Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth

Summary. We prove the existence and efficiency of equilibrium in economies with infinitely many consumers in which there are finitely many agents who own a positive portion of the aggregate endowment. We prove existence for commodity spaces which are employed in the general equilibrium asset pricing models and use incomplete and intransitive preferences. We discuss the importance of existence of finitely many agents who own a positive portion of the aggregate endowment in obtaining efficient equilibrium. For general equilibrium asset pricing applications we require forward properness only at individually rational Pareto optimal allocations. We provide an Arrow-Debreu model for these economies. We also give an application of our approach and results by employing Stochastic Differential Utility as the utility of each consumer in an infinite horizon model.     

Efficiency in an Economy with Fixed Costs

It is by now well known that in an economy with increasing returns, first-best efficiency may be impossible to attain through an equilibrium concept based on market prices, even if firms are regulated to follow marginal cost pricing. We examine the efficiency issue in a special but important class of economies in which the only source of nonconvexities is the presence of fixed costs. Even in this context, it is possible that none of the equilibria based on marginal cost pricing are efficient (unless additional, strong assumptions are made). We argue that available results on the existence of an efficient two-part tariff equilibrium rely on very strong assumptions, and we provide a positive result using a weak surplus condition. Our approach can also be used to establish the existence of an efficient marginal cost pricing equilibrium with endogenously chosen lump-sum taxes if the initial endowment is efficient in the economy without the production technology.     

Value theory with personalized trading

This paper extends existing general equilibrium theory to describe the competitive production and allocation of “personalized commodities:” commodities with only one potential buyer or seller. The basic, novel theoretic possibility introduced into value theory with the introduction of personalized trading—the trading of personalized commodities—is that price discrimination over quantity may occur under perfect competition. Theorems on the existence and optimality of competitive equilibria under discriminatory pricing are proved.     

Equilibrium with nonconvex technologies

Summary We provide an elementary proof of the existence of equilibrium in a general equilibrium model allowing for non-convex production sets. It is shown that when firms follow upper hemicontinuous and convex-valued pricing rules with bounded losses, a price vector and an allocation exist, such that all agents are in equilibrium and all markets clear.The existence result presented in this paper is a particular case of that one in Bonnisseau & Cornet (1988, Th. 2.1). In this respect our contribution consists of presenting an alternative proof which turns-out to be simpler and more intuitive.Thanks are due to Carmen Herrero and two anonymous referees for very helpful comments. Financial support from theDirection General de Investigación Cientiflca y Ténica, under project PS89–0066, is gratefully acknowledged.     

Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

Summary. Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima. Received: February 16, 2000; revised version: July 7, 2001     

To Trade Or Not To Trade: Economies With A Variable Number Of Tradeables*

We present a general equilibrium model that encompasses the endogenous selection and shadow‐pricing of a set of tradeable commodities, with home‐based and social production activities. In the model, a market system is a set of costly social institutions which embody the trade and production technologies available in the economy. Our equilibrium concept describes the pricing of market institutions, thus pricing the tradeability of a commodity. We obtain the existence and the decentralization of Pareto‐efficient allocations. We discuss an example regarding the transition of a guild‐based economy into a market‐based economy.     

FROM RATIONALITY TO BOUNDED RATIONALITY*

We investigate the role of bounded rationality in asset pricing and information efficiency. We show that the market stays between the weak‐form efficiency and the semi‐strong‐form efficiency in a market with a single asymmetric information and without noise supply. We show the existence of an overall equilibrium in which the publicly available information can be priced and is ‘almost free’, and the majority of the agents choose to stay uninformed. We show the existence of a Nash competitive equilibrium in an information game.     

Asset-return anomalies in a monetary economy

This paper provides a general equilibrium, choice theoretic, spatial model which explains the preference for holding barren money rather than interest-bearing securities or capital goods. Put somewhat differently, it examines standard asset pricing relationships in the context of a fully articulated monetary economy and delivers various asset-return anomalies. In seeking to integrate the theory of value with the theory of money, a fairly general proof of the existence of a monetary equilibrium is provided.     

The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.     

Public pricing of final and intermediate goods in the presence of externalities

The purpose of this paper is to investigate the impact of externalities on pricing decisions by a public or a private regulated firm selling both final and intermediate goods. The externalities generate feedbacks in demand that affect both consumers and producers. The model is very general in that it does not impose constant returns to scale on private production, allows for distributional effects of both the publicly determined prices and private sector profits, and captures the general equilibrium effects of public pricing. Socially optimal pricing rules are derived, and the relation of the results with previous models of pricing in the presence of externalities is investigated.     

