A monopoly produces widgets at a marginal cost of $20 per unit and zero fixed costs.It faces an inverse demand function given by P = 100 − 4Q.What are the profits of the monopoly in equilibrium?
A) $800
B) $600
C) $400
D) $200

Question

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we first need to set marginal cost equal to marginal revenue. The marginal revenue can be found by taking the derivative of the inverse demand function:
MR = dTR/dQ = 100 - 8Q
Setting MR = MC, we get:
100 - 8Q = 20
Solving for Q, we get:
Q = 10
Plugging Q back into the inverse demand function, we can find the price:
P = 100 - 4Q = 60
Total revenue is then:
TR = P*Q = 60*10 = 600
Total cost is simply:
TC = MC*Q = 20*10 = 200
Therefore, the profit is:
π = TR - TC = 600 - 200 = 400
The correct answer is therefore C) $400.

A Monopoly Produces Widgets at a Marginal Cost of $20