Economies with Multiple Public Projects

This paper discusses a general equilibrium model of an economy with multiple separately provided public projects. We assume an additively separable cost structure and consider valuation equilibria with separated finance systems, one for each collective good. Under non-Euclidean representation we show the decentralization of Pareto efficient allocations by valuation equilibria and the equivalence of the core and the set of nonnegative valuation equilibria. In the case of Euclidean representation, every Pareto efficient allocation is shown to be supported as an affine valuation equilibrium that is characterized by a personalized price per unit of each public good and a personalized lump sum tax or subsidy. These results complement and clarify already established insights into Lindahl pricing and its generalizations developed in the literature.     

Voluntariness and efficiency in the provision of public goods

This paper presents a characterization of Lindahl allocations which makes no reference to personalized prices. Lindahl equilibria are characterized here by two conditions: Pareto efficiency and a voluntariness condition. Voluntariness requires that no consumer may benefit from a reduction in his contribution if this means that the vector of public goods must be reduced in the same proportion. The intersection of the (large) set of voluntary allocations and that of efficient ones turns out to be (under differentiability) the set of Lindahl allocations.     

A graphic representation of the Nash and Lindahl equilibria in an economy with a public good

In an economy with a public good the noncooperative Nash equilibrium and the cooperative Lindahl equilibrium are represented graphically. The Nash equilibrium is shown to be non-optimal, while the Lindahl equilibrium is shown to be optimal. Simple stability analyses are undertaken. Finally, the two equilibria are compared. It appears that more public good will be allocated in the Lindahl than in the Nash equilibrium, and that in a sufficiently large economy a transition from a Nash to a Lindahl equilibrium will be advantageous for everyone.     

One-sided private provision of public goods with implicit Lindahl pricing

We consider a sequential game in which one player produces a public good and the other player can influence this decision by making an unconditional transfer. An efficient allocation requires the Lindahl property: the sum of the two (implicit) individual prices has to be equal to the resource cost of the public good. Under mild conditions this requires a personal price for the providing player that lies below half of the resource cost. These results can, for example, justify high marginal taxes on wages of secondary earners.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Economics of public good provision: auditing, outsourcing, and bribery

Abstract .  This study investigates a government's contracting decision to audit or outsource the provision of a public good given a potential hidden bribe and information asymmetries. The key findings are the following. First, the bribe and price of the public good are increasing in the corruptibility of the department. Second, the bribe is decreasing in the firm's bargaining power. Third, a bribery equilibrium exists when the department's corruptibility is sufficiently high given the firm's bargaining power. A bribe involves extortion or a compensatory payment depending on the department's corruptibility. Only a compensatory bribe affects the department's contracting decision.     

Existence,uniqueness and some comparative statics for ratio and Lindahl equilibria

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost share or ratio equilibrium. Finally, we indicate how it may be exploited to facilitate comparative static analysis of Lindahl and cost share equilibria.      

Free Riding and Consistent Conjectures in the Provision of Public Goods: An Experimental Study

The aim of this paper is to examine free riding and consistent conjectures in the provision of public goods. In this research, a Lindahl optimum is never reached. The prediction that public goods will inevitably be under-supplied is proven. With repetition, the subjects' contributions move toward the free riding level instead of the Lindahl optimum. However, a surprising observation is that the public goods provided sometimes increase with time. Economists and males behave more selfishly than other people. Most people expect matching behaviour, and most of them do behave accordingly. The extent to which people will match is overestimated, therefore expectations about the amount of public goods and the amount of actually provided public goods will be revised accordingly and tend to decline over time.     

The Asymptotic Voluntary Provision of the Pure Public Goods

This paper analyzes the voluntary provision of the pure public good in a sequence of finite economies. The boundedness of this provision is established under very weak conditions. The Cournot–Nash provision of the public good is bounded. In contrast, the Lindahl provision is unbounded but the proportion of private good devoted to its production may be infinitesimal. Several examples are provided to relate this paper to the literature.     

Opacity in bargaining over public good provision

We consider ultimatum bargaining over the provision of a public good. Offer-maker and responder can delegate their decisions to agents whose actual decision rules are opaque. We show that the responder will benefit from strategic opacity, even with bilateral delegation. The incomplete information created by strategic opacity choices does not lead to inefficient negotiation failure in equilibrium. Inefficiencies arise from an inefficient provision level. While an agreement will always be reached, the public good provision will fall short of the socially desirable level. Compared with unilateral delegation, bilateral delegation is never worse from a welfare perspective.     

Stable Provision vs. Cournot–Nash Equilibria in Pure Public Good Economies

Shitovitz and Spiegel (1998, Journal of Economic Theory 83 , pp. 1–18) demonstrated that in pure public good economies, for some consumers the Lindahl consumption bundles can be inferior (utility-wise) to their Cournot–Nash allocation. In this paper, we prove that in any finite pure public good economy there exists a core allocation that is unanimously preferred, utility-wise, by all consumers over their Cournot–Nash consumption bundles.     

