The Walras core of an economy and its limit theorem

The Walras core of an economy is the set of allocations that are attainable for the consumers when their trades are constrained to be based on some agreed price system, such that no alternative price system exists for any sub-coalition that allows all members to trade to something better. As compared with the Edgeworth core, both coalitional improvements and being a candidate allocation for the Walras core become harder. The Walras core may even contain allocations that violate the usual Pareto efficiency. Nevertheless, the competitive allocations are the same under the two theories, and the equal-treatment Walras core allocations converge under general conditions to the competitive allocations in the process of replication.     

A continuous double implementation of the constrained Walras equilibrium

We provide a continuous and feasible double implementation of the Walras equilibrium. In our game form the set of traders is partitioned intok subsets,k>-2, and for each member of the partition there is an (outside) auctioneer. Also, each agent announces a price-allocation pair so that all agents become price takers. The outcome allocation is defined as the feasible (and budget balanced) allocation which is closest to the aggregate announced allocation. No assumptions are made on the preferences of the traders.     

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 ^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.     

A uniqueness theorem for convex-ranged probabilities

A finitely additive probability measure P defined on a class Σ of subsets of a space Ω is convex-ranged if, for all P(A)>0 and all 0 < α < 1, there exists a set, Σ∋B⊆A, such that P(B)=αP(A).?Our main result shows that, for any two probabilities P and Q, with P convex-ranged and Q countably additive, P=Q whenever there exists a set A∈Σ, with 0 < P(A) < 1, such that (P(A)=P(B)?Q(A)=Q(B)) for all B∈Σ. Received: 18 December 1999 / Accepted: 17 July 2000     

Erratum to “Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only” [J. Math. Econ. 41 (4–5) (2005) 571–601]

We consider a pure exchange economy with a continuum of agents and finitely many indivisible commodities. Every commodity can be consumed only in integer amounts. Thus, agents’ preferences are locally satiated and no commodity bundle has necessarily local cheaper points. We introduce a core which is an intermediate concept between the strong core and the weak core. In our economy, this core is the most natural concept in the sense that it coincides with the set of all exactly feasible Walras allocations.     

Comparison of test vs. control treatments using distance optimality criterion

We consider the problem of comparison of one test treatment (τ₀) with a set of v control treatments (τ₁, τ₂, …, τ_v) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings. It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design. Received: December 1999     

Strategy-proof allocation when preferences are single-plateaued

Abstract. We consider private good economies with single-plateaued preferences. A solution selects for each preference profile a non-empty set of allocations. An agent strictly prefers a set of allocations to another set of allocations if and only if he strictly prefers any allocation in the first set to any in the second set according to his single-plateaued preference relation. We characterize the class of sequential-allotment solutions by essentially single-valuedness, Pareto-indifference, and coalitional stragety-proofness. These solutions are the Pareto-indifferent extensions of the solutions studied by Barberà et al. 1997. Received: 9 May 2000 / Accepted: 1 May 2001     

Existence of balanced sampling plans avoiding cyclic distances

This article considers balanced sampling plans avoiding adjacent units. It is shown, using linear algebraic and design theoretic tools, that such plans exist for all sufficiently large populations. More generally, if any set of m circular distances is to be avoided in balanced sampling with subsets of size k, then such a plan exists, provided the population size N is at least mk ³. Research of the Peter J. Dukes is supported by NSERC.     

Existence of a competitive equilibrium when all goods are indivisible

This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack.     

Nash implementation with an infinite-dimensional trade space

This paper deals with the problem of implementing the Walras correspondence via Nash equilibria, in exchange economies with infinitely many commodities and finitely many households with possibly non-ordered preferences. We explicitly construct a feasible mechanism enjoying some features, which have natural economic meanings. Under a fairly weak boundary condition, this game fully implements the Walras equilibria. If this condition is not fulfilled, our mechanism nevertheless implements the constrained Walras equilibria. Received: 11 December 2003, Accepted: 29 July 2005 JEL Classification: D41, D43, D51 We thank (without implicating) Prof. Jean-Marc Bonnisseau and Cuong Le Van for helpful comments. The views expressed in this paper reflect those of the authors and not necessarily those of Calyon.     

