A risk-neutral monopoly must set output before it knows the market price.There is a 50 percent chance the firm's demand curve will be P = 20 − Q and a 50 percent chance it will be P = 40 − Q.The marginal cost of the firm is MC = Q.What is the expression for the expected marginal revenue function?

Question

Quizplus · Accepted Answer

The expected demand curve is the average of the two possible demand curves:
E(P) = 0.5(20-Q) + 0.5(40-Q) = 30 - Q
The total revenue function is:
TR = P*Q = (30-Q)*Q = 30Q - Q^2
Taking the derivative of TR with respect to Q, we get:
MR = 30 - 2Q
Since this is the expected marginal revenue function, the answer is (B) E(MR) = 30 − 2Q. 
The monopoly will produce the quantity where MR = MC, which is:
30 - 2Q = Q
Q = 10
Therefore, the best choice is to produce Q = 10, which corresponds to a price of P = 10.

A Risk-Neutral Monopoly Must Set Output Before It Knows the Market