Ullguylu_y 1. Two firms, CS Corporation and JL & Associates, make identical goods, GPX units, and sell them in the same market. The demand in the market is @ = 1200 p. Building a unit capacity costs 600 (for either CS or JL). The interest rate is zero. Once production occurs each period, the price in the market adjusts to the level at which all production is sold. (In other words, these firms engage in quantity competition, not price competition.) a. If CS knew that JL were going to build 100 units of capacity, how much would CS want to build? If CS knew that JL were going to build x units of capacity, how much would CS want to build (that is, what is the CS's best response function in capacity)? b. If CS and JL had to decide how much capacity to build without knowing the other's capacity decision, what the one-shot Nash equilibrium be in the amount of capacity built? 2. Two firms compite in prices in a homogeneous market with demand D(p). Both firms have equal constant marginal cost c. Show the Bertrand equilibrium. Now suppose that one of the firms finds an innovation that halves its marginal cost. Explain and depict the new likely equilibrium. 3. Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function g; = 100 2p; + ps, where ; is Firm's 1 output, p; is Firm's 1 price and p, is Firm's 2 price. Similarly, the demand for Firm 2 is g3 = 100 2p5 + p;. Find the Bertrand equilibrium