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) = 40Q + 5Q2. 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 80 percent chance the market price will be $400 and a 20 percent chance it will be $600.

a. Calculate your marginal cost as a function of Q.

b. Calculate the expected market price.

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