A monopolist has the total cost function c(q) = 750 + 5q. The inverse demand fun
ID: 1101110 • Letter: A
Question
A monopolist has the total cost function c(q) = 750 + 5q. The inverse demand function is 140 - 7q, where prices and costs are measured in dollars. If the firm is required by law to meet demand at a price equal to its maginal costs,
a. the firm will make positive profit but not as much profit as it would make if it were allowed to choose its own price.
b. the firm's profits will be zero.
c. the firm will lose $375
d. the firm will lose $750
e. the firm will lose $450
(Please show work or explain. I already have the answer, just want to know how to solve it)
Explanation / Answer
Ideally the firm should operate where the MR=MC. Here your Revenue is demand*quantity=140q - 7q2.
Differentiating revenue we get 140-14q. this should be equal to MC=5. Equating MR=MC we should get the optimum level of output.
However because of government intervention it now has to supply at where the demand meets the marginal cost. The cost functon has two components a fixed cost and a variable cost. Here we are only equating the variable and hence recovering only the variable component according to the new terms. while we are not recovering our fixed costs. Hence a loss of $750.
Option D