# Maximizing Expected Profits

You are the manager of a firm that sells a commodity in a market that resembles perfect competition, and your cost function is C(Q)=Q+2Q squared. Unfortunately, due to production lags, you must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 60% chance the market price will be $100 and a 40% chance it will be $200.

A. Calculate the expected market price

B. What output should you produce in order to maximize expected profits?

C. What are your expected profits?

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#### Solution Preview

A. Calculate the expected market price.

C(Q)=Q+2Q^2

Marginal Cost=dC(Q)/dQ=1+4Q

Expected price=100*60%+200*40%=$140

B. what output should you ...

#### Solution Summary

This solution describes the steps to calculate expected profit in the given case.