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Article Excerpt
This article considers a market served by a monopolist who sells a durable good that depreciates stochastically over time. We show that there exist three types of stationary equilibria: a Coase Conjecture equilibrium, a monopoly equilibrium, and a reputational equilibrium. When the depreciation rate is low, the Coase Conjecture equilibrium is the unique equilibrium. For intermediate values of the depreciation rate, all three equilibrium types' coexist. When the depreciation rate is high, the monopoly equilibrium is the unique equilibrium. Consequently, when selling a good of sufficiently low durability, the monopolist does not lose any of her monopoly power. Furthermore, the steady-state output in the reputational equilibrium falls below the monopoly quantity. Hence, in durable goods markets, welfare losses due to monopoly power may be larger than in markets for perishables.
1. Introduction
* Durable goods make up a significant fraction of GNP and play an important role in the generation and propagation of the business cycle. As a consequence, the special nature of durable goods markets has drawn considerable interest from economists. One issue that has received a lot of attention is whether a durable goods monopolist has the ability to exercise market power. Indeed, Ronald Coase (1972) has argued that a monopoly seller of a perfectly durable good will be unable to exercise any monopoly power unless she can precommit to a production schedule. Coase's logic is that a durable goods monopolist faces an irresistible temptation to keep on cutting her price in order to further penetrate the market. Unless there is a limitation on the rate at which the good can be produced, the competitive outcome will be achieved "in the twinkling of an eye" (Coase, 1972).
Coase's logic has proven to be extremely robust. Stokey (1981), Fudenberg, Levine, and Tirole (1985), and Gul, Sonnenschein, and Wilson (1986) have formalized Coase's intuition under the assumption that the monopolist's product has infinite durability. More precisely, this literature has shown that in stationary equilibria, the monopolist cannot make sales at prices significantly greater than her marginal cost of production (or the lowest buyer valuation, whichever is higher), provided the length of time that elapses between successive price setting periods is sufficiently small. Bond and Samuelson (1984) have demonstrated that Coase's logic extends to products of limited durability, by constructing a stationary equilibrium that satisfies the Coase Conjecture, even when the durability is arbitrarily low.
Coase's prediction presents somewhat of an empirical puzzle, as there does not seem to be any systematic evidence that durable goods monopolists make less profits, or price at lower margins, than their nondurable counterparts. For example, two of the most profitable monopolies in the United States, Microsoft in the market for software and Intel in the market for microprocessors, sell durable goods. Their prices also appear far above the marginal cost of production (which is near zero for software).
Furthermore, if the Coase Conjecture forces significantly constrained the profitability of durable goods manufacturers, we should observe a variety of responses aimed at restoring this profitability, such as leasing, the adoption of most-favored nation clauses (Butz, 1990), or significant reductions in the durability of the product offered for sale (Bulow, 1986). Although such responses do indeed occur, their adoption seems less widespread than theory would predict.
This evidence also presents a theoretical challenge, as in markets served by durable goods monopolies or oligopolies, departures from the competitive outcome can only be explained by lack of patience on the part of manufacturers (which seems hard to justify), the presence of myopic consumers (which is only defensible for consumer durables, and seems to be at variance with available evidence (Chevalier and Goolsbee, 2005), the existence of commitment power (but then the solution is time inconsistent), or the concern for reputation (Ausubel and Deneckere, 1989; Bond and Samuelson, 1987; but this requires nonstationary equilibria). Furthermore, the theoretical prediction that the monopoly outcome obtains whenever the good is nondurable, yet the competitive outcome results whenever the good is durable, no matter how quickly it depreciates, seems unappealing.
In an interesting contribution, Karp (1996) provides a potential resolution to these puzzles. Karp constructs continuous time equilibria for a model with imperfect durability, and shows that the monopolist can earn profits above the competitive level. However, because there always exists a Coase Conjecture equilibrium in his model, proponents of Coase's logic could still argue that there should be no presumption that monopoly results in welfare losses, even in markets for products of relatively low durability.
The current article studies an infinite-horizon discrete-time model of price setting by a monopolist selling a good of finite durability. We establish that when the depreciation factor is sufficiently high, a Coase Conjecture equilibrium never exists. More strikingly, above a certain threshold for the depreciation factor, there is a unique stationary equilibrium, in which the monopolist charges the monopoly price in every period. This equilibrium continues to exist even when the seller becomes arbitrarily patient. Thus, when the product is of sufficiently low durability, the monopoly outcome necessarily obtains. The intuition for this result runs as follows. Coase's logic is that with infinitely durable goods, the monopolist is always tempted to sell additional output until every consumer has been served. However, when the product depreciates, old customers who value the good considerably above average reenter the market whenever the product fails. When the depreciation factor is sufficiently high, selling at a relatively high price to replacement demand is more profitable than lowering the price in an effort to further penetrate the market.
