HANDWRITTING STEP BY STEP PLEASE

Firm 1 is an incumbent in a market that Firm 2 is considering entering. Market demand is described by P = 150 - (9 +9). Each firm has the same fixed costs: F = F = 400. Firm 2 incurs the fixed cost only if it enters the market. Both firms buy capital in the same market where its price is r = 50. Suppose Firm 1's workers are unionized and the wage rate it faces is w = 20. Firm 2's workers are not unionized so it faces a lower wage rate of W = 10. The cost function of firm i is C(q) = F+ (w + r)qi. Suppose, as in the "Capacity Expansion as a Credible Entry-Deterring Commitment" model, Firm 1 has the option of buying some capacity prior to Firm 2's entry decision. Firm 2 observes Firm 1's capacity purchase and decides to enter or not. If entry occurs, the two firms compete in Cournot fashion by setting quantities simultaneously. a. Derive the Best Nash Equilibrium and the Worst Nash Equilibrium (for the entrant) in the post- entry Cournot game. Show your work. b. What is q, the limit quantity produced by Firm 1, that would make entry unprofitable for Firm 2? Show your work. c. How much capital will Firm 1 buy prior to Firm 2's entry decision? Will Firm 2 enter the market? Explain. Firm 1 is an incumbent in a market that Firm 2 is considering entering. Market demand is described by P = 150 - (9 +9). Each firm has the same fixed costs: F = F = 400. Firm 2 incurs the fixed cost only if it enters the market. Both firms buy capital in the same market where its price is r = 50. Suppose Firm 1's workers are unionized and the wage rate it faces is w = 20. Firm 2's workers are not unionized so it faces a lower wage rate of W = 10. The cost function of firm i is C(q) = F+ (w + r)qi. Suppose, as in the "Capacity Expansion as a Credible Entry-Deterring Commitment" model, Firm 1 has the option of buying some capacity prior to Firm 2's entry decision. Firm 2 observes Firm 1's capacity purchase and decides to enter or not. If entry occurs, the two firms compete in Cournot fashion by setting quantities simultaneously. a. Derive the Best Nash Equilibrium and the Worst Nash Equilibrium (for the entrant) in the post- entry Cournot game. Show your work. b. What is q, the limit quantity produced by Firm 1, that would make entry unprofitable for Firm 2? Show your work. c. How much capital will Firm 1 buy prior to Firm 2's entry decision? Will Firm 2 enter the market? Explain