Walras Law Research Articles

The Buckingham’s π Theorem: Consequences for the Price Theory

The present article focuses on the possible interpretation of the pi theorem of physics in the field of the economics' general equilibrium analysis. The physical units of the exchanged goods are de ned as fundamental units and the neoclassical prices as dimensionless derived numbers. Thus, the general equilibrium does not need money metrics, unspeci ed money market and the complementing inappropriate incorporation of the Walras Law. Further, the main function of money is not that of a unit of account, but a means of exchange. If such type of a money market is introduced, the Walras symmetry holds but in the sense that the positive aggregate excess demand on the goods market matches the negative excess demand on the money market. Distinction is de ned between neoclassical, relative and monetary prices. Additional conditions must be met to allow for a closed monetary circulation.

Densely Defined Equilibrium Problems

In the present work, we deal with set-valued equilibrium problems, for which we provide sufficient conditions for the existence of a solution. The conditions, that we consider, are imposed not on the whole domain, but rather on a self-segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu---Gale---Nikaido-type theorem, with a considerably weakened Walras law in its hypothesis. Furthermore, we consider a noncooperative $$n$$n-person game and prove the existence of a Nash equilibrium, under assumptions that are less restrictive than the classical ones.

Walras's Law of Markets as Special Case of the General Triangle Theorem: A Laconic Proof

From the set of the first three structural axioms follows the Period Core theorem. It asserts that the product of the key ratios, which characterize the firm, the market outcome, and the income distribution, is always equal to unity.The theorem contains only unit-free variables, is testable in principle, and involves no behavioral assumptions. The differentiated Period Core theorem applies to an arbitrary number of firms. Therefrom Walras’s Law can be derived without recourse to demand and supply functions or the notion of equilibrium. It is shown that the familiar interpretation is methodologically illegitimate.

Is “Walras' Law” Really Walras's Original Law?

This article shows that “Walras' Law,” which is one of the crucial foundations of modern economic theory as formulated by Lange, and modified by the modern authors, differs essentially from Walras's own original laws. These two versions of “Walras Law” are disconnected from real economics; nevertheless, unfortunately, they replaced Walras's original laws which are compatible with a hypothetical regime of perfectly free competition.

A note on a proof of F. Hahn concerning the gross substitutability

The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn, which have been stated in several other classics of Economic Theory. The results deal with the relations between the gross substitutability and the weak axiom of revealed preference, in a pure exchange economy, ruled by the Walras law.

La controverse entre Clower et Patinkin au sujet de la validité de la loi de Walras

<titre>R&#233;sum&#233;</titre>Cet article propose une analyse de la controverse qui a oppos&#233; Clower et Patinkin au sujet de la validit&#233; de la loi de Walras dans le cadre de la th&#233;orie keyn&#233;sienne. Il d&#233;montre, de fa&#231;on quelque peu paradoxale, que l&#8217;opposition de Clower &#224; Patinkin, sur ce point, est due &#224; la fid&#233;lit&#233; du premier &#224; l&#8217;&#233;gard de la conception de la th&#233;orie keyn&#233;sienne d&#233;fendue par le second dans le chapitre&#160;13 de Money, Interest and Prices. Ce paradoxe s&#8217;explique par le refus de Patinkin d&#8217;admettre la remise en cause de la loi de Walras impliqu&#233;e par sa propre th&#233;orie. Sur cette base, nous proposons une interpr&#233;tation de l&#8217;impasse sur laquelle s&#8217;est achev&#233;e le d&#233;bat, une issue r&#233;v&#233;l&#233;e par la correspondance entre les deux auteurs dat&#233;e du d&#233;but des ann&#233;es 1990.

The equilibrium manifold keeps the memory of individual demand functions

It is shown that the property that the equilibrium manifold keeps the memory of the individual demand functions holds true if every individual demand function satisfies the following three properties: 1) It is a function of commodity prices and of consumer’s income; 2) Consumption belongs to the nonnegative orthant of the commodity space; 3) Walras law. Neither differentiability nor continuity are necessary. In addition, the demand functions do not have to be utility maximizing subject to budget constraints.

A note on the decomposition (at a point) of aggregate excess demand on the Grassmannian

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in R N . It is shown that, if there are at least K agents in the economy, the only general property satisfied by the value of aggregate excess demand and its derivative, at any arbitrary point, is Walras Law. The result is established by considering an economy where agents' preferences are of a `generalized Leontief' type.

