Public good provision rules and income distribution: Some general equilibrium calculations

A central issue in the analysis of public goods is the relationship between the optimal provision level and the distribution of income. Theoretical research has stressed the conditions under which the optimum is independent of the distribution of income. Here we focus on numerical analysis of more policy-relevant concerns. Specifically, to what extent is a given redistribution of income likely to affect the optimal level of public good supply? And how significant are the welfare costs of not adjusting public good supply when income distribution changes? We use an applied general equilibrium (AGE) model of the Australian economy and public sector to generate numerical estimates of the impacts of redistributive policies on these variables. Results suggest that the traditional separation of allocation and distribution in determining the level of public good supply may be a justifiable empirical simplification, except where very dramatic redistributions are involved.     

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     

Non-cooperative bargaining and the incomplete informational core

In an exchange economy with incomplete information, the signaling core is defined by the set of state-contingent allocations to which no coalitions object under informational leakage through proposals by informed agents. An objection underlying the signaling core is supported by a sequential equilibrium of an ultimatum bargaining game with an informed proposer. We prove that a stationary sequential equilibrium allocation in a Rubinstein-type sequential bargaining game with a restart rule belongs to the signaling core if the belief of players satisfies a self-selection property.     

Finitely Repeated Voluntary Provision of a Public Good

This paper theoretically explores the voluntary provision of a public good when either one of the following holds: (i) agents’ utility is the sum of their monetary earnings and a nonmaterial component, or (ii) agents’ exhibit satisficing behavior. We show that a small degree of either nonmaterial payoffs or satisficing behavior can generate large contributions in a finitely repeated game, even if the incentive to free‐ride on others’ contributions calls for negligible public good provision in the static game. The equilibrium is characterized by a sharp decline in contributions toward the end of the game. Several comparative results regarding group size and technology are consistent with laboratory data obtained in experimental studies. The model also predicts the restart effect observed in previous experiments.     

Nash as an Organizing Principle in the Voluntary Provision of Public Goods: Experimental Evidence

Experiments are reported that add to the growing literature on the voluntary provision of public goods. Information conditions are manipulated to address whether early findings of above-equilibrium contributions to a public good are a result of complete information regarding the symmetry of the game. No significant information effect was found. Further, by examining designs with an interior Nash equilibrium, this research suggests that the nonzero contributions observed in the previous dominant strategy environments, where the prediction was a zero level of provision of the public good, were not simply transitional errors as the system converged to a boundary equilibrium.     

Dynamic Voluntary Provision of Public Goods and Optimal Steady-State Subsidies

This paper examines a differential game model of voluntary provision of a public good in which private agents' contributions accumulate over time and derives subsidy rules that achieve the socially efficient steady state. It is shown that the optimal subsidy rule is a simple one when agents use the open‐loop strategy, while under Markovian strategies it intricately depends on the parameters of the economy.     

Public versus private risk sharing

Can public income insurance through progressive income taxation improve the allocation of risk in an economy where private risk sharing is incomplete? The answer depends crucially on the fundamental friction that limits private risk sharing in the first place. If risk sharing is limited because insurance markets are missing for model-exogenous reasons (as in Bewley (1986) [8]) publicly provided risk sharing improves on the allocation of risk. If instead private insurance markets exist but their use is limited by limited enforcement (as in Kehoe and Levine (1993) [23]) then the provision of public insurance interacts with equilibrium private insurance, as, by providing risk sharing, the government affects the value of exclusion from private insurance markets and thus the enforcement mechanism of these contracts. We characterize consumption allocations in an economy with limited enforcement and a continuum of agents facing plausible income risk and tax systems with various degrees of progressivity (public risk sharing). We provide conditions under which more publicly provided insurance actually reduces total insurance for agents (excess crowding-out), or under which more public insurance increases total insurance (partial crowding-out).     

When Does Everyone Contribute in the Private Provision of Local Public Goods?

When does everyone genuinely contribute in the private provision of a local public good? We first introduce a monotonic condition to characterize the relationship between the structure of the network that underlie the noncooperative game of private provision of local public goods on the one hand, and the preferences of the agents on the other, showing that the monotonic condition is a sufficient and necessary condition of existence of a distributed Nash equilibrium (DNE) in which each agent exerts a positive amount of effort to provision of the public good (Theorem 1). We then study the number of equilibria, and, by using the monotonic condition, characterize the condition under which the DNE set is a singleton, a continuum, or null (Theorem 2). As it turns out, the structure of the network and the agents’ preferences jointly shape the effort profile in the provision of local public goods.     

A Core‐Equilibrium Convergence in a Public Goods Economy

This paper shows a core‐equilibrium convergence in a public goods economy where consumers' preferences display warm glow effects. We demonstrate that if each consumer becomes satiated to other consumers' provision, then as the economy grows large the core shrinks to the set of Edgeworth allocations. Moreover, we show that an Edgeworth allocation can be decentralized as a warm glow equilibrium.     

Best-shot network games with continuous action space

This paper presents a model of public good provision in networks where the level of public good that an agent has access to depends on the maximum of contributions by the agents in her neighbourhood. Our analysis shows that the game always has an equilibrium in pure strategies and all equilibria are specialised and stable. Welfare analysis shows that formation of new links in a prevailing network may not always be useful.     

The ratio equilibrium and a voting game in a public goods economy

An economic model of the allocation process with public goods is presented. We define a concept of equilibrium and prove the existence. Next we present a voting game in which a level of the public goods to be produced is decided. We prove that the core of the voting game and the equilibria exist simultaneously, and that they coincide.     