Congestion effects in a public-good economy

This paper considers a public-good economy with congestion, where participants jointly produce a public good from input of a private good. This economic model gives rise to a transferable-utility game, the profit game, that depends on consumer preferences and a congestion parameter. The simplicity of the game allows the maximum level of congestion that guarantees the nonemptiness of the core of the economy to be determined. It is known that the sustainability of the Lindahl equilibrium in the core of the economy depends on the distribution of profits. In this paper two distributions of profits are compared: the Lindahl solution and the marginal-contribution solution. The latter is more often in the core than the Lindahl solution which in turn Lorenz-dominates the marginal-contribution solution.     

Kant and Lindahl*

In 1896 and 1919, respectively, Wicksell and Lindahl analyzed the public provision of public goods through parliamentary negotiation. Later, Roemer applied Kant's 1785 imperatives to the private provision of public goods by voluntary contributions. Our focal equilibrium notions are the balanced linear cost-share equilibrium for the Wicksell–Lindahl approach and the multiplicative Kantian equilibrium in the Kant–Roemer modeling. These turn out to be fundamentally equivalent, being defined by the same individual optimization problem. These notions fit well with the idea that technology is publicly owned, but we also extend them to cover private-ownership economies with exogenously given profit shares. We show that the equivalence between the Wicksell–Lindahl and Kant–Roemer notions carries over to them.     

Efficiency with Non-Convexities: Extending the “Scandinavian Consensus” Approaches

There are two distinct “Scandinavian consensus” approaches to public good supply, both based on agents' willingness to pay. A Wicksell–Foley public competitive equilibrium arises from a negative consensus in which no change of public environment, together with associated taxes and subsidies which finance it, will be unanimously approved. Alternatively, in a Lindahl or valuation equilibrium, charges for the public environment induce a positive consensus. To allow general non-convexities to be regarded as aspects of the public environment, we extend recent generalizations of these equilibrium notions and prove counterparts to both the usual fundamental efficiency theorems of welfare economics.     

Free entry into telecommunications?

The two leading principles of pricing for public enterprises are outlined: Value based and cost based pricing. It is shown that optimal pricing à la Ramsey-Boiteux is closely related to value based pricing which itself is connected with Lindahl pricing of public goods. Cost based pricing is related to the pricing in competitive markets. Opening up of telecommunication to competition implies a change from value based (public good) pricing to cost based (pritate good) pricing. It is shown why specific developments in telecommunication technology make a switch to cost based pricing and a competitive environment appropriate. At the end a proposal is developed for a gradual change towards competition which would meet less political resistance.     

Bartering Games in the Kolm Triangle

We study a public good mechanism that possesses several attractive properties. In particular, the mechanism always produces feasible allocations, induces a game where the Nash equilibria are all individually rational, and, in contrast to the voluntary contribution mechanism, supports the Lindahl allocation as a Nash equilibrium allocation. The geometric framework of the Kolm triangle is employed to illustrate the workings of the mechanism and provide intuition for the main results.     

Bargaining foundation for ratio equilibrium in public‐good economies

We provide a bargaining foundation for the concept of ratio equilibrium in public‐good economies. We define a bargaining game of alternating offers, in which players bargain to determine their cost shares of public‐good production and a level of public good. We study the stationary subgame perfect equilibrium (SSPE) without delay of the bargaining game. We demonstrate that when the players are perfectly patient, they are indifferent between the equilibrium offers of all players. We also show that every SSPE without delay in which the ratios offered by all players are the same leads to a ratio equilibrium. In addition, we demonstrate that all equilibrium ratios are offered by the players at some SSPE without delay. We use these results to discuss the case when the assumption of perfectly patient players is relaxed and the cost of delay vanishes.     

Equivalence of Lindahl equilibrium with participation prices and the core

Summary In a model of an economy with multiple public goods and differentiated crowding, it is shown that asymptotically the core has the equal treatment property and coincides with the equilibrium outcomes. It follows that all individuals of the same type in the same jurisdiction must pay the same Lindahl taxes and, with strict convexity of preferences, the same Lindahl prices. With only one private good, for sufficiently large economies we show (a) the equivalence of the core and the set of equilibrium outcomes and (b) the nonemptiness of approximate cores and their equivalence to the set of approximate equilibrium outcomes.The author is indebted to Vicky Barham, John Conley, Hideo Konishi, Julian Manning and Roma Jakiwczyk for comments on an earlier draft of this paper. The author gratefully acknowledges the research support of the Social Sciences and Humanities Research Council of Canada.     

Property Rights and Efficiency of Voluntary Bargaining under Asymmetric Information

We show that in public good problems under asymmetric information, the success of voluntary bargaining is closely related to the structure of property rights. We characterize property rights structures and mediated bargaining procedures that either lead to an efficient voluntary resolution to public good problems, or achieve the efficient outcome but slightly coerce the agents into participation. In this respect, we identify "efficient" property rights structures.     

Edgeworth and Lindahl–Foley equilibria of a General Equilibrium Model with Private Provision of Pure Public Goods

In this paper, we propose a definition of Edgeworth equilibrium for a private ownership production economy with (possibly infinitely) many private goods and a finite number of pure public goods. We show that Edgeworth equilibria exist whatever be the dimension of the private goods space and can be decentralized, in the finite and infinite dimensional cases, as Lindahl–Foley equilibria. Existence theorems for Lindahl–Foley equilibria are a by‐product of our results.