Stackelberg and Limit Pricing. Consider the Limit pricing and Stackelberg models done in class in which the incumbent chooses capacity first and entrant then chooses whether to enter or not. If they decide to enter then the entrant chooses the level of output in Cournot fashion taking the incumbent’s capacity choice as given. It is assumed that 75% of the incumbent’s marginal cost is sunk once they make the capacity choice. Inverted demand is given by P = a – Q, where ‘a’ is the market size parameter. Marginal cost is 10 and fixed costs are 100 for both entrant and incumbent.
a) Find the minimum level of output needed to deter entry (qID). Find the levels of ‘a’ for which entry can be deterred with the monopoly level of output (qIM). For every level of ‘a’ determine which output the incumbent will choose to deter entry and whether or not it will be credible?
b) Calculate the Stackelberg level of output and profits for the incumbent as a function of ‘a’. For what values of ‘a’ is it credible for the incumbent to produce at the Stackelberg level of output? Pick a value of ‘a’ for which Stackelberg and limit pricing are both credible and determine which strategy is more profitable.