Ethnic identities,public spending and political regimes

Do democracies discriminate less against minorities as compared to non-democracies? How does the dominance of an ethnic group affect discrimination under various political regimes? We build a theory to analyse such questions. In our model, political leaders (democratically elected or not) decide on the allocation of spending on different types of public goods: a general public good and an ethnically-targetable public good which benefits the majority ethnic group while imposing a cost on the other minorities. We show that, under democracy, lower ethnic dominance leads to greater provision of the general public good while higher dominance implies higher provision of the ethnically-targetable good. Interestingly, the opposite relation obtains under dictatorship. This implies that political regime changes can favour or disfavour minorities based on the ambient level of ethnic dominance. Several historical events involving regime changes can be analysed within our framework and are consistent with our results.     

On the voluntary provision of “weakest‐link” public goods: The case of private information

We characterize equilibria in a private‐provision public‐good game where individuals are allowed arbitrary contribution levels and the level of the public good equals the least contribution made by an individual. Equilibrium comparative statics are derived for the interim Pareto‐dominant equilibrium. First, improvements in the cost distribution of even only one player benefit all. Second, even with such “weakest‐link” public goods, for which greater similarity of preferences would seem to facilitate coordination, decreased heterogeneity can actually decrease payoffs. Indeed, increasing the riskiness of cost distributions has an ambiguous effect on welfare. Two mechanisms are provided for improving equilibrium payoffs: Technology transfer and cheap‐talk communication. While substantial welfare gains are possible, examples show that (a) technology transfer may be futile if a “regularity” condition is not satisfied and (b) cheap talk may be useless if the language for communication is not sufficiently rich.     

A Dynamic Tiebout Theory of Voluntary vs. Involuntary Provision of Public Goods

This paper considers a dynamic model of Tiebout-like migration between communities that utilize distinct allocation procedures for public goods. At issue is whether voluntary or compulsory procedures are more likely to prevail over time. We model infinitely lived individuals who make repeated, sequential location decisions over one of two communities. Each community uses a distinct mechanism for allocating public goods. The first is one in which contributions are given voluntarily by the citizenry of the community. The second is a compulsory scheme by which individuals are taxed proportionately to wealth with the tax determined by a majority vote. Opportunities to accumulate wealth exist via accumulation of public capital.
The Markov Perfect equilibria of the dynamic game are studied. Our main result shows that when accumulated wealth converges to a steady state, individuals' locational choices eventually "select" the involuntary provision mechanism. This holds despite the fact that unanimous location in the voluntary provision community may in many cases remain as a Nash equilibrium of the static game each period. We also describe conditions under which voluntary provision survives. These conditions require that accumulation of capital fails to decrease wealth dispersion over time. The results are shown to be consistent with findings relating inequality to school choice.     

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.     

On the private provision of public goods

We consider a general model of the non-cooperative provision of a public good. Under very weak assumptions there will always exist a unique Nash equilibrium in our model. A small redistribution of wealth among the contributing consumers will not change the equilibrium amount of the public good. However, larger redistributions of wealth will change the set of contributors and thereby change the equilibrium provision of the public good. We are able to characterize the properties and the comparative statics of the equilibrium in a quite complete way and to analyze the extent to which government provision of a public good ‘crowds out’ private contributions.     

Membership in citizen groups

We analyze the coordination problem of agents deciding to join a group that uses membership revenues to provide a discrete public good and excludable benefits. The public good and the benefits are jointly produced, so that benefits are valued only if the group succeeds in providing the public good. With asymmetric information about the cost of provision, the static membership game admits a unique equilibrium and we characterize the optimal membership fee. We show that heterogeneity in valuations for the excludable benefits is always detrimental to the group. However, in a dynamic contest in which heterogeneity arises endogenously (returning members receive additional seniority benefits at the expense of junior members), we show that, in the ex-ante optimal contract, offering seniority benefits is beneficial for the group, despite the heterogeneity in valuations created.     

Contribution to a public good under subjective uncertainty

This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two‐state‐dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first‐ and second‐order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision, as does any homogenization of these beliefs around their mean.     

Chores

We analyze situations where the provision of each of c public goods must be voluntarily assumed by exactly one of n private agents in the absence of transfer schemes or binding contracts. We model this problem as a complete information, potentially infinite horizon game where n agents simultaneously wage c wars of attrition. Providing a public good commits an agent not to take on the provision of another public good for a fixed period. We explore the strategic trade-offs that this commitment ability and the multiplicity of tasks provide. Subgame perfect equilibria (SPEs) are characterized completely for games with two agents and two public goods. For games with two identical agents and c > 1 identical public goods, we establish that an equilibrium that yields a surplus-maximizing outcome always exists and we provide sufficient conditions under which it is the unique equilibrium outcome. We show that under mild conditions, the surplus-maximizing SPE is the unique symmetric SPE. Journal of Economic Literature Classification Number: H41, C72, D13.     

Inefficient Public Provision in a Repeated Elections Model

We consider a dynamic setting with no policy commitment. Two parties that compete for election must choose the level of provision of a public good as well as the tax payment needed to finance it. The cost of producing the good may be high or low and this information is not known to the voters. We show that there exists an equilibrium in which the party that does not want much of the public good uses the inefficient (high cost) technology even though the efficient one is available. Using the low cost technology would, by informing the voters about the cost parameter, force it to produce an excessively high level of the good in the future. Interestingly, this equilibrium is not symmetric, suggesting that a party with a strong taste for the public good is less likely to adopt a wasteful policy.