Question

Assume that market demand is Q = 100 – P. Assume that this is a two-period game. The incumbent enters the market in the first time period and chooses its capacity, K1, at a cost of $35 per unit. By choosing its capacity in the first period, capacity is a sunk cost for the incumbent in time period 2. One unit of capacity generates one unit of output per time period. In the second time period the potential entrant decides whether to enter or not. Assume that in addition to the cost of capacity there are labor costs per unit equal to $5 for both firms. While the potential entrant would pay a capacity cost of $35 per unit in the second time period, the capacity cost for the incumbent is sunk up to the capacity determined in the first time period. Any output beyond this has a capacity cost of $35 per unit. Assume further that the potential entrant’s additional fixed costs, F, equal $100. Determine the equilibrium quantity of the incumbent. Show all your work.

Answer 1

Given a two-period game, market demand is Q = 100 – P or P = 100 - Q, the cost of labor costs per unit equal to $5 for both firms. The incumbent enters the market in the first time period and chooses its capacity, K1, at a cost of $35 per unit and if potential entrant choose to enter then in the second time period it will pay a capacity cost of $35 per unit, because any output beyond 35 has a capacity cost of $35 per unit for incumbent he will not choose to increase his capacity also given is potential entrant’s additional fixed costs, F, equal $100. therefore, in second period incumbent will choose to produce

Profit of incumbent = MR = MC, which means 100 - 2Q - 5 = 0
2Q = 95
Q = 47.5

Because second entrant in the market is a lateral entrant the incumbent will not take his equilibrium quantity into account while making his decision.