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49 Pricing the arts Michael Rushton This survey presents general rules for arts organizations setting menus of prices for live performances, museum exhibitions, festivals and the like. The problem facing arts organizations is how to set prices to capture as much of the surplus generated by the events as possible. In practice, this means finding a way to offer lower prices to ‘marginal customers’ – those customers highly sensitive to price – while still collecting a higher price from the average customer, who has a relatively inelastic demand for the events. These practices are commonly known as ‘price discrimination’. Firms selling goods in perfectly competitive markets must take prices as given, and so price discrimination cannot be used, but such situations are rare in the arts, as each performance, exhibition or festival has some unique characteristics. Price discrimination can be achieved in two ways. One method is to charge different prices to different groups of customers, where it is easy for the arts organization to identify the group to which each customer belongs. This is known as direct price discrimination, or third-degree price discrimination. A common example is a performance or museum that gives a discount on the ticket price to students or to individuals above a certain age. This practice can be effective only where there is no arbitrage; students must not be able to purchase cheap tickets and resell them to those ineligible for the discount. Consider for example an arts organization selling tickets for general admission to an event, and that seeks to maximize profits (non-profit firms are dealt with below). Suppose marginal cost is constant at MC, and, for now, that there is no capacity constraint; in this situation MC is nearly zero. There are two groups of consumers. Let MRi and qi be the marginal revenue curves and the quantity of tickets purchased by group i = L, H, where L is the price-sensitive group, and the H group has low elasticity of demand. The first rule-of-thumb is that the organization will maximize profits by setting prices Pi such that MRi = MC for each group. The intuition is clear: if for either group MRi > MC, profits can be increased by lowering the price for that group to sell a few more tickets, and if MRi < MC, profits can be increased by raising the price for that group and selling fewer tickets to them. It is as if the organization is selling two entirely unrelated products. Now suppose there is in fact a capacity constraint – there are only Q seats in the venue – such that setting prices according to the MRi = MC rule would entail excess demand. The second rule-of-thumb is that prices Pi should be set such that (1) MRL = MRH, and (2) qL + qH = Q. The intuition is that if we were satisfying condition (2), but MRi > MRj, it would increase profits to lower Pi (and sell to group i a few more tickets) and raise Pj (and sell fewer tickets to group j); what is gained in increased revenue from group i exceeds the loss in revenue from group j. The second method of price discrimination is called ‘indirect’ or ‘second-degree’, and involves offering to all potential customers a menu of prices for different packages of tickets and complementary goods, and allowing customers to effectively sort themselves 350 Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 350 19/05/2011 16:33 Pricing the arts 351 according to the options they choose. An example is a museum that charges one price for general admission and an additional price for a special exhibit, which customers may or may not choose to see. There are a number of applications. Two-part pricing Suppose the organization can charge a general admission price T, and a price P for additional goods that are available once inside, where these additional goods are supplied with a constant marginal cost, MC (suppose there is zero marginal cost associated with general admission). There are many examples in the arts: a museum might have an additional fee for a special exhibit; there might be refreshments or souvenirs available for sale inside a museum or performing arts venue or film theatre; a company might sell hardware for reading digital books or listening to downloaded music recordings, as well as the actual literary or musical content; or, to use the example from the seminal paper in the subject (Oi, 1971), an amusement park may charge an entry fee and a price for each ride. To get started, imagine a simple case where consumers may differ in their willingness to pay for general admission, but there is no discernible way to classify consumers in terms of their demand for ‘rides’ (to proceed with the amusement park example). Then the profit-maximizing strategy is (1) set P = MC, and (2) set T such that MR = 0. In other words, set T to maximize the revenues from general admission, noting that MR and the willingness to pay for general admission is dependent upon P – the higher is the price per ride P, the lower is the willingness to pay for general admission. The intuition is that setting P > MC is inefficient – at the margin there will be some consumers declining to purchase more rides, because of the price, even though their willingness to pay for rides at the margin exceeds MC. If the organization were to lower P, that creates more consumer surplus, which can be extracted by the organization in its subsequent ability