简化一般均衡模型中一般均衡点的确定

经济学教材在讨论一般均衡的时候,往往以两个人、两种生产要素、两种产品这种最简单的社会作为研究对象,它们通常只阐述了一般均衡的存在,但都没有说明这种最简单的社会一般均衡点的确定即以此作为研究对象。     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

Endogenous Specialisation and Endogenous Principal-agent Relationship

The paper develops a general equilibrium model with endogenous principal-agent relationship within a framework of consumer-producer, economies of specialisation, and transaction costs. It is shown that if transaction efficiency is low, then autarky is chosen as the general equilibrium where no market and principal-agent relationship exists. As transaction efficiency is improved, the equilibrium level of division of labour increases, comparative advantage between ex ante identical individuals emerges from the division of labour, and the number of principal-agent relationships increases. The following features of the model distinguish it from other principal-agent models in the literature. The principal-agent relationships are not only endogenous, but also reciprocal between different specialists. In a general equilibrium environment, choice between pure pricing and contingent pricing is endogenised. In the paper, the implications of endogenous transaction costs caused by moral hazard for the equilibrium extent of the market and related degrees of market integration, production concentration, trade dependence, diversity of economic structure, and productivity are explored. The model predicts two interesting phenomena: a man might work harder for the market with moral hazard than working for himself in the absence of moral hazard; a market with moral hazard might be Pareto superior to autarky with no moral hazard.     

Beauty contest,bounded rationality,and sentiment pricing dynamics

We present a dynamic asset pricing model that incorporates investor sentiment, bounded rationality and higher-order expectations to study how these factors affect asset pricing equilibrium. In the model, we utilize a two-period trading market and investors make decisions based on the heterogeneous expectations principle and the “sparsity-based bounded rational” sentiment. We find that bounded rationality results in mispricing and reduces it in next period. Investor sentiment produces more significant effects than private signals, optimistic investor sentiment increases hedging demand, thus causing prices to soar. Higher-order investors are more rational and attentive to the strategies of other participants rather than private signals. This model also derives the dampening effect of higher-order expectations to price volatility and the heterogeneity expectation depicts inconsistent investor behavior in financial markets. In the model, investors' expectations about future price is distorted by their sentiment and bounded rationality, so they obtain a biased mean from the signal extraction.     

Strategic nonlinear pricing

The objective of this paper is to examine the role of nonlinear strategies in a standard oligopoly framework. We demonstrate that nonlinear pricing may indeed emerge as an equilibrium strategy, but only when firms produce differentiated products, when one firm retains market power due to a cost advantage, or as part of an equilibrium in mixed strategies. In addition, we examine the role of nonlinear pricing in a spatial-competition framework. Our main conclusion is that in highly competitive markets, nonlinear pricing strategies are not likely to emerge as an equilibrium.     

The devil in the details: Non-convexities in ecosystem service provision

Standard economic theory is built on key assumptions regarding concavity and convexity, particular with respect to the production possibility frontier. Non-convexity is readily demonstrated using a two species conventional model. Now that ecosystem services are growing in prominence it is important to confirm that typical natural resource production relations obey these conditions. If not, innocently prescribing price or allocation policies can lead to a minimum rather than a maximum or to wrong equilibrium solutions in general. This is a particular danger in decentralized pricing systems.     

Financial and Thermodynamic Equilibrium

This paper explores general equilibrium asset pricing implications in a two-period model in which the production side explicitly describes the thermodynamic process unavoidably connected with production. We show that steady state of the production process, i.e. thermodynamic equilibrium, has a one-to-one correspondence with the absence of arbitrage possibilities. This provides an alternative definition of the absence of arbitrage.
(J.E.L.: D5, G1, R3)     

Computing minimal state space recursive equilibrium in OLG models with stochastic production

Using order-theoretic methods, we derive sufficient conditions for the existence, characterization, and computation of minimal state space recursive equilibrium (RE), as well as Stationary Markov equilibrium (SME) for various classes of stochastic overlapping generations models. In contrast to previous work, our methods focus on constructive methods. Our existence results are obtained for models that include public policy (e.g., social security policies, transfers, taxes, etc), production nonconvexities, elastic labor supply, non-monotone income processes, and long-lived agents. We distinguish conditions under which there exist various subclasses of minimal state space RE, including bounded, monotone, non-monotone, semicontinuous, Lipschitz continuous RE. Finally, we provide monotone equilibrium comparative statics results on the space of economies for some RE.     

Linear exchange economies with a continuum of agents

The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called “regular” endowment where it is known.     

Credit risk in general equilibrium

This paper contributes to the literature on default in general equilibrium. Borrowing and lending takes place via a clearing house (bank) that monitors agents and enforces contracts. Our model develops a concept of bankruptcy equilibrium that is a direct generalization of the standard general equilibrium model with financial markets. Borrowers may default in equilibrium and returns on loans are determined endogenously. Restricted to a special form of mean variance preferences, we derive a version of the capital asset pricing model with bankruptcy. In this case, we can characterize equilibrium prices and allocations and discuss implications for credit risk modeling.