When the good is of sufficiently high durability, we establish that the Coase Conjecture equilibrium is the unique equilibrium of our model. However, in this case, we show that the manufacturer has an incentive to reduce the durability of the product to a level sufficiently low to destroy the Coase equilibrium. Thus, our model can potentially explain the empirical puzzle described above: either the inherent durability of the product is low enough that the manufacturer can fully exercise his market power, or else the manufacturer can restore his margins and profitability through planned obsolescence (or any of the other techniques just described). Indeed, the evidence suggests that such practices are more prevalent when the inherent durability of the good is high.
For example, textbook publishers produce new editions of popular texts on an accelerated schedule, in order to increase their economic depreciation (Waldman, 2003). In the software example mentioned earlier, the physical durability of the product is essentially infinite, but sellers introduce frequent new versions, which produces economic depreciation. Strong network externalities, discontinuation of support for older versions, and the introduction of new file formats combine to make old software essentially useless to most buyers. There is also evidence that short-term leasing is prevalent for assets that are long lived (commercial aircraft, mainframe computers, copying machines). Finally, Palacios-Huerta and Saracho (2004) report that industries selling products of higher durability employ longer-term managerial compensation schemes, that are more positively sensitive to profits and more negatively sensitive to sales, in order to give managers increased commitment abilities. (1)
From a theoretical perspective, our article contributes by developing a novel method for constructing stationary equilibria of the discrete-time game. Using this construction, we are able to completely characterize the set of stationary equilibria for the special case where consumers' valuations take on only two possible values. We show that, depending upon the parameters, three types of stationary equilibria can exist: a Coase Conjecture equilibrium, a monopoly equilibrium, and a "reputational" equilibrium. The Coase Conjecture equilibrium exists for sufficiently low values of the depreciation factor, and is characterized by a decreasing price path and a unique steady state equal to the competitive quantity. The monopoly equilibrium exists for sufficiently high values of the depreciation factor, and has the seller charging the static monopoly price in every period. For intermediate values of the depreciation factor, all three equilibrium types coexist. In the reputational equilibrium, the steady-state quantity falls below the monopoly quantity. Were the monopolist to increase sales beyond this level, equilibrium play would revert to the Coase Conjecture equilibrium. An important message therefore emerges from our analysis: in markets for durable goods, monopoly power may result in higher margins and larger welfare losses than in markets for perishable goods.
For general "neoclassical" demand functions, our method for constructing stationary equilibria still works, but a complete characterization of the set of stationary equilibria as a function of the parameters becomes unwieldy. Nevertheless, we are able to provide an existence result, and show that the qualitative properties of the two-step demand case generalize to this class.
Surprisingly, the literature on monopoly in markets for new products with imperfect durability is relatively sparse, consisting mainly of contributions by Bond and Samuelson (1984, 1987), Sobel (1991), and Karp (1996). These papers overlap with ours to varying degrees, but none of them provide a complete analysis of the set of stationary equilibria. We defer a detailed discussion of the similarities and differences between the various models and their results to Section 7.
The rest of the article is organized as follows. Section 2 describes a two-type model where resale is allowed, and introduces the equilibrium concept. Section 3 characterizes the steady states of stationary equilibria. Section 4 describes the construction of the stationary equilibria, and delineates when each type of equilibrium exists. Section 5 generalizes the analysis to general N-step demand functions. Section 6 considers endogenous choice of durability. Section 7 discusses the related literature, and Section 8 concludes. Important proofs are relegated to the Appendix; the remaining proofs are available as an online Appendix (idv.sinica.edu.tw/mliang/papers.htm).
2. The model
* Consider a market for an imperfectly durable good which depreciates stochastically along a continuous time path, but is offered for sale at discrete points in time, spaced a length of time z > apart. The durable good is indivisible and provides either full services or no service at all. The probability that the good is still working after a length of time t [member of] [R.sub.+] equals [e.sup.-[lambda]1]. Letting [mu] denote the probability that the good depreciates within one period, we therefore have
[mu] = 1 - [e.sup.-[lambda]z]. (1)
The market is populated by a continuum of infinitely lived consumers, indexed by q [member of] I = [0, 1]. All consumers are risk neutral and have the same discount rate r. Each consumer wishes to possess at most one unit of the durable good. (2) We assume that the flow benefit of the services consumer q derives from owning one unit of the durable good is described by the following inverse demand function:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Our reason for initially focusing on the two-type case is twofold. First, in order to construct stationary equilibria and analyze their properties, we use the method of "backward induction on the state", starting from any potential steady state. Unlike in the model without depreciation, this method only works for the finite-type case. In addition, the two-type model allows us to provide simple closed-form solutions for the equilibria, and to bring out the economics in the most transparent way possible. We analyze the general N-type case in Section 5.
Let f (q) denote consumer q's willingness to pay for the privilege of a one-time opportunity of acquiring one unit of the durable good. That is,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
where [bar.v] = a / r + [lambda]] and [v.bar] = b / r + [lambda]. Thus, if the price at time t is p, then by purchasing or selling a unit of the durable good (and never transacting thereafter), consumer q can derive a net surplus of [e.sup.-rt] (f(q) - p) or [e.sup.-rt](p...
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