please answer this, N=4

Firm ACME has the following technology: fir]: 1'2) = (inll The price of input 1 is 1111 = 2(N + 2) and the price of input 2 is 11.72 = 2- 1. [2!] points] ACME wants to produce 3; units of output, which sells at price )3. Assume that in the short run 32 = 1. \"Fhat is AChIE's short run conditional factor demand of input 1? What is its short run cost function? And its short run supply function? 2. [20 points] Assume from now on that no input is xed [output is still sold at price p). What is the conditional factor demand for the two inputs? What is ACME's cost function? And its supply function? 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 rm faces two types of consumers. The demand function for type I is Dp} = 20 p and the demand function for type 2 is D2 (p) = 40 2p. ACNE-3's cost function is the one you found in (2] where now y = y1 + y; and y,- for i = 1,2 is how much the rm produces for market 3'. In which market will ACNIE 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 optiJnal 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 rm called BACNEE, identical to ACRE both in terms of the product it is selling and of its costs. The two rms compete in the market as Bertrand competitors and face the aggregate demand D{p) = D; (p) + Dp} where D1 [19} and Dga) are the demands in section (3). What prices will these rms set in the equilibrium of this market? 1What will be their prots? Why? 6. [30 points] Compare in detail your answers to sections 3, 4 and 5 in terms of consumer welfare