Double implementation in economies with production technologies unknown to the designer

Summary. This paper considers double implementation of Walrasian allocations and Lindahl allocations in Nash and strong Nash equilibria for both private and public goods economies when preferences, initial endowments, production technologies, and coalition patterns are all unknown to the designer. It will be noted that the mechanisms presented here are feasible and continuous. In addition, unlike most mechanisms proposed in the literature, our mechanism works not only for three or more agents, but also for two-agent economies, and thus it is a unified mechanism which is irrespective of the number of agents. Received: March 12, 1998; revised version: March 12, 1998     

Incentive Mechanism Design for Production Economies with Both Private and Public Ownerships

In this paper we deal with the problem of incentive mechanism design which yields efficient allocations for general mixed ownership economies when preferences, individual endowments, and coalition patterns among individuals are unknown to the planner. We do so by doubly implementing the proportional solution for economies with any number of private sector and public sector commodities and any number of individuals as well as the coexistence of privately and publicly owned firms with general convex production possibility sets. Furthermore, the mechanisms work not only for three or more agents, but also for two-agent economies. Journal of Economic Literature Classification Numbers: C72, D61, D71, D82.     

A Unique Informationally Efficient Allocation Mechanism In Economies With Consumption Externalities*

This article investigates the informational requirements of resource allocation processes in pure exchange economies with consumption externalities. It is shown that the distributive Lindahl mechanism has a minimal informational size of the message space, and thus it is informationally the most efficient allocation process that is informationally decentralized and realizes Pareto‐efficient allocations over the class of economies that include nonmalevolent economies. Furthermore, it is shown that the distributive Lindahl mechanism is the unique informationally efficient decentralized mechanism that realizes Pareto‐efficient and individually rational allocations over a certain class of nonmalevolent economies.     

Kant and Lindahl*

In 1896 and 1919, respectively, Wicksell and Lindahl analyzed the public provision of public goods through parliamentary negotiation. Later, Roemer applied Kant's 1785 imperatives to the private provision of public goods by voluntary contributions. Our focal equilibrium notions are the balanced linear cost-share equilibrium for the Wicksell–Lindahl approach and the multiplicative Kantian equilibrium in the Kant–Roemer modeling. These turn out to be fundamentally equivalent, being defined by the same individual optimization problem. These notions fit well with the idea that technology is publicly owned, but we also extend them to cover private-ownership economies with exogenously given profit shares. We show that the equivalence between the Wicksell–Lindahl and Kant–Roemer notions carries over to them.     

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.     

A reconsideration of the problem of social cost: Free riders and monopolists

Summary. One version of the Coase Theorem is, If property rights are fully allocated, competition leads to efficient allocations. This version implies that the public goods problem can be solved by allocating property rights fully. We show that this mechanism is not likely to work well in economies with global externalities because the privatized economy is highly susceptible to strategic behavior: The free-rider problem manifests itself as a complementary monopoly problem in an associated private goods economy. Thus, our work relates the validity of the Coase Theorem to the literature on the incentives for strategic behavior in economies with complementarities. Received: 12 May 1999; revised version: 9 July 1999     

On the set of Pareto efficient allocations in economies with public goods

Summary We examine the set of Pareto-efficient allocations in economies with public goods. We show that even if preferences are continuous and strongly monotonic, it need not coincide with the set of weakly efficient allocations. We then study topological properties of the Pareto set. We show that it is neither connected nor closed in allocation space. Furthermore, if the public goods are local, the image of the Pareto set in utility space need not be closed or connected. We provide two independent sufficient conditions for the closedness of the Pareto set. The results are directly applicable to private goods economies with joint production. Our results should be of interest for general equilibrium and mechanism design theory; where for example, the properties of the efficient set are important for proving the existence of an equilibrium and for the study of the properties of monotone-path social choice correspondences.We thank Hideo Konishi, Tomoichi Shinotsuka, Nicholas Yannelis and an anonymous referee for valuable comments on previous drafts of this paper.     

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     

Existence of Lindahl equilibria in measure theoretic economies without ordered preferences

A proof of the existence of Lindahl equilibria is given for a class of measure theoretic economies, possibly atomless, in which consumers' preferences need be neither complete nor transitive. This is done as an application of a nonstandard-analytic technique that allows for the derivation of statements concerning measure theoretic economies from analogous finite economy propositions. This approach to the problem allows use of Foley's method of working with an associated private goods economy without the dimension of the commodity space in the associated economy becoming problematic. Potential extensions of the technique used are also discussed.     

Edgeworth and Lindahl–Foley equilibria of a General Equilibrium Model with Private Provision of Pure Public Goods

In this paper, we propose a definition of Edgeworth equilibrium for a private ownership production economy with (possibly infinitely) many private goods and a finite number of pure public goods. We show that Edgeworth equilibria exist whatever be the dimension of the private goods space and can be decentralized, in the finite and infinite dimensional cases, as Lindahl–Foley equilibria. Existence theorems for Lindahl–Foley equilibria are a by‐product of our results.     