Aggregation and Market Demand: An Exterior Differential Calculus Viewpoint

We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior differential calculus provides very useful tools to address these problems. In particular, we show, using these techniques, that any analytic mapping in Rn satisfying Walras Law can be locally decomposed as the sum of n individual, utility-maximizing market demand functions. In addition, we show that the result holds for arbitrary (price-dependent) income distributions, and that the decomposition can be chosen such that it varies continuously with the mapping. Finally, when income distribution can be freely chosen, then decomposition requires only n/2 agents.

Monetary aspects of Walras's law and the stock-flow problem

Walras's Law is a tautology. It illuminates interrelations among supplies and demands for goods, services, securities, and money and among their supply/demand imbalances. The Law emphasizes that no one thing or group of things can be in excess supply or excess demand by itself. It thereby helps focus attention on the role in macroeconomic disorder, especially in depression, of a distinctively functioning object of market exchange—money. Yet complications arise, and Walras's Law has itself sometimes been called into question. The purpose of this paper is to clarify the very concepts that enter into the Law and into supposed difficulties. Distinctions between "notional" and "effective" supplies and demands and between stock and flow conceptions of quantities and imbalances require attention.

Market Demand Functions in the CAPM

We demonstrate that in a CAPM economy Walras Law and the Tobin Separation Property characterize market demand in finite sets of prices. Consequently, for any number n there exist CAPM economies which have at least n equilibria and hence have n different beta pricing fomulas. It is shown that the lower bound on the number of equilibria, n, is robust to pertubations of endowments.

Price makers and nonclearing markets

In a recent survey article, Benassy argues that fixprice theory holds the key to incorporating monopoly and monopolistic competition into general equilibrium theory. This paper argues that the opposite is true. Fixprice theory is an impediment to incorporating monopoly into general equilibrium theory. The reason for this is that fixprice theory virtually jettisons Walras's law. It is demonstrated that Walras's law makes the general equilibrium analysis of monopoly very tractable, although it was long thought that monopoly and general equilibrium were incompatible.

La incorrecta “ley de Walras” y una posible corrección

The so-called Walras law tends to be presented as if to confirm the impossibility of imbalances in a single market. The author provides us with an example that shows us where the "law" is off the mark. The article then proposes a number of alternative versions that correct its errors, imposing sufficient conditions on relations of preference to demonstrate the validity of the correct form of the Walras law.

Money, competitive efficiency, and intergenerational transactions

This paper shows that a three-period overlapping-generations model with an inverse-V life-cycle endowment structure can generally restore the first welfare theorem without imposing price-characterization conditions. Even when Walras's law fails, a Walrasian equilibrium may be optimal in a three-period model, depending on the endowment and generational structure. If middle-aged generations have sufficiently high income so that both the old and the young are net borrowers, transactions are generation-by-generation bilaterally balanced, thus ruling out potentially better but unenforceable contracts in equilibrium and ensuring competitive efficiency. When there are imbalances, fiat money, which serves as a medium of intergenerational exchanges, becomes valuable.

Evolution of viable allocations

The decentralized evolution of allocations of resources among consumers described by their change functions is characterized by a regulation rule associating with each allocation the subset prices regulating them. Sufficient budgetary conditions, analogous to the Walras law, for the viability of such evolutions are then provided. Next, the issue of finding feedback controls is tackled: Conditions under which slow evolutions are given. More to the point, dynamical feedback controls obeying the inertia principle are provided: Prices are changed only when the viability of the evolution mechanism is at stake. We then derive the differential equations governing the heavy evolution of prices: For a given bound on inflation rates, the price evolves with minimal velocity.

Competitive Equilibrium for Incomplete Market Structures

The objective is to analyze, in a general way, problems of existence and determinacy of competitive equilibria when the markets structures are incomplete. The usual properties of demand functions (behavior near the boundary, Slutsky matrix, and Walras law) are carried over from the case in which the typical consumer necessarily chooses his net trade in a hyperplane to the more general case of the consumer choosing in a vector subspace of any dimension. The notion of a price vector is replaced by the notion of a price system or, alternatively, by the notion of a vector of exchange ratios between bundles of commodities. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Efficient Pricing and Budgetary Balance