The strong sequential core for two-period economies

The strong sequential core for two-stage economies with a possibly incomplete set of assets in period zero and trade in commodities in period one consists of those goods allocations that are in the classical core and moreover, after realization of the state of nature, in the core of the economy where executed asset contracts serve as initial endowments. The strong sequential core coincides with the classical core when all possible state-contingent contracts may serve as an asset. For finance economies it is shown that the strong sequential core is generically empty when there is an incomplete set of assets. Outside the setting of finance economies, we show that the strong sequential core can be empty even if there is a complete set of assets. If the set of constrained feasible allocations resulting from trading in assets, is enlarged to include also allocations outside the agents’ consumption sets, then a complete set of assets is sufficient for the equivalence of the resulting semi-strong sequential core and the classical core.     

Accessibility of optima in pure exchange economies

Assuming differentiable monotonicity and differentiable convexity of utility functions, we show that if y and z are allocations of a pure exchange economy with z optimal and preferred to y by every agent, then there is a trade curve of finite length from y to z. We make no assumption on utility functions designed to ‘keep away from the boundary’. The conclusion need not hold if z is not optimal, unless a special boundary condition is assumed and (l, m) ≠ (2, 2).     

Equilibrium participation in public goods allocations

We consider a notion of voluntary participation for mechanism design in public goods economies in which mechanisms select public goods allocations and individuals then choose whether or not to submit their requested transfer to the central planner. The set of allocations that are robust to non-participation is shown to be sub-optimal in a wide variety of environments and may shrink to the endowment as the economy is replicated. When agents become small as the economy becomes large, any non-trivial mechanism suffers from non-participation when agents cannot be coerced to contribute.     

Nominal rigidities equilibria in a non-Ricardian economy

I consider a cash-in-advance economy with nominal price rigidities. Nominal interest rates are the cost of liquidity and fiscal policy sets nominal transfers that affect the distribution of wealth. Under a fiscal policy associated with an unequal distribution of wealth and for policies of low or even zero interest rates, coordination failures exist, that is, involuntary unemployment persist even if prices are set at full employment levels. Coordination failures exist if and only if nominal rates are below a threshold. Moreover, I demonstrate the following result on welfare: full employment allocations at a nominal rate equal to the threshold (high liquidity costs) are better, in terms of welfare, from unemployment allocations at any non-negative interest rates below the threshold. On the other hand, under a sufficiently progressive fiscal system that reduces the inequality in the wealth distribution, coordination failures do not exist.     

On a study of the exponential and Poisson characteristics of the Poisson process

Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations of the Poisson process as a renewal process. More precisely, let γ_t be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γ_t)=E ² (γ_t),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)). Received: August 1999     

Walrasian social orderings in exchange economies

We study social ordering functions in exchange economies. We show that if a social ordering function satisfies certain Pareto, individual rationality, and local independence conditions, then (i) the set of top allocations of the chosen social ordering is contained in the set of Walrasian allocations and is typically non-empty, and (ii) all individually rational but non-Walrasian allocations are typically ranked indifferently. Thus, such a social ordering function is quite similar to the Walrasian correspondence, which can be regarded as the social ordering function whose associated indifference classes are the set of Walrasian allocations and the set of other allocations.     

A count-amount model with endogenous recording of observations

This paper discusses some of the problems which are encountered if an event ? is only recorded if its value satisfies a recording criterion A. It follows that we get an incorrect idea of the frequency of the events and of its true distribution. In order to solve these problems, an econometric model has been constructed by means of which consistent estimation of the true parameters is possible. The model is estimated on consumer purchases, where the number of purchases is assumed to be NEGBIN-distributed and the purchase amounts obey a lognormal distribution. Purchases are only recorded if their value exceeds Dfl. 10. It is shown that ignoring the recording condition will result in biased estimates and invalid predictions. Apart from this, the model is, among others, relevant for insurance problems, marketing surveys and criminological and epidemiological phenomena.