A monopolist has the following short-run total cost function and demand function:
Total Cost: TC = 32 + 2Q + 1/2Q^2
Marginal Cost: MC = 2 + Q
Demand: Q = 52-2P
where P is the price per unit of output, and Q is the quantity of output.
(a) What price and quantity combination maximizes the monopolist's total revenues?
(b) What price will the profit-maximizing monopolist charge? What will profits equal?