- Email: [email protected]
Durable good celebrities
Journal of Economic Behavior & Organization Vol. 66 (2008) 312–321
Durable good celebrities Todd D. Kendall ∗ The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, SC 29634, USA Received 3 May 2005; accepted 16 January 2006 Available online 28 December 2006
Abstract Celebrity musicians and other famous touring performers face problems similar to those of a durable good seller with market power, since the number of tickets sold (or expected to be sold) at a given time has intertemporal demand effects. I show that the durability of celebrity output leads to “excessively” long tours and that there is a strong incentive to take actions early in one’s career that will increase costs later in one’s career. These effects may help explain high rates of drug abuse and other anomalous self-destructive behavior observed among celebrities. © 2006 Elsevier B.V. All rights reserved. JEL classification: L82; K42; J28 Keywords: Celebrity; Durable goods; Performance; Drug abuse
Led Zeppelin, one of the most popular rock bands of the 1970s, often performed six nights each week for months at a time. In one 15-month period, the band took six tours of the United States. On tour, lead guitarist Jimmy Page suffered from frequent nausea and was often close to nervous and physical breakdown, vocalist Robert Plant collapsed from exhaustion after the end of the fifth tour, and drummer John Bonham was driven to alcoholism to calm his frayed nerves, dying at age 32 to alcohol abuse.1 Zeppelin’s story is not unique. Similar problems have plagued many, if not most, other star musicians, from Mozart to Metallica. Given the high wealth levels of top-selling artists, it may seem surprising that their labor supply curves apparently do not bend backwards significantly; other high-income professionals ∗ 1
Tel.: +1 864 639 2682; fax: +1 864 656 4192. E-mail address: [email protected]. This history is gleaned from the account in Wills and Cooper (1988).
0167-2681/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2006.01.009
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do not have anything like the same popular reputation for self-destructive behavior as that of star musicians. Some such behavior may be explained by performers’ purposive attempts develop an interesting or exciting reputation, which their audiences may value; however, similar behavior is observed with many of the greatest classical composers and performers as well, where audience preferences are generally tamer. Pathologies in the labor market for celebrity performers undoubtedly have many causal factors, and significant literature in other social sciences has addressed some of these.2 In this paper, I note that the unusual behavior of performing artists may also be driven partially by economic factors, in particular, the well-known problems of the durable good monopolist. All performers produce durable goods in the sense that consumers who buy tickets to a performance receive an “experience” they carry with them. Thus, a consumer who sees tonight’s show is generally unwilling to pay as much for a ticket to tomorrow’s show. To the extent that their talents and stardom are irreplicable, top-selling performers hold some measure of market power over their output. Coase (1972) conjectured that firms with market power selling a durable good face a dynamic inconsistency problem. The firm prefers to set a price above marginal cost, but after consumers have purchased the product at this price, the firm faces an incentive to drop prices in order to attract additional sales. Foreseeing this outcome, consumers choose not to purchase the product at the monopoly price in the first place. Under appropriate assumptions established by Stokey (1981), Bagnoli et al. (1989), Thepot (1998), and Horner and Kamien (2004), this implies that the firm will not be able to take advantage of its market power. Celebrity performers face similar problems. For instance, a star musician on tour must find a way to convince fans in each city that there will be no “cut-rate” performances in the near future if they wish to extract rents from their fans. Thus, promotional materials carry the familiar phrase “One Performance Only”, although by itself, such notice constitutes little more than cheap talk. As another example, stars must convince current fans that they are unlikely to become “sell-outs” later in their careers by appealing to mass audiences, thus diminishing early fans’ utility. In this paper, I show that the time-inconsistent nature of durable good monopoly decisionmaking among celebrity performers may result in many of the behaviors that have long puzzled and fascinated observers. I show that: (1) performers run excessively long tours, a factor which may lead to the mental breakdowns, substance abuse, and other problems so common in the celebrity labor market; (2) regardless of their personal discount rates, performers have an incentive to engage in activities that lower their costs of production in the present and raise them in the future, of which the abuse of drugs and alcohol might be considered an example; and (3) performers may produce at levels consistent with inelastic demand, despite their market power. The issue of celebrity behavior has received little attention in economics, despite its prominence in social discourse and the status of celebrities as cultural symbols and “leaders” in the formation and evolution of preferences, social norms, fashions, and so on. Cowen (2000) discusses the
2 See, for instance, Csikszentmihalyi (1998) and Giles (2000) in psychology, and Stack (1987) and Parnaby and Sacco (2004) in sociology.
