CAPACITY AS A STRATEGIC BARRIER TO ENTRY 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 demand is given by: p =900 qy gy, where, as usual, p is the market price, g, is the output of firm 1 and g, is the output of firm 2. To enter the industry a company must build a production facility. Capacity is typ- ically lumpy. This is captured by allowing the firms to build one out of two possible facilities: small facility, large facility. A small facility costs $50,000 and it allows the firm to produce as many as 100 units at (for sake of simplicity) 0 marginal cost. Alternatively, the firm can pay $175,000 to construct a large facility that will allow the firm to produce as many as 700 units at zero marginal cost. You are asked to analyze two games: Simultaneous game: The firms decide secretly and simultaneously the facility to con- struct and the output to produce. Then, given the resulting total output, the market price is determined by the industry (inverse) demand. The goal of both firms is to maximize their profits. Find the Nash equilibrium of this game. Fin the equilibrium prices and profits. Sequential game: Firm 1 moves first. It must decide whether to construct a small or a large facility. Then, firm 2 after having observed the facility built by firm 1, de- cides whether to enter the industry or not, and, if it enters the industry, what facility to construct. Finally, after having observed the facilities built, both firm secretly and simultaneously decide the production levels. The goal of both firms is to maximize their profits. Analyze this game. Find the credible Nash equilibrium. Does the existence of a competitor affect the decision taken by the first firm