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Toward an economic theory of fashion.

Strong as is the desire for variety, it is weak compared with the desire for distinction: a feeling which if we consider its universality, and its constancy, that it affects all men at all times, that it comes with us from the cradle and never leaves us until we go to the grave, may be pronounced to be the most powerful of human passions.

Nassau Senior(1)

With the greater part of rich people, the chief enjoyment of riches consists in the parade of riches, which in their eyes is never so complete as when they appear to possess those decisive marks of opulence which nobody can possess but themselves.

Adam Smith(2)

I. INTRODUCTION

Positively sloped "demand" curves are used in marketing textbooks to explain the pricing of fashion merchandise.(3) "Snob" or "prestige" effects are alluded to in support of the claim that price increases can lead to an increase in the quantity demanded. In the tenth edition of their text, E. Jerome McCarthy and William D. Perreault [1990] offer a demand curve with a positively sloped segment. They explain:

Prestige pricing is setting a rather high price to suggest high quality or high status. Some target customers want the "best," so they will buy at a high price. But if the price seems "cheap," they worry about quality and don't buy. (P. 506; footnote omitted, emphasis in the original.)

In another text, Ralph M. Gaedeke and Dennis Tootelian [1983] also discuss a positively sloped demand curve:

Some products do not have the traditional downward sloping demand curve previously described, but a more curved slope, illustrated in Exhibit 13-6 [demand curve with upward sloping portion--not shown]. This reflects the real impact of price as a part of the product's value. Quite obviously, as a product's price rises above [P.sub.0], demand will begin to drop as some consumers will simply be unable to afford the product. However, that decline is rather slow until very high prices are reached. But demand also begins to drop at prices below [P.sub.0], showing that part of the reason for owning the product lies in its high price--it has prestige value.

Economists react by asserting that marketing explanations are ad hoc, devoid of economic content. Conversely, marketers say that economic models are naive and incapable of explaining the marketing of fashion goods. As economists, we have a bias towards economic explanations, but these explanations are incomplete and not highly valued by the market. In stark contrast, the advice of professional marketers (that economists contend is muddled or worse) is amply rewarded in consulting work. Is there a market failure in the consulting market, or does marketing provide an insight that economics lacks?

We start with the premise that the intuition behind marketing explanations, that people desire prestige, has validity. This notion can be incorporated into economic theory using Kelvin Lancaster's [1971] notion that when a purchase is made, what is bought is a bundle of services or characteristics. The salient feature of a fashion good is its ability to confer prestige or status.(4)

The argument is straightforward: There is a sociobiological basis for status-seeking behavior. Status-seeking is an evolved trait that is innate to humans as well as to many other animals. Given the pervasiveness of status-seeking, human cultures have developed effective signals of status--fashion being just one. We incorporate the status yielding nature of fashion goods into a standard demand model by assuming that the value consumers attach to a fashion good depends on the stock held by other consumers. This interdependency among consumers allows us to explain the upward sloping constructs (labeled demand curves) that populate marketing texts. Our model has downward sloping demand curves throughout, but (because of the interdependencies) generates cyclical price behavior that can be misconstrued as aberrant (positively sloped) demand functions. The result is more complete in an economic analysis of fashion than marketing explanations, and less naive than most economic theories, while still maintaining downward sloping demand curves.

II. THE LITERATURE

The literature on product pricing, fashion and human status is vast.(5) The prefatory quotation from Nassau Senior clearly supports the notion that both he and Alfred Marshall (who preserved Senior's remarks in his own work) regarded this quest as fundamental and powerful. Adam Smith wrote in The Theory of Moral Sentiments:

...vanity is always founded upon the belief of our being the object of attention and approbation. The rich man glories in his riches, because he feels that they naturally draw upon him the attention of the world, and that mankind are disposed to go along with him in all those agreeable emotions which the advantages of his situation so readily inspire.

In this passage, Smith suggests that riches are desired primarily for their ability to enhance one's status.

Other prominent nineteenth century economists who wrote on status were John Rae, and Thorstein Veblen.(6) In The Theory of the Leisure Class, Veblen espoused a view of human nature which contended that some aspects of human behavior were a way of proclaiming rank.(7) Veblen's approach was adopted by fringe economists and sociologists,(8) and in mainstream economics by Harvey Leibenstein [1950].

Relying on consumer interdependencies he developed propositions about the elasticity of demand for "snob" and "bandwagon" goods, and generated demand functions that were positively sloped for "Veblen" goods.(9) Leibenstein's approach is an excellent introduction to the economics of fashion, but it provides no rationale for the way consumers behave.(10) Further, it focuses solely on the demand side with no explanation of firm behavior, market supply, nor equilibrium dynamics.

