Consider a homogeneous product industry with inverse demand given by p(Q) = 100 – 2Q. There is currently one incumbent firm and one potential competitor. Entry into the industry requires a sunk cost of F. Both firms have the same variable cost function: C(q) = 10q.
(a) Determine the incumbent's optimal output in the absence of the entry threat.
(b) What output should the incumbent firm set to deter entry? (Your answer will be a function of F!) (c) Assuming that the incumbent firm decides to deter entry, determine the Lerner index as a function of F. Discuss the result.
(d) Will the incumbent firm prefer to deter entry when F = 12.5? Will the incumbent firm prefer to deter entry when F = 25?
(e) Is entry deterrence optimal from a social point of view when F = 25?