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value and costs of fame in society, and Kendall (2006) illustrates how labor supply inelasticity can lead to anti-social behavior among stars. Some empirical work in other fields documents self-destructive celebrity behavior: Wills and Cooper (1988) and Valhouli (1998) present case studies of psychological meltdown by musicians, while Fowles (1992) shows celebrities have higher mortality rates than non-celebrities, and Redelmeier and Singh (2001a,b) debate whether success reduces longevity among movie stars. In Section 1 below, I amend the cost structure of a typical durable good monopolist model to include a term that rises convexly with time, which is intended to encapsulate the psychological costs of stress and of being away from home, as well as the pecuniary costs of moving people and equipment on tour. Thus, performers can commit to a non-falling price for early consumers by selling tickets to performances sufficiently far in the future that additional “surprise” performances beyond those would be unprofitable. In other words, the model predicts that celebrities will “burn out” as a price-commitment mechanism. It also follows that performers will exert less market power in larger markets than in smaller ones, since for a given duration of production, unexpectedly lowering prices is a more profitable strategy in larger markets. In Section 2, I show that seemingly “myopic” behavior that shifts costs into the future, such as drug abuse or reckless living, can be an effective substitute commitment device, a result that echoes Bulow’s (1986) “planned obsolescence” model of durable good sellers.3 I do not mean to claim that price-commitment issues explain all the pathologies in the labor market for stars; however, durability issues play an undoubtedly large role in the career choices these performers make, and this paper opens the economic question related thereto for greater consideration. 1. Burnouts The basic model sketched here is one of a celebrity performer who can observe the level of demand for his services in a number of different markets, which could represent a number of different cities for a touring musical group, or a number of periods over which his career spans, for instance. The performer must choose his level of output in each market as well as the number of different markets to enter. Let us consider specifically the case of a touring musical band, making choices in two consecutive periods. The model timeline is as follows: in the first period, the band sets a number of concert tour dates in different cities, as well as the number of tickets they will sell in each city.4 In the second period, after tickets have been sold for the previously announced tour dates, the band may choose to add additional concerts to the tour and if so, also chooses the number of tickets sold in each “return engagement” based on residual demand after the original tour date. For simplicity of explication, assume that cities are real numbers along a continuum (0, ∞), and that the cities are ordered by decreasing size (demand). Thus, performers choose a measure 3 To be sure, other commitment mechanisms may exist. Quickly changing tastes and age-specific product provide natural obsolescence for many celebrity outputs. Moreover, Bulow (1982) implies that leasing is an optimal strategy for durable good monopolists; however, it is usually infeasible to “lease” a performance experience. Anderson (1985) suggests that sellers can take appropriate positions in futures markets that make lowering prices ex post unprofitable. Recently, futures contracts for specific movies have begun trading on the Hollywood Stock Exchange (http://www.hsx.com). It is not known whether celebrities take advantage of this investment vehicle, and no similar market seems to exist for musicians or other classes of celebrity. 4 I ignore potential non-convexities due to fixed venue sizes, as well as the issue of how to price different seats within the same venue. For an explication of this latter problem, see Rosen and Rosenfield (1997).
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of cities, not a discrete number. This allows for analytic solutions throughout, but all results that follow are robust to a discrete framework. Let the inverse demand in city j be given by pj = A − jxj where pj and xj denote price and quantity of tickets in city j, and A is a positive constant. There are three assumptions implicit in these demand equations. First, note that by construction, there is an inverse relationship between demand and city rank, such that city j is simply 1/j times the size of city 1.5 In other words, the frequency distribution of consumer valuations is constant across cities, so that fans are not differentially concentrated in some cities.6 Second, demand curves are independent across cities. If cities are distant enough from each other so that relatively few fans travel between tour cities to buy tickets, then this assumption is innocuous. Thirdly, the linear functional form allows for analytic solutions below, but neither of the Propositions that follow rely on this assumption.7 Performers face a constant marginal cost for tickets within a given city, which, without loss of generality, is set at zero. However, there is also a separate cost incurred in each city, which includes the psychological costs of stress and of being away from home for another set of performances, as well as the costs of moving and setting up equipment and personnel. Assume that this cost varies with the number of cities toured, N, according to a power function: C(N) =
N 1+μ . 1+μ
If the psychological stress of being away from home and/or the cost of time spent moving between cities increases over time, then μ > 0 is appropriate, making the cost function convex.8 As a baseline case for use as a comparison, suppose that performers have access to some costless perfect commitment technology (PC) that allows them to make binding contracts with fans to add no further dates to the tour schedule in period 2. Then, in the first period the band chooses the number of cities, N, and the number of tickets in each city, xj , to maximize profits by solving the following problem: N 1+μ N PC max π = . (1) [(A − jxj )xj ] dj − N,{xj }j 1+μ 0 The first-order conditions imply the following solutions9 : xjPC =
5
A , 2j
1/1+μ
N PC = ( 41 A2 )
.
This matches well the empirical distribution of city sizes in the U.S. and most other countries (see Gabaix, 1999). A band that was more popular in some cities than others could still fit in this framework if the inverse relationship between city rank and size held within the band’s favored region. 7 Derivation of all results under a general model with demand curves of the form p = p(jx ) is available upon request j j from the author. 8 Even if psychological costs were not convex, the complexity (and hence, computational costs) of finding the travel cost-minimizing tour schedule (a “traveling salesman” problem) increase convexly in the number of nodes (Papadimitriou and Steiglitz, 1998). 9 Here I assume the band is literally a monopolist. Oligopoly is probably a more accurate description of the industrial organization of top-selling artists; nevertheless, it is market power, not strict monopoly, that drives the results. 6
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Hereafter, these will be referred to as the “perfect commitment” solutions since they involve the band setting its profit-maximizing price in each market separately10 and scheduling a tour in which the marginal cost of the last tour date equals the marginal revenue. Note that while all cities j ≤ NPC will be included in the concert tour, this does not imply that these cities must be visited in order of decreasing size.11 Now consider the problem of imperfect commitment. If, in the first period, the band were to offer the perfect commitment quantity of tickets in city j, fans may be concerned that the band will, ex post, announce additional concerts at a lower price in the second period. This concern would lead fans to decrease their demand for the original tour dates, and the band’s potential to extract profits would be thereby lessened. One way of ameliorating this problem is for the band to take no breaks between concerts during the first period. Ex ante, they announce a full schedule of concerts across many cities—a “whirlwind” tour. Thus, fans can rest assured that the band will not extend its engagement in a particular city immediately because it has already contracted to perform in another city, preferably a distant one. This may help explain why bands typically take so few breaks in their concert tours and why their tour schedules often call for a large number of coast-to-coast flights. However, even whirlwind tours may not entirely solve the commitment problem if fans are concerned that the band may schedule a return engagement at the end of the tour. Specifically, consider what would happen if the band did schedule a return engagement to a particular city j in period 2.12 Let rj denote the number of tickets offered for this concert. Given a number of tickets sold in the original run, xj , the band would choose rj to solve the following problem: max(A − j(xj + rj ))rj , rj
which gives the following first-order condition: rj (xj ) =
A − jxj , 2j
and the profit to the band from returning to city j, given the sales of tickets in the original run in city j, can then be written as (A − jxj )2 . 4j Now, the cost of a return to city j at the end of a tour with N dates would simply be the marginal cost of another city, Nμ .
