PLEASE SOLVE PARTS C & D

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=5Q, where p is price, and Q is market quantity. Let k 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