ON THE ASSUMED INELASTICITY OF DEMAND FOR THE PERFORMING ARTS

Marianne Victorlus Felton

For the past decade, cultural economists have been telling per- forming arts organlratious that they can increase their box office receipts by raising ticket prices; or, as an economist would put it, that their price elasticity of demand is inelastic. This conclusion has in- variably been reached for groups of companies, either for a specific medium such as orchestras, or across a number of performing mediums (Withers, 1980; Touchstone, 1980; Lange and Luksetich, 1984; Throsby and Withers, 1987). Furthermore, these studies have treated sub- scribers and nonsubscribers as a single entity. The implication is that, as with socks, "one size fits all."

This paper attempts to examine this claim more closely. The rationale for doing so is the concern that, what may be true for companies as a group, may not hold for an individual company. Since pricing decisions are made at the company level, preaching the gospel of inelasticity will give false assurances of rising box office receipts to companies whose price elasticity may, in fact, be elastic, or greater than one. These companies would experience declining box office receipts since they would lose a greater percentage of their customers than the percent increase in their price. Evidence that this might be the case for some companies has been encountered in some previous research (Lange and Luksetich, 1984; Greckel and Felton, 1987; Felton, 1989).

Three kinds of U.S. companies were chosen for this investigation: 24 orchestras, 14 ballet companies, and 12 opera companies. An attempt was made wherever possible to choose more than one kind of company for anygiven city. Using pooled time series and cross section data for each medium separately, along with dummy variables to represent the individual companies, a price elasticity of demand is

calculated for each company. Income elasticities and, where possible, cross elasticities of demand are also investigated. Previous work with

- opera data (Felton, 1989) revealed that season subscribers do react to ticket price changes while non-subscribers do not. Thus, I decided to limit the present investigation to demand for subscription tickets.

The Role of Econometrics

The methodology used in this paper, indeed, employed by many economists to study a large variety of subjects, has in the past been the cause of some friction between cultural economists and arts ad- mlnistrators as well as some of our colleagues in other social sciences. The tool of econometrics, sometimes referred to as "number crunch- ing," is exactly that, a tool. Its purpose is to uncover some crucial information which might otherwise remain hidden, much as a physician uses his stethoscope or a dentist his probe. In the hands of a skillful practitioner, some important relationships can be discovered with this tool. It is certainly an improvement over conjecture.

The objection on the part of artists and arts administrators has mainly been that it is crass to try to reduce the arts to numbers. Agreed. How could one ever express the lyricism of a Mendelssohn violin concerto, the heartbreak of a Traviata, the flirtatiousness of a Coppelia, the majesty of a Mahler symphony, or the energy of a Yo-Yo Ma in numbers? But that is not the object of the exercise.

The objections on the part of some social scientists are somewhat more difficult to comprehend. I believe they can largely be explained by a mixture of distrust, misunderstanding, and perhaps a bit of fear of the unknown. It is human to distrust things we do not understand. I, for one, drive a car whose mechanics I will never be able to explain, fly in airplanes even though I don't understand the principles of flight, and work on a computer whose inner workings escape me. I simply have to trust that, when competently operated, these vehicles will function as they are supposed to. Econometrics is a similar vehicle, and it too functions well when skillfully used. The skill comes in building the right model; i.e., in choosing the right level of abstraction and the right variables to "explain" the behavior of whatever is under examination.

The misunderstanding comes with the belief that, once a satisfac- tory model has been selected, we have all the answers. Far from it! All we have uncovered are the "what" and the "how much." But we still do not know the answer to the most important question of all: "Why?" Nor do we necessarily know how to use our results. This is where the

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expertise of the sociologist, the psychologist, the historian, the political scientist, the finance and marketing experts, and the arts ad- ministrators must take over.

Presumably we are all working towards the same goal, not only the survival, but the flourishing of the arts, without which fife would be very glum indeed. We need all the talents we can muster to achieve this end. If numbers have something to contribute, why not use them?

The Model

The model employed is the usual microeconomic demand function where the number of subscription seats sold is assumed to vary with ticket price and income. Additional variables were included to try to capture the effects of the number of performances, marketing efforts, the cost of attending a different kind of performance, and the size of the city in which the company is located. The model may be repre- sented as follows.