10 Further note that these solutions imply a constant price across cities, a characteristic that finds empirical support in Krueger (2005). 11 Technically, the cost function C(N) is the minimum cost of visiting the first N cities and implicitly assumes that a “traveling salesman”-style linear programming problem has been solved to find the lowest cost permutation of the N cities among all possible permutations. Thus, for instance if the band is touring New York, Los Angeles, and Minneapolis, Minneapolis would likely be the second tour date, even though it ranks third in size. 12 Here, I assume fans do not discount the future, though clearly the model could be extended to include this detail without changing the general results.
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Thus, consumers in city j will be convinced in the first period that the band is not planning a return engagement to their city in the second period if and only if: (A − jxj )2 ≤ N μ. 4j
(2)
Without a perfect commitment technology, then, the band’s first period problem is to maximize profits, as in Eq. (1), but subject to the constraint of Eq. (2) for all cities j: 1+μ N N max πIC = [(A − jxj )xj ] dj − (3) N,{xj }j 1+μ 0 subject to Eq. (2) for all j. For a given value of N, the constraint in Eq. (2) must hold for all j ∈ [0, N]. For some j, the constraint may strictly bind, such that: (A − jxj )2 = N μ. 4j Rearranging the binding form of Eq. (2), the number of tickets sold in any “binding” city, which I will denote xjB , has an obvious relationship with tour length, N: xjB =
A − 2j 1/2 N μ/2 . j
For other j, however, the constraint may not bind. If, for a particular city j, the constraint does not bind, then there is no reason why the band should not choose the perfect commitment ticket quantity: xjNB = xjPC =
A . 2j
In other words, a city in which the constraint in Eq. (2) does not bind is one in which the band can freely produce the perfect commitment quantity of tickets in that city while remaining fully committed to not returning to the city. A city in which the constraint in Eq. (2) does bind is one in which the band would like to sell fewer tickets, but cannot do so in the absence of an enforceable commitment device. Substituting the perfect commitment value of xj into the constraint in Eq. (2), we find that, given the length of the tour N, the cities with non-binding constraints are those that satisfy: A2 ≤ N μ, 16j or in other words, the cities with non-binding constraints are those j > j* , where j∗ =
1 2 −μ . 16 A N
Thus, we can reconsider the imperfect commitment problem specified in Eq. (3): the band must choose N, knowing that on the margin, an increase in N has both direct and indirect effects. The direct effect of increasing N is increased revenues from ticket sales in the additional city and fixed cost expenditures for adding a city to the tour. The indirect effect is to strengthen the band’s commitment not to hold return engagements in more cities in period 2, causing more cities to
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become “non-binding”. In other words, a longer tour allows the band to exert market power in more cities. We can then rewrite the problem in Eq. (3), including the constraint as ∗ 1+μ N j N NB NB B B . (4) [A − jxj ]xj dj − [A − jxj ]xj dj + max N 1+μ j∗ 0 The first integration term is the revenue from cities in which the constraint binds, the second integration term is the revenue from cities in which the constraint does not bind, and the final term is the cost function for tour length. Substituting in the values of xjB and xjNB , the first-order condition to this problem implies 1/1+μ
N IC = ( 41 A2 )
(1 + μ)1/1+μ .
Comparing this solution to the perfect commitment solution, we see that NIC is higher than the perfect commitment solution, NPC , whenever (1 + μ)1/1+μ is greater than 1, or in other words, when μ > 0. Thus, we have shown the following proposition: Proposition 1. Celebrity performers will extend the lengths of their tours beyond the length they would choose with a perfect commitment technology. Corollary. Celebrity performers will undertake performances in which the revenue derived from the performance is less than the cost. Proof. Consider the Nth and final city. This is clearly a “non-binding” constraint city. Then the revenue derived from city N is A2 /4N. Substituting the value of N derived above, the band’s profit in the Nth city is μ/1+μ
( 41 A2 )
[(1 + μ)1/1+μ − (1 + μ)μ/1+μ ].
This expression is negative so long as μ > 0.
Thus, the band “burns out”, performing on a tour that is excessively long, in the sense that on the margin, the costs of being on the road are greater than the profits derived. A further implication of the equilibrium derived above is that, in larger markets, which are more likely to be binding, prices are lower than the monopoly price. This may help explain why a number of empirical studies (for instance, Moore, 1968; Houthakker and Taylor, 1970; Throsby and Withers, 1979; Goudriaan and de Kam, 1983) on arts-related outputs have counter-intuitively found cases of inelastic demand.13 2. Self-destruction Suppose there were a technology available to celebrity performers that had some effect on the magnitude of μ. To be concrete, increasing μ means making the cost function more convex (lowering costs for the initial few concerts while increasing costs dramatically for later concerts). Mind-altering drugs might be considered one example of such a technology. The use of marijuana, LSD, heroin, cocaine, and other drugs can lower the present costs of production by loosening a performer’s inhibitions on stage, helping him to relax, cope with stress, and so on. Of course, 13
Heilbrun and Gray (2001) catalog some alternative explanations for these results.
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abuse of these drugs comes at an often terrible price; the potential for addiction, dangerous overdoses, and loss of self-control and reason are significant. However, these costs are, for the most part, incurred during the later stages of drug use, not at the beginning. Another such cost-function altering “technology” would be the development of a taste for reckless driving or other risky behaviors generally. Most other commentators assume that celebrities who abuse drugs or engage in other such “myopic” behaviors do so because of excessively high subjective discount rates.14 However, the theory presented here provides another avenue for such behavior, one that does not rely on arbitrary differences in preferences. Consider first the perfect commitment case, and now assume that, through the use of drugs or similar behaviors, μ can be costlessly varied over some set [μ, μ]. ¯ The band’s first period problem (analogous to Eq. (1)) is now N 1+μ N max πPC = . [(A − jxj )xj ] dj − N,{xj }j ,μ 1 +μ 0 As before, the first-order conditions for xj and N give the results: xjPC =
A , 2j
1/1+μ
N PC = ( 41 A2 )
.
