Perfect Price Discrimination by a Monopolist
The demand for a good X in a town is Q = 10 − P , where P is the price of good X per pound and Q is the quantity demanded in pounds. The marginal cost of producing the good is $2 per pound. There is no fixed cost of producing the good. There is only one firm, Abe, who can produce the good. Abe can perfectly price discriminate. Rather than naming the price for each quantity sold, Abe uses two-part tariff that names a per-unit price and a fixed-fee to maximize his profit.
What are the per-unit price and the fixed fee in his optimal two-part tariff?
How much do consumers demand under the optimal two-part tariff?
How much are the consumer surplus, the producer surplus, and the aggregate surplus under optimal two-part tariff?