(Price Discrimination of Second Degree)
A monopolist has 2 sets of customers distinguished by their demand functions p1=15-p1 and p2=25-2(q2)respectively. The total cost function of the firm is of the form C(Q)=5+3Q , where Q=q1+q2
(a) Derive the aggregate demand function of the monopolist and draw it in a clearly labeled diagram.
(b) Derive the aggregate marginal revenue function and graph it in the same diagram.
(c) Derive the optimal uniform price and the equilibrium level of profit. Illustrate the equilibrium in the figure you drew for parts (a) and (b).
(d) Obtain the consumer surplus in each market under uniform pricing and the total producer surplus in the two markets combined.
(e) Now assume that the monopolist can practice group pricing. What are the profit maximizing prices and levels of consumer surplus in the 2 markets?
(f) Defining total surplus as the sum of consumer and producer surplus in the 2 markets, does price discrimination increase or reduce total surplus?