Optimal Replacement Timing And Monopoly Choice Of Durability

The "Swan Independence Result" states that a monopolist producer of durable goods will set product durability equal to the competitive or socially optimal level. This paper presents a new model of a durable asset market which, unlike the standard Wicksellian model used to prove the Swan result, recognizes that new and used assets are imperfect substitutes and that scrappage of durables is endogenously determined. We show that equilibrium scrappage is the solution to a particular optimal stopping or replacement timing problem. We formulate the problem of producer choice of price and durability as the solution to a two stage Stackelberg game between monopolist and consumers and demonstrate that under general conditions the Swan result is false. Although our model validates the intuitive notion that a monopolist can increase profits through planned obsolescence, paradoxically equilibrium durability can be greater than the social optimum and increasing competition from substitute products can cause the monopolist to decrease rather than increase product durability. We show that equilibrium durability depends critically on two factors; the magnitude of fixed costs of production and the degree of monopoly power. If fixed costs are sufficiently low and the monopoly is sufficiently strong, the monopolist will eliminate the secondary market by producing assets of zero durability. Numerical examples demonstrate that this can occur at moderate levels of monopoly power.