However, the marginal effect of changing μ is now dπPC N 1+μ 1 = − log N . dμ 1+μ 1+μ Substituting in the value of NPC , we find dπPC 1/4A2 1 2 . A = 1 − log 4 dμ 1+μ Assuming a reasonably high value for A,15 the band would choose the corner solution μ = μ. In other words, with a perfect commitment technology, self-destruction would be only counterproductive. Now let us consider the case without perfect commitment. Analogous to Eq. (4), the band’s maximization problem is now ∗ 1+μ N j N B B NB max [A − jxj ]xj dj + [A − jxj ] dj − . N,μ 1+μ j∗ 0 The first-order condition for N implies, as before: 1/1+μ
N IC = ( 41 A2 )
(1 + μ)1/1+μ .
However, the effect of changing μ is dπIC 1 1 N 1+μ = A2 log N − log N − . dμ 4 1+μ 1+μ 14 See, for instance, Adam Smith’s (1776/1976) discussion of celebrity, in which he designates a particular “contempt of risk” to which young people are particularly prone. 15 In particular, A > 2√e, where e is euler’s constant.
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Substituting in the value of NIC : dπIC 1/4A2 = > 0. dμ 1+μ As in the perfect commitment case, this condition implies a corner solution to the choice of μ. However, now the optimal value of μ is μ. In other words, due to the commitment problem, self-destruction becomes an optimal strategy for the band. This result echoes Bulow’s (1982) finding that monopolist sellers are led to produce goods that are less durable than those of competitive markets. In this case, celebrity performers have an incentive to diminish their own durability purposely as a commitment device to consumers. Celebrity self-destruction thus may be thought of as “planned obsolescence,” in the words of Bulow (1986). 3. Conclusion Celebrities are social leaders, where fashions and trends in speech and action begin. They also serve as visible symbols of the societies in which they live. Their behavior, therefore, deserves special attention and further research from economists, as it has received in other social sciences. Connolly and Krueger (2005) provide additional evidence for the importance of understanding the economics of celebrity in popular music. The question of why celebrities appear so inclined to burn-outs and self-destructive behavior is a problem not inclined to a simple solution. For instance, while celebrities are wealthy, so are Fortune 500 CEOs, yet the stereotypical behaviors of these groups differ markedly. Also, while it may be true that rock stars can use bad behavior as advertising appealing to the preferences of their target audience, many of the great classical composers, whose audience was significantly older and more culturally refined, exhibited similarly self-destructive tendencies.16 Moreover, performing in front of large crowds is very stressful, but many other jobs are also very stressful, yet workers in these jobs do not seem to turn nearly as quickly to drugs and other self-destructive behavior as do performing artists. This paper has suggested the special nature of the output of celebrity performers as an important part of the puzzle and has applied a simple extension of the well-known results related to durable good monopolists to explain this behavior. Further empirical work on the question might focus on the model’s implication that elasticities of demand for celebrity performances should be correlated with city size. In addition, further theoretical work is likely necessary to understand more fully celebrity behavior.
16 Mozart or Paganini, for instance. Of course, not all great composers exhibited such behavior, just as not all rock stars abuse drugs. Handel, Liszt, Rodrigo, and Telemann all composed until relatively late ages for their times. In many other cases, composers died at early ages, though perhaps not always from reckless living: Franz Schubert from syphilis, Tchaikovsky from poisoning, Chopin from consumption, Alban Berg from blood poisoning, Henry Purcell from tuberculosis, and Anton Webern from accidental shooting. All of these, however, it may be argued, are to various degrees preventable forms of death, and these composers made lifestyle choices that increased their probability of early death. For instance, Purcell is believed to have become sick after being locked out of his house by his wife. I am grateful to a referee for suggesting some of these interesting cases.
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Acknowledgements I acknowledge helpful suggestions from Gary Becker, Julie Hilden, Casey Mulligan, Allen Sanderson, Curtis Simon, and Robert Tamura. References Anderson, R.W., 1985. Market Power and Futures Trading for a Durable Good. Mimeo, Graduate Center, City University of New York. Bagnoli, M., Salant, S., Swierzbinski, S., 1989. Durable-goods monopoly with discrete demand. Journal of Political Economy 97, 511–531. Bulow, J., 1982. Durable-goods monopolists. Journal of Political Economy 90, 143–149. Bulow, J., 1986. An economic theory of planned obsolescence. Quarterly Journal of Economics 101, 729–749. Coase, R., 1972. Durability and monopoly. Journal of Law and Economics 15, 143–149. Connolly, M., Krueger, A., 2005. Rockonomics: The Economics of Popular Music. Mimeo, Industrial Relations Section, Princeton University. Cowen, T., 2000. What Price Fame? Harvard University Press, Cambridge, MA. Csikszentmihalyi, M., 1998. Genius and Mind: Studies of Creativity and Temperament. Oxford University Press, London. Fowles, J., 1992. Starstruck. Smithsonian Institution Press, Washington, DC. Gabaix, X., 1999. Zipf’s law for cities. Quarterly Journal of Economics 114, 739–767. Giles, D., 2000. Illusions of Immortality: A Psychology of Fame and Celebrity. St. Martin’s Press, New York. Goudriaan, R., de Kam, C.A., 1983. Demand in the performing arts and the effects of subsidy. In: Hendon, W.S., Shanahan, J., Hilhorst, I., Van Straalen, J. (Eds.), Economic Research in the Performing Arts. Association for Cultural Economics, Akron, OH, pp. 35–44. Heilbrun, J., Gray, C.M., 2001. The Economics of Art and Culture: An American Perspective. Cambridge University Press, New York. Horner, J., Kamien, M.I., 2004. Coase and Hotelling: a meeting of the minds. Journal of Political Economy 112, 718–722. Houthakker, H.S., Taylor, L.D., 1970. Consumer Demand in the United States. Harvard University Press, Cambridge, MA. Kendall, T.D., 2006. Celebrity Misbehavior. Mimeo, The John E. Walker Department of Economics, Clemson University. Krueger, A.B., 2005. The economics of real superstars: the market for rock concerts in the material world. Journal of Labor Economics 23, 1–30. Moore, T.G., 1968. The Economics of the American Theater. Duke University Press, Durham, NC. Papadimitriou, C.H., Steiglitz, K., 1998. Combinatorial Optimization: Algorithms and Complexity. Dover Books, Mineola, NY. Parnaby, P.F., Sacco, V.F., 2004. Fame and strain: the contributions of Mertonian deviance