Positional goods were introduced into economics by Fred Hirsch [1978]. Positional goods, such as rank or titles, establish one's place in society.(11) Their unique features are their zero-sum characteristics. The zero-sum nature of fashion goods was elegantly noted by George J. Stigler and Gary S. Becker [1977]:

The commodity apparently produced by fashion goods is social distinction: the demonstration of alert leadership, or at least not lethargy, in recognizing and adopting that which will in due time be widely approved. This commodity--it might be termed style-- sounds somewhat circular, because new things appear to be chosen simply because they are new. Such circularity is no more peculiar than that which is literally displayed in a race--the runners obviously do not run around a track in order to reach a new destination.(12)

Positional goods convey distinction, but the larger the number of people who claim it, the less distinction it confers. Work on positional consumption is growing; notable among those currently working in this area is Robert H. Frank (1985a; 1985b; 1988; 1991b).(13)

III. A SOCIOBIOLOGICAL EXPLANATION OF STATUS-SEEKING

Both economics and evolutionary theory assume the pervasiveness of scarcity. Evolution favors organisms that are superior competitors in a given environment.(14) Sociobiology, an extension of evolutionary theory, contends that some behaviors are innate and can be culled or selected through evolution. To grasp the importance of status (rank) for evolutionary success,(15) it is necessary to examine genes, the instrument by which evolutionary forces work.(16)

The characteristics of an individual are determined by its genetic inheritance. In species that reproduce sexually, evolution works through sexual selection as well as the external environment.(17) Any gene that enhances the reproductive success of an individual is pro-adaptive and will tend to be more heavily represented in future gene pools.(18) Present-day humans have existed for at least 40,000 years,(19) or between 1,400 to 2,000 human generations.(20) Evolutionary mechanisms have had more than enough generations to work on the human species.(21)

Humans are social animals propagating in sexual pairs. Neither infants nor individual adults can survive for long periods without the assistance of their fellows. All available evidence suggests that for hundreds of millennia humans have been subject to these conditions. There is substantial evidence that the status of social animals is positively correlated with reproductive success.(22) Human psychology and physiology is affected by the individual's rank or status in society.(23) Anthropological, historical, and psychological studies indicate that status within human society enhances an individual's chances for survival and reproduction.(24)

Competition for status is typically among individuals of the same sex.(25) High status in the relevant sexual peer group signals that the individual is a relatively good mate for members of the opposite sex. Because it enhances survival and reproduction, the genetic forces causing humans to crave status could be as strong as the sex drive.(26)

Evolutionary forces have had millennia to shape humanity into a race of status seekers.(27) The specific signals that connote one's rank in society tend to be idiosyncratic to a culture. Evolutionary forces will also work on signals of status. Signals that are false or easily counterfeited will be culled, while accurate signals will prevail. Fashion is a pervasive signal, but its manifestations are peculiar to each society.(28)

IV. AN ECONOMIC ANALYSIS OF FASHION/STATUS GOODS

Fashion goods signal status.(29) To be an effective signal(30) the fashion good must be more costly to obtain for those who do not possess the status than for those who do.(31) If fashionable clothing is to be an effective signal of status, it must change. An unchanging fashion and a second-hand market would allow everyone to be "fashionable," negating the value of fashion as a signal.

The resources required to attain the fashion signal may be rationed in a variety of ways, wealth being only one of them. In the Western world, until well into the eighteenth century, sumptuary laws existed detailing who had the right (not the monetary resources) to wear various garments.(32) The non-wealth constraints on the purchase of "status" goods enabled the fashion or status signal to be easily recognized as an indicator of relative rank.(33) Increasing material abundance raised the cost of enforcing legal constraints upon an individual's ability to purchase clothes and other consumables that were legally constrained. In the recent modern era (post 1750 in the West) sumptuary laws fell by the wayside.

Absent sumptuary laws, in a society of status seekers individuals are continually attempting to elevate their perceived social rank by acquiring the signal. Social ranking is a zero-sum game: gains are offset by losses.

Consider an archetypical example of a pure fashion good, "neck ties" worn by men.(34) Ties are solely decorative and indicate that the wearers' activities are not physical. Ties cost resources, and are uncomfortable if one has to make physical exertions. Wearing a tie to work indicates that a man's professional status is such that physical exertions are not required. Ties signal effectively because they are easily discernable, and they impose costs upon men who attempt to acquire the signal (the tie) without actually having the characteristic (the employment that does not require physical exertions).(35)

If a group of men agree not to wear ties, their social ranking vis a vis one another will be unaffected. They will save the resources they would have spent on ties, and they will not suffer the physical constraints that a tie imposes. But a man who breaks the agreement gains in perceived rank. This "prisoner's dilemma" has a dominant solution in which men wear ties.(36)

The absence of enforceable contracts and competition for the fashion signal leads to the prisoner's dilemma. The marginal value of a fashion good falls as more people hold it: in Leibenstein's terminology, a snob effect exists. This effect is incorporated into two models of fashion goods: (A) the competitive case; and (B) the noncompetitive case. The results lead to an explanation of apparently upward sloping "demand" curves.

