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.     

Social network and private provision of public goods

Using a simple model with interdependent utilities, we study how social networks influence individual voluntary contributions to the provision of a public good. Departing from the standard model of public good provision, we assume that an agent’s utility has two terms: (a) ‘ego’-utility derived from the agent’s consumption of public and private goods, and (b) a social utility which is the sum of utility spillovers from other agents with whom the agent has social relationships. We establish conditions for the existence of a unique interior Nash equilibrium and describe the equilibrium in terms of network characteristics. We show that social network always has a positive effect on the provision of the public good. We also find that, in networks with “small world”-like modular structures, ‘bridging’ ties connecting distant parts of social network play an important role inducing an agent’s contribution to public good. Assumptions and results of the model are discussed in relation to the role of social capital in community-level development projects and to the effect of innovation networks on firms’ R&D investments.     

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.     

Rewards and the private provision of public goods on dynamic networks

We study an evolutionary model of a public good game with rewards played on a network. Giving rewards to contributors transforms the game but gives rise to a second-order dilemma. By allowing for coevolution of strategies and network structure, the evolutionary dynamics operate on both structure and strategy. Players learn with whom to interact and how to act and can overcome the second-order dilemma. More specifically, the network represents social distance which changes as players interact. Through the change in social distance, players learn with whom to interact, which we model using reinforcement dynamics. We find that, for certain parameter constellations, a social institution, prescribing prosocial behavior and thus solving the second-order dilemma, can emerge from a population of selfish players. Due to the dynamic structure of the network, the institution has an endogenous punishment mechanism ensuring that defectors will be excluded from the benefits of the institution and the public good will be supplied efficiently.     

Depreciation and intergenerational altruism in the private provision of public goods

The static model of the private provision of public goods is refuted by empirical and experimental evidence which shows that contributions are above the levels predicted by the theory. The model is reconsidered here in an intertemporal framework that allows the formation of a stock of public good over time and admits intergenerational altruism into preferences. Both of these factors affect the level of private provision. An intertemporal version of the Samuelson rule is derived and it is shown that, for some parameter values, the provision level determined by this is matched by private provision. For other parameter values, it is shown how a system of taxation can achieve the optimum.     

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.     

Effect of an audience in public goods provision

This paper investigates a novel public goods game where contributions to the public goods require effort that is observable. When the players are observed, they exert more effort to contribute to the public goods, and free-riding diminishes significantly compared to the no observer case. These effects are absent when no effort is required in order to contribute to the public goods. Furthermore, in the presence of an audience, the contributions to the public goods do not diminish when the game is repeated in the effort-required environment. Being observed does not affect the performance of the players if there is no strategic aspect of the game, in other words, when they play a private goods game. These results indicate that an individual wants to avoid appearing lazy when her effort helps the society.     

Public provision of private child goods

This paper analyzes the public provision of private goods for children in a politico-economic model with endogenous fertility. The government provides every child with goods that can also be purchased by parents in private markets, and the level of provision is determined by majority rule. Households with many children benefit from the public provision more than those with fewer children; thus, a political conflict arises between them. The distribution of the number of children across households, which is a crucial factor for determining which group is politically dominant, is endogenously determined by households' fertility decision. The sequential interaction between fertility and political decisions might lead to multiple equilibria: equilibrium with high fertility and low-private/public-spending ratio and equilibrium with low fertility and high-private/public-spending ratio. Our model could explain the large differences in fertility and structure of child-related spending across countries.     

A further look at consistent conjectures and private provision of public goods

A model of private provision of a public good under conjectural variations is discussed and the rule for a symmetric consistent conjectures equilibrium (CCE) derived. It is shown that in a number of reasonable cases symmetric CCEs fail to exist in economies with identical individuals, while there may exist asymmetric ones. The relevance of these results for the use of the conjectural variations approach in public good theory is then discussed together with some suggestions for further research.     

Dynamic provision of public goods

Summary. This paper deals with implementing the efficient level of public good provision in a dynamic setting. First, we prove that when the good is provided in several stages, no sequence of Groves' mechanisms guarantees that agents will reveal their true valuations as a dominant strategy. The contribution of this paper is the characterization of those mechanisms which guarantee truthful revelation in this environment.Received: 30 December 2001, Revised: 27 March 2003, JEL Classification Numbers: D61, D78, D82, H41.This paper has greatly benefited from the ideas and comments of Sandro Brusco, Luis Corchón and Roberto Burguet. I would also like to thank José Alcalde, Luis J. Alías, Javier López-Cuñat, Juan Vicente Llinares, Ashley Piggins, Juan Perote and Antonio Quesada for very helpful suggestions. I am also grateful to an anonymous referee whose suggestions aided the quality of exposition in the paper and led me to Proposition 4.     