theory to an understanding of the relationship between celebrity and deviant behavior. Deviant Behavior 25, 1–26. Redelmeier, D.A., Singh, S.M., 2001a. Survival in Academy award-winning actors and actresses. Annals of Internal Medicine 134, 955–962. Redelmeier, D.A., Singh, S.M., 2001b. Longevity of screenwriters who win an Academy award: longitudinal study. British Medical Journal 323, 22–29. Rosen, S., Rosenfield, A.M., 1997. Ticket pricing. Journal of Law and Economics 40, 351–376. Smith, A., 1976. An Inquiry into the Nature and Causes of the Wealth of Nations. University of Chicago Press, Chicago (Original work published 1776). Stack, S., 1987. Celebrities and suicide: a taxonomy and analysis 1948–1983. American Sociological Review 52, 401–412. Stokey, N.L., 1981. Rational expectations and durable good pricing. Bell Journal of Economics 12, 112–128. Thepot, J., 1998. A direct proof of the Coase conjecture. Journal of Mathematical Economics 29, 57–66. Throsby, C.D., Withers, G.A., 1979. The Economics of the Performing Arts. St. Martin’s Press, New York. Valhouli, C., 1998. Taking Care of Business: Managing the Death and Legacy of Celebrity Musicians. Master’s Thesis, Georgetown University. Wills, G., Cooper, C.L., 1988. Pressure Sensitive: Popular Musicians Under Stress. Sage Publications, London.
Durable good celebrities Todd D. Kendall ∗ The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, SC 29634, USA Received 3 May 2005; accepted 16 January 2006 Available online 28 December 2006
Abstract Celebrity musicians and other famous touring performers face problems similar to those of a durable good seller with market power, since the number of tickets sold (or expected to be sold) at a given time has intertemporal demand effects. I show that the durability of celebrity output leads to “excessively” long tours and that there is a strong incentive to take actions early in one’s career that will increase costs later in one’s career. These effects may help explain high rates of drug abuse and other anomalous self-destructive behavior observed among celebrities. © 2006 Elsevier B.V. All rights reserved. JEL classification: L82; K42; J28 Keywords: Celebrity; Durable goods; Performance; Drug abuse
Led Zeppelin, one of the most popular rock bands of the 1970s, often performed six nights each week for months at a time. In one 15-month period, the band took six tours of the United States. On tour, lead guitarist Jimmy Page suffered from frequent nausea and was often close to nervous and physical breakdown, vocalist Robert Plant collapsed from exhaustion after the end of the fifth tour, and drummer John Bonham was driven to alcoholism to calm his frayed nerves, dying at age 32 to alcohol abuse.1 Zeppelin’s story is not unique. Similar problems have plagued many, if not most, other star musicians, from Mozart to Metallica. Given the high wealth levels of top-selling artists, it may seem surprising that their labor supply curves apparently do not bend backwards significantly; other high-income professionals ∗ 1
Tel.: +1 864 639 2682; fax: +1 864 656 4192. E-mail address: [email protected]. This history is gleaned from the account in Wills and Cooper (1988).
0167-2681/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2006.01.009
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do not have anything like the same popular reputation for self-destructive behavior as that of star musicians. Some such behavior may be explained by performers’ purposive attempts develop an interesting or exciting reputation, which their audiences may value; however, similar behavior is observed with many of the greatest classical composers and performers as well, where audience preferences are generally tamer. Pathologies in the labor market for celebrity performers undoubtedly have many causal factors, and significant literature in other social sciences has addressed some of these.2 In this paper, I note that the unusual behavior of performing artists may also be driven partially by economic factors, in particular, the well-known problems of the durable good monopolist. All performers produce durable goods in the sense that consumers who buy tickets to a performance receive an “experience” they carry with them. Thus, a consumer who sees tonight’s show is generally unwilling to pay as much for a ticket to tomorrow’s show. To the extent that their talents and stardom are irreplicable, top-selling performers hold some measure of market power over their output. Coase (1972) conjectured that firms with market power selling a durable good face a dynamic inconsistency problem. The firm prefers to set a price above marginal cost, but after consumers have purchased the product at this price, the firm faces an incentive to drop prices in order to attract additional sales. Foreseeing this outcome, consumers choose not to purchase the product at the monopoly price in the first place. Under appropriate assumptions established by Stokey (1981), Bagnoli et al. (1989), Thepot (1998), and Horner and Kamien (2004), this implies that the firm will not be able to take advantage of its market power. Celebrity performers face similar problems. For instance, a star musician on tour must find a way to convince fans in each city that there will be no “cut-rate” performances in the near future if they wish to extract rents from their fans. Thus, promotional materials carry the familiar phrase “One Performance Only”, although by itself, such notice constitutes little more than cheap talk. As another example, stars must convince current fans that they are unlikely to become “sell-outs” later in their careers by appealing to mass audiences, thus diminishing early fans’ utility. In this paper, I show that the time-inconsistent nature of durable good monopoly decisionmaking among celebrity performers may result in many of the behaviors that have long puzzled and fascinated observers. I show that: (1) performers run excessively long tours, a factor which may lead to the mental breakdowns, substance abuse, and other problems so common in the celebrity labor market; (2) regardless of their personal discount rates, performers have an incentive to engage in activities that lower their costs of production in the present and raise them in the future, of which the abuse of drugs and alcohol might be considered an example; and (3) performers may produce at levels consistent with inelastic demand, despite their market power. The issue of celebrity behavior has received little attention in economics, despite its prominence in social discourse and the status of celebrities as cultural symbols and “leaders” in the formation and evolution of preferences, social norms, fashions, and so on. Cowen (2000) discusses the
2 See, for instance, Csikszentmihalyi (1998) and Giles (2000) in psychology, and Stack (1987) and Parnaby and Sacco (2004) in sociology.