SUBSCRIBit --- f(Pit, Yit, Nit, Mit, SUBPit, POPit, Dit, Sit)

where:

SUBSCRIBit = the number of subscribers to the home season of the i th company during the tth season

Pit = the real average subscription ticket price of the i th company

Yit = the real per capita income for its metropolitan area

Nit = the number of home performances

Mit = real marketing expenses

SUBPit = the average real subscription price of attending another performance medium in the same city

POPit = the population of the company's metropolitan statistical area (In the ease of larger cities, the PMSA was used)

Dit = a dummy variable reflecting the presence of a particular company, where Dit = 1 for the i th company, i = 2 ...... N; 0 otherwise

Si t = a dummy variable to capture differences in slope across com- panies, where Sit = Dit * Pit, i - 2, .... ,N

For the orchestra and ballet data, the number of subscribers or number of subscription seats sold was used as the dependent variable instead of attendance. This was done for two reasons. Since our

primary interest here is what happens at the box office, what matters is how many seats are sold, not how many people show up for the

-performance. Second, attendance figures-are generally less reliable and, except for opera companies, no distinction is made between subscribing and non-subscribing attenders. For opera companies, sub- scriber attendance was the only data available.

The average subscription price was calculated by dividing total subscription revenue by the number of subscribers. All real dollar figures were arrived at by dividing the nominal dollar figures by the fixed weight consumption price index of the National Income and Product Accounts.

It was expected that subscriber attendance would be negatively related to subscription price, and positively related to income, the number of performances, marketing expenses, and population. No a priori judgment was made with respect to the effect of the price of attending a different type of performance. It was deemed equallylikely that the two experiences would be substitutes or complements.

The Data

The American Symphony Orchestra League was kind enough to provide all the orchestra data required, upon being given assurance that the confidentiality of all data pertaining to individual companies would be strictly guarded, and that the results of the investigation would be made available to them. The data for the 24 orchestras chosen span the nine years from 1979 through 1987. The orchestras were chosen partly on the basis of their prominence, partly to match up with the cities for which opera and ballet data were available. An attempt was made to take a balanced sample from different budget categories and from various regions of the country.

Dance/USA cooperated in making ballet data available, based on the same assurances. The dance companies selected were the only ones for which at least five years of data were available. Six years were included, 1982 through 1987. The opera data were partially obtained from Opera America, and for the most part include the seven years from 1979 through 1985. Demographic and economic data of the geographic areas were obtained from published government sources.

Methodology Each data set was first divided into separate budget groups. For

orchestras and ballet companies, the criterion used to assign categories

was total concert income. Orchestras were divided into four budget groups. Group 1 includes the five "mega-orchestras" with concert

- income of $9 million and above during the 1987-88 season; group 2, the other "major" orchestras with incomes of at least $2 million but under $9 million; group 3, the "regional" orchestras with incomes of between $1 million and $2 million; and group 4, the "metropofitan" orchestras with incomes under $1 million. Ballet's budget group 1 includes com- panies with 1987 total ticket revenues of over $1 million; budget group 2, those with revenues of up to $1 million. For opera companies, budget groups are divided by total expenses. Budget group 1 includes compa- nies with expenses above $3 million during the 1985 season, budget group 2, those with expenses between $1 million and $3 million. No smaller opera companies were included in the sample.

Ordinaryleast squares (OLS) regressions were in'st run separately on each budget group in each medium without dummyvariables. Little muiticollinearity was encountered, but autocorrelation of the error terms was si~ificant. A scattergram of the number of subscribers with subscription price confirmed the suspicion that both intercepts and slopes tend to vary among companies. Further plots of the data revealed that some of the relationships were nonlinear. Additional tests identified the growth model to be the best fitting model. This suited our purposes perfectly, since a double logarithmic transforma- tion of all variables except intercept d-mmles would render the model linear, and the resulting regression coefficients would represent the elasticities in which we are interested.

