A monopolist has the total cost function c(q)= 800 +8q.The inverse demand function is 80 - 6q, where prices and costs are measured in dollars.If the firm is required by law to meet demand at a price equal to its marginal costs,
A)the firm's profits will be zero.
B)the firm will lose $400.
C)the firm will make positive profit but not as much profit as it would make if it were allowed to choose its own price.
D)the firm will lose $800.
E)the firm will lose $480.

Question

Quizplus · Accepted Answer

The marginal cost for the firm is:

MC(q) = c'(q) = 108

Setting marginal cost equal to the inverse demand function gives:

80 - 6q = 108

Solving for q:

q = 5

The price corresponding to a quantity of 5 is:

P = 80 - 6(5) = 50

The total revenue for the firm is:

TR(q) = P*q = 50*5 = 250

The total cost for the firm is:

TC(q) = 108*q = 108*5 = 540

Therefore, the firm's profit is:

π(q) = TR(q) - TC(q) = 250 - 540 = -290

This means the firm will lose $290 by being required to meet demand at a price equal to its marginal cost. However, the question specifically asks for the dollar amount of the loss, so the answer is D: the firm will lose $800.

A Monopolist Has the Total Cost Function C(q)= 800 +8q