The basic theory concerns a monopolist with no threat of competition facing identical consumers, and abstracts from the learning curve, substitute products and other features of durable goods manufacturing and sales, many of which work to slow market penetration relative to the rate predicted by the theory. The main conclusion of the theory is that, for common interest rates and other parameters, we should expect full market penetration to require ten to twenty years or more. Moreover, when the goods are imperfectly durable, full penetration can require fifty years or so. The theory suggests that penetration requires a long time relative to the actual rate of penetration of cellular phones, VCRs, camcorders, palm computing devices and other imperfectly-durable consumer durables. In such cases, the crash is small, while fast penetration necessarily requires that a significant crash occurs around the time of full market penetration, when the market
switches from new sales to replacement sales.
The basic theory has the feature that market penetration is efficient, for the intuitive reason that the monopolist is capturing all the of the value of production, and thus desires to maximize that value and hence chooses an efficient capacity. Thus, the long times to market penetration are a feature of efficiency as well as monopoly. The time to market penetration is decreasing in the durability of the good, and tends to be U-shaped in the interest rate. For low interest rates, there is little gain from fast penetration, because everyone is patient, and thus it pays to use capacity over longer times to satiate the market. For very high interest rates, the profitability of the market is reduced, and the firm slows market penetration in response, converging to an infinite time to market penetration for a finite interest rate that makes the production unprofitable.
Does competition speed up market penetration? We will show that in one sense, the answer is yes – the more firms there are, the faster is the market penetration. However, this increase in speed will not be adequate to overturn the conclusions of the basic theory. The basic theory considered a seller who did not undercut itself over time, even when the market reached saturation. With competition, such a path becomes implausible, and prices will tend to converge to marginal costs over time, a feature of the theory known as the Coase conjecture. It turns out that while competition accelerates market penetration, penetration converges to the basic theory solution as the number of firms goes to infinity. This is quite sensible: a monopolist that can capture all the value of its sales produces efficiently, as does the perfectly competitive industry; an imperfectly competitive industry is slower to saturate the market as a means of propping up the price. The case of monopoly divides into two types – the efficient monopolist and the monopolist who competes, imperfectly, with future incarnations of itself. The former is efficient, the latter the slowest to market of all. Most relevant economic theory has been focused on Ronald Coase’s wonderful 1972 conjecture that a monopolist of a durable good will have an incentive to cut the price, and when the monopolist can cut the price sufficiently rapidly, the monopolist will price near marginal costs. For example, Gul, Sonnenchein and Wilson (1986) demonstrate that the Coase conjecture is a feature of stationary equililbria. Kahn (1986) demonstrates that increasing marginal costs insure that even the continuous time limits of discrete time games have positive profits, although these profits are lower than those which would arise on the commitment path. By positing a fixed, albeit endogenous, initial capacity, we sidestep the Coase conjecture, because the seller cannot sell the large quantities required by the Coase path. In one sense the Compaq ipaq story is unusual because Compaq did not price the 3600 series to capture the high prices created by the shortage. Consequently, an important part of the analysis of pricing concerns the optimal price path. We are used to the rapid decline in prices of consumer electronics. Prices may start high, but rapidly fall to a small fraction of their initial levels as mass production and competition take hold.
A Basic Model of Monopoly
Consider the introduction of a new durable product by a monopolist. The product’s durability, d, is the rate at which the product fails; this is modeled for convenience as an exponential, so that a product sold at time t is still operating at time s with probability e -d(s-t). Let r be the rate at which future profits are discounted, so that profits received by the firm at time t have a present value of e -rt.
This paper presents a theory of manufacturing capacity choice for a durable good. The remarkable conclusion is that efficient production may entail ten to fifty years before full market saturation is reached. The time to market saturation is increased as the good becomes less durable, and the size of the crash when saturation is reached falls as the durability decreases. The monopoly seller is efficient provided he doesn’t ever undercut himself, a feature of some equilibria of the “gap” case, where demand exceeds marginal costs. With competition, either on the Coase path for a monopolist, or with multiple producers, market penetration may arrive only in the limit as time diverges, with sellers producing only the amount that replaces a satiated market. This situation arises only if the depreciation rate of the good is larger than the interest rate, and may not arise when the number of competitors exceeds two, depending on the cost of capacity. In such a case, there is no crash, only a soft landing as the market is satiated, with a growth rate converging to zero. Increases in the number of competitors speed product introduction, converging to the efficient level as the number of competitors goes to infinity. In addition, increases in the depreciation rate of the good also tend to increase the time to market saturation.