to set a higher general admission price T. This model is amenable to direct price discrimination; the organization might want to set a lower T for students or seniors, following the rule of setting T such that MRi = 0 for each group i. But it would remain the case that all groups would be charged the same price P per ride. But now suppose a situation where consumer preferences for ‘rides’ differ between customers, but we have no way of knowing, as we do with direct price discrimination, whether any specific individual is a great fan of rides or quickly tires of them. In such a situation we should depart from P = MC in the following way: if our marginal, price-sensitive customer has a strong (relative to others) preference for ‘rides’, then set P < MC, and capture the associated increase in consumer surplus by increasing T; and if the marginal customer has a low (relative to others) preference for rides, then set P > MC, which will necessitate a lower T. The intuition is as follows. Suppose the first case, where the price-sensitive visitors have a high preference for rides. Then offering subsidized rides is a way to bring them into the venue. The organization won’t need to worry about losing too much of the custom of average customers, since they value general admission highly but have a low demand for rides in any case. When we observe an amusement park offering a high general admission fee but free rides, even though the marginal cost per ride is positive, it is probably the case that marginal consumers have a high preference for lots of rides. Offering rides for Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 351 19/05/2011 16:33 352 A handbook of cultural economics free is not all that costly to the firm, since it is only the marginal consumers who will take advantage of the free rides from opening until closing. Now consider the opposite case, where the typical customer has a greater demand for rides than the marginal customer. Then the organization can entice the marginal consumer into the venue with a low entry fee T, and capture the high surplus of the average customer through charging them for the rides they so enjoy. This provides an explanation of the phenomenon so often remarked upon by laypersons: ‘Why is popcorn so expensive in movie theatres?’ It turns out that marginal, infrequent attendees of the cinema buy less popcorn than those who attend more often. So it makes sense for the theatre owner to lower the price of admission into the theatre, and earn high profits on popcorn sales (Gil and Hartmann, 2009). Bundling Suppose there is some good X, not necessarily an arts-related good, for which there is some demand by price-sensitive, marginal consumers of the arts, but for which there is little interest from the average ticket-buyer for the arts. Then the arts organization might effectively price-discriminate by offering to all ticket-buyers a special discount on good X. This will help lure marginal consumers to the arts venue, but without having to provide any sort of discount in price to the average price-inelastic attendees, who will not be interested in exercising their rights to buy X at a subsidized price. This practice is known as ‘bundling’. As an example, consider a theatre in London’s West End. It might charge high ticket prices, knowing that average theatre-attendees will pay the high price, and offer a ‘bundle’ of a pair of theatre tickets, a pair of tickets on a sightseeing bus, and dinner at a good, but not excellent, restaurant, where the price for the bundle is significantly less (although still above cost) than the price of buying all three goods separately. Here, the marginal customers are tourists, probably on a tight budget, and with many different things on offer in the city to compete for their limited time. They might not be willing to pay full price for theatre tickets, but will find the bundle an attractive option. And the theatre is able to attract their business without lowering the price for ordinary, unbundled tickets that would be purchased by London residents. Differential quality Arts organizations can charge different prices for customer experiences of different characteristics and quality. For example, preferred seats, or preferred times of performances can command a higher price than lower-quality seats or tickets for performances at low-demand times of day or days of the week. Publishers offer different versions of books: hardcovers have the advantage of more durable binding and being immediately available, while paperbacks have the disadvantages of less durable binding and a delay (usually at least a year) in release. Seats in the upper balcony, and paperback versions of novels, are priced to attract marginal, price-sensitive consumers, while seats in the orchestra, and immediately available hardcover books, are priced higher, with the knowledge that some consumers will be willing to pay the higher price in order to obtain the highest quality. The challenge for the arts organization is to ensure that the quality difference is high enough relative to the price differential to avoid having too many consumers opting for the lower-quality/lower-priced alternative. Thus, while it makes sense to charge for the Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 352 19/05/2011 16:33 Pricing the arts 353 lower-quality version a price as close as possible to the marginal customer’s willingness to pay, in