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1981 TheEconomicsofSuperstars

Subject Headings: Superstar, Mediocre Agent.

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Abstract

The phenomenon of Superstars, wherein relatively small numbers of people earn enormous amounts of money and dominate the activities in which they engage, seems to be increasingly important in the modern world. While some may argue that it is all an illusion of world inflation, its currency may be signaling a deeper issue.[1] Realizing that world inflation may command the title, if not the content of this paper, quickly to the scrap heap, I have found no better term to describe the phenomenon. In certain kinds of economic activity there is concentration of output among a few individuals, marked skewness in the associated distributions of income and very large rewards at the top.

Confidentiality laws and other difficulties make it virtually impossible to obtain systematic data in this field. However, consider the following: (i) Informed opinion places the number of full-time comedians in the United States at approximately two hundred. This is perhaps a smaller number than were employed in vaudevillian days, though it hardly can be maintained that the demand for (intended) comic relief is in a state of secular decline. Some of the more popular performers today earn extraordinary sums, particularly those appearing on television. The capacity for television to produce high incomes is also manifest in the enormous salaries paid to network news broadcasters.

(ii) The market for classical music has never been larger than it is now, yet the number of full-time soloists on any given instrument is also on the order of only a few hundred (and much smaller for instruments other than voice, violin, and piano). Performers of first rank comprise a limited handful out of these small totals and have very large incomes. There are also known to be substantial differences in income between them and those in the second rank, even though most consumers would have difficulty detecting more than minor differences in a " blind " hearing.

(iii) Switching to more familiar territory, sales of elementary textbooks in economics are concentrated on a group of best sellers, though there exists a large number of very good and highly substitutable alternatives in the market (the apparent inexhaustable supply of authors willing to gamble on breaking into the select group is one of the reasons why so many are available). A small number of graduate schools account for a large fraction of Ph.D. s. A relatively small number of researchers account for a large fraction of citations and perhaps even articles written.

Countless other examples from the worlds of sports, arts and letters, and show business will be well known to readers. Still others can be found in several of the professions. There are two common elements in all of them: first, a close connection between personal reward and the size of one's own market; and second, a strong tendency for both market size and reward to be skewed toward the most talented people in the activity. True, standard theory suggests that those who sell more generally earn more. But that principle applies as well to shoemakers as to rock musicians, so something more is involved. In fact the competitive model is virtually silent about any special role played by either the size of the total market or the amount of it controlled by any single person, because products are assumed to be undifferentiated and one seller's products are assumed to be as good as those of any other.

The elusive quality of " box office appeal," the ability to attract an audience and generate a large volume of transactions, is the issue that must be confronted.

Recognition that one's personal market scale is important in the theory of income distribution has a long history, but the idea has not been developed very extensively in the literature.[2] I hope to fill in some of the gaps in what follows.

The analytical framework used is a special type of assignment problem, the marriage of buyers to sellers, including the assignment of audiences to performers, of students to textbooks, patients to doctors, and so forth. Rest assured that prospective impresarios will receive no guidance here on what makes for box office appeal, sometimes said to involve a combination of talent and charisma in uncertain proportions. In the formal model all that is taken for granted and represented by a single factor rather than by two, an index q labeled talent or quality. The distribution of talent is assumed to be fixed in the population of potential sellers and costlessly observable to all economic agents. Let p be the price of a unit of service (for example, a performance, a record, a visit, etc.) and let m be the size of the market, the number of "tickets" sold by a given seller. Then an overall market equilibrium is a pair of functions p(q) and m(q) indicating price and market size of sellers of every observable talent and a domain of q such that: (a) all sellers maximize profit and cannot earn larger amounts in other activities, and (b) all buyers maximize utility and cannot improve themselves by purchasing from another seller.