Toward ‘privatization’ of public sector output: decentralized contracting for public and private goods

Public sector goods and services can be produced in the private sector. The challenge is to provide incentives for allocative and technological efficiency. Either of two mechanisms is proposed to accomplish this. To ensure allocative efficiency, the proposed mechanisms require knowledge of the complete schedule of benefits. Alternatively, they can use information available on benefits in an efficient manner. Costs need not be known to authorities. Profit maximization leads to efficient private sector responses to cost changes over time. Either mechanism can be combined with the demand revealing process to circumvent the need for ex ante information on benefits.     

Minimum participation rules for the provision of public goods

This paper considers the endogenous formation of an institution to provide a public good. If the institution governs only its members, players have an incentive to free ride on the institution formation of others and the social dilemma is simply shifted to a higher level. Addressing this second-order social dilemma, we study the effectiveness of three different minimum participation requirements: (1) full participation/unanimity rule; (2) partial participation; (3) unanimity first and in case of failure partial participation. While unanimity is most effective once established, one might suspect that a weaker minimum participation rule is preferable in practice as it might facilitate the formation of the institution. The data of our laboratory experiment do not support this latter view, though. In fact, weakening the participation requirement does not increase the number of implemented institutions. Thus, we conclude that the most effective participation requirement is the unanimity rule which leaves no room for free riding on either level of the social dilemma.     

Private provision of discrete public goods

We investigate private provision of discrete public goods under refund and cost-sharing. If it is commonly believed that individuals may be warm-glow altruists and the group-size is a Poisson random variable, then the equilibrium distribution of collected contributions is uniquely determined. If composition uncertainty is very small and the expected group-size sufficiently large, the distribution of contributions can be described by concentrating in a symmetric mixed-strategy equilibrium. As the expected group-size increases, the probability a randomly selected player contributes and the associated expected number of contributions converge to the corresponding ones in the symmetric mixed-strategy equilibrium of the game with no uncertainty.     

The importance of considering optimal government policy when social norms matter for the private provision of public goods

We study optimal government policy in a reference model (Rege, 2004, Journal of Public Economic Theory, 6, 65–77) of public good provision and social approval in a dynamic setting. We show that even if complete adherence to the social norm maximizes social welfare it is by no means necessarily optimal to push society toward it. We stress the different roles of social externality and the public good problem. We discuss the problem with the standard crowding in and out argument and analyze the relationship with Pigouvian taxes. We discuss the role of the cost of public funds and show how it can create path dependency, the multiplicity of both optimal equilibria and optimal paths, and discuss the role of parameter instability.     

A pigovian rule for the optimum provision of public goods

The integrated treatment of optimal taxation and public expenditure presented here is based on the dual relationship between the prices of private goods and the quantities of public goods. The conditions for optimum public good provision can be expressed as a modification of the Samuelson conditions with extra terms representing (a) the distortionary effect of taxes on the willingness to pay for the public good, and (b) distributional effects. The former captures Pigou's notion of the indirect damage caused by the need to finance public expenditure out of distortionary taxes, and we call this the ‘Pigou term’. In certain cases a very simple benefit-cost ratio for public projects emerges that is equivalent to measuring benefits as if they were taxed.     

The scope of satisfactory mechanisms for the provision of public goods

This paper establishes the existence of satisfactory public-good provision mechanisms when utilities are nonseparable. The assumptions used to obtain this result are: (1) that the public good is continuously variable; (2) that utility functions are parametrically representable and twice continuously differentiable; and (3) that the provision rule is a strictly increasing function of the reported marginal rates of substitution between the public good and the private good. The satisfactory mechanisms derived are all augmented Groves mechanisms and are equivalent to Groves mechanisms if, and only if, each consumer's utility function is additive in income.     

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.     

On commodity tax harmonization and public goods provision

This paper argues that Pareto improvements based on harmonizing tax reforms expressed in terms of the divergence between actual and optimal tax structures and over/under provision of public goods require the use of ‘pseudo-optimal’ taxes instead of optimal ones. ‘Pseudo-optimal’ taxes are defined as those obtained using the optimal tax formulas but evaluated at any arbitrary initial tax structure. Within this context the paper reconfirms existing results showing that tax harmonization emerges as a strong policy instrument in achieving a potential Pareto-improvement.