Public Good Model Research Articles

Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model

Fershtman and Nitzan (1991) presented a continuous dynamic public good game model and solved the model for feedback Nash-equilibria. Wirl (1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case the volatility of the diffusion term is dependent on the current level of the public good. This setup will in principle lead to the same feedback strategies computed under certainty. In the second case the volatility is dependent on the current rate of public good provision by the agents. The result in this case is qualitatively different from the first one. We provide a detailed discussion of our results as well as numerical examples.

Spatial dynamics of ecological public goods

The production, consumption, and exploitation of common resources ranging from extracellular products in microorganisms to global issues of climate change refer to public goods interactions. Individuals can cooperate and sustain common resources at some cost or defect and exploit the resources without contributing. This generates a conflict of interest, which characterizes social dilemmas: Individual selection favors defectors, but for the community, it is best if everybody cooperates. Traditional models of public goods do not take into account that benefits of the common resource enable cooperators to maintain higher population densities. This leads to a natural feedback between population dynamics and interaction group sizes as captured by "ecological public goods." Here, we show that the spatial evolutionary dynamics of ecological public goods in "selection-diffusion" systems promotes cooperation based on different types of pattern formation processes. In spatial settings, individuals can migrate (diffuse) to populate new territories. Slow diffusion of cooperators fosters aggregation in highly productive patches (activation), whereas fast diffusion enables defectors to readily locate and exploit these patches (inhibition). These antagonistic forces promote coexistence of cooperators and defectors in static or dynamic patterns, including spatial chaos of ever-changing configurations. The local environment of cooperators and defectors is shaped by the production or consumption of common resources. Hence, diffusion-induced self-organization into spatial patterns not only enhances cooperation but also provides simple mechanisms for the spontaneous generation of habitat diversity, which denotes a crucial determinant of the viability of ecological systems.

Dynamic Voluntary Provision of Public Goods with Uncertainty: A Stochastic Differential Game Model

Fershtman and Nitzan (1991) presented a continuous dynamic public good game model and solved the model for feedback Nash-equilibria. Wirl (1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case the volatility of the diffusion term is dependent on the current level of the public good. This setup will in principle lead to the same feedback strategies computed under certainty. In the second case the volatility is dependent on the current rate of public good provision by the agents. The result in this case is qualitatively different from the first one. We provide a detailed discussion of our results as well as numerical examples.

THE EFFECTS OF UNCERTAINTY ON THE VOLUNTARY PRIVATE PROVISION OF IMPURE PUBLIC GOODS

This paper examines the effects of uncertainty on an individual's own contribution to the provision of the collective good using an impure public good model. Two types of uncertainty analyzing free-riding behavior are evaluated: (i) uncertainty surrounding the contributions of others to the public characteristic and (ii) uncertainty surrounding the response of others to an individual's own contribution. We extend previous studies by examining both the compensated and uncompensated effects of increases in such risks on the provision of the collective good. We also establish the conditions that are sufficient to determine both compensated and the total, uncompensated effects of an increase in risk on the voluntary provision of the collective good.

Voluntary Provision of Public Goods for Bads: A Theory of Environmental Offsets

This article examines voluntary provision of a public good that is motivated, in part, to compensate for activities that diminish the public good. Markets for environmental offsets, such as those that promote carbon neutrality, provide an increasingly salient example. An important result is that mean donations do not converge to zero as the economy grows large. The equilibrium is solved to show how direct donations and net contributions depend on wealth and heterogeneous preferences. Comparative static analysis demonstrates how public good provision and social welfare depend on the technology, individual wealth and an initial level of the public good. Why do individuals voluntarily provide public goods? The question has received much attention in the economics literature, and two general answers have emerged. The first is based on a standard model of private provision of a pure public good. Agents are assumed to benefit from the aggregate level of a public good and thus have some incentive for private provision. While the additional incentive to free ride ensures that the equilibrium level of the public good will fall short of the Pareto-efficient level, the theory nevertheless predicts some degree of voluntary provision. 1 The second explanation has grown out of the need to reconcile why observed levels of private provision regularly exceed those that the standard theory predicts. Research in this area can be characterised broadly as refinements or extensions on the impure public good model. The general approach is to assume that agents obtain a private benefit from some aspect of their own provision and this encourages provision beyond that which would occur if benefits came from only the public good itself. Different interpretations of the private benefit range from a feeling of warm-glow satisfaction, social approval, prestige and signalling about income. 2 The present article pursues a further explanation for voluntary provision of a public good. The idea is that provision may occur, in part, to offset other activities that have an adverse effect on a public good. Consider an activity that produces a negative externality through diminishing the level of a public good. Assuming the individual cares enough about the public good, she may seek to minimise her adverse effect on it. One possibility is for the individual to restrain her behaviour voluntarily. 3 Another possibility, which need not be mutually exclusive, is for the individual to offset some (or all) of her detrimental effect through direct provision of the public good.

