A market is made up of two consumers. The first has a demand P1 = 1200 – 3q1 and the other has demand P2 = 1200 – 6q2. There is one firm in the market acting like a monopolist with costs = Q2 + 90,000

a) If the firm must charge the same price to both consumers, show that q1 = 400/3 and q2 = 200/3 and find the firm’s profit.

b) Now assume the firm can perfectly price discriminate on a continuous level. Show that q1 = 200, q2 = 100, and that the firm’s profit = 90,000

c) Show that if the firm can identify the two consumers separately, following the profit maximizing rule for 3rd degree (2-part) price discrimination will end up with the same result as in (a).

d) Suppose the firm implemented at 2 part tariff where each consumer is charged a price of 600 per unit plus a flat fee of 25,000.

i) Show that the low demand consumers will not choose q2 = 0 with this system.

ii) Show that the result of this system is generates a more efficient market quantity and more profit for the firm that the result in (a)