Mises and the moderns on the inessentiality of money in equilibrium

The challenge of rendering monetary exchange intelligible within a Walrasian general equilibrium framework is well known. Perhaps less well known is the difficulty of integrating monetary and exchange economies in decentralized conceptions of equilibrium, of which the evenly rotating economy of Ludwig von Mises (1949) is an early example. After reviewing the prospect for money in the evenly rotating economy, I survey the modern literature on frictions that make money useful for exchange. While exploring techniques commonly used to generate a useful role for money in this environment, I make a distinction between exchange frictions and epistemic frictions. Although theoretical efforts have largely focused on exchange frictions, recent experimental evidence suggests that epistemic frictions warrant further attention. I conclude that Mises should be seen as a pioneer in this literature, though recent advances demonstrate that the set of frictions capable of rendering money useful is much larger than he envisioned.     

The Arrow-Debreu model: How math can hide a fatal conceptual error

I argue that math, like love, can cover a multitude of sins, and I use the neoclassical object of adoration, the Arrow-Debreu model, as the case in point. It is commonplace that the Arrow-Debreu (AD) model of general equilibrium does not describe the real world, but it is equally commonplace to accept it as representing the pure logic of the competitive capitalist economy in an idealized world free of transactions costs. I show that the AD model fails even as an idealized model; it actually mistakes the logic of pure capitalism. Unlike McKenzie’s model of idealized general equilibrium under constant returns to scale, Arrow and Debreu claim to have shown the existence of competitive equilibrium under decreasing returns to scale and positive pure profits. The AD model (again unlike the McKinzie model) needs to assign the profits to individuals and this is done using the notion of “ownership of the production set.” But this notion suffers from a fatal ambiguity. If Arrow and Debreu interpret it to mean “ownership of a corporation” then a simple argument in the form “labor can hire capital or capital can hire labor” defeats the alleged necessity of assigning residual claimancy to the corporation. A given corporation may or may not end up exploiting a set of production opportunities (represented by a production set) depending on whether it hires in labor and undertakes production or hires out its capital to others (all by assumption at the parametrically given prices). In the latter case, residual claimancy is elsewhere. There is no such property right as “ownership of a production set” in a private property market economy. The legal party which purchases or already owns all the inputs used up in production has the defensible legal claim on the outputs: there is no need to also “purchase the production set.” At any set of prices that allow positive pure profits, anyone in the idealized AD model could bid up the price of the inputs and thus try to reap a smaller but still positive profit. Therefore,pace Arrow and Debreu, there could be no equilibrium with positive pure profits. In the Appendix, the property rights fallacy that afflicts the AD model is shown to also afflict orthodox capital theory and corporate finance theory.     

The Arrow-Debreu model: How math can hide a fatal conceptual error

I argue that math, like love, can cover a multitude of sins, and I use the neoclassical object of adoration, the Arrow-Debreu model, as the case in point. It is commonplace that the Arrow-Debreu (AD) model of general equilibrium does not describe the real world, but it is equally commonplace to accept it as representing the pure logic of the competitive capitalist economy in an idealized world free of transactions costs. I show that the AD model fails even as an idealized model; it actually mistakes the logic of pure capitalism. Unlike McKenzie’s model of idealized general equilibrium under constant returns to scale, Arrow and Debreu claim to have shown the existence of competitive equilibrium under decreasing returns to scale and positive pure profits. The AD model (again unlike the McKinzie model) needs to assign the profits to individuals and this is done using the notion of “ownership of the production set.” But this notion suffers from a fatal ambiguity. If Arrow and Debreu interpret it to mean “ownership of a corporation” then a simple argument in the form “labor can hire capital or capital can hire labor” defeats the alleged necessity of assigning residual claimancy to the corporation. A given corporation may or may not end up exploiting a set of production opportunities (represented by a production set) depending on whether it hires in labor and undertakes production or hires out its capital to others (all by assumption at the parametrically given prices). In the latter case, residual claimancy is elsewhere. There is no such property right as “ownership of a production set” in a private property market economy. The legal party which purchases or already owns all the inputs used up in production has the defensible legal claim on the outputs: there is no need to also “purchase the production set.” At any set of prices that allow positive pure profits, anyone in the idealized AD model could bid up the price of the inputs and thus try to reap a smaller but still positive profit. Therefore,pace Arrow and Debreu, there could be no equilibrium with positive pure profits. In the Appendix, the property rights fallacy that afflicts the AD model is shown to also afflict orthodox capital theory and corporate finance theory. World Bank The findings, interpretations and conclusions expressed in this paper are entirely those of the author and should not be attributed in any manner to the World Bank, to its affiliated organizations or to the members of its Board of Directors or the countries they represent.     

