Economics 461: Industrial Organization Assignment 2 1. An incumbent, firm 1, faces a potential entrant and can pre-purchase capacity in an attempt to deter entry. The entrant, firm 2, observes the amount of capacity chosen by firm 1 before its entry decision. Each firm needs a unit of capacity to produce a unit of output, and capacity costs 1 per unit. Market demand is p = 5 - Q, where p is price, and Q is market quantity. Let & denote the amount of capacity that firm 1 purchases prior to firm 2's entry decision. Any post-entry competition is standard Cournot competition. a) Suppose that firm 1 purchases no capacity in the initial period. Compute the resulting equilibrium quantities and profits in the post-entry period given that firm 2 has entered. Show this equilibrium on a graph. b) Suppose that firm 1 has purchased 3 units of capacity in the initial period. Compute the resulting equilibrium quantities and profits in the post-entry period given that firm 2 has entered. Show this equilibrium on a graph. c) Show on a graph the post-entry equilibrium if firm 1 purchases 1.5 units of capacity. d) If entry is costless, solve for firm 1's equilibrium choice of capacity if it does not deter entry. Given this choice of capacity, solve for both firm's equilibrium post-entry quantities and profits. e) Can firm 1 deter entry in this case? Explain. f) Now suppose the cost of entry is 1.4. Solve for the level of initial capacity that will deter entry in this case. g) Will firm 1 choose to deter entry when the entry cost equals 1.4? Explain. 2. An incumbent, firm 1, is in a market with demand p = 9 - Q. An entrant, firm 2, observes the initial-period quantity chosen by the incumbent, and decides whether or not to enter. There is one period of Cournot competition post-entry. The entrant knows that the incumbent has a unit cost equal to 1 with probability .6, and equal to 3 with probability .4. Firm 1, of course, knows the actual value of its own cost. The entrant is known to have a unit cost equal to 2. a) Solve for the post-entry equilibrium quantities and profits if firm 2 enters this market. Show this equilibrium on a graph b) Use a graph to show the effect of increase in the probability that firm 1 is low cost on the equilibrium outcome, and provide a written explanation. c) If the cost of entry is 5, solve for the smallest initial-period quantity that will deter entry (q ) given a separating equilibrium in which a firm is thought to be high cost if it produces any quantity less than q'. Show the determination of q' on a graph. d) Explain in words the effect of an increase in the probability that the incumbent is low cost on your answer. e) In this example do you think that firm 1 would attempt to deter entry or not? Explain. What if the entry cost is increased to 7? Explain