Durable Good Monopolies with Rational Expectations and Replacement Sales

A monopoly producer of a durable good is examined under the (previously uninvoked) assumption that the good depreciates, and hence that replacement sales must occur if a fixed stock of the good is to be maintained. We find two ways in which the no-depreciation result, that the monopoly will always (at least eventually) produce a stock equal to that produced by a competitive market, may not hold. If the length of the trading period is nonzero, the limiting stock produced by the firm will be lower than the competitive stock, to ensure the profitability of future replacement sales. If the firm is able to constrain its production capacity, it may choose a constraint that always binds in the sense that it will be impossible for the firm to achieve a stock equal to the competitive stock.