Premise: You are asked to analyze a sequential game illustrating the strategic role of capacity. The goal is to have a game theoretic understanding of how excess capacity can limit entry in an industry, that is, how the incumbent can build an endogenous barrier to entry. Consider an industry whose (inverse) demand is given by P = 900 Q1 Q2, where P is the market price, Q1 is the output of rm 1 and Q2 is the output of rm 2. To enter the industry, a company must build a production facility. Capacity is often lumpy. This is captured by allowing the rms to build one out of two possible facilities: a small facility, or a large facility. A small facility costs $50,000 and it allows the rm to produce as many as 100 units at (for sake of simplicity) zero marginal cost. Alternatively, the rm can pay $175,000 to construct a large facility that will allow the rm to produce as many as 700 units at zero marginal cost. You are asked to analyze two games. (a) SIMULTANEOUS CAPACITY CONSTRUCTION. Each rm decides secretly and simulta- neously which facility to construct. Once the facilities are built (and they can observe each other's capacity), the rms decide simultaneously the output to produce. Then, given the resulting total output, the market price is determined by the industry (inverse) demand. The goal of both rms is to maximize their prots. Find the subgame perfect Nash equilibrium of the game. (b) SEQUENTIAL CAPACITY CONSTRUCTION. Consider now the case in which Firm 1 moves rst, and it must decide whether to construct a small or a large facility. Then, after having observed the facility built by Firm 1, Firm 2 decides whether to stay out of the industry, enter the industry with a small facility, or enter the industry with a large facility. Finally, after having observed the facilities built, both rm secretly and simultaneously decide the production levels. The goal of both rms is to maximize their prots. Find the subgame perfect Nash equilibrium of the game