Two profit-maximizing firms, firm I and firm 2, must decide whether to enter a new industry with an inverse demand function that is equal to p =900-0 =900 -(q, + q, ) . To enter a firm must build a production facility, an investment that is completely irreversible and observable to the other firm. Two types of facilities can be built, a small one or a large one. A small facility requires an investment of $50,000 and it allows the firm to produce as many as 100 units of the good at a constant marginal cost of zero. However, producing more than 100 units is technologically impossible, i.e., the small facility imposes an absolute capacity constraint at 100 units of output. The large facility, by contrast, does not: for an investment of $175,000, it allows the firm to produce any quantity of output at a constant marginal cost of zero. Firm 1 makes its entry decision first. It has three alternatives to choose from: enter with a large facility, enter with a small facility, or don't enter at all. Then, after observing firm I's irreversible decision, firm 2 makes its entry decision, choosing from the same three alternatives. A firm that does not enter earns a profit of zero. If only one firm enters the industry, it then selects a quantity of output and sells it at the corresponding price. If both firms enter the industry, the market becomes a Cournot duopoly. a) Draw the extensive for game that represents the above situation. b) What is the outcome (use backward induction to rule out non-credible threats)? Does firm 1 enter and at what size? Does firm 2 enter and at what size? c) Is there any predatory conduct in equilibrium? d) Suppose that it is possible to downsize the large production facility to a small one for a cost of $10000. Would this change the equilibrium outcome and, if so, how