In exercise 25.2, we considered quantity competition in the simultaneous Cournot setting. We now turn the sequential Stackelberg version of the same problem.
A: Suppose that firm1 decides its quantity first and firm2 follows after observing x1. Assume initially that there are no recurring fixed costs and that marginal cost is constant as in the text.
(a) Suppose that both firms have a recurring FC (that does not have to be paid if the firm chooses not to produce). Will the Stackelberg equilibrium derived in the text change for low levels of FC?
(b) Is there a range of FC under which firm1 can strategically produce in a way that keeps firm2 from producing?
(c) At what FC does firm1 not have to worry about firm2?
(d) Could FC be so high that no one produces?
(e) Suppose instead (i.e. suppose again FC = 0) that the firms have linear upward sloping MC curves, with MC for the first output unit equal to what the constant MC was in the text. Can you guess how the Stackelberg equilibrium will change?
(f) Will firm1 be able to engage in entry deterrence to keep firm 2 from producing?
B: Consider again the demand function x(p) = 100−0.1p and the cost function c(x) = FC +5x2 (as you did in exercise 25.1 and implicitly in the latter portion of exercise 25.2).
(a) Suppose first that FC = 0. Derive firm 2’s best response function to observing firm 1’s output level x1.
(b)What output level will firm1 choose?
(c) What output level does that imply firm2 will choose?
(d) What is the equilibrium Stackelberg price?
(e) Now suppose there is a recurring fixed cost FC > 0. Given that firm1 has an incentive to keep firm 2 out of the market, what is the highest FC that will keep firm 2 producing a positive output level?
(f) What is the lowest FC at which firm1 does not have to engage in strategic entry deterrence in order to keep firm 2 out of the market?
(g)What is the lowest FC at which neither firm will produce?
(h) Characterize the equilibrium in this case for the range of FC from0 to 20,000.