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value and costs of fame in society, and Kendall (2006) illustrates how labor supply inelasticity can lead to anti-social behavior among stars. Some empirical work in other fields documents self-destructive celebrity behavior: Wills and Cooper (1988) and Valhouli (1998) present case studies of psychological meltdown by musicians, while Fowles (1992) shows celebrities have higher mortality rates than non-celebrities, and Redelmeier and Singh (2001a,b) debate whether success reduces longevity among movie stars. In Section 1 below, I amend the cost structure of a typical durable good monopolist model to include a term that rises convexly with time, which is intended to encapsulate the psychological costs of stress and of being away from home, as well as the pecuniary costs of moving people and equipment on tour. Thus, performers can commit to a non-falling price for early consumers by selling tickets to performances sufficiently far in the future that additional “surprise” performances beyond those would be unprofitable. In other words, the model predicts that celebrities will “burn out” as a price-commitment mechanism. It also follows that performers will exert less market power in larger markets than in smaller ones, since for a given duration of production, unexpectedly lowering prices is a more profitable strategy in larger markets. In Section 2, I show that seemingly “myopic” behavior that shifts costs into the future, such as drug abuse or reckless living, can be an effective substitute commitment device, a result that echoes Bulow’s (1986) “planned obsolescence” model of durable good sellers.3 I do not mean to claim that price-commitment issues explain all the pathologies in the labor market for stars; however, durability issues play an undoubtedly large role in the career choices these performers make, and this paper opens the economic question related thereto for greater consideration. 1. Burnouts The basic model sketched here is one of a celebrity performer who can observe the level of demand for his services in a number of different markets, which could represent a number of different cities for a touring musical group, or a number of periods over which his career spans, for instance. The performer must choose his level of output in each market as well as the number of different markets to enter. Let us consider specifically the case of a touring musical band, making choices in two consecutive periods. The model timeline is as follows: in the first period, the band sets a number of concert tour dates in different cities, as well as the number of tickets they will sell in each city.4 In the second period, after tickets have been sold for the previously announced tour dates, the band may choose to add additional concerts to the tour and if so, also chooses the number of tickets sold in each “return engagement” based on residual demand after the original tour date. For simplicity of explication, assume that cities are real numbers along a continuum (0, ∞), and that the cities are ordered by decreasing size (demand). Thus, performers choose a measure 3 To be sure, other commitment mechanisms may exist. Quickly changing tastes and age-specific product provide natural obsolescence for many celebrity outputs. Moreover, Bulow (1982) implies that leasing is an optimal strategy for durable good monopolists; however, it is usually infeasible to “lease” a performance experience. Anderson (1985) suggests that sellers can take appropriate positions in futures markets that make lowering prices ex post unprofitable. Recently, futures contracts for specific movies have begun trading on the Hollywood Stock Exchange (http://www.hsx.com). It is not known whether celebrities take advantage of this investment vehicle, and no similar market seems to exist for musicians or other classes of celebrity. 4 I ignore potential non-convexities due to fixed venue sizes, as well as the issue of how to price different seats within the same venue. For an explication of this latter problem, see Rosen and Rosenfield (1997).
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of cities, not a discrete number. This allows for analytic solutions throughout, but all results that follow are robust to a discrete framework. Let the inverse demand in city j be given by pj = A − jxj where pj and xj denote price and quantity of tickets in city j, and A is a positive constant. There are three assumptions implicit in these demand equations. First, note that by construction, there is an inverse relationship between demand and city rank, such that city j is simply 1/j times the size of city 1.5 In other words, the frequency distribution of consumer valuations is constant across cities, so that fans are not differentially concentrated in some cities.6 Second, demand curves are independent across cities. If cities are distant enough from each other so that relatively few fans travel between tour cities to buy tickets, then this assumption is innocuous. Thirdly, the linear functional form allows for analytic solutions below, but neither of the Propositions that follow rely on this assumption.7 Performers face a constant marginal cost for tickets within a given city, which, without loss of generality, is set at zero. However, there is also a separate cost incurred in each city, which includes the psychological costs of stress and of being away from home for another set of performances, as well as the costs of moving and setting up equipment and personnel. Assume that this cost varies with the number of cities toured, N, according to a power function: C(N) =
N 1+μ . 1+μ
If the psychological stress of being away from home and/or the cost of time spent moving between cities increases over time, then μ > 0 is appropriate, making the cost function convex.8 As a baseline case for use as a comparison, suppose that performers have access to some costless perfect commitment technology (PC) that allows them to make binding contracts with fans to add no further dates to the tour schedule in period 2. Then, in the first period the band chooses the number of cities, N, and the number of tickets in each city, xj , to maximize profits by solving the following problem: N 1+μ N PC max π = . (1) [(A − jxj )xj ] dj − N,{xj }j 1+μ 0 The first-order conditions imply the following solutions9 : xjPC =
5
A , 2j
1/1+μ
N PC = ( 41 A2 )
.
