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     

Congestion effects in a public-good economy

This paper considers a public-good economy with congestion, where participants jointly produce a public good from input of a private good. This economic model gives rise to a transferable-utility game, the profit game, that depends on consumer preferences and a congestion parameter. The simplicity of the game allows the maximum level of congestion that guarantees the nonemptiness of the core of the economy to be determined. It is known that the sustainability of the Lindahl equilibrium in the core of the economy depends on the distribution of profits. In this paper two distributions of profits are compared: the Lindahl solution and the marginal-contribution solution. The latter is more often in the core than the Lindahl solution which in turn Lorenz-dominates the marginal-contribution solution.     

A graphic representation of the Nash and Lindahl equilibria in an economy with a public good

In an economy with a public good the noncooperative Nash equilibrium and the cooperative Lindahl equilibrium are represented graphically. The Nash equilibrium is shown to be non-optimal, while the Lindahl equilibrium is shown to be optimal. Simple stability analyses are undertaken. Finally, the two equilibria are compared. It appears that more public good will be allocated in the Lindahl than in the Nash equilibrium, and that in a sufficiently large economy a transition from a Nash to a Lindahl equilibrium will be advantageous for everyone.     

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.     

A competitive idea-based growth model

ABSTRACT

In this paper, we present a model in which endogenous growth arises in competitive markets. Knowledge is described as a factor used directly in the final goods' production. Firms demand both basic nonrival knowledge contents, which are supplied jointly and inelastically with raw labor, and further contents supplied by patent holders. This fact, together with Lindahl prices for knowledge, allows competition to work, while it also implies that workers' income share declines overtime. In a first version of the model with constant cost of knowledge production, the first best is attained. In a further version of the model, in which the cost of knowledge production is allowed to change over time and thus intertemporal externalities arise, in a decentralized economy a second best equilibrium occurs in the transitional period, while in the long run there is convergence to efficiency.     

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.     

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.     

Economies with Multiple Public Projects

This paper discusses a general equilibrium model of an economy with multiple separately provided public projects. We assume an additively separable cost structure and consider valuation equilibria with separated finance systems, one for each collective good. Under non-Euclidean representation we show the decentralization of Pareto efficient allocations by valuation equilibria and the equivalence of the core and the set of nonnegative valuation equilibria. In the case of Euclidean representation, every Pareto efficient allocation is shown to be supported as an affine valuation equilibrium that is characterized by a personalized price per unit of each public good and a personalized lump sum tax or subsidy. These results complement and clarify already established insights into Lindahl pricing and its generalizations developed in the literature.     

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.     

Efficiency with Non-Convexities: Extending the “Scandinavian Consensus” Approaches

There are two distinct “Scandinavian consensus” approaches to public good supply, both based on agents' willingness to pay. A Wicksell–Foley public competitive equilibrium arises from a negative consensus in which no change of public environment, together with associated taxes and subsidies which finance it, will be unanimously approved. Alternatively, in a Lindahl or valuation equilibrium, charges for the public environment induce a positive consensus. To allow general non-convexities to be regarded as aspects of the public environment, we extend recent generalizations of these equilibrium notions and prove counterparts to both the usual fundamental efficiency theorems of welfare economics.     

Stackelberg thresholds in network routing games or the value of altruism

It is well known that the Nash equilibrium in network routing games can have strictly higher cost than the optimum cost. In Stackelberg routing games, where a fraction of flow is centrally-controlled, a natural problem is to route the centrally-controlled flow such that the overall cost of the resulting equilibrium is minimized.We consider the scenario where the network administrator wants to know the minimum amount of centrally-controlled flow such that the cost of the resulting equilibrium solution is strictly less than the cost of the Nash equilibrium. We call this threshold the Stackelberg threshold and prove that for networks of parallel links with linear latency functions, it is equal to the minimum of the Nash flows on links carrying more optimum flow than Nash flow.Our approach also provides a simpler proof of characterization of the minimum fraction that must be centrally controlled to induce the optimum solution.     

Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models

Summary. This paper extends the Samuelsonian overlapping generations general equilibrium framework to encompass a variety of altruistic preferences by recasting it into a Lindahl equilibrium framework. The First and the Second Welfare theorems hold for Lindahl equilibrium with respect to the Malinvaud optimality criterion but not with respect to the Pareto optimality criterion. A complete characterization of Pareto optimal allocations is provided using the Lindahl equilibrium prices.Received: 2 October 2003, Revised: 13 September 2004, JEL Classification Numbers: D51, D62, D64, C62.An earlier draft of the paper was prepared for presentation at the Sixth World Congress of the Econometric Society, 1990, Barcelona, Spain. Much of this work was done when I was at Yale University and University of California-San Diego. I am grateful to an anonymous referee of this journal and to Don Brown, Vince Crawford and Joel Sobel for many insightful comments and encouragements on an earlier draft of the paper.     

