The market demand in a particular market is Q = 2000 4P. Production of a unit of the good requires use of one unit of labour input and one unit of capital input. The wage paid to labour is w = $160. The rental rate for capital is r = $140. Firm 1 is an incumbent firm and can choose to invest in production capacity (pre-purchase capital), K1 before Firm 2, the entrant, decides whether or not to enter. If Firm 2 enters, the firms will compete as simultaneous quantity-setters. The investment in capacity by firm 1 is a sunk cost that can not be recovered. Firm 2 faces a fixed cost of entry, f > 0.
(a) Find the Cournot equilibrium (quantities for each firm, total quantity, price, profits to each firm) when both firms have mc = w + r = $300.
(b) Find the Cournot equilibrium (quantities for each firm, total quantity ,price , profits to each firm) when firm 1 has mc = w = $160 and firm 2 has mc = w + r = $300.
(c) For what values of fixed costs f of firm 2 will firm 2 always choose to enter the market? (For any K1)
(d) For what values of fixed costs f of firm 2 will firm 2 always choose to stay out of the market? (For any K1)
(e) If the fixed costs of the entrant (firm 2) are f = $6400 find the limit point B (point on R2 where 2 = 0).
(f) What is a strategy for firm 1 in this game? (I am asking what a strategy for firm 1 must describe).
(g) What is a strategy for firm 2 in this game?
(h) Solve for the subgame perfect Nash equilibrium for fixed costs as in (e).