general the price of the high-quality version is something less than the maximum willingness to pay by high-demand customers, in order to avoid their ‘switching’ to the lower-priced option. Cheung (1977) adds that high-quality seats might also be ‘underpriced’ to prevent them from going unsold and, subsequently, occupied by those who bought lower-quality seats and then snuck past the ushers into the vacant highquality seats. An interesting empirical study concerns tickets for Broadway theatre, and the halfprice day-of-show tickets that can be bought in person at selected outlets in New York. The day-of-show tickets are lower ‘quality’ in the sense that there is great uncertainty as to whether any will in fact be available on the day of the show, and also in the (deliberate) inconvenience in obtaining them – they cannot be purchased online or by telephone even though such purchases would be easy for theatres to accommodate, since regular tickets can be bought that way. Leslie (2004) used data on sales to find that the theatres were not engaged in profit-maximizing pricing, because the discount for day-of-show tickets was too high – the high price differential combined with the relatively small difference in ‘quality’ was inducing too much ‘switching’ by high-demand customers into purchasing the discounted tickets. Leslie suggests a discount on day-of-show tickets of about 30 per cent would have been more profitable for the theatres. See also Courty (2003a, 2003b) on the timing of price discounts. Quantity discounts It is commonplace for museums to offer single-day tickets or memberships for families that cost less on a per-person basis than would be charged to a single individual, and this is a fairly obvious recognition of the differential willingness to pay by a single individual and set of two parents with children. In addition, discounts are given on the number of events attended: festivals offer menus of different numbers of performances to attend, where the cost per event is lower the more events are purchased; performing arts organizations offer season tickets; and museums offer memberships that lower the effective price per visit. For individuals, diminishing marginal benefits work on two levels here. Consider an opera season, where there are options for tickets to individual operas as well as season tickets. The more operas one sees in a season, the lower the marginal benefit for attending one more. But that reasoning applies equally to purchases of oranges or shirts. In addition, however, if one were to purchase tickets for the opera on an individual basis, the person would first choose a ticket to their favourite opera of the season. If they were to buy tickets for a second opera during the season, the second ticket would be for an opera that is less preferred than the first one, and so the reservation price for that ticket will be less. In general, it is best for the arts organization to ensure that there is a variety of ticketpurchase options, to best capture the surplus from individuals with different willingness to pay not only for a single ticket, but who experience differing rates of decline in marginal benefits. Pricing when profits are not the only goal Suppose a museum or orchestra is run by the state or a non-profit. How would pricing depart from the profit-maximizing rules given above? Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 353 19/05/2011 16:33 354 A handbook of cultural economics It might be the case that prices do not change at all; the goals of outreach to underserved communities might best be reached by maximizing profits from museum admissions or concert tickets, and using the proceeds to fund educational programmes. On the other hand, suppose the goal is simply to increase attendance at the museum or concerts. First note that the means of price discrimination used by profit-maximizing firms already work to the benefit of those with a lower willingness to pay, who can get discounted admission on times and days of the week when demand is typically low, and who can get ‘basic’ admission at a low rate without paying for special exhibits or prime-location orchestra seats. But a state-owned or non-profit arts organization might discount the basic offering even further to achieve their goals of broad dissemination of the arts. Would the discount in prices ever extend to charging a basic admission price below marginal cost? We can imagine a few possibilities: the target customer of the deeply discounted price has a willingness to pay above marginal cost, but this is a means of transferring consumer surplus to that person; or, the target customer’s willingness to pay is below marginal cost, but (1) there are positive externalities associated with consumption, or (2) consumption now will alter preferences and willingness to pay in the future. If none of these factors is present, it is difficult to justify prices below marginal cost. New directions in pricing Arts organizations continue to experiment with new methods of price-setting, owing to the possibilities created by technological change in online transactions and data management. For example, concert tickets can now be sold through online auctions (Halcoussis and Mathews, 2007). And as sports franchises adopt methods of variable pricing through their seasons, where prices adjust according to shifting demand for specific matches, we might also begin to see the