This matches well the empirical distribution of city sizes in the U.S. and most other countries (see Gabaix, 1999). A band that was more popular in some cities than others could still fit in this framework if the inverse relationship between city rank and size held within the band’s favored region. 7 Derivation of all results under a general model with demand curves of the form p = p(jx ) is available upon request j j from the author. 8 Even if psychological costs were not convex, the complexity (and hence, computational costs) of finding the travel cost-minimizing tour schedule (a “traveling salesman” problem) increase convexly in the number of nodes (Papadimitriou and Steiglitz, 1998). 9 Here I assume the band is literally a monopolist. Oligopoly is probably a more accurate description of the industrial organization of top-selling artists; nevertheless, it is market power, not strict monopoly, that drives the results. 6
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Hereafter, these will be referred to as the “perfect commitment” solutions since they involve the band setting its profit-maximizing price in each market separately10 and scheduling a tour in which the marginal cost of the last tour date equals the marginal revenue. Note that while all cities j ≤ NPC will be included in the concert tour, this does not imply that these cities must be visited in order of decreasing size.11 Now consider the problem of imperfect commitment. If, in the first period, the band were to offer the perfect commitment quantity of tickets in city j, fans may be concerned that the band will, ex post, announce additional concerts at a lower price in the second period. This concern would lead fans to decrease their demand for the original tour dates, and the band’s potential to extract profits would be thereby lessened. One way of ameliorating this problem is for the band to take no breaks between concerts during the first period. Ex ante, they announce a full schedule of concerts across many cities—a “whirlwind” tour. Thus, fans can rest assured that the band will not extend its engagement in a particular city immediately because it has already contracted to perform in another city, preferably a distant one. This may help explain why bands typically take so few breaks in their concert tours and why their tour schedules often call for a large number of coast-to-coast flights. However, even whirlwind tours may not entirely solve the commitment problem if fans are concerned that the band may schedule a return engagement at the end of the tour. Specifically, consider what would happen if the band did schedule a return engagement to a particular city j in period 2.12 Let rj denote the number of tickets offered for this concert. Given a number of tickets sold in the original run, xj , the band would choose rj to solve the following problem: max(A − j(xj + rj ))rj , rj
which gives the following first-order condition: rj (xj ) =
A − jxj , 2j
and the profit to the band from returning to city j, given the sales of tickets in the original run in city j, can then be written as (A − jxj )2 . 4j Now, the cost of a return to city j at the end of a tour with N dates would simply be the marginal cost of another city, Nμ .
10 Further note that these solutions imply a constant price across cities, a characteristic that finds empirical support in Krueger (2005). 11 Technically, the cost function C(N) is the minimum cost of visiting the first N cities and implicitly assumes that a “traveling salesman”-style linear programming problem has been solved to find the lowest cost permutation of the N cities among all possible permutations. Thus, for instance if the band is touring New York, Los Angeles, and Minneapolis, Minneapolis would likely be the second tour date, even though it ranks third in size. 12 Here, I assume fans do not discount the future, though clearly the model could be extended to include this detail without changing the general results.
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Thus, consumers in city j will be convinced in the first period that the band is not planning a return engagement to their city in the second period if and only if: (A − jxj )2 ≤ N μ. 4j
(2)
Without a perfect commitment technology, then, the band’s first period problem is to maximize profits, as in Eq. (1), but subject to the constraint of Eq. (2) for all cities j: 1+μ N N max πIC = [(A − jxj )xj ] dj − (3) N,{xj }j 1+μ 0 subject to Eq. (2) for all j. For a given value of N, the constraint in Eq. (2) must hold for all j ∈ [0, N]. For some j, the constraint may strictly bind, such that: (A − jxj )2 = N μ. 4j Rearranging the binding form of Eq. (2), the number of tickets sold in any “binding” city, which I will denote xjB , has an obvious relationship with tour length, N: xjB =
A − 2j 1/2 N μ/2 . j
For other j, however, the constraint may not bind. If, for a particular city j, the constraint does not bind, then there is no reason why the band should not choose the perfect commitment ticket quantity: xjNB = xjPC =
A . 2j
In other words, a city in which the constraint in Eq. (2) does not bind is one in which the band can freely produce the perfect commitment quantity of tickets in that city while remaining fully committed to not returning to the city. A city in which the constraint in Eq. (2) does bind is one in which the band would like to sell fewer tickets, but cannot do so in the absence of an enforceable commitment device. Substituting the perfect commitment value of xj into the constraint in Eq. (2), we find that, given the length of the tour N, the cities with non-binding constraints are those that satisfy: A2 ≤ N μ, 16j or in other words, the cities with non-binding constraints are those j > j* , where j∗ =
1 2 −μ . 16 A N
Thus, we can reconsider the imperfect commitment problem specified in Eq. (3): the band must choose N, knowing that on the margin, an increase in N has both direct and indirect effects. The direct effect of increasing N is increased revenues from ticket sales in the additional city and fixed cost expenditures for adding a city to the tour. The indirect effect is to strengthen the band’s commitment not to hold return engagements in more cities in period 2, causing more cities to
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become “non-binding”. In other words, a longer tour allows the band to exert market power in more cities. We can then rewrite the problem in Eq. (3), including the constraint as ∗ 1+μ N j N NB NB B B . (4) [A − jxj ]xj dj − [A − jxj ]xj dj + max N 1+μ j∗ 0 The first integration term is the revenue from cities in which the constraint binds, the second integration term is the revenue from cities in which the constraint does not bind, and the final term is the cost function for tour length. Substituting in the values of xjB and xjNB , the first-order condition to this problem implies 1/1+μ
N IC = ( 41 A2 )
(1 + μ)1/1+μ .
Comparing this solution to the perfect commitment solution, we see that NIC is higher than the perfect commitment solution, NPC , whenever (1 + μ)1/1+μ is greater than 1, or in other words, when μ > 0. Thus, we have shown the following proposition: Proposition 1. Celebrity performers will extend the lengths of their tours beyond the length they would choose with a perfect commitment technology. Corollary. Celebrity performers will undertake performances in which the revenue derived from the performance is less than the cost. Proof. Consider the Nth and final city. This is clearly a “non-binding” constraint city. Then the revenue derived from city N is A2 /4N. Substituting the value of N derived above, the band’s profit in the Nth city is μ/1+μ
( 41 A2 )
[(1 + μ)1/1+μ − (1 + μ)μ/1+μ ].
