Public subsidies and the location and pricing of sports.

• Author: Porter, Philip K.

1. Introduction

   Municipal subsidies to private owners of sports team franchises are now so large that sports team subsidies threaten to crowd out local public spending on schools, infrastructure maintenance and expansion, and other high-valued municipal services. Adding insult to injury, many local officials believe that if every city would withhold subsidies to team owners, the teams would stay right where they currently reside and in the very same stadiums. (1) Using public choice analysis, this article examines the effect of government subsidies on the location and pricing decisions of for-profit sports teams. Understanding the role of these government subsidies in sports team location and pricing decisions enables us to identify the winners and losers in subsidy bidding wars among cities and to understand how voter referendums can create suboptimal outcomes for local communities. We also show that municipal subsidies play an important role in sport ticket pricing. By including public choice analysis of subsidies in the pricing decision of team owners, we reconcile a long-standing conundrum in sport ticket pricing: Why do empirical studies consistently find ticket prices in the inelastic region of demand? Although this article focuses on municipal subsidies to sports teams, the importance of linking a firm's location and pricing decisions to the firm's pursuit of voter support for public subsidies may extend well beyond the business of sports to include bidding wars among cities to win corporate relocations.

   This article begins by employing a widely accepted public choice model to determine a region's political support for team subsidies. Integrating this public choice model with private market demand for a sports team allows us to measure and compare the profit and subsidy potential of a region. We then demonstrate that the two are positively related in nearly all cases. Rational team owners locate where the sum of private profits and public subsidies are greatest. Because the maximum subsidy a region will support is directly related to the level of market demand, our model reveals that subsidy bidding among communities anxious to host a sports team will not alter the geographic distribution of teams--a principle we call "location invariance." This principle is analogous to Rottenberg's famous principle describing the invariance in the distribution of player talent to rules governing bidding for players in sport labor markets (Rottenberg 1956). We find that community bidding serves only to redistribute wealth: in our case, from citizens at large to team owners (and players) and from non-fan taxpayers to fans.

   Having established a formal public choice linkage between voter support and ticket prices, we next investigate the pricing decision of a team owner. Team owners can influence the political outcome of a subsidy vote by actions that build fan loyalty and community interest in the team. In particular, owners realize that lower ticket prices stimulate public support for greater subsidies. It is precisely the ability to trade lower ticket prices for increased subsidy support that resolves the troublesome observation that teams frequently price tickets in the inelastic region of demand, a practice that many sports economists have argued reduces profit for team owners. Using the more complete model of ticket pricing developed in this article, we show that inelastic ticket pricing can indeed be profit maximizing, and these "low" prices can also explain the persistent excess demand for tickets when stadium capacity is fixed. In addition, our analysis of sport subsidies suggests that owners will practice a form of politically motivated price discrimination in which persons of exceptional political influence are showered with valuable team-related consumption packages.

   The article begins by examining the location decision. In section 2 we develop a formal public choice model of voter behavior and preferences for sports team subsidies, which leads to the location invariance principle. The article then turns to the ticket pricing decision. Section 3 reviews the sport pricing literature, and section 4 utilizes the public choice model developed in section 2 to explain why profit-maximizing team owners set ticket prices so low. Section 5 offers concluding remarks and suggestions for further research.

2. Subsidy Bidding and the Invariance of Team Location

   Consider two cities or locations that might host a professional team. In the absence of a subsidy offer from either location, the team locates where demand is highest. We wish to know whether competition between locations that results in subsidy offers can alter a team's location decision. (2) Specifically, can a location with less market demand offer a subsidy sufficiently greater than that of a location with more demand to attract a team? Because subsidy determination is a political process, public choice analysis provides the means to determine the maximum subsidy any particular location will support and to identify the winners and losers when cities compete for sports teams through subsidies. We demonstrate that, in general, municipal team subsidies cannot be used by "smaller" cities to lure teams away from "larger" cities, a principle we call location invariance. (3)

   We employ the public choice model developed by Goodman and Porter (1985, 1988, 2004) that characterizes the outcome of a vote--either a referendum or a vote among elected representatives--as a function of the "effort" that proponents and opponents supply to the political process to secure their preferred outcome. Effort can take many forms. Individuals can vote, contribute money, organize get-out-the-vote campaigns, and help to persuade others. A mayor or city official can combine the proposal with other proposals (logrolling), choose the time of the election, and control the agenda. Individuals in the print and broadcast media can provide an influential source of voter information and so on. (4) Because effort, unlike votes, can be continuously varied, the model highlights the different influence individuals can have on the political outcome. In what follows, we assume the subsidy decision is determined by a direct referendum vote; although, the analysis would apply in the same fashion to representative voting.

