A risk-neutral, price-taking firm must set output before it knows the market price. There is a 50 percent chance the market demand curve will be Qd = 10 - 2P and a 50 percent chance it will be Qd = 20 - 2P. The market supply cur–e is estimated to be QS = 2 + P.
a. Calculate the expected (mean) market price.
b. Calculate the variance of the market price.
c. If the firm's marginal cost is given by MC = 0.01 + 5Q, what level of output maximizes’ expected profits?