q,
Q = 1,000 units,
Total profits TP = TR - TC = 100*1,000 - (25,000 + 10*1,000) = $65,000.
ROA = $65,000/500,000 = 0.13 or 13%.
c. If the commission has ordered the firm to charge a price that will provide the firm with no more than a 10 percent return on its assets, then:
ROA = TP/500,000 = 0.1,
TP = $50,000,
P*Q - (25,000 + 10*Q) = 50,000,
P*Q - 10Q = 75,000,
P = $250 − $0.15Q,
(250 − 0.15Q)Q - 10Q = 75,000,
0.15Q^2 - 240Q + 75,000 = 0,
Q^2 - 1,600Q + 500,000 = 0,
D = 1,600^2 - 4*500,000 = 560,000,
Q1 = (1600 + 748.33)/2 = 1,174 units,
Q2 = (1600 - 748.33)/2 = 426 units,
P1 = 250 - 0.15*1174 = $73.9,
P2 = 250 - 0.15*426 = $186.1.