(a) Suppose that m = 30, f = 100, L = 0, H = 20, and w = 0.5. Find the optimal first period price for the incumbent if its MC is L. Find the optimal first period price for the incumbent if its MC is H.
(b) Suppose that m = 30, f = 200, L = 0, H = 20, and w = 0.5. Find the optimal first period price for the incumbent if its MC is L. Find the optimal first period price for the incumbent if its MC is H.
(c) Suppose that m = 30, f = 350, L = 0, H = 20, and w = 0.5. Find the optimal first period price for the incumbent if its MC is L. Find the optimal first period price for the incumbent if its MC is H.

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1. An incumbent firm operates in a market on its own in period 1. During that period, a potential entrant observes the price the incumbent sets. The incumbent's output is denoted by Q. The potential entrant's cost function is c(q)=f+mq, where q is the quantity produced by the entrant. The entrant believes that the demand in the market is given by y(p)=100-p, where total market output y=Q+q. And the entrant believes that the marginal cost of the incumbent is either L (with probability w) or H (with probability 1-w). The entrant, having observed price in the first period, must decide whether to enter and compete in the second period. If it does enter, competition will be based on simultaneous quantity-setting (i.e., Cournot). The discount factor for the second period is 0.9 (i.e., a dollar in the second period has present value in the first period of 0.9). Prices must be integers. 1. An incumbent firm operates in a market on its own in period 1. During that period, a potential entrant observes the price the incumbent sets. The incumbent's output is denoted by Q. The potential entrant's cost function is c(q)=f+mq, where q is the quantity produced by the entrant. The entrant believes that the demand in the market is given by y(p)=100-p, where total market output y=Q+q. And the entrant believes that the marginal cost of the incumbent is either L (with probability w) or H (with probability 1-w). The entrant, having observed price in the first period, must decide whether to enter and compete in the second period. If it does enter, competition will be based on simultaneous quantity-setting (i.e., Cournot). The discount factor for the second period is 0.9 (i.e., a dollar in the second period has present value in the first period of 0.9). Prices must be integers.

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a When MC is L ie L 0 1 Calculate the entrants reaction function q 100 p 2 m 100 p 60 2 Calculate th... View the full answer