Effects of the CDM on poverty eradication and global climate protection

In an impure public good model we analyze the effects of CDM transfers on poverty as well as on the global climate protection level. We construct an analytical model of a developing and an industrialized region, both of which independently seek to maximize their utility – a function of private consumption, domestic air quality, and global climate protection. They do so by distributing their finite expenditures across (1) the aggregate consumption good, (2) end-of-pipe pollution control technologies, and (3) greenhouse gas abatement. Based on our analytical findings, we develop two sets of simulations for China in which we vary the rate of the CDM transfer. The simulations differ by the assumption of China’s domestic air quality policy – the first assumes a technology-standards policy which fixes a level of end-of-pipe SO2 control, whereas the second assumes a technology-neutral policy which simply fixes the level of total SO2 emissions.

Effects of the CDM on Poverty Eradication and Global Climate Protection

In an impure public good model we analyze the effects of CDM transfers on poverty as well as on the global climate protection level. We construct an analytical model of a developing and an industrialized region, both of which independently seek to maximize their utility - a function of private consumption, domestic air quality, and global climate protection. They do so by distributing their finite expenditures across (1) the aggregate consumption good, (2) end-of-pipe pollution control technologies, and (3) greenhouse gas abatement. Based on our analytical findings, we develop two sets of simulations for China in which we vary the rate of the CDM transfer. The simulations differ by the assumption of China's domestic air quality policy - the first assumes a technology-standards policy which fixes a level of end-of-pipe SO2 control, whereas the second assumes a technology-neutral policy which simply fixes the level of total SO2 emissions.

An Experimental Study on the Gap between Willingness to Pay and Willingness to Donate for Green Electricity

According to Champ et al. (1997), we have to differentiate between willingness to pay (WTP) and willingness to donate (WTD) in eliciting individual preferences for public goods. Because strong incentives exist to understate the willingness to spend on the public good and to freeride on other people’s contributions, WTP forms the upper limit for WTD. This paper presents an experimental study on the size of the gap between WTP and WTD in the context of green electricity promotion, where making electricity markets ‘‘greener’’ can be interpreted contributing to the public good “environmental quality”. Our theoretical model is based on the impure public good model (Cornes and Sandler, 1984, 1994). It enables us to directly investigate the extent of free-riding in the sample. In the individual-choice scenario, subjects are induced to act as market participants and thereby reveal their WTP, while the public-choice scenario is designed as a majority vote on the preferred level of green electricity. Since free-riding is impossible, the latter treatment reveals subjects’ WTD. The data analysis reveals a strong treatment effect concerning the decision mode: under the public choice treatments, participants were willing to pay about three times higher contributions to green electricity than under the individual choice treatments. This observation highlights the large extent of free-riding in the private provision of the public good “environmental quality”.

Political Cycles: Issue Ownership and the Opposition Advantage

AbstractIn modern democracies, common wisdom suggests that political parties alternate in power due to voters' disappointment. The aim of this paper is to show that parties' turnover may be due to voters' “satisfaction.” Our model is built on two main assumptions: Parties “own” different issues, and investments in the provision of public goods create a linkage between successive elections. We show that no party can maintain itself in power forever when the median voter is moderate enough. This result holds when the parties' main objective is to win the election and is compatible with a large range of candidates subobjectives that may change from one election to the next. We also provide some novel welfare implications. Whereas rent‐seeker candidates always dominate reelection‐concerned candidates in one public good models, rent‐seeker candidates may be welfare improving compared with reelection‐concerned candidates.

Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization

We introduce a model of a local public goods economy with a continuum of agents and jurisdictions with finite but unbounded populations, where the set of possible projects for each jurisdiction/club is unrestricted in size. Under boundedness of per capita payoffs, which simply ensures that equal treatment payoffs are bounded above, we apply results of Kaneko and Wooders (1986) to obtain nonemptiness of the core of the economy. We then demonstrate, under the stronger condition of strict small group effectiveness, that the equal treatment core coincides with the set of price-taking equilibrium outcomes with anonymous prices—that is, prices for public goods depend only on observable characteristics of agents. Existence of equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach provides a new technique for showing existence of equilibrium in economies with a continuum of agents.

Choosing How to Cooperate: A Repeated Public-Goods Model of International Relations

International relations theory has borrowed important intuitions from Olson’s static public-goods model (hegemonic stability) and the repeated prisoners’ dilemma (theories of international cooperation), and arguments often combine implications from both models. We develop a general, repeated public-goods model. We then allow the qualitative dimensions of cooperation to emerge endogenously: agreements can have broad or narrow membership and entail deep or shallow commitments; they can be multilateral or discriminatory; they can be ad hoc or institutionalized. We find that the relationship between the distribution of power and international cooperation is complex: a large leading state forms a narrow coalition of intensive contributors, and builds institutions, while a smaller leading state forms a broader coalition that makes shallow contributions, and is more inclined to multilateralism.

The Vancouver Community Network, Social Investing and Public Good Models of ICT development

This paper links discussions of community access to ICTs to discussions of sustainability in the non-profit community and the viability of public good models of ICT development. It addresses the concepts of public goods and social entrepreneurship and their relationship to new funding sources for non-profit organizations. The paper examines the Vancouver Community Network’s investigation of for-profit service models to diversify the organization’s revenue stream. The paper suggests that the VCN has the potential to develop a project that may provide the basis for a new generation of community networking in Canada, based upon a new organizational structure model.

