You are a risk-neutral monopolist that makes and sells a unique T-shirt. You must set your output before you know the market price for your product. There is a 50 percent chance that your firm's demand curve will be P = 20 – Q2. Your total cost function is estimated to be C(Q) = 0.5Q2.
a. What is your expected profit-maximizing quantity? Show your work.
b. What is your profit-maximizing price? Show your work.
c. What are your expected profits? Show your work.