Equilibria in large economies with differentiated commodities and non-ordered preferences

Summary. The purpose of this paper is to provide an equilibrium existence result for economies with a measure space of agents, a finite set of producers and infinitely many differentiated commodities. The approach proposed in this paper, based on the discretization of measurable correspondences, allows us to extend the existence results in Ostroy and Zame (1994) and Podczeck (1997) to economies with a non-trivial production sector and with possibly non-ordered preferences. Moreover, our approach allows for more general consumption sets than the positive cone and following the direction introduced by Podczeck (1998), the uniform substitutability assumptions of Mas-Colell (1975), Jones (1983), and Ostroy and Zame (1994), are replaced by the weaker assumptions of uniform properness.Received: 11 June 2001, Revised: 6 March 2003, JEL Classification Numbers: C62, D51.Thanks to Charalambos D. Aliprantis, Erik J. Balder, Jean-Marc Bonnisseau, Bernard Cornet, Monique Florenzano, Konrad Podczeck, Rabee Tourky, Nicholas C. Yannelis and two anonymous referee for helpful discussions and suggestions.     

Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

Distance measures between free trade and autarky for the world economy

We develop a methodology to determine numerically how globalized the world economy is. We present a global general equilibrium model capturing major OECD economies and a residual rest of world for which alternative metrics of distance between observed, free trade and autarky equilibria can be developed. We use data for 2000 and report a number of distance measures between the 2000 observed trade restricted equilibrium and both free trade and autarky equilibria noting the absence of prior literature on metrics of distance between equilibria. The measures are used to determine the degree to which the world economy is globalized.     

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 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.     

Environmental adders in the real world

This paper evaluates the use of environmental ‘adders’ as a regulatory instrument. It evaluates their likely performance in meeting the policy objective of social costing given the changes in the electric utility industry's structure and in environmental policy since the efforts to estimate these costs were initiated. The prognosis is largely negative — suggesting that environmental adders are inconsistent with the increased competition already underway in the utility industry, as well as with the trend toward greater use of true market-based approaches to environmental policy that are not subject to detailed economic regulation.     

关于商品对人类福利贡献的研究

毫无疑问，商品消费在人类福利的实现过程中发挥着非常重要的作用。但是，商品并不总对我们的福利有贡献，其甚至会使我们的福利受损。因此，随之产生的问题便是：“商品是如何及在什么条件下对我们的福利有贡献？”本文即试图从哲学视角回答这两个问题且形成一些政策建议。福利通常被定义为一个人的利益所在。然而，对什么是一个人的利益所在却有着不同的解释。根据福利的偏好满足观，我们想要的便是对我们有益的；实体价值观意味着一些客观、可确定的价值是对每一个人都有益的；享乐主义则认为愉快是唯一的实体价值。我认为，要为福利做出任何可信的阐释，个人偏好必须在其中发挥重要的作用；特别是只有在我们的终极偏好得以实现时，它才会对福利作出贡献。工具性偏好也许是错误的，它或许会导致人们终极目标的落空。基于对福利的讨论，本文考察了商品和福利之间的联系。我们不太可能对商品有终极性偏好，因此，我们或不会因自己的选择而降低了自身的福祉。在现实生活中，我们却观察到因商品消费而致使福利损失的现象，例如，食用变质食品而得病。可见，我们尤为关心的是一件商品所提供的特质而非直接的商品的本身。当然，即使一件商品包含了被冀望得到的特质，对该商品的消费也不总会提高福利，原因在于我们有可能缺乏使用这些对我们有益的属性的能力。一言以蔽之，我们通过消费而旨在实现的实际上是那些有价值的机能（functionings）。我们的生活恰恰由这些“存在（beings）”和“活动（doings）”组成，其质量也就可以通过机能的质量来判断。机能是我们终极偏好的目标，而商品只是实现终极偏好的工具。这里关于商品对人类福利贡献的解释可成功地用以处理各种可能出现的目标。我们不需进一步论述机能和福利之间的关系：愉快不是我们一生追求的全部，它更应被看作是一种特定的机能。类似地，对于自由、能力等概念，我们都可以有同样的理解。商品从不会直接影响我们的福利。换言之，存在内在价值的商品也会在工具层面有益于我们，因为前者贡献了某些有价值的机能。总之，商品对人类福利的作用并不受制于福利诠释的选择；在福利的实体价值观和偏好满足观框架中，这一逻辑是成立的。为使商品对福利有积极、正面的贡献，消费过程须满足两个条件。首先，商品需具备贡献有价值的机能的特性；其次，消费者将这些特性转换成有价值机能的能力。理解这些条件有助于我们形成提高消费者福利水平的政策。在商品供应充足的情况下，政策的首要目标必须是向消费者提供信息和教育，从而使之能够作出有效的选择。如果人们被剥夺了基本机能（如营养或健康），公共权力部门会经常性地直接向其提供必需的商品。他们必须确保解决这些根本问题的方法是最有效的，而且在商品提供过程中还应兼顾社会和文化结构等背景因素的影响。对商品和福利之间的关系进行详尽的考察可以让我们学到很多东西。消费者理论中消费者对商品信息完全掌握的假设事实上已将选择与福利视为等价，它忽视了消费过程中减少福利的所有问题。当我们允许这些问题发生时，我们才会明白这些错误到底是来自何处。福利的偏好满足的哲学理念及其实际应用都存在着一个关键问题：人们经常想得到的和最终选择的事物往往对他们毫无益处。本文的研究表明，这一问题通常因缺乏信息和能力而起。增进对商品的了解会提高改福利；不过，商品只是消费过程中的一个因素，政府更应关注商品的特定属性及人们应用这些属性的能力。     

