On the Third Law of Demand

I. INTRODUCTION The Alchian and Allen (1967, 63-64) theorem, sometimes elevated to the status of a third law of demand, as in Bertonazzi et al. (1993), is a clever application of the fundamental principle of economizing behavior. As usually stated, the theorem suggests that by reducing the price of higher quality relative to lower quality versions of the same good, a fixed transportation charge will trigger a predictable shift in the mix of quality grades purchased by consumers in distant markets, as compared to the mix purchased locally. Producers will respond rationally to this difference in behavior. Relatively more high-quality goods will be included in outbound shipments, leaving more low-quality goods to be sold nearer the point of origin. Hence, other things being the same, the theorem predicts that it will be harder to find "good" apples in the State of Washington, a prime apple-growing region, than in, say, New York City, where "bad" apples are comparatively more expensive. The first law of demand still holds, of co urse, in that fewer apples of both types will be consumed in New York than in Seattle, ceteris paribus. Similarly, given that the cost of a babysitter will be the same no matter where the parents of young children decide to spend the evening Out, they are more likely than an otherwise identical childless couple to choose an upscale restaurant over an inexpensive eatery and to go to the theater rather than to the movies. Moreover, if both couples plan to see a play or a concert, the couple with children will opt for better seats. The foregoing examples indicate that the Alchian and Allen theorem is rich in empirical implications. In what follows, however, we show that placed in the context of a market model, its range of applications is narrower than has been acknowledged in the literature heretofore. More specifically, our analysis demonstrates that a fixed charge unambiguously reduces the price of a higher-quality good, relative to a lower-quality version of the same good, only when that good is sold by a perfectly competitive, constant-cost industry. Under increasing-cost conditions or imperfectly competitive industry structures, by contrast, it is possible for relative prices either to be unaffected by the addition of a fixed charge or, indeed, for the lower-quality good to become relatively cheaper in distant markets, depending on the elasticity characteristics of relevant market demand and supply functions. Our analysis is in no way intended as an attack on Alchian and Allen or their fine textbook, which has taught more than one generation of economists to be better price theorists. We do not quarrel in the least with the pedagogical value of their theorem, which has been immense. Our purpose is to identify some plausible scenarios under which the third law of demand may fail to hold. The present article is thus in the spirit of Yang and Stitt (1995), who show that the Ramsey (1927) rule for optimal commodity taxation is changed in important ways when the assumption of constant production costs is relaxed. It is organized as follows. In the next section, the fundamentals of the Alchian and Allen theorem are described in more detail and its predictions are situated within the existing literature. Section III explores the theorem's operations under alternative cost conditions and industry structures. Factors complicating the analysis of the effects of a fixed charge on the relative prices of high-and low-quality goods are also addressed in this section. Finally, section IV contains some concluding remarks. II. SHIPPING THE GOOD APPLES OUT To borrow an example from a classic statement of the Alchian and Allen theorem, (1) suppose that "good" Washington apples sell for 10 cents each in Seattle and "bad" apples each cost a nickel there. Because the price of a good apple is twice that of a bad apple, Seattle's consumers must sacrifice the opportunity of buying two bad apples to obtain a good one. …