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 = 40 − Q and a 50 percent chance it will be P = 60 − Q.The marginal cost of the firm is MC = 3Q.What is the expression for the expected marginal revenue function?

Question

Quizplus · Accepted Answer

To calculate the expected marginal revenue (MR), we need to find the average of the two possible MR functions weighted by their probabilities.

When the demand curve is P = 40 − Q, the corresponding MR curve will be 
MR = 40 − 2Q 
When the demand curve is P = 60 − Q, the corresponding MR curve will be 
MR = 60 − 2Q

Therefore, the expected MR function is: 
E(MR) = (0.5)*(40 − 2Q) + (0.5)*(60 − 2Q) 
Simplifying this expression gives E(MR) = 50 − 2Q.

To find the optimal output level, the company should produce where MR=MC (marginal revenue equals marginal cost). Plugging in the given MC function, we get: 
50 − 2Q = 3Q 
Solving for Q gives Q = 10, and therefore P = 30 (using either of the given demand curves).

So the company should produce 10 units and charge a price of $30.

Therefore, the best choice is C.

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