same for tickets for live performances in the arts. See also: Chapter 1: Application of welfare economics; Chapter 26: Demand; Chapter 37: Marketing the arts; Chapter 40: Museums; Chapter 47: Performing arts. References Adams, William James and Janet L. Yellen (1976), ‘Commodity Bundling and the Burden of Monopoly’, Quarterly Journal of Economics, 90, 475–98. Ansari, Asim, S. Siddarth and Charles B. Weinberg (1996), ‘Pricing a Bundle of Products or Services: The Case of Nonprofits’, Journal of Marketing Research, 33, 86–93. Cheung, Steven N.S. (1977), ‘Why are Better Seats “Underpriced”?’, Economic Inquiry, 15, 513–22. Clerides, Sofronis K. (2002), ‘Book Value: Intertemporal Pricing and Quality Discrimination in the US Market for Books’, International Journal of Industrial Organization, 20, 1385–408. Connolly, Marie and Alan B. Kreuger (2006), ‘Rockonomics: The Economics of Popular Music’, in V.A. Ginsburgh and D. Throsby (eds), Handbook of the Economics of Art and Culture, Amsterdam: NorthHolland, pp. 667–719. Courty, Pascal (2000), ‘An Economic Guide to Ticket Pricing in the Entertainment Industry’, Recherches Économiques de Louvain, 66, 167–92. Courty, Pascal (2003a), ‘Ticket Pricing Under Demand Uncertainty’, Journal of Law and Economics, 46, 627–52. Courty, Pascal (2003b), ‘Some Economics of Ticket Resale’, Journal of Economic Perspectives, 17, 85–97. Courty, Pascal and Mario Pagliero (2009), ‘Price Discrimination in the Concert Industry’, CEPR Discussion Paper No. 7143. Cowell, Ben (2007), ‘Measuring the Impact of Free Admission’, Cultural Trends, 16, 203–24. Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 354 19/05/2011 16:33 Pricing the arts 355 Currim, Imran S., Charles B. Weinberg and Dick R. Wittink (1981), ‘Design of Subscription Programs for a Performing Arts Series’, Journal of Consumer Research, 8, 67–75. Gil, Ricard and Wesley R. Hartmann (2009), ‘Empirical Analysis of Metering Price Discrimination: Evidence from Concession Sales at Movie Theatres’, Marketing Science, 28, 1046–62. Halcoussis, Dennis and Timothy Mathews (2007), ‘eBay Auctions for Third Eye Blind Concert Tickets’, Journal of Cultural Economics, 31, 65–78. Leslie, Phillip (2004), ‘Price Discrimination in Broadway Theater’, Rand Journal of Economics, 35, 520–41. Leslie, Phillip and Alan Sorenson (2009), ‘The Welfare Effects of Ticket Resale’, NBER Working Paper No. 15476. Maddison, David and Terry Foster (2003), ‘Valuing Congestion Costs in the British Museum’, Oxford Economic Papers, 55, 173–90. Mortimer, Julie Holland (2007), ‘Price Discrimination, Copyright Law, and Technological Innovation: Evidence from the Introduction of DVDs’, Quarterly Journal of Economics, 122, 1307–50. Oi, Walter Y. (1971), ‘A Disneyland Dilemma: Two-part Tariffs for a Mickey Mouse Monopoly’, Quarterly Journal of Economics, 85, 77–96. Prieto-Rodríguez, Juan and Víctor Fernández-Blanco (2006), ‘Optimal Pricing and Grant Policies for Museums’, Journal of Cultural Economics, 30, 169–81. Ravanas, Philippe (2008), ‘Hitting a High Note: The Chicago Symphony Orchestra Reverses a Decade of Decline with New Programs, New Services and New Prices’, International Journal of Arts Management, 10, 68–87. Rentschler, Ruth, Anne-Marie Hede and Tabitha R. White (2007), ‘Museum Pricing: Challenges to Theory Development and Practice’, International Journal of Nonprofit and Voluntary Sector Marketing, 12, 163–73. Rosen, Sherwin and Andrew M. Rosenfield (1997), ‘Ticket Pricing’, Journal of Law and Economics, 40, 351–76. Shiller, Ben and Joel Waldfogel (2009), ‘Music for a Song: An Empirical Look at Uniform Song Pricing and its Alternatives’, NBER Working Paper No. 15390. Shy, Oz (2008), How to Price, Cambridge, UK: Cambridge University Press. Steinberg, Richard and Burton A. Weisbrod (1998), ‘Pricing and Rationing by Nonprofit Organizations with Distributional Objectives’, in B. Weisbrod (ed.), To Profit or Not to Profit, Cambridge, UK: Cambridge University Press, pp. 65–82. Steinberg, Richard and Burton A. Weisbrod (2005), ‘Nonprofits with Distributional Objectives: Price Discrimination and Corner Solutions’, Journal of Public Economics, 89, 2205–30. Further reading Shy (2008) is a comprehensive text on pricing, and Courty (2000) provides a survey of ticket pricing. On differential levels of quality and price discrimination see Rosen and Rosenfield (1997) on tickets, Clerides (2002) on books, and Mortimer (2007) on evidence from VHS and DVD versions of movies. On bundling and subscriptions, see Adams and Yellen (1976), Ansari et al. (1996), Currim et al. (1981), and Ravanas (2008). Connolly and Kreuger (2006) and Courty and Pagliero (2009) consider when popular music performers will use price discrimination. On price discrimination methods for online music downloads, see Shiller and Waldfogel (2009). Leslie and Sorenson (2009) consider pricing strategies when there are secondary markets in tickets. On museum pricing see Cowell (2007), Prieto-Rodríguez and Fernández-Blanco (2006) and Rentschler et al. (2007). Maddison and Foster (2003) examine optimal museum pricing when consumers are willing to pay to reduce crowding. On departures from profit-maximizing pricing when there are distributional objectives, see Steinberg and Weisbrod (1998, 2005). Ruth Towse - 9781848448872 Downloaded from Elgar Online at 11/16/2015 07:01:21AM via Universita Degli Studi Roma Tre TOWSE PAGINATION (M2613).indd 355 19/05/2011 16:33