Existence of competitive equilibrium when incomes may be zero

Summary In a pure exchange economy, there exists a price vector which is a quasi-equilibrium (Debreu 1962), but this may not be a competitive equilibrium if some individuals' demand functions are discontinuous because their incomes may be zero. We show nonetheless, in a pure exchange economy with free disposal, that there is asequence of prices approaching the quasi-equilibrium along which total excess demands tend to a non-positive limit.Comments on earlier drafts from K. J. Arrow, D. Duffie, H. E. Scarf, and D. Schmeidler are gratefully acknowledged.     

General equilibrium and the new neoclassical synthesis

We present a general equilibrium model of the new neoclassical synthesis that has the same level of generality as the Arrow–Debreu model. This involves a stochastic multi-period economy with a monetary sector and sticky commodity prices. We formulate the notion of a sticky price equilibrium where all agents form rational expectations on prices for commodities and assets, interest rates, and rationing. We present a general result showing that monetary policy imposes no restrictions whatsoever on nominal equilibrium price levels and that the set of sticky price equilibria has a dimension equal to the number of terminal date-events. Stickiness of prices implies that this indeterminacy is real.     

Non-causal understanding with economic models: the case of general equilibrium

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly explanation which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding.     

Core convergence with asymmetric information

We analyze the ex ante incentive compatible core for replicated private information economies. We show that any allocation in the core when the economy is replicated sufficiently often is approximately Walrasian for the associated Arrow–Debreu economy.     

Regulating collateral-requirements when markets are incomplete

In this paper we examine the effects of default and collateral on risk sharing. We assume that there is a large set of assets which all promise a risk less payoff but which distinguish themselves by their collateral requirements. In equilibrium agents default, the assets have different payoffs, and there are as many linearly independent assets available for trade as there are states of the world. We derive necessary and sufficient conditions for equilibria to be Pareto-efficient in the presence of uncertainty. We explore some examples for which the collateral equilibrium allocation is identical to the Arrow–Debreu allocation, either when agents have a high preference for the durable good, or when the endowment distribution of the durable good is relatively homogeneous. We examine a series of examples to understand which collateral-levels prevail in equilibrium and under which conditions there is scope for regulating margin-requirements, that is, restricting the sets of tradable assets through government intervention. In these examples equilibrium is always sub-optimal but regulation never leads to a Pareto-improvement. While the competitive equilibria are constrained efficient, there do exist regulations which make large groups of agents in the economy better off. These regulations typically restrict all trades to take place in the low-collateral loans and benefit the poor and the rich agents in the economy through their effects on the equilibrium interest rate and the equilibrium prices of the durable goods.     

MISERY LOVES COMPANY: EQUILIBRIUM PORTFOLIOS WITH HETEROGENEOUS CONSUMPTION EXTERNALITIES*

The present article extends the Arrow–Debreu portfolio model to consumption externalities. It is assumed that each investor has a von Neumann–Morgenstern utility that is a function of her own consumption and of the average consumption in the group to which she belongs. Individual degrees of risk aversion and conformism are heterogeneous within each group and between the different groups in the economy. We show that, under some conditions on the degree of conformism in the economy, the optimal portfolio and consumption choices observed at equilibrium in each group with consumption externalities are equivalent to those that are optimal without any externality, but with an adjusted degree of risk aversion. If these conditions are not fulfilled, groups have no representative agent and the demand for pure zero‐mean lotteries may be positive, thereby showing that not all diversifiable risks are washed away at equilibrium. We characterize the relationship between the distribution of conformism in the economy to the competitive allocation of risk and to the equity premium. We provide conditions for the two‐fund separation property to hold.     