Status Goods and Fashion Cycles Under Competition

The unique feature of the market demand curve for a fashion good is that it varies inversely with the contemporaneous stock of the good (Q.sub.t).(37) This incorporates the impact that an increase in the stock has upon the fashion/status services derived from a commodity, the "snob effect" that is mentioned in the literature. If others hold a large stock of the fashion good, its ability to provide distinction is reduced. Because consumers cannot instantly perceive this stock, they form an expectation [Mathematical Expression Omitted] of its value based on experience. The following "adaptive" expectations equation represents consumers' expectations:(38)

[Mathematical Expression Omitted],

where [Alpha] [is greater than] 0.

Equation (1) is incorporated into the otherwise standard linear demand function as shown below:

[Mathematical Expression Omitted]

where [q.sub.t] is the flow quantity demanded in period t, with a [is greater than] 0, b [is less than] 0, and c [is less than] 0. The parameter "c" is referred to as the status coefficient. Its negative sign indicates a snob effect.

The market supply curve is given the simple linear form:

(3) [P.sub.t] = r + s[q.sub.t]

where r and s are positive. The resultant equilibrium quantity at time t is

(4) [q.sub.t]* = [1/(s-b)]

[a - r + c(1 + [Alpha])[Q.sub.t-1] - c[Alpha][Q.sub.t-2]].

This assumes that resale markets do not exist, or are of little consequence.(39) The equilibrium is a function of only past values of the stock and current demand/supply flows.

Completing the model is an identity that equates the current stock with the undepreciated stock plus new production:

(5) [Q.sub.t] = (1-[Delta])[Q.sub.t-1] + [q.sub.t]

where [Delta], 0 [is less than] [Delta] [is less than] 1, denotes the rate of depreciation. Substituting equilibrium condition (4) into the stock identity (5) and simplifying, we find

(6) [Q.sub.t] = A + [T.sub.1][Q.sub.t-1] + [T.sub.2][Q.sub.t-2]

where

(7) [T.sub.1] = 1-[Delta]+[c(1+[Alpha])/(s-b)],

[T.sub.2] = [-c[Alpha]/(s-b)],

and

A = (a-r)/(s-b).

The side conditions for the stability of this second-order difference equation are known. The stock converges to a stable path if (i) [T.sub.2] [is greater than] -1, (ii) 1 + [T.sub.1] - [T.sub.2] [is greater than] 0, and (iii) 1 -[T.sub.1] - [T.sub.2] [is greater than] 0. If [T.sub.2] [is less than] -1 while conditions (ii) and (iii) hold, explosive oscillations occur. If 1 + [T.sub.1] - [T.sub.2] [is less than] 0, and (i) and (iii) hold, explosive oscillations occur. Finally, if 1 - [T.sub.1] - [T.sub.2] [is less than] 0, and conditions (i) and (ii) hold, explosive growth occurs.(40)

These results have implications for fashion goods. Given the assumptions of the model (c [is less than] 0, b [is less than] 0, s [is greater than] 0, [Delta] [is greater than] 0 and [Alpha] [is greater than] 0), it follows that [T.sub.2] [is greater than] 0 (ruling out one case of explosive oscillation), and explosive growth is ruled out as 1 - [T.sub.1] - [T.sub.2] is unambiguously positive.(41)

The final possibility of explosive oscillation occurs if 1 + [T.sub.1] -[T.sub.2] [is less than] 0. In our model the inequality implies

(8) c(2[Alpha] + 1) [is less than] (s - b)([Delta] - 2).

Both sides of this inequality are negative; the left side is negative because of our assumptions that c [is less than] 0 and [Alpha] [is greater than] 0, the right side is negative because s [is greater than] 0, b [is less than] 0, and [Delta] [is less than] 1.

A major result of the model is that if the product is not a fashion good (c = 0), the stock always converges to a stable path over time.(42) Only for a fashion good (c [is less than] 0) can the stock be subject to explosive oscillation. In this case, the likelihood that inequality (8) will hold increases as: (i) [Delta] rises, (ii) s falls, (iii) b becomes more negative, (iv) c becomes more negative, and (v) [Alpha] rises.