This expression is negative so long as μ > 0.
Thus, the band “burns out”, performing on a tour that is excessively long, in the sense that on the margin, the costs of being on the road are greater than the profits derived. A further implication of the equilibrium derived above is that, in larger markets, which are more likely to be binding, prices are lower than the monopoly price. This may help explain why a number of empirical studies (for instance, Moore, 1968; Houthakker and Taylor, 1970; Throsby and Withers, 1979; Goudriaan and de Kam, 1983) on arts-related outputs have counter-intuitively found cases of inelastic demand.13 2. Self-destruction Suppose there were a technology available to celebrity performers that had some effect on the magnitude of μ. To be concrete, increasing μ means making the cost function more convex (lowering costs for the initial few concerts while increasing costs dramatically for later concerts). Mind-altering drugs might be considered one example of such a technology. The use of marijuana, LSD, heroin, cocaine, and other drugs can lower the present costs of production by loosening a performer’s inhibitions on stage, helping him to relax, cope with stress, and so on. Of course, 13
Heilbrun and Gray (2001) catalog some alternative explanations for these results.
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abuse of these drugs comes at an often terrible price; the potential for addiction, dangerous overdoses, and loss of self-control and reason are significant. However, these costs are, for the most part, incurred during the later stages of drug use, not at the beginning. Another such cost-function altering “technology” would be the development of a taste for reckless driving or other risky behaviors generally. Most other commentators assume that celebrities who abuse drugs or engage in other such “myopic” behaviors do so because of excessively high subjective discount rates.14 However, the theory presented here provides another avenue for such behavior, one that does not rely on arbitrary differences in preferences. Consider first the perfect commitment case, and now assume that, through the use of drugs or similar behaviors, μ can be costlessly varied over some set [μ, μ]. ¯ The band’s first period problem (analogous to Eq. (1)) is now N 1+μ N max πPC = . [(A − jxj )xj ] dj − N,{xj }j ,μ 1 +μ 0 As before, the first-order conditions for xj and N give the results: xjPC =
A , 2j
1/1+μ
N PC = ( 41 A2 )
.
However, the marginal effect of changing μ is now dπPC N 1+μ 1 = − log N . dμ 1+μ 1+μ Substituting in the value of NPC , we find dπPC 1/4A2 1 2 . A = 1 − log 4 dμ 1+μ Assuming a reasonably high value for A,15 the band would choose the corner solution μ = μ. In other words, with a perfect commitment technology, self-destruction would be only counterproductive. Now let us consider the case without perfect commitment. Analogous to Eq. (4), the band’s maximization problem is now ∗ 1+μ N j N B B NB max [A − jxj ]xj dj + [A − jxj ] dj − . N,μ 1+μ j∗ 0 The first-order condition for N implies, as before: 1/1+μ
N IC = ( 41 A2 )
(1 + μ)1/1+μ .
However, the effect of changing μ is dπIC 1 1 N 1+μ = A2 log N − log N − . dμ 4 1+μ 1+μ 14 See, for instance, Adam Smith’s (1776/1976) discussion of celebrity, in which he designates a particular “contempt of risk” to which young people are particularly prone. 15 In particular, A > 2√e, where e is euler’s constant.
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Substituting in the value of NIC : dπIC 1/4A2 = > 0. dμ 1+μ As in the perfect commitment case, this condition implies a corner solution to the choice of μ. However, now the optimal value of μ is μ. In other words, due to the commitment problem, self-destruction becomes an optimal strategy for the band. This result echoes Bulow’s (1982) finding that monopolist sellers are led to produce goods that are less durable than those of competitive markets. In this case, celebrity performers have an incentive to diminish their own durability purposely as a commitment device to consumers. Celebrity self-destruction thus may be thought of as “planned obsolescence,” in the words of Bulow (1986). 3. Conclusion Celebrities are social leaders, where fashions and trends in speech and action begin. They also serve as visible symbols of the societies in which they live. Their behavior, therefore, deserves special attention and further research from economists, as it has received in other social sciences. Connolly and Krueger (2005) provide additional evidence for the importance of understanding the economics of celebrity in popular music. The question of why celebrities appear so inclined to burn-outs and self-destructive behavior is a problem not inclined to a simple solution. For instance, while celebrities are wealthy, so are Fortune 500 CEOs, yet the stereotypical behaviors of these groups differ markedly. Also, while it may be true that rock stars can use bad behavior as advertising appealing to the preferences of their target audience, many of the great classical composers, whose audience was significantly older and more culturally refined, exhibited similarly self-destructive tendencies.16 Moreover, performing in front of large crowds is very stressful, but many other jobs are also very stressful, yet workers in these jobs do not seem to turn nearly as quickly to drugs and other self-destructive behavior as do performing artists. This paper has suggested the special nature of the output of celebrity performers as an important part of the puzzle and has applied a simple extension of the well-known results related to durable good monopolists to explain this behavior. Further empirical work on the question might focus on the model’s implication that elasticities of demand for celebrity performances should be correlated with city size. In addition, further theoretical work is likely necessary to understand more fully celebrity behavior.
16 Mozart or Paganini, for instance. Of course, not all great composers exhibited such behavior, just as not all rock stars abuse drugs. Handel, Liszt, Rodrigo, and Telemann all composed until relatively late ages for their times. In many other cases, composers died at early ages, though perhaps not always from reckless living: Franz Schubert from syphilis, Tchaikovsky from poisoning, Chopin from consumption, Alban Berg from blood poisoning, Henry Purcell from tuberculosis, and Anton Webern from accidental shooting. All of these, however, it may be argued, are to various degrees preventable forms of death, and these composers made lifestyle choices that increased their probability of early death. For instance, Purcell is believed to have become sick after being locked out of his house by his wife. I am grateful to a referee for suggesting some of these interesting cases.
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