OLS regressions including dummy variables were then run. Cal- culation of the F statistic confirmed in each case that the gain in accuracy outweighed the loss of degrees of freedom. The problem of autocorrelation also disappeared, but examination of the error terms revealed heteroscedasticity across companies. This was not unex- pected, since the accuracy of the data varies from company to com- pany. To resolve this problem, weighted least squares (WI.S) regres- sions were then run for each budget group of each performing medium, using the standard deviation of the OLS residuals as the basis for the weights. The results are shown in Tables 1 and 2.

The Regression Results

Table I lists the regression results of the WLS double-log model for the four orchestra budget groups. The model appears to be more than adequate, as evidenced by the high R square, high F, and low

standard error. The Durbin-Watson statistic confirms the absence of autocorrelation of the error terms. Each of the coefficients exhibits

- the expected sign with the exception of population for Budget Group 3, which turned out not to be sionificant.

The price coefficients are significant at the .01 level for each of the budget groups. The coefficients represent the price elasticity of demand for the reference company in each group (the company not assigned a dummy variable) -- the Boston Symphony in group 1, the National Symphony in group 2, the San Diego Symphony in group 3, and the Tulsa Symphony in group 4. For each of these companies, the elasticity is inelastic (less than one), but bordering on unit elasticity, or one, for San Diego. A coefficient of -.90 for Boston means that a one percent change in the real (inflation adjusted) average subscription price is associated with a 0.9% change in the opposite direction in the number of subscription seats sold; or, a ten percent increase in price is associated with a nine percent decrease in the number of seats sold. As long as the percentage drop in seats is less than the percent increase in price, box office revenue will rise. Interpretation of all other coeffi- cients is such that each represents the percent change in the dependent variable if the independent variable changes by one percent.

Income per capita was sitmificant at the .01 level for budget groups 1 and 2, but not significant for groups 3 and 4. This is not surprising, since subscriptions to the smaller orchestras are much more affor- dable. Consequently, we would expect income to be less of a factor in deciding whether or not to become a subscriber. Higher income elasticities than those encountered would have been more beneficial for the orchestras.

As expected, the number of concerts turned out to be highly significant for each of the four budget groups. More concerts mean more subscription seats sold, although it is not known whether the additional revenue would be enough to cover the cost of additional concerts.

Marketing expenses were only si~mificant for budget group 2. Even here, the size of the impact as measured by the coefficient of .14 appears small.

Population was dropped from budget group i because of a col- linearity problem. For groups 2 and 4, the number of subscription seats sold was positively associated with population and the coefficients are

TABLE 1

ORCHESI*RA DEMAND FUNCrlON ESTIMATF~

Dependent Variable: Number of Subscription Seats fold I I I II I II

Budget Group 2

80

Budget Group 3

48

Budget G r p u p 4

28

.981 .951 .946

199.66.* 62.42** 44.04**

Standard . 087 Error

1.91

Budget Group X

n 45

Adj. R 2 .948

F 67.78**

.043

Durbln- 2.14 Watson I

-.900"* (-4.59) .767** (4.47)

.528"* (4.71)

.051 (1.25)

4.604** Constant (3.02)

Notes:

Subscrlp- t ion Price

Per Capita Income

Number of Concerts

- . 4 2 8 " * (-2.e9) 1.048"* (3.97)

.510"* (5.09)

.142"* (3.73)

1.171"* (3.95)

-4.501.* ( -2-9,4)

Marketing Expenses

Population

�9 110 .132

1.95 2.01

-.961"* (-5.52)

.758 (1.54)

.380"* (3.75)

. 080 (1.1o)

-.405 ( - 0 . 7 3 )

5.432 ( 1 . 3 8 )

Numbers in parentheses represent t-values ** Significant at the .01 level * Significant at the .05 level # Significant at the .10 level I Derived from O1_5 regressions

-.890"* (-3~83)

.510 (0 .38)

.987"* ( 4 . 4 0 )

.019 (0.28)

2.802* (2.74)

-. 680 (-o.o6!

large, especially for group 4. Since population was not a factor for group 3, no impfieations are attached to the negative sign.

The price of a ballet or opera ticket was not included in this model since not enough years of data were available for either medium. Therefore, no cross elasticity could be calculated.

