Problem: You are the manager that sells a commodity in a market that is, for all intents and purposes, a perfectly competitive market. Your cost function is TC = C(Q) = 50+0.01*Q^2. Your marginal cost function is MC(Q) = 0.02*Q. Unfortunately, due to production lags, you must make your output decision prior to knowing for certain what price will prevail in the market. You believe that there is a 20% chance that the market price will be $500 otherwise, the other possible value for the market price is $600.
Question 1. Calculate the expected market price.
Question 2. What output should you produce in order to maximize expected profits?