(i) Increases in Product Depreciation Rate ([Delta])

The stock depreciation rate increases if the rate of physical deterioration increases or if the goods are discarded as unfashionable at an increased rate. In the tie example, ties are relatively inexpensive and are often discarded long before they physically deteriorate.(43)

"Premature" disposal occurs because some characteristic or combination of characteristics of the tie no longer gives the appropriate fashion signal. The probability of disposal will increase the more costly it is to store, the more difficult it is to resell, the larger or more uncertain is the variance of the fashion cycle, and the lower is its replacement cost.(44)

(ii) Changing the Slope of the Supply Curve (s)

A decline in the slope of the supply curve causes both an increase in the elasticity of supply and the likelihood of explosive oscillations. With any change in demand, existing producers and new entrants react rapidly in changing the amount supplied. There are few obstacles to adjusting production--manufacturers can easily change their input purchases to alter production or shift inputs between product lines.(45)

(iii) Changing the Slope of the Demand Curve (b)

A decline in the slope of the demand curve causes the elasticity of demand to decrease and the likelihood of explosive oscillations to increase. As demand becomes more inelastic, any change in the stock of the commodity leads to a larger change in the equilibrium amount traded. In the extreme case where demand is completely inelastic, the equilibrium quantity changes by the same amount that demand shifts.(46)

In the tie example we speculate that the demand for fashionable ties is relatively inelastic. While ties are a necessary component of the standard wardrobe of a white collar male, the fraction of the clothing budget spent on ties is minuscule. Marshallian demand theory predicts that demand becomes less elastic as the availability of substitutes declines and as the budget share spent on the commodity declines. Because there are few close substitutes for ties and they constitute a minor portion of a consumer's budget, fashionable ties and their stocks are likely to cycle.

(iv) Changing the Status Coefficient (c)

The coefficient c is negative for status goods. The larger its absolute value, the more important status is as a component of demand, and the larger demand shifts will be for any given change in the stock. Too large a stock of a given fashion good will provide few status services. The larger its stock, the greater the likelihood that the demand for it will implode.

(v) Changing the Expectations Coefficient ([Alpha])

The expectations coefficient indicates the importance of past changes in the stock on expectations. As [Alpha] rises, the stock is more likely to oscillate explosively. This coefficient regulates the magnitude of the demand shift that results from revisioned consumer expectations. If the stock is expanding, consumers will increase their assessment of the expected stock to a greater degree the greater is [Alpha]. The size of the demand shift and the consequent supply response determine the cycle.

This concludes our discussion of the parameters that affect fashion goods in the competitive case. The unique feature of this model is that, given appropriate values for the parameters, equilibrium values for both the stock of and demand for fashion goods fluctuates cyclically. Graphing the resulting price/stock combinations over time, the plotted values are sometimes upward sloping. Such evidence might suggest an upward sloping demand to the casual observer. Of course, such a plot is not a demand curve at all. A demand curve is a plot of the amount demanded (not the existing stock) at various prices (per unit time) measured at a given instant, ceteris paribus.(47) The people who argue for upward sloping "demand" functions are not economists. The positive price/stock relationship they observe and use is not a demand curve, but their advice passes the market test.

B. Status Goods in Non-Competitive Markets

With minor modifications the standard model of price discrimination can be used to analyze a fashion good. The standard model has four assumptions: (1) resale is not feasible; (2) markets can be segmented at low cost; (3) the amount that one group consumes does not affect the amount that another group desires (this is the non- status good case); (4) the seller sets a fixed (uniform) price for each group of consumers. Maximum profit is obtained by price/quantity combinations for which marginal revenue for each consumer group is equal to marginal cost. This is shown in Figure 1; because the good cannot be resold, the monopolist can charge group one demanders [P.sub.1]* and group two demanders [P.sub.2]*, where [P.sub.2]* [is greater than] [P.sub.1]*.(48)

If the stock of a commodity affects the flow of services from an incremental purchase, a "snob effect" is present and must be added to the analysis of price discrimination. Assume two distinct customer groups: first-period demanders, and second-period demanders.(49) The snob effect is between period-one users and period-two users; the greater the quantity purchased by first- period demanders, [Q.sub.1], the lower its marginal value to second-period users.

The theory depends upon the absence of resale markets. Resale markets do not exist where transactions costs are prohibitively high. Transactions costs can be viewed as infinitely high for services such as those provided by restaurants, medical procedures, educational institutions, and entertainment establishments. An archetypical example of a firm supplying "fashion services" would be a "fashionable" nightclub. It could maintain its cachet only by restricting entry to clientele disproportionately composed of the "fashionable" or "powerful."

The Vertigo Club in Los Angeles is such an establishment. It is being sued for discrimination because it limits entry to "fashionable" people. Management claims that limited entry "increases demand" and without it the club would be less successful. Nine out of ten nightclubs in Los Angeles fail within one year of opening, yet the Vertigo Club has been in business for over six years. The policy of discriminating in favor of "fashionable" people has apparently maintained the Vertigo Club's demand, passing the market test.(50)

The apparent circularity reinforces the basic point that fashion goods are desirable because they signal one's social rank. The more easily attainable, the less valuable is the signal to consumers. That is, the greater the amount supplied in the current period, the lower demand is in the future.

