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5. (25 points) Strategic Entry Deterrence In a market with two firms facing zero marginal cost and inverse market demand given by P=2000-20, each firm's best response function is BRi(q;)= % (1000-q). a. If the firms play a Stackelberg (quantity) game with firm 1 as the leader, find firm 1's profit maximizing choice of qi and its profits. b. If firm 2 must pay a sunk cost of $5,000 to enter the market after firm 1 (say, through a licensing fee), what minimum output must firm 1 choose if they want to deter firm 2's entry? What will firm 1's profits be in this case?3. (17 points) Price Discrimination Find the profit maximizing choice of prices and quantities sold in the two markets characterized by the inverse demand functions P1=120-Q1 and P2=60-0.502 when both markets are serviced by a monopolist engaging in 3" degree price discrimination. What are total profits for the firm? What would the profits be if the firm were forced to charge a single price in both markets? (Hint: Feel free to ignore the case of the firm choosing to only sell in one of the markets.)2. (16 points) Monopoly a. Show that if the market inverse demand function is P(Q), the profit maximizing monopoly will charge a price equal to MC(1 + 2)-1, where MC is the firm's marginal cost of production and epp is the price elasticity of market demand. b. Calculate the deadweight loss to monopoly when the demand function is given by Q=100-P and C(Q)=4Q.1. (12 points) Derive the cost function C(v,w,q) for a firm facing constant input prices w and v and production function f(k, !) = k-25125. Find the firm's demand for k and I contingent on their choice of output q (k' and 1")