Market economies with many commodities

In this survey problems from the consideration of infinite dimensional commodity spaces in the Arrow-Debreu-McKenzie model are discussed. It has become clear in the last couple of decades that in order to address real policy questions, economic models that are both stochastic and dynamic have to be employed. These models lead naturally to infinite dimensional commodity spaces.

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Riassunto In questo lavoro si discutono i problemi che si presentano quando, in connessione all'esistenza e all'efficienza di equilibri Walrasiani nel modello di Arrow-Debreu-McKenzie, si ammette che lo spazio dei beni sia di dimensione non finita. è diventato chiaro nei due ultimi decenni che per affrontare questioni reali è necessario usare modelli sia dinamici che stocastici e ciò conduce in modo naturale alla considerazione di spazi infinito-dimensionali. Si rimane principalmente confinati alle economie di puro scambio al solo scopo di semplificare la trattazione.

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This paper has been presented atWorkshop in Economic Theory, Venice-June 2–7, 1997 organized by Istituto Veneto di Scienze, Lettere ed Arti and atXXI Convegno AMASES, Rome-September 10–13, 1997. It is an expanded version of our paper [5] that appeared inJournal of Economic Theory, vol. 74, n. 1, 1997, pp. 62–105. We are grateful to Karl Shell and Academic Press for permission to include that portion of the material here. The research of C. D. Aliprantis was supported in part by the NATO Collaborative Research Grant #941059.     

Finitely additive economies with free extremely desirable commodities

Continuing the investigation on finitely additive economies with infinite dimensional commodity space, we state a core-walras individualistic equivalence for an economy where preferences admit a summable map of extremely desirable commodities. The main result extends previous equivalences obtained both in the countably additive and in the finitely additive setting. Extra assumptions on the model are discussed via a pair of examples.     

Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.     

Equilibria in markets with a Riesz space of commodities

We present a new proof of the existence of competitive equilibrium for an economy with an infinite dimensional space of commodities.     

Hedonic prices and composite commodities

In this paper we conjecture and, to an extent, prove that recently noted restrictions required for the logical coherence and empirical relevance of hedonic price models make these models no more general than traditional housing services models. In particular, intra-urban variation in hedonic prices may not be substantively related to market equilibration at all, and therefore is not evidence for the existence of housing sub-markets. Moreover, in the case of jointly produced housing characteristics, the hedonic price models are found to be less general than the traditional homogeneous housing services models.     

论商品质量特性

准确地评价、检验和监督商品的质量，有赖于对质量特征的正确理解和把握。由于消费的需求是多种多样的，所以反映商品质量的特性也是多种多样的，商品质量的适用性就是建立在质量特性基础之上的。     

Learning cycles in Bertrand competition with differentiated commodities and competing learning rules

This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

浅析零售企业的商品陈列策略

随着我国商品经济的日益发展,零售业经营的商品品种是越来越丰富,人们日常生活所需商品可以说是一应俱全.但是由于零售业通常是开架销售、自由选购,所以商品的摆放就显得致关重要.文中针对零售企业商品陈列中存在的问题提出了相应的解决方案.     

Positioning of commodities using the Kraljic Portfolio Matrix

This article proposes a more objective methodology to classify and position commodities (works and services) in the Kraljic Portfolio Matrix (KPM) in a continuous scale around the two dimensions of supply risk and profit impact—the two dimensions which mainly influence the choice of a firm's purchasing strategy. Fuzzy multi-attribute scoring is used to assign performance scores to different commodities on supply risk as well as profit impact attributes. With a multidimensional scaling approach the commodities are placed in the KPM. An application of the proposed approach is attempted on commodities procured by the Rural Development Department of a state government in India.     

具有质量竞争的供应链网络均衡研究

文章研究了具有质量竞争的供应链网络均衡问题。借助Lagrange对偶理论和有限维变分不等式理论,刻画了供应市场、零售市场及供应链网络的均衡条件,并利用投影算法对模型进行求解。结合算例,讨论了质量标准、质量成本系数对网络均衡的影响。数值结果表明:当质量标准较低时,制造商存在一个高于质量标准的均衡质量水平;当行业质量标准超过该均衡质量水平时,随着行业质量标准的提高,制造商利润会降低,而零售商利润会增加;随着行业质量标准的增加,供应链网络总利润呈现出先增后减规律,因此从供应链网络整体来看,行业质量标准应当适当,不能定得过高。同时,具有质量成本优势的制造商,会提高均衡质量水平,而具有质量成本劣势的制造商,会降低均衡质量水平,目的是增加产品质量差异以增加利润。     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题.借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型.结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响.结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大.     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题。借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型。结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响。结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大。     

Indivisible commodities and the nonemptiness of the weak core

We consider a sufficient condition for the nonemptiness of the weak core in a finite exchange economy where every commodity is available only in integer quantities. We show that if the aggregate upper contour set is discretely convex, then the weak core is nonempty. In addition, we give two sufficient conditions for the aggregate upper contour set to be discretely convex. One is that every upper contour set of every agent is M^?${\text{M}}^{?}$-convex. The other is that the number of commodities is two and every agent’s preference relation is weakly monotone and discretely convex.     

Equilibrium unemployment with outsourcing under labour market imperfections

We study the effects of international outsourcing on equilibrium unemployment in a high-wage economy with labour market imperfections. We demonstrate, consistent with empirical results, that the wage elasticity of labour demand is increasing as a function of outsourcing. Furthermore, we show that a production mode with more outsourcing reduces the negotiated wage in a high-wage country with labour market imperfections if the relative bargaining power of the labour union is sufficiently high. Under such circumstances outsourcing reduces equilibrium unemployment. Finally, we characterize the optimal production mode showing that stronger labour market imperfections induce a production mode with more outsourcing.     

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Received: 2 February 1996 / Accepted: 28 March 1997     

Indivisible commodities and an equivalence theorem on the strong core

We consider a pure exchange economy with finitely many indivisible commodities that are available only in integer quantities. We prove that in such an economy with a sufficiently large number of agents, but finitely many agents, the strong core coincides with the set of expenditure-minimizing Walrasian allocations. Because of the indivisibility, the preference maximization does not imply the expenditure minimization. An expenditure-minimizing Walrasian equilibrium is a state where, under some price vector, all agents satisfy both the preference maximization and the expenditure minimization.