The snob effect results in an additional cost to the monopolistic seller in the first period. As [Q.sub.1] rises, the total revenue the firm can obtain in the following period, [R.sub.2], is reduced. The full marginal cost in period one, M[C.sub.1], may be expressed as

(9) M[C.sub.1] = [MC.sub.p1] - d[R.sub.2]/d[Q.sub.1],

where M[C.sub.p1] denotes the marginal cost of production in period one and dR2/d[Q.sub.1] is the marginal reduction in second-period revenue resulting from increasing period-one sales.(51)

Figure 2 illustrates the effect on the monopolist's pricing policy in the first period. The equilibrium quantity in the first period, [Q.sub.1]**, will be lower and the equilibrium price, [P.sub.1]**, higher than in the absence of the snob effect. Additionally, the snob effect drives a wedge between the within-period marginal cost of production and marginal revenue for fashion goods.

The snob effect implies that a higher price in period one increases demand in period two. Ceteris paribus, this results in increased sales in period two. Perhaps this is the meaning of the upward sloping "demand" curves found in marketing texts--a higher price today leads to greater sales in future periods.

V. CONCLUDING REMARKS

From an evolutionary perspective, there is strong evidence that there is an innate drive for status among humans. This drive is fundamental to the existence of fashion goods. Simple economic models that incorporate a "snob" effect are derived that can be used to analyze competitive and noncompetitive markets for fashion.

The competitive model generates cycles producing fashion "booms" and "busts." In the noncompetitive model, a discrepancy between the marginal cost of physically producing the output and the marginal cost that actually faces the producer is predicted. In both the models, a rationale for apparently upward sloping "demand" functions emerges--if time is not held constant one can obtain a positive relationship between price and the equilibrium stock purchased over the relevant time periods. Such a construction is not, of course, a demand curve.

Our models abstracted away the possibility of resale. The status approach could be extended to include durables. In markets for durable fashion goods, resale markets may exist. With a resale market, stock supply and demand drive the model. This complicates the analysis considerably because parameters other than current supply and demand enter. The analysis of resale markets and stocks has appeared in the literature for non-fashion commodities.(52) However, a theory that combines consumer interdependencies for fashion durables with a stock/flow analysis awaits future research.

1. This quotation has been preserved in Alfred Marshall [1961] p. 87.

2. This quotation comes from Heilbroner [1986, 190].

3. The term "prestige pricing" in a marketing text usually indicates a "demand" function that has a positive slope through a portion of its range. The texts that do not have sections on "prestige pricing" either have a section on the perceived valuation of consumers as a function of price (Richard P. Bagozzi [1986, 507]), or take a completely economic approach and say quality is higher in higher priced goods (Philip Kotler [1991, 393-475]).

4. Consumers buy cars, for example, to travel from point A to point B, to maintain a certain degree of comfort, and to acquire status. The relative importance of these characteristics change in different automobiles. The buyer of a Yugo automobile is purchasing a substantially different amount of status relative to the buyer of a Mercedes Benz--yet they are both European cars.

5. The literature combining these topics is not very substantial. An incomplete survey of the Social Science Citation Index for the past ten years reveals few articles by economists devoted to either status or fashion, the major exception being the work by Robert H. Frank. Further, an unsystematic search of undergraduate texts revealed only one reference to status in an intermediate microeconomics text (Robert H. Frank, 1991a, pp. 177-79, 511-15), although another intermediate text had an insightful analysis of a prestige product (Donald N. McClosky, 1985, pp. 127-28).

6. For a more extensive review of the pre-1950 literature, see Leibenstein [1950].

7. For example, Veblen hypothesized that men during the late nineteenth century carried walking sticks to show that their hands were "busy," leaving no room for manual labor--the user of a walking stick was signaling that he was not a manual laborer.

8. John Kenneth Galbraith [1984] is an example of the economists and Vance O. Packard [1959] an example of the sociologists.

9. If a snob effect exists, the amount that others possess of some product reduces the marginal value to any consumer. If a bandwagon effect exists, the amount that others possess of some product enhances any consumer's marginal valuation. If a Veblen effect exists, the price that others perceive a buyer to have paid for the good enhances the buyer's marginal valuation. Only in the presence of a Veblen good was Leibenstein able to derive an upward sloping "virtual" market demand curve.

