On the privatization of excludable public goods.

• Author: Gronberg, Timothy J.

There is a growing interest among state and local government officials in the possibility of privatization of the provision of public goods. In the face of increasing opposition to tax increases and government growth, the transfer of responsibility for the delivery and pricing of services from the public sector to the private sector becomes an attractive option. Assessment of the impact of the transfer from public to private institutional arrangements upon provision of public goods requires that properties of the private and public equilibria be established.

In a series of provocative papers the possibility of private market provision of public goods has been explored. Building upon early contributions by Thompson [10] and Demsetz [5], both competitive [7] and monopoly [3; 2; 4] models have been developed in an attempt to characterize private market solutions to the public goods allocation problem under conditions of costless exclusion. A common conclusion of these recent papers is that private provision of excludable public goods is inefficient. The private pricing mechanism results in underallocation of resources to the production of public goods capacity and in the underutilization of the capacity which is produced. The implication is that, relative to the first-best Lindahl-type public equilibrium, the private equilibrium represents an inferior alternative.

Although the Lindahl solution provides an appropriate benchmark for pure theoretical inquiry, the actual process of privatization develops from a majority voting status quo in the public sector. In this paper we wish to extend the scope of comparative analysis to the case of private market versus majority voting public sector provision of excludable public goods. The concept of public sector equilibrium employed is that of median voter equilibrium. This concept has become a standard within the theoretical public goods literature [1] and has enjoyed some recent empirical support as well [6]. The particular research issue we will address is the identification of conditions under which a majority of the consumer/voters would prefer the private monopoly outcome to the public monopoly outcome. Given the increasing interest in the privatization of public service delivery, the framework of analysis contained in this paper would seem to be of significant potential public policy import. A nonexhaustive list of potential candidate services for monopoly privatization would include roads, waterways, parks, museums, zoos, and airports.

We employ consumer surplus analysis to determine the percentage of voters who prefer the private monopoly solution to the public outcome. Successful privatization requires majority support from an interesting coalition of low and high demanders of the public good. Low demanders can benefit from the voluntary purchase nature of the private regime. High demanders can secure surplus increases in situations where the private monopolist selects a larger capacity than that chosen under public provision. Identification of surplus gains and losses requires specific solutions for the equilibrium prices and quantities (capacities) which obtain under the public and private institutional arrangements. We first generate solutions within a linear demand framework introduced by Burns and Walsh [4]. In this case each individual's preference between monopoly and public provision and hence, the percentage of voters who support the privatization initiative can be determined analytically. The numerical analysis is employed for the cases involving non-uniform distributions of individuals and nonlinear demand functions.

For the linear demand distribution case, we prove that public sector provision always dominates monopoly provision under a majority voting ranking. The requisite coalition of high and low demands in support of the private outcome never materializes. The only support for privatization comes from the low demand group. The dominance result prove to be robust with respect to a variety of demand and distributional specifications.

The negative conclusions concerning privatization above follow from the significant increase in price and concomitant transfer of surplus which accompany the movement from public to pure private monopoly. These price and transfer effects can be ameliorated by considering partial privatization alternatives. We explore three mixed public/private arrangement: (1) price regulation, (2) quantity regulation, and (3) public auction. For the linear demand distribution case we demonstrate the existence of successful privatization proposals for each three mixed schemes. Parameter conditions amenable to passage of the privatization measures are also identified.

The paper is organized as follows. In section I we introduce the basic privatization issue and identify the motivation for coalition formation. In sections II and III we present the basic model structure and define the public and private monopoly solution concepts used in the comparative analysis. Section IV includes the presentation and discussion of the analytical and numerical results of equilibrium quantity and price and the two modes of provision, and the comparisons of majority voters' choice. In section V we describes and analyze the three partial privatization alternatives. Conclusions and suggestions for further research are found in section V.

1. A Simple Privatization Model

   The basic issue raised in this paper can best be introduced within the context of a simple three person community model. Assume that each consumer possess a linear demand curve for the public good, q, of the form. (1) [q.sup.i] = [a.sup.i] + bp, i = 1, 2, 3. If we denote the total quantity of the public good available as q0, and if we allow individual consumption of the pure public service to be discretionary, then the constraint (2) [q.sup.i] [is less than or equal to] q0 must hold.

   Under public sector provision the choice of capacity, qv, will be determined via majority voting. If we assume that the marginal cost of producing is a constant. C, and if we assume that a head tax is used to finance the production costs, then each individual faces a fixed tax price, pv, where (3) [P.sub.v] = C/3. Substituting into [1], each individual determines his most preferred output, [Mathematical Expression Omitted]. If we assume that [a.sup.3] > [a.sup.2] > [a.sup.1], then appeal to the median voter theorem yields [Mathematical Expression Omitted] as the public sector equilibrium output. Each consumer thus faces a tax bill of [p.sub.v] [q.sub.v] = [Cq.sub.v] /3. If the government then employs a zero user charge for access to the public good, individual consumption will equal min [[a.sup.i], [q.sub.v]].

   Suppose now the possibility of provision of q under conditions of monopoly is introduced. Assume that it is both feasible and costless to monitor and to exclude individuals from consuming all of the monopolist's output. Assume further that...