Equilibrium with arbitrary market structure

Summary. Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The complete market predicted by this theory is clearly unrealistic, and Radner [10] formulated and proved existence of equilibrium in a multiperiod model with incomplete markets.In this paper the Radner result is extended. Radner assumed a specific structure of markets, independence of preferences, indifference of preferences, and total and transitive preferences. All of these assumptions are dropped here. We - like Radner - keep assumptions implying compactness.Received: 17 April 2003, Revised: 26 March 2004, JEL Classification Numbers: D52, D40.     

Durable capital inputs: Conditions for price ratios to be invariant to profit-rate changes

Conclusion It has been shown that the simplicities of the nondurable Leontief-Sraffa model can for the most part be preserved so long as durability obeys the strict laws of exponential depreciation that is independent of a tool's age. But, as soon as the real world fails to obey the strict rules of this fairy tale, Sraffian Standard Comodities fail to exist and the conditions for price-ratio invariance at all profit rates become both complicated and restrictive.The complexities are in the nature of things, not a fabrication of the equilibrium analyst. Only the modern paradigm of general equilibrium — as begun by Smith and Ricardo and as improved by Walras, Fisher, Pareto, Dimitriev, von Bortkiewicz, von Neumann, Debreu, Arrow, Leontief, and Sraffa — can do justice to the realities of technology and arbitrage.     

A theory of cooperation in games with an application to market socialism

Abstract

Economic theory has focused almost exclusively on how humans compete with each other in their economic activity, culminating in general equilibrium (Walras–Arrow–Debreu) and game theory (Cournot–Nash). Cooperation in economic activity is, however, important, and is virtually ignored. Because our models influence our view of the world, this theoretical lacuna biases economists’ interpretation of economic behavior. Here, I propose models that provide micro-foundations for how cooperation is decentralized by economic agents. It is incorrect, in particular, to view competition as decentralized and cooperation as organized only by central diktat. My approach is not to alter preferences, which is the strategy behavioral economists have adopted to model cooperation, but rather to alter the way that agents optimize. Whereas Nash optimizers view other players in the game as part of the environment (parameters), Kantian optimizers view them as part of action. When formalized, this approach resolves the two major failures of Nash optimization from a welfare viewpoint – the Pareto inefficiency of equilibria in common-pool resource problems (the tragedy of the commons) and the inefficiency of equilibria in public-good games (the free rider problem). An application to market socialism shows that the problems of efficiency and distribution can be completely separated: the dead-weight loss of taxation disappears.     

Limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium with or without short sales

Summary A condition oflimited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. Theorem 1 establishes thatlimited arbitrage is necessary and sufficient for the existence of a competitive equilibrium in markets with or without short sales. Limited arbitrage bounds utility arbitrages, the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments (Proposition 2); it is related to but nonetheless different from the no-arbitrage condition used in finance. Theorem 2 establishes that an Arrow — Debreu economy has a competitive equilibrium if and only if every one of its subeconomies withN + 1 traders does, whereN is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the existence of the core [16], to the contractibility of spaces of preferences and to the existence of continuous anonymous social choice rules which respect unanimity [10], [14], [15], [16].This paper was circulated in December 1991 as a Working Paper of the Department of Economics, Columbia University, New York, and presented at seminars at Mathematics, Economics, and Operations Research Departments at Columbia, Harvard, Stanford University of California at Berkeley, University of Bonn and the University of Siena, at an invited presentation at the European Congress of Mathematicians, July 1992, and the Winter Meetings of the Econometric Society in Boston, January 1994. Valuable comments and suggestions from Roko Aliprantis, Masahiko Aoki, Kenneth Arrow, Duncan Foley, Geoffrey Heal, Lionel McKenzie, Paul Milgrom and two anonymous referees, and research support from NSF Grant No. 92-16028 and the Stanford Institute for Theoretical Economics are gratefully acknowledged.     

Is dynamic general equilibrium a theory of everything?