10. Leibenstein's contribution has also been generally neglected. Robert A. Pollack [1970] is an exception; he addressed the problem of the creation of demands in a dynamic setting. In Pollack's conclusions, he notes that interdependence of consumer demands may usefully be incorporated into his model. Another more recent exception, Jeff Biddle [1991], tested Leibenstein's 1950 hypothesis on consumer interdependencies (bandwagon effects). Finally, Uhlaner [1989] analyzes the consumption of "relational goods." These goods are like bandwagon goods in that they generate utility only when consumed by a group of people.

11. Positional goods have to be very limited if they are to serve their purpose as indicators of social rank. For example, if everyone were addressed as "your excellency" it would convey no distinction; consequently that form of address would not yield status.

12. One of the most interesting aspects of the Stigler and Becker article is that they do not recognize the existence or similarities of Kelvin Lancaster's contributions [1966; 1971] to their work.

13. For recent examples of scholarship relating to these issues, see Mark Stegman [1991] on advertising, and Kyle Bagwell and Michael H. Riordan [1991] on pricing. In an already noted exception, Biddle [1991] evinces a direct interest in the subject. Also, Bilkhchandani, Sushil, Hirshleifer and Welch directly address the status issue.

14. This refers both to competition for an ecological niche between species and among conspecifics of the same species.

15. Evolutionary "success" is defined as the long-run viability of the genetic inheritance of a species (or an individual).

16. Social Darwinism, a precursor of sociology, heavily influenced nineteenth century economists and other social scientists.

17. "Environment" refers to the material resources available, as well as ecological relationships such as predator/prey and parasites/symbionts.

18. Genes that stimulate behavior that enhances reproductive success will be more abundant in future gene pools. For more on this point, see Richard Dawkins [1989].

19. The exact lineage of modern man (Homo sapiens sapiens) has not been determined. A branch of the Homo sapiens line, Neanderthal man, has been dated over one-half million years ago (Erik Trinkhaus and William H. Howells [1979] and Sherwood L. Washburn [1978]). Archeological remains of Homo sapiens sapiens have been dated at approximately forty thousand years ago. Skulls very similar to those of modern man and very much older than this suggest that our lineage may have been extant for much more than forty thousand years. For further discussion see Rodney Steel and Anthony Harvey [1979], Trinkhaus and Howells, and Washburn.

20. A generation is calculated to be between twenty to twenty-five years. This might surprise the reader because contemporary usage for the term generation is thirty to thirty-three years. The difference arises because we are looking into the evolutionary history of humanity. Up until the last two hundred years, life expectancies were less than forty years. That would imply a span of between twenty to twenty-five years between generations.

21. Population geneticists have calculated that a dark-skinned Mediterranean-type population may evolve into a fair-skinned Scandinavian-type population in as little as five thousand years if fair-skin coloration confers an advantage of 2 percent more surviving offspring per generation (Marvin Harris [1985, 146]). Charles J. Lumsden and Edward O. Wilson [1983] calculate that a single gene that gives "... a small survival advantage on those who use it..." would spread to almost the entire population in fifty generations. In human history before the modern era a generation was about twenty years; consequently, fifty generations would equal one thousand years. Thus the "thousand-year rule" of Lumsden and Wilson.

22. Evidence for this statement comes from a variety of sources. For studies linking wolves' reproductive success to their status see: Erik Zimen [1979], Durward Allen [1979], Micheal Fox [1980] and Fred H. Harrington and Paul C. Paquet, eds. [1979]. For literature on primates, see: Charles J. Lumsden and Edward O. Wilson [1981; 1983] and Frans De Waal [1982]. For an introduction to human sexuality and status see: Doris Jonas and David Jonas [1980], Donald Symons [1979], and Robert H. Frank [1985a]. For an exhaustive approach to the sociobiological literature as it pertains to animals and humans, see John Alcock [1989].

Some of the physiological changes that accompany changes in status in the animal world are quite amazing. A fish, labroides diminiatus, lives in groups of one male and a female harem. The male is superior to any female and there is a rank ordering among the females. If the male is removed from the group, the ranking female undergoes a metamorphosis and becomes a male, and he (formerly she) controls the harem and supplies sperm to the females' eggs. See Jonas and Jonas [1980, 54].

23. Frank [1985a], devotes an entire chapter to a detailed account of the biological/evolutionary basis for human (also with non-human examples) status-seeking.

24. Jonas and Jonas have devoted an entire book to this proposition, similarly Alcock, Symon, and Edward O. Wilson [1975] attest to the importance of status in both human and non-human populations. From the behavior of other social mammals (wolves, baboons, hyenas, and gorillas are some examples), it appears that there is an innate (genetic) quest for status within peer groupings of these species. Sources for this statement are contained in footnote 20 and footnote 26; especially see Alcock [1989].

