(Requires calculus.) A monopolist faces an inverse demand function P = 10 − Q in each of two periods A and B. Her marginal costs are 5 for period A and 5 − q A for period B. Thus, the monopolist “learns” about production in period A, so that her marginal costs fall in period B. Assume that there is no discounting of second-period income.
(a) Derive the monopoly output for period A, disregarding production in period B.
(b) Now consider the dynamic (two-period) monopoly problem. Derive the monopolist’s profit maximizing quantities in both periods. Does the monopolist’s output in period A stay the same as in the first part of the question? Explain.
(c) Suppose that in period B the monopolist (incumbent) faces an entrant with unit cost ce = 5.
Write down the first order condition for this two-stage duopoly game. Just by inspection of the first order conditions, can you compare q A 1 in the dynamic monopoly case with the strategic duopoly case? What explains the difference? What kind of equilibrium in terms of top dogs, etc. is this?