Probability of survival in a random exchange economy with dependent agents

Summary. In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy. Received June 7, 2001; revised version: January 7, 2002 RID="*" ID="*" I would like to thank Mukul Majumdar and Thomas DiCiccio for helpful discussion and an anonymous referee for valuable comments and suggestions.     

Incentive compatible core and competitive equilibria in differential information economies

Summary. If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core. Furthermore, any competitive equilibrium allocation can be viewed as an element of the core of the n-fold replicated economy, for every n. The converse holds under the further assumption of independent private values but not in general, as shown by a counter-example. Received: August 9, 1999; revised version: September 12, 1999     

Growth dynamics in a model of endogenous time preference

We incorporate endogenous time preference in a simple Diamond-type economy with production and analyze the resulting dynamics both for the competitive and command equilibrium. We assume an individual's rate of time preference is decreasing in consumption (decreasing marginal impatience) and show that this intuitively more appealing assumption is consistent with a stable, non-trivial competitive equilibrium. Analysis of the competitive equilibrium indicates that the observed ‘non-convergence’ of cross-country per capita income could partially be explained by cross-country differences in ‘innate patience’. Examination of the local dynamics around the ‘optimal’ solution suggests that this particular preference structure exhibiting diminishing marginal impatience may generate endogenous business cycle phenomenon.     

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     

Incomplete risk sharing arrangements and the value of information

Summary. The paper constructs a theoretical framework in which the value of information in general equilibrium is determined by the interaction of two opposing mechanisms: first, more information about future random events leads to better individual decisions and, therefore, higher welfare. This is the ‘Blackwell effect’ where information has positive value. Second, more information in advance of trading limits the risk sharing opportunities in the economy and, therefore, reduces welfare. This is the ‘Hirshleifer effect’ where information has negative value. We demonstrate that in an economy with production information has positive value if the information refers to non-tradable risks; hence, such information does not destroy the Blackwell theorem. Information which refers to tradable risks may invalidate the Blackwell theorem if the consumers are highly risk averse. The critical level of relative risk aversion beyond which the value of information becomes negative is less than 0.5. Received: May 14, 2001; revised version: March 5, 2002     

Continuity of the payoff functions

Summary. In his Nash equilibrium paper, Glicksberg states that the payoff functions are continuous. Such a function is defined on the product of mixed strategies, which are the Borel probability measures on a compactum, endowed with the product of the weak topologies. The continuity property is used in proving the existence of Nash equilibria. This note proves that the payoff functions are continuous, which is not immediate to establish. Received: June 10, 1999; revised version: June 24, 1999     

Mending the family tree a reconciliation of the linearization and levels schools of AGE modelling

