Consider a market where demand is given by = 150 2(₁+ ₂)

There is an incumbent, Firm 1, who moves first by making an irreversible purchase of some hours of machine time (capacity), which costs$30per/hr. The other input of production is labor which costs$25/hr. To produceunits of output,hours of machine time andhours of labor time are required. Firm 1 has no fixed costs.

There is a potential entrant, Firm 2, who observes the incumbent's capacity choice and

then decides to enter or not. If entry occurs, the two firms compete by setting quantities

simultaneously. If entry does not occur, the incumbent produces her optimal output level

in that case. The entrant can buy machine time and labor at the same prices as the

incumbent after entering the market. Her fixed cost of entering the market by ₂=120.

(a) What are the best and worst Nash equilibria for the entrant in the post-entry game? Show your work.

(b) How much capacity would the incumbent need to install to deter entry in this game? Show your work.