Wealth inequality and collective action

We study the effect of inequality in the distribution of endowments of private inputs (e.g., land, wealth) that are complementary in production with collective inputs (e.g., contribution to public goods such as irrigation and extraction from common-property resources) on efficiency in a class of collective action problems. We focus on characterizing the joint surplus maximizing level of inequality, making due distinction between contributors and non-contributors, in a framework that allows us to consider a wide variety of collective action problems ranging from pure public goods to impure public goods to commons. We show that while efficiency increases with greater equality within the groups of contributors and non-contributors, so long the externalities (positive or negative) are significant, there is an optimal degree of inequality between these groups.     

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.     

Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

Income Distribution, Taxation, and the Private Provision of Public Goods

This article investigates the role of taxation when public goods are privately provided. Externalities between consumers via the public good are shown to cause kinks in social indifference curves. As a result, a government restricted to income taxation should engineer enough inequality to ensure there are some non-contributors to the public good. Whether commodity taxation changes this conclusion depends on the extent to which consumers "see through" the government budget constraint. If they can, inequality should still be sought. When they cannot, in contrast to the case of an economy with only private goods, commodity taxation can be used in conjunction with income transfers to achieve the first-best.     

Participation and the provision of discrete public goods: a strategic analysis

This paper considers the Nash equilibria to a game where a discrete public good is to be provided. Each individual may participate by making a fixed contribution. If a sufficient number of contributions are made, the good is provided. Otherwise, the good is not provided. One variant of the rules allows for contributions to be refunded when the good is not provided. For pure strategies, we find that the Nash equilibria with a refund are a superset of those without a refund. For both rules, the efficient number of players contributing is an equilibrium. For mixed strategies, to every equilibrium without a refund there is a corresponding equilibrium with a refund with a higher number of expected contributors. Mixed strategy equilibria ‘disappear’ as the number of players grows large. Some results reported in the experimental literature are discussed in light of these theoretical results.     

On the Frequency of Interior Cournot–Nash Equilibria in a Public Good Economy

In a public good economy the distribution of initial income is an important determinant of how many individuals contribute to the public good in Cournot–Nash equilibrium. In this paper, first a simple formula is derived that provides a measure for the size of the set of income distributions leading to an interior Cournot–Nash equilibrium in which all individuals contribute to the public good. Furthermore, we give an estimate for the frequency that all members of a certain subgroup of the population are contributors.     

Giving is a Question of Time: Response Times and Contributions to an Environmental Public Good

Does it matter whether contribution decisions regarding environmental public goods are arrived at through intuition or reflection? Experimental research in behavioral economics has recently adopted dual-system theories of the mind from psychology in order to address this question. This research uses response time data in public good games to distinguish between the two distinct cognitive processes. We extend this literature towards environmental public goods by analyzing response time data from an online experiment in which over 3400 subjects from the general population faced a dichotomous choice between receiving a monetary payment or contributing to climate change mitigation efforts. Our evidence confirms a strong positive link between response times and contributions: The average response time of contributors is 40 % higher than that of non-contributors. This suggests that reflection, not intuition, is at the root of pro-environmental contributions. This result is robust to a comprehensive set of robustness checks, including a within-subjects analysis that controls for potentially unobserved confounds and recovers the relationship at the individual level.     

Group efforts when performance is determined by the “best shot”

We investigate the private provision of a public good whose level is determined by the maximum effort made by a group member. Costs of effort are either commonly known or privately known. For symmetric perfect-information games, any number of players may be active and we characterize the unique (mixed-strategy) equilibrium in which active contributors use the same strategy. Increasing the number of active players leads to stochastically lower individual efforts and level of the public good. When information is private, the symmetric equilibrium is in pure strategies. Increasing the number of players yields a pointwise reduction in the equilibrium contribution strategy but an increase in equilibrium payoffs. Comparative statics with respect to costs and levels of risk aversion are derived. Finally, whether information is public or private, equilibria are inefficient—we provide mechanisms that improve efficiency.     

Public Good Provision Under Monopolistic Competition

This paper presents a model of voluntary private provision of public good under monopolistic competition following Pecorino. Consumers prefer product varieties and a public good. Marginal utility of income depends inversely upon the aggregate consumption of private goods in this model. As population size increases, aggregate consumption of private goods goes up and marginal utility of income falls. This explains the positive relationship between population size and public good provision. Any technological changes in the production of private goods are shown to be neutral to the aggregate provision of public good. These results are in contrast to Pecorino.     

