Suppose that market demand is described by P = 100 - (Q + q ), where P is the market price, Q is the output of the incumbent ?rm and q is the output of a potential entrant to the market. The incumbent ?rm's total cost function is T C (Q) = 40Q, whereas the cost function of the entrant is T C (q ) = 100 + 40q , where 100 is a sunk cost incurred to enter the market.
a. If the entrant observes the incumbent producing Q units of output and expects this output level to be maintained, write down the equation for the residual demand curve that the entrant ?rm faces.
b. If the entrant ?rm maximizes pro?t given the residual demand curve in a., what output q e will the entrant produce? (Your answer should be a function of Q.)
c. How much output would the incumbent ?rm have to produce to just keep the entrant out of the market? That is, solve for the limit output QL . At what price will the incumbent sell the limit output?