A monopolist can produce at a constant marginal and average cost of $1/unit and faces a market demand curve of Q = 100 - 20P and MR = 5 - Q/10, where Q is quantity (in thousands), MR is marginal revenue, and P is price

A monopolist can produce at a constant marginal and average cost of $1/unit and faces a market demand curve of Q = 100 - 20P and MR = 5 - Q/10, where Q is quantity (in thousands), MR is marginal revenue, and P is price.

a. Calculate the quantity and price that maximizes the profit for the monopolist.

b. What is the efficient level of output (maximizes social welfare) of the market?

c. Calculate the consumer surplus, producer surplus, and deadweight loss under monopoly. Show these areas on a graph.

d. What is the profit of the monopolist?

e. If the monopolist finds a way to perfectly discriminate prices of each consumer, what is the size of producer surplus and consumer surplus?