A monopoly faces a market demand Q = 30 - P and has a cost function C(Q) = 0.5Q2 and marginal cost function MC = Q

1. Find the profit maximizing price and output and the resulting profit for the monopoly.

2. What is the social optimal price? Find the dead weight loss (DWL) due to monopoly?

3. Assume the government set a price ceiling on the monopolist at $18. How much output will the monopolist produce? Calculate the DWL

4. Assume the government set a price ceiling in order to maximize the total surplus. What price ceiling should it choose? What will the profit of the monopoly will be? What is the DWL?