Question: Stackelberg and Limit Pricing

Consider the Limit pricing and Stackelberg models in which the incumbent chooses

capacity first and then the entrant chooses whether or not to enter. If the entrant enters

they choose output in Cournot fashion taking the incumbent's capacity choice as given. It

is assumed that 90% of the incumbent's marginal cost is sunk (s = .9) once they make the

capacity choice. Inverted demand is given by P = a - Q, where 'a' is the market size

parameter. Marginal cost is c = 300 and fixed costs are F = 400 for both entrant and

incumbent.

a) Limit pricing. (i) Solve for the incumbent's entry deterring level of output,

limit price and profits as a function of 'a'. (ii) Find the levels of 'a' for which entry is

blockaded. (iii) Find the levels of 'a' for which limit pricing is 'credible'.

b) Stackelberg. (i) Solve for the incumbent's Stackelberg level of output and

profits as a function of 'a'. (ii) Find the values of 'a' for which Stackelberg is credible.

c) Profit comparison and credibility. (i) Are there values of 'a' for which entry

is not blockaded and both limit pricing and Stackelberg are credible. (ii) If so then

determine whether limit pricing or Stackelberg is more profitable for these values of 'a'.

(iii) Based on your analysis what is your prediction about the impact of market size on the

likelihood that entry deterring behavior will be observed in the data?