Efficient provision of public goods with endogenous redistribution

We study a balanced mechanism that is capable of implementing in Nash equilibrium all the Pareto-efficient individually rational allocations for an economy with public goods. The Government chooses a set of weights directly related to the Lindahl prices corresponding to the Pareto-efficient allocation to be implemented. The mechanism then guarantees that initial endowments are re-allocated so that the chosen vector of Lindahl prices is indeed a Lindahl equilibrium, and implements the corresponding Lindahl allocation. Finally, besides being balanced, our mechanism is simple. Each agent has to declare a desired increase in the amount of public good, and a vector of redistributive transfers of initial endowments (across other agents).Received: 9 May 2003, Accepted: 22 October 2003, JEL Classification: C79, H21, H30, H41We wish to thank Jeremy Edwards, Andrew Postlewaite and Emanuela Sciubba for helpful comments. Of course, any remaining errors are our own.     

Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

The graph of Lindahl correspondence as the unique von Neumann-Morgenstern abstract stable set

In this paper, we consider a continuum economy with a finite number of types of agent, and several private and public goods. The main result of the paper is that the graph of the equal-treatment Lindahl equilibria mapping is the unique abstract stable set with respect to the dominance relation in economies with crowding effects introduced by Vasil'ev et al. in 1995. The external stability of this mapping implies that, for any equal-treatment allocation x in , that is not a Lindahl equilibrium, there exists a subeconomy of such that one of its equal-treatment Lindahl allocations blocks x. This result is a counterpart of the theorem of Mas-Colell for Aumann's atomless market with private goods.     

Taxation in an economy with private provision of public goods

This paper analyses the effects of taxation and subsidies in an economy with private provision of a public good. It is shown that in a situation where all individuals contribute, taxation affects the equilibrium allocation if and only if at least one individual's voluntary contribution to the public good has an impact on the aggregate tax payments of the others. We then consider linear nonneutral tax-subsidy schemes and analyse efficiency and uniqueness of the resulting Nash equilibria. We show that an efficient Nash equilibrium, where all individuals contribute, will in general not be unique, and establish a non-uniformity property which a tax-subsidy scheme must fulfil in order to induce a unique interior equilibrium that is efficient. Throughout the paper it is assumed that individuals fully understand and take into account the government's budget constraint. Received: 3 November 1997 / Accepted: 23 March 1999     

Double implementation of the ratio correspondence by a market mechanism

To overcome deficits of the Lindahl solution concept when the economy does not exhibit constant returns to scale, Kaneko (1977a) introduced the concept of aratio equilibrium. Theratio correspondence selects for each economy its set of ratio equilibrium allocations. In this paper we provide a simple market game thatdouble implements the ratio correspondence in Nash and strong equilibria.     

Endogenous household interaction

Most econometric models of intrahousehold behavior assume that household decision making is efficient, i.e., utility realizations lie on the Pareto frontier. In this paper, we investigate this claim by adding a number of participation constraints to the household allocation problem. Short-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize under (inefficient) Nash equilibrium. Long-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize by cheating on the efficient allocation and receiving Nash equilibrium payoffs in all successive periods. Given household characteristics and the (common) discount factor of the spouses, not all households may be able to attain payoffs on the Pareto frontier. We estimate these models using a Method of Simulated Moments estimator and data from one wave of the Panel Study of Income Dynamics. We find that both short- and long-run constraints are binding for sizable proportions of households in the sample. We conclude that it is important to carefully model the constraint sets household members face when modeling household allocation decisions, and to allow for the possibility that efficient outcomes may not be implementable for some households.     

Information complexity, punishment, and stability in two Nash efficient Lindahl mechanisms

Earlier experimental work on public good mechanisms has focused almost exclusively on stability issues, finding that institutions with robust equilibrium stability properties were better at achieving their equilibrium. In this study, we continue to explore this insight and, in addition, look at issues such as out-of-equilibrium punishment and complexity. The experiment varies stability conditions and group size in two Nash efficient Lindahl mechanisms. These mechanisms have similar stability properties. However, when groups are large, they differ both in the severity with which they punish out-of-equilibrium behavior and their informational complexity. We examine how these differences impact mechanism performance.     

Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

A decentralized and informationally efficient mechanism realizing fair outcomes in economies with public goods

We present a decentralized mechanism (called Lindahl Egalitarian), which yields Pareto efficient and envy free allocations (i.e. fair outcomes). We show that the mechanism is informationally efficient in general production economies with an arbitrary, but finite, number of private and public goods, and a finite number of agents. The mechanism reduces to the Walrasian mechanism starting from equal wealth when no agent cares about public goods. We also prove that the set of Public Competitive equilibrium allocations (from equal endowments and proportional taxation), and the set of the Lindahl Egalitarian equilibrium allocations are the same. We are grateful to Xavier Calsamiglia and Albert Marcet for helpful conversations, and to A. de la Fuente, I. Macho, and an anonimous referee for useful suggestions. A. Manresa’s research has been supported by the grant CICYT PB90-0172. J. Aizpurua acknowledges financial support from the Government of Navarra.     

Optimal mechanisms for siting noxious facilities

We study Bayesian mechanism design in the context of the siting of noxious facilities. Under incomplete information, we characterize optimal mechanisms facilitating the siting and cost sharing of the facility. These mechanisms are allocatively and Pareto efficient. However, it appears that transfers occur when the good is not provided. This result is due to the weakening of the incentive notion to Bayesian–Nash equilibrium and to the balanced budget condition. This phenomenon disappears if the setting is perfectly symmetric.      