Baumol (1979), denying the general feasibility of pricing everything at marginal cost, presents a counterexample in which such pricing is clearly infeasible. He draws the following conclusions: Generally, the best that any set of fixed prices can achieve is the Ramsey solution constrained by Walras's law. resulting welfare loss is the price society must pay for using a price system to allocate resources (p. 578). It will be argued here that the loss results not from use of a price system but from nonoptimal population density and that a remedy for the latter is to extend the price system into the area of population policy. Baumol's counterexample (pp. 581-86) would seem to allow more generality than necessary, for it is general enough to permit optimal population to be infinite. He has one consumer, one resource (labor/ leisure), one product, and continually increasing returns to labor. Utility, an increasing function of leisure and product, is to be maximized. consumer pays the firm labor for product. The firm and the government are operated by (nonhuman) agents who do not consume anything themselves (p. 581). Marginal cost pricing yields the firm a deficit. Lump-sum payments are held to be impossible, and so the budget cannot be balanced. If the model permitted entry of consumers identical to the first consumer, then under Ramsey pricing the utility of any current member of the society would rise every time another consumer entered, ad infinitum. argument that the welfare loss stems from nonoptimal population will run as follows. I assume that a second resource-landexists and is jointly owned. Some of it is used in production and the rest is leased by society to individuals as residential space. In an efficient society the ratio of labor to leisure will be optimal, as well as that of per capita residential land to per capita leisure. Given these optimal ratios, per capita levels of residential land and leisure are

WALRAS'S LAW IN MACROECONOMIC DISEQUILIBRIUM*

Australian Economic PapersVolume 25, Issue 47 p. 257-260 WALRAS'S LAW IN MACROECONOMIC DISEQUILIBRIUM* ROBERT L. GREENFIELD, ROBERT L. GREENFIELD Fairleigh Dickinson University, MadisonSearch for more papers by this author ROBERT L. GREENFIELD, ROBERT L. GREENFIELD Fairleigh Dickinson University, MadisonSearch for more papers by this author First published: December 1986 https://doi.org/10.1111/j.1467-8454.1986.tb00800.xCitations: 6 † *This note draws heavily on Leland Yeager's unpublished manuscript “What Remains of Walras's Law?” as well as his many published and unpublished writings on the theory of monetary disequilibrim. Yeager himself, of course, bears no responsibility for my interpretation of what he says. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume25, Issue47December 1986Pages 257-260 RelatedInformation

Monetary Policy Devaluation and Capital Accumulation in an Open Developing Economy with Fixed Exchange Rates

Tobin has pointed out that in an economy with n assets, Walras Law allows only for n — 1 independent market equilibrium equations linking the n corresponding real rates of return. If the real rate of return on money is fixed and the price level is fixed then asset markets can adjust to monetary policy only through changes in the real rates of return on the [n — 1) other assets. However one of the other assets is physical capital. Everything else equal, its rate of return is inversely related to its valuation relative to its replacement cost. Therefore the adjustment to monetary policy requires a departure of the real rate of return from the value of the marginal productivity of capital or a divergence of the market valuation from the reproduction cost of capital. In turn the latter divergence makes the production of new capital more or less profitable and leads to a change in the level of gross investment which in turn may alter real national income and will necessarily alter the rate of accumulation of capital. In the long run this may lead to a change in the demand for real money balances because of the change in the marginal productivity of capital and in the total wealth. Therefore in the long run if the price level is allowed to change, the price level may not change in the way predicted by classical economics (new and old). In this paper we attempt to detail this process in the case of a small open developing economy with fixed exchange rates and two sectors, the sector of traded goods whose inter national price is given and a home good with a flexible price. Since the exchange rate is fixed the domestic price of the traded goods is also fixed and we used this price to deflate nominal money balances. This world is not unlike that of a fixed price world. In addition we assume that the economy does not produce capital

Existence and uniqueness of price equilibria: Theory and application to discrete choice models

Continuous excess demand systems which do not obey homogeneity of degree zero or Walras's Law are proved to have equilibria if they satisfy certain mild regularity conditions when prices tend to the extremes of a price domain which need not be closed or bounded. A straightforward generalization of Brouwer's theorem is used. Systems also obeying a weak balance condition (of which Walras's Law is a special case) and homogeneity are treated as corollaries to the main theorem. Sufficient conditions for differentiable excess demand systems to have unique equilibria are developed in three separate theorems. The usefulness of these general existence and uniqueness theorems is demonstrated by applying them to three specific models constructed from discrete choice theory: (1) a competitive rental housing market, (2) a regulated rental housing market with fixed rents and rationing and (3) an interregional labor market in which laborers can choose among regions for employment (or voluntary unemployment) as well as the work hours they will supply.