A STABLE NASH MECHANISM FOR QUASI-ADDITIVE PUBLIC-GOOD ENVIRONMENTS*

In this paper we present a simple game form implementing Lindahl allocations as Nash equilibrium outcomes, which has nice stability properties. we show that if the preferences of eaach consumer are representable by a utility function of the form a(y)x_i+b_i(y), where x_i(y), where x_i is the amount of private good and y, the amount of public good, then the Nash equilibrium of our geme is locally stable under the gradient adjustment process. This restriction on the preferences has been known in hte literature as the necessary and sufficient condition for the Pareto optimal amount of pukic goods to be independent of the private goods distribution. This type of preference includes quasi-linear preferences as a special case. but unlike quasi-linearity, this allows a non zero income effect of demand for public goods as well as private goods, which is often supported by empirical evidence. Our result shows how an equilbirium can be achieved over time by a decentralized strategy adjustement process for a fairly general class of environments, even in the absence of a dominant-strategy equilibrium.     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Bargaining over Public Goods

In a simple public good economy, we propose a natural bargaining procedure, the equilibria of which converge to Lindahl allocations as the cost of bargaining vanishes. The procedure splits the decision over the allocation in a decision about personalized prices and a decision about output levels for the public good. Since this procedure does not assume price-taking behavior, it provides a strategic foundation for the personalized taxes inherent in the Lindahl solution to the public goods problem.     

An Allocation Rule with Wealth-Regressive Tax Rates

We introduce a public good allocation rule whose direct implementation by asking agents their endowments leads to Nash equilibrium outcomes—always Pareto dominating voluntary contributions outcomes. Although the Nash equilibrium allocations induced by this rule are not Pareto optimal in general, they are so in two-person economies.     

Equivalence of Lindahl equilibrium with participation prices and the core

Summary In a model of an economy with multiple public goods and differentiated crowding, it is shown that asymptotically the core has the equal treatment property and coincides with the equilibrium outcomes. It follows that all individuals of the same type in the same jurisdiction must pay the same Lindahl taxes and, with strict convexity of preferences, the same Lindahl prices. With only one private good, for sufficiently large economies we show (a) the equivalence of the core and the set of equilibrium outcomes and (b) the nonemptiness of approximate cores and their equivalence to the set of approximate equilibrium outcomes.The author is indebted to Vicky Barham, John Conley, Hideo Konishi, Julian Manning and Roma Jakiwczyk for comments on an earlier draft of this paper. The author gratefully acknowledges the research support of the Social Sciences and Humanities Research Council of Canada.     

Coalitional instability of the distributive Lindahl equilibrium

Summary Bergstrom [3] has showed that the Lindahlian approach to the analysis of public goods may also be used to analyze a model of wide-spread externalities in which agents have preferences defined on allocations rather than on individual commodity bundles. He has provided versions of the first and second welfare theorem for adistributive Lindahl equilibrium and also presented sufficient conditions for its existence. However, we shall show that, in contrast to Foley's [4] result on the core stability of a Lindahl equilibrium, a distributive Lindahl equilibrium need not satisfy coalitional stability. We will provide a robust example in which the unique, distributive Lindahl equilibrium does not belong to the -core defined either as in Scarf [11] or as in Yannelis [12].I would like to thank F. Canova, R. Serrano, M. Spagat, R. Vohra at Brown University, P. C. Padoan at University of Rome and an anonymous referee for their comments. I am also grateful to the participants at the Third Annual MeetingColloquia on Economic Research at I.G.I.E.R. in Milan, Italy, and to the participants at the Citibank Workshop in Economic Theory at Brown University.     

Nash implementation in production economies

Summary This paper provides a general way to incorporate private ownership production economies into the implementation of the Walrasian correspondence. We present two mechanisms, both of which permit agents to behave strategically with respect to their initial endowments, preferences, and production possibility sets. The first mechanism deals with the case of endowment destruction, the second deals with the case of endowment withholding. We show that each mechanism Nash implements the Walrasian correspondence. In addition, both mechanisms are individually feasible, balanced, continuous and only require the transmission of prices and quantities of goods as messages.This paper is based on Chapters 2 and 3 of my dissertation submitted to the University of Minnesota. I want to thank E. Green, J. Jordan, M. Richter, H. Weinberger and especially L. Hurwicz for their many helpful suggestions and comments.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

A revised concept of distributional equity

Recent studies have shown that in a private goods economy with production, allocations which are considered to be distributionally fair may not exist. As a solution for such cases, just allocations are introduced and examined in some detail. Such allocations are shown, by rigorous proof, to exist in general.