Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 2

Consider the example of the Stackelberg model discussed in the text. Firms choose quantities, with firm A moving first, and then firm B. As in the text, market demand is given by
Q = 120 - P
and production is costless.
a. Recall that firm B's best-response function is
Substitute this best-response function into the equation for A's profit, (Equation), to express A's profit as a function of qA, labeled pA. Next, substitute this best-response function into the analogous equation for B's profit to compute B's profit as a function of qA, labeled pB. Finally, write the expression for A's profit if B produces zero as a function of qA, labeled pM (where the M subscript stands for the fact that A is a monopoly if B produces zero).
b. Use the formulae from part a to fill in the following table. c. Does your table from part b confirm the result from the text that firm A would choose qA = 60 in the Stackelberg game? How much would A have to produce to deter B's entry if B had a fixed cost of entry equal to a bit more than 400? If B had a fixed cost of entry a bit more than 100? Would it be worthwhile for A to deter B's entry in these cases?