Table 2 shows the regression results for the ballet and opera companies. Because of the smaller number of companies and fewer years of data, the results are somewhat more nebulous, especially for the smaller companies. Subscription price and number of performan- ces were sitrnificant for both budget groups 1. Income and marketing expenses were significant for ballet companies, but not for opera companies. It should be noted that the coefficient for marketing was small but negative for the larger ballet companies. By using orchestra prices as the substitute price, it was possible to calculate a cross elasticity of demand for ballet companies. The result was positive and significant for the group of larger ballet companies, indicating that ballet and orchestra subscriptions are substitutes; i.e., as orchestra subscription prices rise, more people subscribe to the ballet instead. For the smaller companies, the coefficient was negative. Had it also been si~ificant, it would have revealed complementarity. With the relatively lower cost of attendance in smaller cities, such a result would have been plausible. Unfortunately, not enough orchestra prices were available to match up with the opera companies.

Price Elasticities of Demand

The summary table lists the average price elasticities of demand for each of the budget groups. It confirms the finding of inelastic demand of previous research. It also confirms the Lange/Luksetich (1984) result of somewhat higher elasticities for smaller orchestras.

AVERAGE PRICE ELASTICITIES OF DEMAND

Orchestra Ballet Opera

Budget #1 -.57 -.29 -.28

Budget #2 -.62 -.13 -.56

Budget #3 -.75

Budget #4 -.95

TABLE 2

BALLET AND OPERA DEMAND ~3NCTION F.ffFIMATES

Ballet Dependent Variable: Number of Subscribers Opera Dependent Variable: Subscriber Attendance

B~I~ Companies

Budget Group 1

Budget Group 2

n 29 33

Adj. R z .989 .761

F 163.09-* 8.29*

Standard .203 .119 Error

Durbin- 2.95 2.71 Watson I

Subscrlp- -.481. -.993 tion Price (-2.36) (-1.17)

Per Caplta Income

Number of Perform- ances

3.088** (9.39)

.119. (2.21)

-.084" ( -2 .82)

.670* ( 2 . 9 6 )

Marketing Expenses

Substitute Price

.457 ( 0 . 6 6 )

-.061 ( -0 .23)

.258 Population (0.23)

Opera Companies

Budget Budget Group 2 Group 1

32 30

.954 .984

38.44** 119.25.*

.352 .044

2.27 2.85

+.271 -.672# (0.88) ( -1.80)

1.868" .306 (2.16) (0.43)

�9 148 .295# (1.20) (2.08)

.368* .159 (2.20) (-1.30)

- .083 ( 0 . 7 8 )

-1 .253 -2.093 (-0.88) (-1.44)

-9.286 6.189" ( -0 .25) (2.65) Constant

- 20 .55 " * ( -8 .74)

Notes: Number of parentheses represent t-values ** significant at the .01 level * significant at the .05 level # significant at the .10 level

Derived from OLS regressions

2.348 ( 0 . 7 6 )

Table 3 exhibits the individual price elasticity of demand of subscribers for each individual orchestra, ballet company, and opera

-company. Scanning the columns, it becomes immediately apparent that the elasticities vary widely within the same medium and budget group. For example, for the "mega-orchestras," they run the gamut from -.10 for the San Francisco orchestra to -1.18 for the New York Philharmonic. (The minus sign, normally dropped, has been retained here because some of the elasticities turned out to be positive.) Each group cont~in.~ at least one company with elastic demand.

An even more surprising result is the one of positive elasticities, defying the law of demand. Where these coefficients are not sig- nificant, the logical interpretation is that price is of little importance compared with other considerations such as available leisure time and expected quality. Where the positive coefficient is significant, how- ever, it may well be that price is being perceived in some sense as a measure of quality. Throsby demonstrated that "quality characteristics are much more important influences on demand than price." (Throsby 1982) The real challenge, of course, is to explain why the elasticities differ, not only among companies of similar size and in the same performing medium, but across companies in the same city. Economists have identified a number of determinants of elasticity." the availability of substitutes, the size of the expense in proportion to one's income, and whether the good is a luxury or a necessity. Based on the first two criteria, one would expect to fred greater elasticity in the larger cities. Not only does the opposite seem to be the case, but it doesn't begin to explain the kinds of diversity uncovered in this paper. Surely the degree of loyalty subscribers feel towards the organiTation must be considered a factor. But what elicits loyalty? Is it the charisma of the conductor? the quality of the performers? the repertoire? the am- biance of the hall? the sociability of being with friends? The answers to these and other questions will have to await further research.

