Problem: You are a manager of a firm that sells a "commodity" in market that resembles perfect competition, and your cost function is C(Q) = Q + 1Q^2. 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 percent chance the market price will be $100.00 and a 40 percent 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?