Efficient Mechanisms For Public Goods With Use Exclusions
Peter Norman, University of Wisconsin
Most theory on public goods considers the "pure'' case where the collective goods are non-exhaustible and non-excludable. Clearly, these properties don't necessarily go hand in hand and it is easier to think of real world examples of excludable public goods, that is, non-rival goods where it is technologically feasible to exclude individuals from usage. To the extent that copying can be prevented, a recording of a song or anything else that can be stored in digital format is an almost perfect example of an excludable public good. Other examples include cable TV, public facilities with controlled access and excess capacity (parks, gyms, zoos, swimming pools, trains), innovations, services by the police and the fire department, access to databases and gated communities. One can also reinterpret fixed costs of production of private goods as excludable public goods.
Until recently, excludable public goods had only been studied in complete information models. But, excluding consumers from use of a non-rival good is pure waste. The Pareto frontier is the same no matter whether use exclusions are feasible or not and first best can be implemented with, say, the Lindahl equilibrium mechanism, so exclusions seem irrelevant. The literature typically assumes this problem away by restricting the ability to price discriminate. This is dealt with most explicitly by Dreze (1980) who argues that the individualized Lindahl prices are simply not observed in the real world and that there are "many good reasons'' for this, for example the lack of incentives for truthful revelation of preferences. Imposing a uniform price as a constraint, Dreze shows that some consumers are excluded from use if the planner faces a binding budget constraint. The reason for exclusions to be beneficial is that they serve as an imperfect substitute for price discrimination.
While suggestive, the complete information analysis raises the question whether it is possible to formalize any of the "many good reasons'' for why prices can not be individualized. Observe here that asymmetric information in itself is not sufficient. Versions of "pivot mechanisms'' are capable of implementing the first best outcome for a pure public good. Excluding consumers is then again a pure waste of resources.
This paper studies use exclusions in "voluntary bargaining agreements''. I ask how to optimally design mechanisms which besides the usual incentive compatibility constraints also satisfies a voluntary participation constraint and budget balance. Neither of these "extra'' constraints is sufficient to create a role for exclusions in isolation. There are pivot mechanisms that satisfy either constraint (but not both) that can implement the ex post optimal rule, under which there will be no exclusions when the good is provided for the same reasons as in a perfect information environment.
In combination, voluntary participation and budget balance makes it impossible to implement the ex post efficient rule. Better outcomes can then be achieved by excluding some customers from using the public good. The basic intuition is that excluding some low types makes it less appealing for high types to mimic lower types, so the downwards incentive constraints are relaxed.
I focus on results for a large economy. It is then well known that it is "asymptotically impossible'' to provide a pure public good in a voluntary bargaining agreement: the probability of provision in a large economy is near zero. In contrast, I establish a simple non-trivial condition in terms of the distribution of valuations for when the surplus maximizing mechanism generates a provision probability near unity in a large economy with use exclusions.
An appealing aspect of the analysis is that a very simple mechanism can generate a per capita surplus arbitrarily close to that of the efficient mechanism for a sufficiently large economy. This simple mechanism sets a fixed fee for each agent (possibly depending on observables, but not on unobservables) and is similar to monopoly pricing, except that the price need not be the price that maximizes revenue. The good is provided if the user fees collected cover the costs and an agent is allowed to consume the good if and only if she is willing to pay the price. This may be thought of as the obvious arrangement, but solutions to mechanism designs problem are usually not this simple. Moreover, this is not what would happen if the mechanism designer could force consumers to participate or if resources from outside the model were available.
While it is unclear whether participation constraints are relevant for "governments" it seems to be a very natural restriction for "private market arrangements". The comparison with the results obtained by others for the (nonexcludable) pure public goods case thus indicates that one should expect to see private markets for collective goods being able to operate only if consumers can be excluded, which seem to correspond reasonably well with the collective goods actually provided privately in the real world.
The paper focuses on surplus maximizing mechanisms, but little changes when the objective is to maximize profits. The asymptotic condition for when the good is provided is exactly the same, so the good will be provided by a profit maximizing monopolist whenever a benevolent planner would provide the good. However, the monopolist will tend to charge a higher price and exclude more people from use in order to generate higher profits.