Equity as a Prerequisite for Stable Cooperation in a Public-Good Economy - The Core Revisited

In this paper we explore the relationship between an equitable distribution of the cost shares in public-good provision on the one hand and the core property of an allocation on the other. In particular we show that it is an inhomogeneous distribution of cost shares that motivates some coalition of agents to separate and to block an initially given Pareto optimal allocation which can be interpreted as the outcome of a negotiation process when all agents form a grand coalition. Distributional equity of the individual burdens of public-good contribution is assessed by a specific sacrifice measure (the “Moulin sacrifice”) which is derived from the egalitarian-equivalent concept suggested by Moulin (1987). We also develop a simple core test by which it can be checked whether a given allocation is in the core thus being a possible outcome of a cooperative agreement in the public-good economy.public goods, core, equity, stability of cooperation

Justifying the Lindahl Solution as an Outcome of Fair Cooperation

The Lindahl equilibrium is mostly motivated by a rather artificial price mechanism. Even though the analogy to a competitive market has been emphasised by Lindahl himself his approach does not directly explain the normative ideas, which are behind this concept. In the present paper we therefore show how the Lindahl equilibrium can be deduced from some simple equity axioms that in particular are related to the equal sacrifice principle and a non-envy postulate as norms for distributional equity. Fairness among agents with different preferences is taken into account by considering their marginal willingnesses to pay as virtual prices. In this way it might also become more understandable why the Lindahl solution can be perceived as an outcome of fair cooperation.public goods, Lindahl equilibrium, fairness, equity

The Edgeworth Conjecture in a Public Goods Economy: An Elementary Example

We show by a simple example that in a public goods economy consisting of identical individuals with symmetric Cobb-Douglas preferences the core of the economy does not con-verge to the Lindahl solution when the number of agents goes to infinity. This confirms in an elementary way that the Edgeworth conjecture does not necessarily hold in an economy with a public good.core

Equal Sacrifice and Fair Burden Sharing in a Public Goods Economy

Applying a willingness to pay approach known from contingent valuation in environmental economics, we develop an ordinally based measure for the size of individual sacrifice that is connected with an agent's contribution to a public good. We construct a selection mechanism that picks the unique efficient solution among all allocations that have an equal sacrifice as defined in this way. We show that the solution thus obtained correspond to Moulin’s egalitarian equivalent allocation, conforms to both the ability to pay and the benefit principles, and has much in common with the Lindahl equilibrium.public goods, cooperative solutions, fairness, egalitarian equivalent solutions

EXISTENCE, UNIQUENESS AND SOME COMPARATIVE STATICS FOR RATIO- AND LINDAHL EQUILIBRIA: NEW WINE IN OLD BOTTLES

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 ex-ploited to facilitate comparative static analysis of Lindahl and cost share equilibria.Public goods, Lindahl equilibrium, ratio equilibrium.

Existence, Uniqueness and Some Comparative Statics for Ratio- and Lindahl Equilibria: New Wine in Old Bottles

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 ex-ploited to facilitate comparative static analysis of Lindahl and cost share equilibria.public goods, Lindahl equilibrium, ratio equilibrium

Expected Utility theory and the tyranny of catastrophic risks

Expected Utility theory is not only applied to individual choices but also to ethical decisions, e.g. in cost-benefit analysis of climate change policy measures that affect future generations. In this context the crucial question arises whether EU theory is able to deal with 'catastrophic risks', i.e. risks of high, but very unlikely losses, in an ethically appealing way. In this paper we show that this is not the case. Rather, if in the framework of EU theory a plausible level of risk aversion is assumed, a 'tyranny of catastrophic risk' (TCR) emerges, i.e. project evaluation may be dominated by the catastrophic event even if its probability is negligibly small. With low degrees of risk aversion, however the catastrophic risk eventually has no impact at all when its probability goes to zero which is ethically not acceptable as well. --utilitarianism,Expected Utility theory,catastrophic risks

Discounting the Long-Distant Future: A Simple Explanation for the Weitzman-Gollier-Puzzle

In this paper, we reconsider the debate on Weitzman's (1998) suggestion to discount the long-run future at the lowest possible rate, referring to Gollier (2004) and Hepburn & Groom (2007). We show that, while Weitzman's use of the present value approach may indeed seem questionable, its outcome, i.e. a discount rate that is declining over time, is nevertheless reasonable, since it can be justified by assuming a plausible degree of risk aversion.discount rates, uncertainty, risk aversion

Intertemporal evaluation criteria for climate change policy: the basic ethical issues

The evaluation of long-term effects of climate change in cost-benefit analysis has a long tradition in environmental economics. Since the publication of the Stern Review in 2006 the debate about the 'appropriate' discounting of future welfare and utility levels was revived and the most renowned scholars of the profession participated in this debate. But it seems that some contributions dealing with the Stern Review and the Review itself mixed up normative and positive issues to defend the own position. Furthermore, as we argue in this contribution, it also seems that the debate misses the heart of the problem. The aim of this work is to bring together economic and philosophical reasoning about justice and intergenerational equity in the context of climate change. So we adopt the normative view in order to present the most important ethical issues that, particularly in the context of climate policy, are most relevant for the choice of intertemporal welfare criteria. Subsequently we explore whether ethical considerations may also be helpful to determine the parameter values (or at least to delimit their range) which, after the choice of some type of intertemporal social welfare function, are needed to specify the concrete criterion that is employed to make decisions on climate policy. --Intertemporal ethics,Distribution,Discounting,Climate Change

Discounting and Welfare Analysis Over Time: Choosing the ç

Based on the Ramsey equation and an ethically motivated rejection of pure utility time discount, the Stern Review on the Economics of Climate Change concentrates on the use of the elasticity of marginal utility ç in the intergenerational social welfare function. We support this position by showing that, also from the view point of sustainability, application of ç is preferable to the use of the pure time discount parameter ñ when a balanced distribution of utility across generations is to be brought about. After reviewing empirical studies on the size of ç we develop a novel axiomatic approach based on non–envy criteria by which we obtain values for ç lying in a range between 1 and 2. Whereas the starting point of the Stern Review quite explicitly is an ethical one, many critics of the Review deny this ethical stance and thus – as described in our paper – miss a crucial element of the Stern Review.Ramsey equation, discounting, sustainability, non-envy