25. The evidence presented in footnote 26 is pertinent to intra- sexual competition. Males compete with other males for access to females, and similarly females compete with females. Alcock [1989] has two chapters that separately examine male competition and female competition. The discussions of Jonas and Jonas [1980] are also pertinent.

26. Perhaps it is even stronger than the sex drive, because status confers not only sexual opportunities but increased feeding opportunities. In social animals, high ranking individuals feed before others. See Melvin Fredlund [1976], Alcock [1989], and Wilson [1975]. In animal societies, the progeny of high-status parents have significantly greater chances of reaching maturity and mating than those of low-status parents. The analogy between the genetic basis for a sex drive and status-seeking is apropos. Sexual desires are genetically transmitted, but not all individuals have the same sexual desires and appetites, and there are many cultural forces that constrain and channel it into forms that differ widely between different societies and individuals within a society. We expect that a genetically determined quest for status would be at least as equally variable and subject to a multitude of cultural and environmental influences. See Alcock [1989], Jonas and Jonas [1980], and Richard Dawkins [1989] for further elaboration.

In some species, the probability of mating is so skewed that on a probabilistic basis only high-status individuals reproduce, and there are significant impediments that prevent the lower-ranking members of these societies from mating. In wolves, low-ranking females seem to be physiologically inhibited from coming into estrus by the presence of the alpha (highest-ranking) female. Furthermore, the alpha female tries to prevent any subordinate female from mating. (See Zimen, Allen, Fox, and Harrington and Paquet). In other species, the social ranking of the individual is just as important for reproductive success as in wolves (see Wilson [1975]).

Alcock [1989] reports on the reproductive success of individuals in various species. On South Georgia Island the top-ranking male in a population of elephant seals had approximately 37 percent of all copulations that occurred (the absolute number of males was substantially greater than ten, but only ten were "ranked" in the study). The top two males between them had over 55 percent of all the copulations that occurred during the breeding season. In these animal societies, adequate status is a necessary condition before the sex drive can be satisfied.

27. Innate urges are basic to the organism's survival and reproduction. The desire for food, sex, warmth, and shelter are all examples of innate or genetic urges. It is important to note that because an urge is genetic, it does NOT mean that it cannot be resisted. After all, some humans are voluntary celibates and dieters.

28. There have been human societies that have conferred status upon people who collected the most scalps, heads, cattle, horses, sea- shells, stones, and, at the other spectrum, some societies have conferred status upon those who have given away or destroyed more of their possessions than other members of their peer groups. Like the sex urge, we expect status-seeking to be a genetic trait, but subject to the whims of stochastic cultural and environmental factors.

29. Fashion goods are distinguished from other goods for which "prestige pricing" is recommended by marketers such as pharmaceuticals and imported beers. In their marketing text, William M. Pride and O.C. Ferrell state:

In Prestige Pricing, prices are set at an artificially high level to provide prestige or a quality image. Pharmacists report that some consumers complain if a prescription does not cost enough. Apparently, some consumers equate a drug's price with its potency. Consumers may also associate the quality of a good with its price.

In the economic literature there have been numerous studies showing that consumers perceive that price can be used as a signal of product quality in the absence of costless information. See, Kent B. Monroe [1973], Paul Milgrom and John Roberts [1986], and David J. Curry and Peter C. Riesz [1988] for examples of the relationship between price and perceived quality.

30. A. Michael Spence [1973; 1974] has made valuable contributions to the literature on signaling and elaborates on the effectiveness of a signal.

31. The signal must be accurate, otherwise the signal would have conferred a disadvantage. If signals cost resources and are not accurate predictors, then individuals who invest resources in signaling and those who believe the false signals will be culled over generations.

32. For more information and a review of the literature see, Philip R. P. Coelho [1985]. For information on these restrictions, see Thomas B. Costain [1958]. Outside the field of clothing, other laws existed forbidding some social classes the right to do what other classes were legally entitled to do. For example, in Scotland under James I it was illegal for people with less than baronial ranking to consume baked meat pies. During the same period in England, it was illegal for servants to have more than one meal of meat or fish per day, nor was it legal for them to spend more than three shillings and four pence per year on clothing. These examples also come from Costain [1958, 263].

33. As an anonymous referee pointed out, the laws discussed in this paragraph may have been enacted for the purpose of curbing fashion "arms races." He provided us with the additional example of school uniforms that are required by some private schools.

34. The "neck tie" example that we use may be descriptive of reality, but is meant to be illustrative rather than literal. The example may be modified without damaging the argument.

35. Ties can also be viewed as a signal of wealth. As long as tie styles (the combination of width, pattern, color, material, etc.) continually change, the cost of consistently wearing a fashionable tie is higher for the poor than for the wealthy.

36. The addition of more individuals enhances the argument. The more anonymous individuals are, the more "free riding" is expected. This is because if there are very many people, one individual will benefit materially from violating an agreement if all but one keep it. If all break it but one, the additional cost of one more breaking it is negligible.

