F(X1,X2)=(x1x2)^1/4, Price of input 1 is w1 = 20 and the price of input 2 is w2 =2

The demand function for type 1 is D1(p) = 20-p and the demand function for type 2 is D2(p) = 40-2p. Firm A cost function is 4 ?(10)q² where now y = y1+y2 and yi for i = 1; 2

3. [20 points] Assume the market is no longer competitive and ACME is now a mo- nopolist who can practice third degree price discrimination. The firm faces two types of consumers. The demand function for type 1 is Di(p) = 20 -p and the demand function for type 2 is D2(p) = 40 - 2p. ACME's cost function is the one you found in (2) where now y = $1 + 12 and y; for i = 1, 2 is how much the firm produces for market i. In which market will ACME exert more market power in equilibrium? 4. [30 points] Assume now ACME cannot tell these two types of consumers apart any more and decides to set a unique two part tariff . Compute the optimal two part tariff if ACME decided to serve only to consumers of type 2. Compute the optimal part tariff if ACME decided to serve to both types of consumers. Which one is best for ACME assuming there is only one consumer of each type? 5. [30 points] Now suppose there exist another firm called BACME, identical to ACME both in terms of the product it is selling and of its costs. The two firms compete in the market as Bertrand competitors and face the aggregate demand D(p) = D,(p) + D2(p) where Di(p) and D2(p) are the demands in section (3). What prices will these firms set in the equilibrium of this market? What will be their profits? Why