1. 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 generates a more efficient market quantity and more profit for the firm than that the result in (a) .