Conclusions

This paper has demonstrated that, while average price elasticities of demand for the performing arts are inelastic as claimed, elasticities vary widely among companies. There are many with elastic demand. One size does not fit all. Consequently, care must be taken not to give the impression that higher box office receipts can be achieved by raising subscription ticket prices. Such a policy could prove unfor- tunate for companies whose price elasticity of demand is greater than one. Some of the mystery has also been removed from the income

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TABLE 3

c~Y

New York Chicago B o s t o n P h i l a d e l p h i a San Francisco

Cleveland Pittsburgh Dallas Houston Seattle

Washington, D.C. Atlanta Milwaukee

PRICE ELASTICITIES OF DEMAND

ORCHESTRA BALLET

Budget #1 Budget #1 -1.18 - .41 - .24 j - .90,, r - .48 r

- . 43 ' - . 86

- - . 10" - 1 . 13"

B u d g e t #2 + . 2 0 " - . 5 2 - . 80

- . 64

- . 88 +1 .34"

- 1 . 2 0 ' - . 7 7

B u d g e t #2 - .43" *r + .76 - .96 s - .61 I - ~ + .27 t

Baltimore

San Diego Louisville Charlotte Phoenix Hartford Orlando

Tulsa Akron Little Rock Winston-Salem Portland, OR Cincinnati

- . 3 3

B u d g e t #3 - . 9 6 * * r - . 99 - . 61"

- . 90

- . 41 *

- . 19 s - . 52

- 1 . 0 2

B u d g e t #4 - . 8 9 * * r - . 67 - . 02

-1.04 -1.21 + .40

(1) Belongs to Opera Budget Group 1 * * Signif icant at the .01 level * Significant at the .05 level

# Signif icant at the .10 level r Reference company �9 significantly different from the reference company

OPERA

B u d g e t #1

- 1 , 0 7

+ . 5 9 + . 4 6 - . 6 7

- . 2 9

B u d g e t #2 - , 2 8

- . 6 7 [ r - , 93 r - 1 . 3 0

+ , 0 8

- . 77

- . 16

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elasticities of demand, at least as they pertain to orchestras. They are positive, but si~ificant only for the larger orchestras. Some tantalizing

-evidence has also been uncovered with respectkto cross elasticities of demand, results which invite further research.

Indiana University Southeast

References

Felton, Marianne V. "Major Influences on the Demand for Opera Tickets," Journal of Cultural Economics, 13,1 (June, 1989) pp. 53-64

Greckel, Fay R. and Marianne V. Felton, "Price and Income Elas- ticities of Demand: A Case Study of Louisville," in Economic Efficiency and the PerfonningArts, Nancy K. Grant, W. S. Hendon, V. L. Owen (eds.), Akron: Association for Cultural Economics, 1987, pp. 62-73.

Lange, Mark D. and William A. Luksetich, "Demand Elasticities for Symphony Orchestras," Journal of Cultural Economics, 8,1 (June, 1984) pp. 29-48.

Throsby, C. D., "Perceptions of Quality in Demand for the Theatre," in Markets for theArts, James L. Shanahan, W. S. Hendon, I. H. Hilhorst, J. van Straalen (eds.) Akron: Association for Cultural Economics, 1983, pp. 6-21.

Touchstone, Susan K., "The Effects of Contributions on Price and Attendance in the Lively Arts," Journal of Cultural Economics, 4,1 (June, 1980) pp. 33-46.

Withers, Glenn A., "Unbalanced Growth and the Demand for Per- forming Arts: an Econometric Analysis," Southern Economic Journal, (January, 1980).

Note: an ealier version of this paper was presented at the cultural economics meetings in Sweden in 1990.

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