   Referendum Voting Model

   Suppose a community is composed of N persons who share the tax cost of the subsidy. Individual demand for the sport is [q.sub.i](P, [alpha]), where P is the team-determined price and [alpha] is a shift parameter that accounts for all non-price demand factors. Assume that [partial derivative][q.sub.i]/[partial derivative]P [less than or equal to] 0 and [partial derivative][q.sub.i]/ [partial derivative]a [greater than or equal to] 0. The subsidy's tax cost for individuals is [t.sub.i]S, where [t.sub.i] is voter i's tax share and S is the amount of the subsidy. For any particular ticket price, [bar.P], the net benefit of the subsidy for voter i is

   N[B.sub.i] (S) = [V.sub.i] + C[S.sub.i]([bar.P]) - [t.sub.i]S, (1)

   where [V.sub.i] is any value not related to consumption and C[S.sub.i]([bar.P]) = [[integral].sup.[infinity].sub.[bar.P]] [q.sub.i](p) dp is consumer's surplus for individual i.

   We assume there exists a homogeneous measure of the effort that individuals contribute to the voting process. Let [H.sup.i.sub.yes] and [H.sup.i.sub.no] be the effort that individual i contributes, respectively, in support of or in opposition to a team subsidy proposal:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

   We also assume that y,(x)and ni(x)are continuous functions with [y.sub.i](0) = [n.sub.i](0) = 0. Voter indifference (Smithies 1941) and rational voter behavior (Downs 1957) imply that when alternatives in elections are of nearly equal value, voters will be nearly indifferent between outcomes and so exert little effort to influence elections. Conversely, when the stakes are high, voters will expend greater effort to secure their favored alternatives. Therefore, [y'.sub.i] >0 and [n'.sub.i] < 0. Individuals may differ, then, in their support or opposition for the team subsidy according to the functions [y.sub.i](x) and [n.sub.i](x). For all individuals the greater the net benefit (loss), the greater will be the effort for (opposition to) the subsidy. Assume that voter effort is equally productive in generating "yes" or "no" votes, and that votes are positive monotonic functions of effort. Thus, a subsidy referendum passes if [[summation].sup.N.sub.i=1] [H.sup.i.sub.yes] > [[summation].sup.N.sub.i=1] [H.sup.i.sub.no] and fails if [[summation].sup.N.sub.i=1] [H.sup.i.sub.yes] < [[summation].sup.N.sub.i=1] [H.sup.i.sub.no].

   The maximum subsidy a community will support is the solution to the following constrained optimization problem: Maximize S subject to [[summation].sup.N.sub.i=1] ([H.sup.i.sub.yes] - [H.sup.i.sub.no] > 0. The solution to this optimization problem, [S.sup.*], satisfies the following condition:

   [summation over (F)] [y.sub.f]([V.sub.f] + C[S.sub.f]([bar.P]) - [t.sub.f][S.sup.*]) = [summation over (A)] [n.sub.a]( [V.sub.a] + C[S.sub.a]([bar.P]) - [t.sub.a][S.sup.*]) + [delta], (3)

   where F = {f: N[B.sub.f] > 0} is the set of voters that favor the subsidy, A = {a : N[B.sub.a] < 0} is the set of voters who oppose the subsidy, and [gamma] is an arbitrarily small positive number.

   For any [gamma], [S.sup.*] is unique. To see this, consider Equation 3 when S = 0. The left-hand side of Equation 3 is positive--representing fans with consumer surplus or other value--and the right-hand side is zero. Now let the size of the proposed subsidy increase. For each individual there is a maximum subsidy they will not oppose, defined as

   [S.sup.max.sub.i] = [[V.sub.i] + C[S.sub.i]([bar.P])]/[t.sub.i]. (5) (4)

   As the subsidy amount passes each individual fan's maximum level, that fan moves from set F to set A, causing the set of voters who favor the subsidy to...