N5

2. Entry deterrence in Stackbelberg model

Suppose the inverse demand is given by P(Q) = 56 - 2Q, where Q= q1 + q2. The cost function is C(qi) = 20qi + f, where f is the fixed cost of entry. Firm 1, the leader/incumbent firm, first chooses q1. Potential entrant Firm 2 then chooses q2 after observing q1. Like the lecture notes, we assume only Firm 2 needs to pay this entry cost in the event that it enters the industry.

(a) Find the backward-induction equilibrium assuming that f= 0. (Be sure to state the full strategy profile, i.e., the quantity each firm plans to choose at every decision node, no matter whether it is reached or unreached. The same remark applies to part (c) below).

(b) Find the limit outputs for fixed costs (f) equal to 50, 18, and 2.

(c) What is the backward-induction equilibrium for each case of f= 50, f= 18, and f= 2?