Properties of sellers' maximum net revenue functions, R(q), will have special interest. Specifically, convexity of this function describes much of the observable consequences of Superstars. Since R(q) is the transformation that takes the distribution of talent to the distribution of rewards, convexity implies that the income distribution is stretched out in its right-hand tail compared to the distribution of talent. Hence a genuine behavioral economic explanation is provided for differential skew between the distributions of income and talent, a problem that has been an interesting and important preoccupation of the literature on income distribution down through the years.[3] Convexity of R(q) literally means that small differences in talent become magnified in larger earnings differences, with great magnification if the earnings-talent gradient increases sharply near the top of the scale. This magnification effect is characteristic of the phenomenon under consideration.

Convexity of returns and the extra skew it imparts to the distribution of earnings can be sustained by imperfect substitution among different sellers, which is one of the hallmarks of the types of activities where Superstars are encountered. Lesser talent often is a poor substitute for greater talent. The worse it is the larger the sustainable rent accruing to higher quality sellers because demand for the better sellers increases more than proportionately: hearing a succession of mediocre singers does not add up to a single outstanding performance. If a surgeon is 10 percent more successful in saving lives than his fellows, most people would be willing to pay more than a 10 percent premium for his services. A company involved in a $30 million law suit is rash to scrimp on the legal talent it engages.

Imperfect substitution alone implies convexity and provides a very general explanation of skewed earnings distributions which applies to myriad economic service activities.

However, preferences alone are incapable of explaining the other aspect of the Superstar phenomenon, the marked concentration of output on those few sellers who have the most talent. This second feature is best explained by technology rather than by tastes.[4] In many instances rendering the service is described as a form of joint consumption, not dissimilar to a public good. Thus a performer or an author must put out more or less the same effort whether 10 or 1,000 people show up in the audience or buy the book. More generally, the costs of production (writing, performing, etc.) do not rise in proportion to the size of a seller's market.

The key difference between this technology and public goods is that property rights are legally assigned to the seller: there are no issues of free riding due to nonexclusion; customers are excluded if they are unwilling to pay the appropriate admission fee. The implied scale economy of joint consumption allows relatively few sellers to service the entire market. And fewer are needed to serve it the more capable they are. When the joint consumption technology and imperfect substitution features of preferences are combined, the possibility for talented persons to command both very large markets and very large incomes is apparent.

A theory of the assignment of buyers to sellers is required to make these ideas precise. The demand and supply structure of one such model is set forth in Sections I and II. The nature of market equilibrium and its implications for income and output distributions are discussed in Sections III and IV. Comparative static predictions of the model are sketched in Section V and conclusions appear in Section VI.

Footnotes

  1. That escalation is not confined to wars and prices is established by the fact that Stars would have sufficed not long ago. Academics have a certain fondness for Giants, while businessmen prefer Kings. Obviously there is a fair bit of substitution among all these terms in depicting related data in different contexts.
  2. Albert Rees is a good introduction to the size distribution of income. The selectivity effects of differential talent and comparative advantage on the skew in income distributions are spelled out in my 1978 article, also see the references there. Melvin Reder's survey touches some of the issues raised here. Of course social scientists and statisticians have had a long standing fascination with rank-size relationships, as perusal of the many entries in the Encyclopedia of the Social Sciences will attest.
  3. Few economic behavioral models exist in the literature. On this see Harold Lydall. Jacob Mincer has shown that investment can produce skewness through the force of discounting, and established that as an important source of skewness empirically. Learning is not treated here because those issues are well understood, whereas the assignment problem has received little attention. Some recent works, but with different focus and emphasis than is discussed here, are Gary Becker (1973), David Grubb, and Michael Sattinger.
  4. Milton Friedman proposed a model based on preferences for risk taking, but did not explain why or how the market sustains the equilibrium ex post with few sellers earning enormous incomes (for example, why the losers in the lottery rest content with such low incomes if they have the same talents as the winners). Issues of uncertainty that make these elements of supply more interesting are abstracted from here. A model of prizes based on effort-incentive monitoring and the principal agency relation is found in my article with Edward Lazear

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