As an anonymous referee pointed out, the process may be desirable in an evolutionary sense because status-seeking may enhance the viability of the species. A species' evolutionary chances are improved if their social system allows reproductive success to the "fittest."

37. There is an important distinction between market demand and an individual's demand. If an individual is offered a unique "deal" on a fashion commodity, he will typically take it. The question that interests us is what would the market response be if all consumers were offered the same "deal"--this question is the issue that this paper addresses.

38. One can imagine more elaborate equations with which to represent expectations. The assumed equation has the advantage of making the analysis of the cycle tractable. There appears to be no consensus in the profession on the form of such equations, and, in defense of our formation, it has a historic lineage: in summarizing Phillip Cagan's results [1956], Sargent [1987, 195] employs this form of adaptive expectations for prices.

In a world of rational expectations, the model changes according to the costs and benefits of information. If information were free, accurate, and instantly available, then there would be no fashion cycle. But resources are scarce, and information is costly and imperfect. In such a world adaptive expectations could be rational. (Adaptive expectations are a subset of rational expectations. Depending upon the costs/benefits of information, adaptive expectations could be fully rational.)

39. Resale markets complicate the analysis by conflating the stock of the commodity with both demand and supply equations. Whether an individual is a demander or a supplier in such a model becomes problematic. We found these problems intractable.

40. For a description and proof of the characteristics of differential equations and cycling, see William Baumol [1959, 221].

41. This proposition is easily verified:

1 - [T.sub.1] - [T.sub.2] [is equivalent to] 1 - 1 - [Delta] + [c (1+[Alpha])/(s-b)]}

- [-c[Alpha]/(s-b)]

= 1 - 1+[Delta] - [c/(s-b)] [is greater than] 0.

42. If c = 0 in equation (8), a contradiction emerges because the right side will be negative while the left side will be zero; the condition for explosive oscillation cannot be met.

43. Cf. footnote 33.

44. If the stock implodes, the model's condition for cycling is that the stock becomes negative. Negative stocks are not possible; consequently, the cycle terminates. Exogenous events at some future date may give new life to the fashion good. Such events are not predictable, giving the cycle an unpredictable variance.

45. Imagine an initial situation in which the stock is expanding rapidly (extra wide ties in the mid-1960s). Recognizing this, consumers revise their expectations of the stock upward; this decreases the demand for ties. Because of the high supply elasticity, the demand shift sharply reduces the equilibrium quantity traded. This process predictably leads the stock of extra wide ties to implode in a subsequent period; wide ties fall from the height of fashion to objects of derision.

46. From an initial situation in which stock has been expanding, consumers subsequently revise their expectations causing demand to implode. With inelastic demand, the leftward shift has a greater effect on the current equilibrium amount sold as well as future stocks.

47. There is an interesting and subtle point here; if demand theory is to be operational then demand (and supply) must be stable over some period. Consequently, applying the ceteris paribus assumption to time and holding to it strictly--i.e., not allowing time to pass--makes the concepts of supply and demand operationally meaningless. Just generating a quantitative estimate employs time, thus any test of the theory means that the strict assumption of ceteris paribus has been violated.

48. Subscripts denote consumer groups: [D.sub.1] is the demand of group one, [D.sub.2] is the demand of group two, and so forth.

49. Consumers in groups one and two may be the same consumers. Particularly in the case of a fashion service, we expect repeat customers.

50. This summary is taken from the radio program Morning Edition for 26 June 1991; a transcript is available from National Public Radio in Washington, D.C.

Another product that fits the analysis is Soviet caviar. Jane Mayer writes, "The mood in the Soviet caviar business is as black as beluga--not because this most luxurious of bourgeois treats is so rare, but because it is in danger of becoming too plentiful.... Soviet and Western experts who oversee the rarefied and lucrative caviar trade worry that the delicacy is on the verge of becoming, of all horrors, common." The Wall Street Journal, 18 November 1991, pp. Al, A12.

51. The term d[R.sub.2]/d[Q.sub.1] should actually be discounted into present values. In order to simplify this presentation we will omit an explicit consideration of the discount rate. It should be noted that as the interest rate rises, d[R.sub.2]/d[Q.sub.1] becomes smaller.

52. Robert W. Clower [1954] investigated the relationships between stocks and flows in investment.

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PHILIP R. P. COELHO and JAMES E. MCCLURE, Professor, Ball State University, and Associate Professor, Ball State University. We gratefully acknowledge the support of a John W. Fisher grant awarded by the Ball State University Foundation, the contributions made by our colleagues at Ball State University, anonymous referees, and the editor of this Journal. All remaining errors are our own.
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