This paper offers a critical comparison between the North American levels school of applied general equilibrium modelling, and the Norwegian/Australian school of linearizers. The paper develops both the levels and linearized representations of a neoclassical multiregion trade model. This is used as a vehicle for focusing attention on similarities and differences between the two schools. The main conclusions are: (i) that both the levels and linearized versions of non-linear AGE model offer a valid starting point for obtaining accurate solutions to the non-linear equilibrium problem; (ii) when update formulae are not employed, linearized representations are particularly prone to erroneous welfare conclusions; (iii) the levels representation offers a more natural starting point for expressing accounting conditions, whereas behavioural relationships are relatively more easily expressed in a linearized representation. Recent software developments now make both approaches to the representation and solution of non-linear AGE models convenient to implement. Thus the choice of which approach to use will depend on the special needs and preferences of the economist implementing the model. The two traditions of AGE modelling have a great deal in common and both would benefit from greater cooperation.     

Sensitivity analysis for applied general equilibrium models in the presence of multiple Walrasian equilibria

Summary. Pagan and Shannon's (1985) widely used approach employs local linearizations of a system of non-linear equations to obtain asymptotic distributions for the endogenous parameters (such as prices) from distributions over the exogenous parameters (such as estimates of taste, technology, or policy variables, for example). However, this approach ignores both the possibility of multiple equilibria as well as the problem (related to that of multiplicity) that critical points might be contained in the confidence interval of an exogenous parameter. We generalize Pagan and Shannon's approach to account for multiple equilibria by assuming that the choice of equilibrium is described by a random selection. We develop an asymptotic theory regarding equilibrium prices, which establishes that their probability density function is multimodal and that it converges to a weighted sum of normal density functions. An important insight is that if a model allows multiple equilibria, say , but multiplicity is ignored, then the computed solution for the i-th equilibrium generally no longer coincides with the expected value of that i-th equilibrium. The error can be large and correspond to several standard deviations of the mean's estimate. Received: December 7, 1999; revised version: December 4, 2000     

Adjusting the model to adjust the world: constructive mechanisms in postwar general equilibrium theory

Economic methodologists most often study the relations between models and reality while focusing on the issues of the model's epistemic relevance in terms of its relation to the ‘real world’ and representing the real world in a model. We complement the discussion by bringing the model's constructive mechanisms or self-implementing technologies in play. By this, we mean the elements of the economic model that are aimed at ‘implementing’ it by envisaging the ways to change the reality in order to bring it more in line with the model. We are thus concerned mainly not with the ways to change the model to ‘fit’ the reality, but rather with the model's own armature that is supposed to transform the world along theoretical lines. The case we study is Arrow–Debreu–McKenzie general equilibrium model. In particular, we show the following: gradient methods and stability could be regarded as constructive mechanisms of general equilibrium modeling in the context of market socialism debates; the obsession of general equilibrium theorists with these concepts can be partly explained by the fact that they hoped not to be faithful to reality, but rather to adjust it to fit the theoretical model; mechanism design theory initiated by the stability theorist Leonid Hurwicz could be seen as a successor of this position. We conclude by showing the relevance of this analysis for epistemic culture of much of contemporary economics and hence, claim that it is an important complement to the traditional philosophy of economic modeling.     

The role of miniatures in computable general equilibrium modelling : Experience from ORANI

ORANI is a large general equilibrium model of the Australian economy used by policy analysts and university research workers. This paper describes the role of miniature models in the development and application of ORANI. Miniature versions of ORANI have been useful in (a) explaining results; (b) detecting errors; (c) conducting sensitivity analyses; (d) experimenting with new specifications; and (e) teaching. The present paper concentrates mainly on (a) and (b). A miniature model is developed to explain ORANI results for the effects of increases in protection, reductions in the real costs of labour, increases in oil prices and increases in real aggregate demand.     

传统价格理论的局限--以软件产品价格形成机理解释为例

软件产品在产权、信息及交易上所表现出的特别性使传统的以物质产品为研究对象的价格理论及即使在其具有最强解释力的成本价值与使用价值均衡领域均陷入困境.本文分析了传统价格理论解释无力的局限性原因.