Should we interpret the contributions of Edward C. Prescott and his collaborators, especially Finn Kydland and Rajnish Mehra, to dynamic general equilibrium as just a mathematical restatement of pre-Keynesian business cycle theory in the language of Arrow and Debreu? This essay advances the contrary view that Prescott has been laying the foundations for a theory of everything in macroeconomics that will stretch well beyond the frictionless environments treated in its early version. A theory of everything is an attempt to explain key empirical observations in nearly every subfield of macroeconomics from a simple, logically coherent conceptual platform with a minimum of institutional detail. After reviewing the current state of Prescott’s agenda, we examine several examples of dynamic equilibrium in economies with constant returns to scale, complete markets, idiosyncratic productivity shocks, and limited capital mobility. These examples suggest that the Solow residual controls the entire path of aggregate output if redefined more broadly to include financial, distributional and institutional variables; that the discount factor used in pricing streams of income will shift autonomously over time in response to endogenous changes in the set of unconstrained asset traders; and that a dynamic general equilibrium model with substantive frictions in financial markets goes some distance towards a joint account of well-known empirical anomalies in growth, business cycles, and asset returns.     

ON THE EIGHT BASIC UNITS OF A DYNAMIC ECONOMY CONTROLLED BY FINANCIAL INSTITUTIONS*

The elegant general equilibrium world of Arrow and Debreu has had a considerable mathematical development in the last decade. Underlying this work is an extremely parsimonious model of the economic system. In particular, only one economic actor is distinguished, the consumer who maximizes his welfare (the firm which maximizes profit is an automation). One class of economic entities is considered. These are goods and services. There is no important operational distinction made between a good, which is durable, and a service, which is not. It is suggested here that a more fruitful basic economic model needed to achieve a unification of micro and macroeconomic theory needs both more actors and more basic economic units. Specifically, the structure of process in a political-economy is such that even at the level of relatively abstract theory operational differences among consumers, entreprenuers, administrators, financiers, and politicans should be discernible. Furthermore, several basic economic entities (or “basic particle”) must play important discernible roles in an adequate theory. In partiuclar, in the “real sector” physical assets should play a mahor role, i.e., the distinction between durable goods and consumables or services should be important. The paper sector must also be present with the roles of flat money, ownership claims and contracts all distinguished. It is argued here that any economy can be characterized in terms of two real and six paper basic units: goods, services and six financial instruments. All other financial instruments can be obtained as mixtures of this basic set.     

The Mordukhovich Normal Cone and the Foundations of Welfare Economics

The statement that Pareto optimal allocations require the equalization of marginal rates of substitution, or in an economy with public goods, require the equalization of the aggregate of the marginal rates in consumption to those in production, is formalized through the use of the Mordukhovich normal cone. Since this cone is strictly contained, in general, in the Clarke normal cone, the results generalize earlier work of Khan and Vohra, Quinzii, Yun, and Cornet. The results are an application of Mordukhovich's 1980 theorem on necessary conditions for optimality in constrained optimization problems involving functions that are not necessarily differentiable or quasi-concave. As such, the results suggest a distinction between the mathematical programming approach to the "second welfare theorem," as in the work of Hicks, Lange, and Samuelson, and that based on the separation of sets, as pioneered by Arrow and Debreu.     

The phenomenon of equifinality in innovative development of the monetary private ownership economy —An axiomatic set-up

The phenomenon of the equifinality can be understood as a possibility to achieve a given final state in many potential ways, regardless of the initial state. The study of this phenomenon is particularly relevant in today's world, where one of the main problems is the transformation of post-communist countries' economies so that they reach the states close to the economic systems of developed countries. This transformation takes place in the process of economic development stimulated by innovation, with the active role of the banking sphere.Thus, the main purpose of this study is to define the concept of equifinality achieved in a finite time, in an innovative development of the economic system controlled by the banks and the analysis of its properties. For this purpose the possible trajectories of development are studied here in a space of innovative extensions of private ownership economy with money, for which the target state is an innovative extension of a given model.This analysis uses the apparatus of an Arrow–Debreu general equilibrium theory and the theory of dynamical systems. Simultaneously, the work presented is a development of earlier studies in modeling of the Schumpeter's vision of the economic development (Ciałowicz and Malawski, 2007, 2011).     

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.     

Wealth Inequality and Asset Pricing

In an Arrow–Debreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the risk-free rate. We first show that wealth inequality raises the equity premium if and only if the inverse of absolute risk aversion is concave in wealth. We then show that the equilibrium risk-free rate is reduced by wealth inequality if the inverse of the coefficient of absolute prudence is concave. We also prove that the combination of a small uninsurable background risk with wealth inequality biases asset pricing towards a larger equity premium and a smaller risk-free rate.     

Pricing rules and Arrow–Debreu ambiguous valuation

This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow–Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow–Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.