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?