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.

EVALUATING GAINS FROM MERGERS IN A NON-PARAMETRIC PUBLIC GOOD MODEL OF POLICE SERVICES

ABSTRACT**: The merger of police services in the UK has been suggested on the grounds that efficiency improvements will be possible. This paper applies a public good model of the police service to evaluate the potential efficiency gains from mergers of police services in England and Wales. It uses a non-parametric method suggested by Bogetoft and Wang (2005). We construct a dataset that reflects the public good nature of police service and allows for the exogenous imposition by government on the level of police service budgets. Our main finding is that English and Welsh police service mergers could lead to increases in police staff resource efficiencies between 10 per cent and 70 per cent. Hence, we confirm the government's decision to merge English and Welsh police services.

Equilibrium existence and uniqueness in impure public good models

Despite widespread application of the impure public good model, surprisingly little attention has been given to the model's equilibrium properties. This paper presents a proof that clearly shows sufficient conditions for existence and uniqueness of a Nash equilibrium.

The complementarity of Tiebout and Alonso

While residential location is an important aspect of both models of urban spatial structure and local public goods, previous modeling efforts have most commonly separated these. The resulting models yield unrealistic locational predictions. This paper incorporates both motivations simultaneously and finds that the equilibrium outcomes are more consistent with empirical observation. Having a more realistic model permits analysis of current school finance proposals. Because school finance is focused on local jurisdictions, having a more realistic general equilibrium model is essential to assess the impact of governmental involvement on the K-12 school system.

Aggregative Public Good Games

AbstractWe exploit the aggregative structure of the public good model to provide a simple analysis of the voluntary contribution game. In contrast to the best response function approach, ours avoids the proliferation of dimensions as the number of players is increased, and can readily analyze games involving many heterogeneous players. We demonstrate the approach at work on the standard pure public good model and show how it can analyze extensions of the basic model.

Climate Coalitions: A Theoretical and Computational Appraisal

Using an updated version of the CWS model (introduced by Eyckmans and Tulkens in Resource and Energy Economics 2003), this paper intends to evaluate with numbers the respective merits of two competing notions of coalition stability in the standard global public goods model as customarily applied to the climate change problem. After a reminder of the model structure and of the definition of the two game theoretical stability notions involved - namely, core stability and internal-external stability, the former property is shown to hold for the grand coalition in the CWS model only if resource transfers of a specific form between countries are introduced. It is further shown that while the latter property holds neither for the grand coalition nor for most large coalitions, it is nevertheless verified in a weak sense that involves transfers (dubbed potential internal stability) for most small coalitions. The reason for this difference is brought to light, namely the differing rationale that inspires the transfers in either case. Finally, it is shown that the stable coalitions that perform best (in terms of carbon concentration and global welfare) are always composed of both industrialized and developing countries. Two sensitivity analyses confirm the robustness of all these results.

Jack Hirshleifer: A Nobel Prize left unbestowed

Jack Hirshleifer (1925–2005) contributed to investment theory, information economics, conflict, and bioeconomics, clarified the foundations of investment and capital theory in the spirit of Fisher, and made basic contributions to the analysis of covariance risk, gambling and insurance, the Modigliani–Miller Theorem, and public investment through a focus on time, uncertainty and information. He formulated new models of public goods, added to understanding of contest success functions, and explained the paradox of power. He developed a general equilibrium approach to conflict jointly encompassing production, exchange, appropriation and defense. He analyzed the emotions as guarantors of threats and promises, proposed alternatives to the tit-for-tat strategy, considered the bioeconomic causes of war, and investigated the truthful signaling hypothesis. Jack Hirshleifer was a leading scholar and original thinker of the 20th century. His scientific contributions have left a Nobel Prize unbestowed.

Global Environment and International Transfer: A Case without the Transfer of Initial Endowments

In recent years, the global environment has been regarded as one of the most important international public goods. Using the simple public good model, this paper examines an economic implication of the transfer from home country to a foreign country on the global environment and each country's economic welfare. In the literature of international transfers, it has been shown that any slight reallocations of initial endowment between two countries have no effect on the quantity of an international public good and the level of each country's economic welfare. It is important, however, to notice that there are some cases initial endowment of one country can not been transfered to the other country. This paper constructs a model where home country sends to a foreign country an amount of a good which is produced in home country. The result in this paper is as follows. If home country produces a good more efficiently and less harmfully to the global environment than a foreign country, the increase of transfer of the good makes better the global environment and improves the economic welfare of not only the foreign country which receives the transfer but also home country which sends it. On the contrary, if home country produces a good less efficiently and more harmfully to the global environment than the foreign country, the increase of transfer of the good makes worse the global environment and deteriorates the economic welfare of not only home country which sends the transfer but also the foreign country which receives it.JEL classification: H87, R13, Q58