Stackelberg leadership and transfers in private provision of public goods

We consider transfers in a Stackelberg game of private provision of a public good. It turns out that the agent who is the follower in the process of making voluntary contributions to a public good may have an incentive to make monetary transfers to the Stackelberg leader even in a situation where neither has a comparative advantage in making contributions to the public good. The Stackelberg leader is willing to accept such transfers if the actual contribution game is fully non-cooperative because the transfer generates a Pareto superior outcome. If the contributions in the Stackelberg equilibrium is the threat point of a possible cooperative Nash bargaining game, the Stackelberg leader will refuse to accept the transfer if she can. Received: 30 June 1995 / Accepted: 18 February 1997     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

Lindahl's solution and values for a public-goods example

An example of an economy with a public good is presented with a non-atomic measure space of agents and money (transferable utility medium). Three solutions are computed: the Lindahl solution, the Shapley value, and the Harsanyi-Selten value. The three are found to differ significantly in their assignment of the societal benefits attributable to the presence of the public good.     

Symmetry and continuity properties of Lindahl equilibria

In this paper it is shown that: (1) some non-symmetric Lindahl equilibria may exist; (2) under usual assumptions, the set of symmetric Lindahl equilibria is non-empty; (3) however, the correspondence which associates with every economy the set of symmetric Lindahl equilibria is not a closed correspondence; (4) there are economies with a measure space of economic agents in which every Lindahl equilibrium is discontinuous.     

Counting Groves-Ledyard equilibria via degree theory

We study the Groves-Ledyard mechanism for determining optimal amounts of public goods in economies whose agents have the most general class of preferences for which a Pareto amount of public goods can be computed independently of income distribution. We use degree theory on affine spaces to show that the number of equilibria in such economies grows exponentially as the number of agents in the economy increases. The large number of equilibria in such simple economic models raises doubts as to whether the Groves-Ledyard mechanism is a workable solution to the Free Rider Problem since individuals may have incentives to falsify their preferences in order to drive the adjustment process to a preferred Nash equilibrium.     

The allocation of public funds in a hierarchical educational system

This paper studies the dynamic effects of allocating public funds between basic and advanced education. Holding the size of total public education funds fixed, I identify the effects of their composition on aggregate efficiency and (in)equality. First, since basic education is a prerequisite for attending advanced education, there exists a lower bound on funding it: allocation policies below this lower bound are strictly Pareto dominated. Whether a corresponding lower bound on funding advanced education exists or not depends on the development stage of the economy and the size of total public funds. Secondly, while an allocation policy favoring basic education generates the usual redistribution from top to bottom, one favoring advanced education may result in reverse redistribution from bottom to top. Last, through the inter-generational link, short-run allocation policies may have long-run effects. A simple rule-of-thumb is that for an economy in its early development stage, focusing on basic education for sufficiently long duration is the only way out of polarization and low aggregate efficiency, contrary to the actual policies pursued by many of the less developed economies.     

Convergence in games with continua of equilibria

In game theory, the question of convergence of dynamical systems to the set of Nash equilibria has often been tackled. When the game admits a continuum of Nash equilibria, however, a natural and challenging question is whether convergence to the set of Nash equilibria implies convergence to a Nash equilibrium. In this paper we introduce a technique developed in Bhat and Bernstein (2003) as a useful way to answer this question. We illustrate it with the best-response dynamics in the local public good game played on a network, where continua of Nash equilibria often appear.     

Central government subsidies to local public goods

We examine the welfare effects of a central government's subsidy for a local public good in a Nash equilibrium model with two types of public goods. We first show that the welfare effect depends on the substitution and evaluation effects. We also investigate the optimal subsidy rate in a second-best framework and explore how the optimal subsidy scheme depends on the relative evaluation of the two types of public goods. Received: August 20, 1998/accepted: February 12, 2002 RID="*" ID="*" We are grateful to John Quigley, Minoru Kunisaki, Tom Panella, Andy Haughwout, Steven Craig, William Hoyt, Michael Ash, Konrad Stahl, Amihai Glazer, David Wildasin and two referees for helpful comments and suggestions, An early version of this paper was presented at a seminar at University of California, Berkeley and at conferences at JAEE Annual Meeting in Japan, North American Meetings of The RSAI in Washington, WSAI conference in Hawaii, Public Choice Meeting in San Francisco.     

Pareto efficiency in the jungle

We revisit the jungle economy of Piccione and Rubinstein (Econ J 117(July):883–896, 2007) in which the allocation of resources is driven by coercion. In this economy the unique equilibrium satisfies lexicographic maximization. We show that relaxing the assumptions on consumption sets and preferences slightly, allocations other than lexicographic maximizers can be jungle equilibria. We attribute this result to single unilateral taking where a stronger agent takes goods from only one weaker agent. Once multiple unilateral takings are introduced, we show that jungle equilibria coincide with lexicographic maximization under weak assumptions. However, we also present examples of equilibria that are Pareto inefficient, where voluntary gift giving by stronger agents is needed to achieve Pareto efficiency and even voluntary trade has a role in the jungle.     

Pareto improving interventions in a general equilibrium model with private provision of public goods

Most of the literature on government intervention in models of voluntary public goods supply focuses on interventions that increase the total level of a public good, which is considered to be typically underprovided. However, an intervention that is successful in increasing the public good level need not benefit everyone. In this paper we take a direct approach to welfare properties of voluntary provision equilibria in a full blown general equilibrium model with public goods and study interventions that have the goal of Pareto improving on the voluntary provision outcome. Towards this end, we study a model with many private goods and non-linear production technology for the public good, and hence allow for relative price effects to serve as a powerful channel of intervention. In this setup we show that Pareto improving interventions generally do exist. In particular, direct government provision financed by “small” , or “local” , lump-sum taxes can be used generically to Pareto improve upon the voluntary provision outcome.