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     

On the Neutrality of Redistribution in a General Equilibrium Model with Public Goods

Models on private provision of public goods typically involve a single private good and linear production technology for the public good. We study a model with several private goods and nonlinear (strictly concave) production technology. We revisit the question of „neutrality” of government interventions on equilibrium outcomes and show that relative price effects that are absent with a single private good and linear production technology become a powerful channel of redistribution in this case. Contrary to previous results, redistributing endowments in favor of contributors is shown to be neither necessary nor sufficient for increasing the equilibrium level of public good.     

Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via Contraction

This paper presents a proof for existence and uniqueness of a Nash equilibrium of a public good model that exploits a simple contraction mapping. The proof establishes both existence and uniqueness in a single exercise that provides intuition about sufficiency. The method of proof is applied not only to the basic pure public good model but also to the impure model. In the latter model, income normality does not play the same pivotal role for existence and uniqueness.     

Income distribution and firm formation

This paper investigates equilibria associated with alternative income-distribution schemes in economies where firm formation is endogenous. The income realizable by a firm depends upon the membership of the firm. An entrepreneurial equilibrium, where agents form and/or join firms so as to maximize their individual incomes, has firm structures that maximize aggregate income but does not have good existence properties. Two alternative equilibrium concepts that have better existence properties than the entrepreneurial equilibrium but weaker optimality properties are considered. The results are applied to the debate on the optimality of average-income-per-worker maximization within a market-socialist firm.     

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.     

Indeterminacy, underground activities and tax evasion

This paper introduces underground activities and tax evasion into a one-sector dynamic general equilibrium model with aggregate external effects. The model presents a novel mechanism driving the self-fulfilling prophecies, which is characterized by well behaved (downward sloping) labor demand schedules. This mechanism differs from the customary one, and it is complementary to it. Compared to traditional labor market income, the income derived from underground labor activity is subject to a lower expected tax rate when considering both the probability of detection and the evasion penalty. During a belief-driven expansion, the household allocates more time to both traditional and underground labor supply. In equilibrium, this action serves to lower the effective labor tax rate faced by the household, thus providing stimulus to aggregate labor supply so as to make the initial expansion self-fulfilling. The mechanism here is akin to a “regressive tax”; the household's effective tax rate depends negatively on the level of total labor income. We argue that an underground sector, and the associated tax evasion, offer a good economic rationale for a regressive tax rate.     

The public and private provision of pure public goods and the distortionary effects of income taxation: a political economy approach

Abstract .  A pure public good is provided by the government and the voluntary contributions of two types of households. The government finances its contribution by means of income taxation. The latter has distortionary effects. A third type of household never makes contributions. We analyse the effects of changes in the income tax rate on (a) the provision of the public good, (b) the private contributions of the households, and (c) changes in the distribution of income and welfare between contributing and non-contributing households. We derive a simple and testable condition under which the lowering of the income tax entails a Pareto improvement.     

Private Information in the BBV Model of Public Goods

To analyze the private provision of a public good in the presence of private information, we explore the connections between two frameworks: the binary public good model with threshold uncertainty and the standard continuous model à la Bergstrom et al. Linearity of best responses in others' contributions is key to matching the two frameworks. We identify all utility functions that display this linearity, and we provide conditions ensuring that the minimal properties that Bergstrom et al. require for utilities are satisfied. Using techniques developed in the threshold uncertainty framework, we show existence and uniqueness of the Bayes‐Nash equilibrium—thus generalizing existing results—and we analyze its comparative statics properties. In particular, under the reasonable assumption that agents' income is stochastic and private information, we complement the full‐information crowding‐out and redistribution results of Bergstrom et al. If the government taxes agents' income proportionally and redistributes (expected) revenues lump sum, equilibrium public good provision can increase or decrease, even if the set of contributors is unchanged. Similarly, we show that crowding‐out can be one‐for‐one, less than one‐for‐one, or more than one‐for‐one. Finally, we extend our results to a multidimensional framework in which agents' unit costs of contributions are also private information.     

Keynes,Employment Policy and the Question of Public Debt

This article provides a simple formalization of income–expenditure equilibrium in accordance with the Principle of Effective Demand, but augmented to explicitly incorporate public debt. This is utilized to explore the conditions required for simultaneous achievement of full-employment growth and a sustainable public debt trajectory—the latter understood as stabilization of the ratio of public debt to aggregate income, at some desired level. In the spirit of Keynes's economics, demand-led, full-employment growth, driven by government spending, is reconciled with public debt sustainability so understood. The policy implications, illustrative of Keynes's policy views, are then drawn out.