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Price variation over differentiated products is the profit-maximizing solution corresponding to differing price elasticities of demand. A significant exception, the uniform price across different motion pictures at the box office, has been challenging economists for years. Market practitioners justify a persistent uniform pricing regime, with demand uncertainty (i.e. inflexible price helps in eliminating demand uncertainty), quality signal by pricing (i.e. lower priced movies will lead to a significant decline of demand), potential loss of goodwill (i.e. variable pricing will confuse and antagonize patrons), and the agency problem (i.e. exhibitors' major profits come from sales of concession rather than from box office). Orbach (2004) argues, however, that none of the above plays an important role in determining uniform pricing over different
movies. The key objection for price variation comes simply from the distributors' illegal intervention. They enforce uniform pricing by refusing to deal with exhibitors that wish to exercise variable pricing. Furthermore, Orbach and Einav (2007) conclude that if the antitrust prohibition (1) can be enacted more strictly; that is, if exhibitors can really choose an optimal pricing regime, then variable pricing, at least tiered pricing over regular and event movies, should be the profit-maximizing choice of movie theaters and would benefit patrons. Given their assertion, a premium added on regular admission price at box office for event movies such as Spiderman 4 will benefit the movie theaters.
This paper considers the agency problem associated with concession sales between the exhibitors' profit maximization and the distributors' revenue maximization to examine the assertion in Orbach (2004) and Orbach and Einav (2007). The model derived in this paper explores the nature of price rigidity at the current uniform price regime. It develops the criteria for both exhibitors' and distributors' preferences over the tiered pricing for regular and event movies, with and without concession sales. The uniform price regime is shown to be optimal for the exhibitor's profit maximization from both box office revenue and concession sales together, without the distributor's intervention. High concession profit not only defends uniform pricing for the exhibitor, but also relaxes the agency problem between the exhibitor's profit maximization and the distributor's revenue maximization. Unless many event movies are expected to be blockbusters, tiered pricing cannot benefit either exhibitors or distributors. The condemnation of distributors in Orbach (2004) and Orbach and Einav (2007) is undeserved. In addition, the model shows how the distributor can eliminate an agency problem by its choice of the share of gross box office revenue and the minimum dollar amount collected per seat.
The paper is organized as follows. The next section reviews the literature and clarifies how to represent demand for analyzing uniform vs. two-tiered pricing in the motion picture industry. The theoretical model develops the profit-maximizing criteria for both exhibitor and distributor to favor tiered pricing, given the estimation for the event movie's popularity. The criteria varies significantly with and without concession sales, and a simple example illustrating the findings will follow. The final section summarizes and provides possible extension for the future.
Literature Review
Although few empirical studies (Cheung 1977; Groves 2000) from the foreign movie theater industry have proven that price variation increases exhibitors' profits from the box office, concession sales have not been considered in these studies. Luis and Rodriguez (1992) explore how concession pricing affects the movie price, and they conclude the exhibitor's profit comes substantially from over priced (i.e. above its marginal cost) popcorn. They do not explain why the exhibitors stick with the motion picture industry: (a) no direct or indirect intervention in admission price setting by producers and distributors; (b) no licensing negotiations except on theater-by-theater and movie-by-movie bases; and (c) no vertical integration between the Paramount defendants and exhibitors. uniform price at the box office. Marburger (1997) considers concession sales theoretically, to explain the inelastic demand of performance goods which is against the clear pursuit of a price searcher's profit-maximizing pricing by charging at the segment of elastic or unitary-elastic demand. (2) The paper confirms several empirical findings (Noll 1974; Whitney 1993; Whitney 1988) about the demand inelasticity for performance goods if the exhibitors can charge varied optimal ticket prices. However, none of the above considers the agency problem associated with concession sales, to examine the exhibitor's and the distributor's incentives for retaining the uniform price.