Public policies as specification errors

Treating public policies as computable dynamic general equilibrium model specification errors offers computational and conceptional advantages for comparing models with data. The set of policies calculated to rationalize observed behaviors raises the substantive economic question whether, in any particular market, actual public policies sufficiently coincide with the model's behavior-rationalizing policies, or whether the model offers correct hypotheses about the determinants of demand and supply. As illustrations, public policies are calculated to rationalize, with respect to the stochastic neoclassical growth model, capital market behavior since WWII and labor market behavior in 1929–1950. One conclusion is that capital taxation drives a wedge between consumption growth and the expected pre-tax capital return, in the direction and amount predicted by the theory, and that capital taxation is the major intertemporal distortion in the postwar capital market. Second, a good theory of the Great Depression labor market must explain why measured MRS and MPL diverged so dramatically in 1929–1933 and why the wedge persisted.     

Cooperative oligopoly equilibrium

Oligopoly cooperation is investigated in an industry with N firms: each firm selects its own output. We show that such oligopoly problems have the same structure as problems of allocating public goods since each firm views its own output as a private good while viewing the outputs of others as public bads. This leads to ‘cooperative oligopoly equilibria’ which are the Lindahl equilibria of the oligopoly model. Agreements are modeled by the selection of a mechanism or ‘game form’ which obeys certain axioms. Under the postulated axioms we show the equivalence of agreed allocations with the set of oligopoly equilibria.It is argued that the principle of ‘Lindahl agreements’ may have wider applications.     

Chores

We analyze situations where the provision of each of c public goods must be voluntarily assumed by exactly one of n private agents in the absence of transfer schemes or binding contracts. We model this problem as a complete information, potentially infinite horizon game where n agents simultaneously wage c wars of attrition. Providing a public good commits an agent not to take on the provision of another public good for a fixed period. We explore the strategic trade-offs that this commitment ability and the multiplicity of tasks provide. Subgame perfect equilibria (SPEs) are characterized completely for games with two agents and two public goods. For games with two identical agents and c > 1 identical public goods, we establish that an equilibrium that yields a surplus-maximizing outcome always exists and we provide sufficient conditions under which it is the unique equilibrium outcome. We show that under mild conditions, the surplus-maximizing SPE is the unique symmetric SPE. Journal of Economic Literature Classification Number: H41, C72, D13.     

Free entry into telecommunications?

The two leading principles of pricing for public enterprises are outlined: Value based and cost based pricing. It is shown that optimal pricing à la Ramsey-Boiteux is closely related to value based pricing which itself is connected with Lindahl pricing of public goods. Cost based pricing is related to the pricing in competitive markets. Opening up of telecommunication to competition implies a change from value based (public good) pricing to cost based (pritate good) pricing. It is shown why specific developments in telecommunication technology make a switch to cost based pricing and a competitive environment appropriate. At the end a proposal is developed for a gradual change towards competition which would meet less political resistance.     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Strength of the Social Dilemma in a Public Goods Experiment: An Exploration of the Error Hypothesis

We present the results of an experiment on voluntary contributions to a public good with a unique dominant strategy equilibrium in the interior of the strategy space. The treatment variable is the equilibrium contribution level. By increasing the equilibrium contribution level, we reduce the strength of the social dilemma. Though we observe that the average level of contribution rises with the equilibrium contribution level, the average rate of over-contribution is not affected in a systematic way. Over-contribution is statistically significant only at the lower level of equilibrium contribution but not at the higher levels. We show that the Anderson et al. (1998, Journal of Public Economics. 70, 297–323) logit equilibrium model which combines altruism and decision errors fits quite well our laboratory data.     

The Lindahl equilibrium in Schumpeterian growth models

The main motivation of the paper is to determine the social value of innovations in a standard scale-invariant Schumpeterian growth model, which explicitly introduces knowledge diffusion over a Salop (Bell J Econ 10(1):141–156 1979) circle. The social value of an innovation is defined as the optimal value of the knowledge inherent in this innovation. We thus have to price optimally knowledge. For that purpose, contrary to what is done in standard growth theory, we complete the markets using Lindahl prices for knowledge. The Lindahl equilibrium, which provides the system of prices that sustains the first-best social optimum in an economy with non rival goods, appears as a benchmark. First, its comparison with the standard Schumpeterian equilibrium à la Aghion and Howitt (Econometrica (60)2:323–351 1992) enables us to shed a new light on the issue of non-optimality of the latter. Second, the Lindahl equilibrium also allows us to revisit the issue of R&D incentives in presence of cumulative innovations. Finally, this benchmark may be a first step to understand how knowledge is exchanged in new technology sectors.     

Petty corruption

This paper analyzes a petty corruption model in which the entrepreneur’s type is drawn from an absolutely continuous probability distribution function F over [0, 1], and perfect Bayesian equilibrium is adopted as the solution concept for a one-stage game. In the one-stage game, if there is more than one bureaucrat, no project is approved with a strictly positive probability. For an infinitely repeated game, I show that the single window policy strictly increases the social benefits in a socially optimal equilibrium. I would like to thank Mukul Majumdar for valuable guidance and encouragement. I am also grateful to Kaushik Basu, Fernando Vega-Redondo, an anonymous referee, seminar participants at the international meeting for public economic theory (PET07) and especially Ani Guerdjikova and Roy Radner for helpful comments. Thanks are due to Hideaki Goto and Eunkyeong Lee for useful conversation.