Any attempt to explore box office pricing over movies will face a key difficulty: demand uncertainty. The classic phrase in Goldman (1983, p. 39), Nobody Knows Anything, about the predictability of a movie's success, is confirmed by Walls (2005) associated with an infinite variance in the conditional distribution of films' returns. However, when the focus is shifted from individual movies to two tiers of movies, regular and event, the demand uncertainty can be reduced significantly. As Orbach (2004, p. 356) notes, "...empirical evidence shows that demand uncertainty is not as great as particularly argued and that the determinants of success in the industry are not totally random." Market practitioners may be unable to predict box office revenues for most movies, but identifiable event movies are likely to perform much better than the regular movies at the box office. De Vany and Lee (2001) conclude that if there is only one good (event) among many regular movies, a large opening audience for the event movie will initiate an information cascade to generate revenues with stronger demand as a result. Basil (2001) tests empirically the US adult moviegoers with video rental competition, and concludes that the demand of new release event movies is more inelastic. Patrons are willing to pay a higher price to see event movies in theaters. In addition, both Orbach (2004) and Orbach and Einav (2007) have conducted a survey with practitioners to show that even if uniform pricing is not the profit-maximizing choice of exhibitors, they still hesitate to be the first mover to apply variable pricing across different movies. The potential loss of goodwill, particularly when competitors maintain the uniform pricing scheme, discourages the attempt of price increase for event movies. On the other hand, lowering the price for movies is believed to convey quality signals although there is no empirical test to prove it. The demand in which the price is lower than the current uniform price will shift down as another weaker demand segment. All the market characteristics and findings in the above literatures support the feasibility to distinguish the differentiated demands between regular and event movies, and to break the demand on movies into two segments at the current uniform price.
The Model
Consider that an exhibitor is playing only two movies, one regular and one event, in its multiplex. Demands for regular and event movies are De and DE respectively. The current uniform price breaks each demand curve into two segments. The upper, the more elastic segments, [D'.sub.R] and [D.sub.E], reflects the consideration of potential loss of goodwill when the rivals are assumed not to match a rise in price. The lower segment reveals a possibly weaker demand by the quality signals from price reduction. It is the game-strategic reaction from competitors and similar to the kinked demand model. Developed by Sweezy (1939), the kinked demand assumes that the firm reacts quickly to match the rival's price cut, but has little or no motivation to match a price increase. Although a number of criticisms question the kinked demand's silence on how the initial price is set, the unexplained prevailing price just reflects the puzzle of uniform pricing at the box office.
At the current uniform price, [P.sup.*], the point elasticities for both movies with [D.sub.R] and [D.sub.E] are assumed to be inelastic and the latter is more price-inelastic than the former, in harmony with the empirical findings in Cameron (1986). (3) The total quantity demanded for both movies in a given period is assumed to equal 1 (i.e. 100%) for simplicity. The proportion (percentage) of quantity demanded on the event, denoted by [alpha], also decides the quantity demanded on the regular as 1-[alpha]. The exhibitor can easily adjust the number of screens to match the percentage of quantity demanded over movies. From the preview opening, or from estimates by market practitioners, [alpha] >0.5 defines the event movie. Figure 1 shows the differentiated demand curves over movies.
For demand estimation, there exists a maximum tiered premium function, which predicts the highest movie price charged above the current uniform price for either the regular or the event, as a strictly increasing function in the expected proportion of box office sales:
f(x), where f' [??] 0, f" [??] 0, and f(0.5) = [P.sup.*] ; (1)
x=[alpha] for the event movie and x = 1 - [alpha] for the regular movie.
Consistent with De Vany and Lee (2001), the first and second derivatives of the premium function define the effect of an information cascade which increases demand by more willing patrons for the movie. For the event, more observed or expected patrons in the same period (i.e. [alpha] > 0.5) will induce a higher maximum premium compared with that for the regular. To ensure the demand-elastic segment above the kink for the regular movie (i.e. 1- [alpha] <0.5) corresponding to the consideration for potential loss of goodwill and competitors' non-matching behavior, the maximum premium is capped by f (0.5)= [P.sup.*], which implies that the highest possible prices charged for the regular movie cannot be greater than twice the current uniform price. The maximum movie prices, [[bar.P].sub.E] and [[bar.P].sub.R], should satisfy
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