Essay on Trade Rules for Uncleared Markets

Trade rules for uncleared markets ∗ Özgür
July 5, 2005
Abstract
We analyze markets in which the price of a traded commodity is such that the supply and the demand are unequal. Under standard assumptions, the agents then have single peaked preferences on their consumption or production choices. For such markets, we propose a class of Uniform Trade rules each of which determines the volume of trade as the median of total demand, total supply, and an exogenous constant. Then these rules allocate this volume “uniformly” on either side of the market. We evaluate these “trade rules” on the basis of some standard axioms in the literature. We show that they uniquely satisfy Pareto optimality, strategy proofness, no-envy, and an informational simplicity axiom that we introduce. We also analyze the implications of anonymity, renegotiation proofness, and voluntary trade on this domain.
JEL Classification Numbers: D5, D6, D7
Keywords: market disequilibrium, trade rule, efficiency, strategy proofness, anonymity, no-envy, renegotiation proofness, voluntary trade
∗We gratefully acknowledge Ipek Gursel for a very useful observation. We also thank William Thomson, Tayfun Sönmez, Utku Ünver, Anirban Kar as well as the seminar participants at Sabancı University, Koç University, ASSET 2004, SED 2004, and the Murat Sertel Memorial Conference on Economic Theory for their comments and suggestions on an earlier version of this paper.
†Corresponding author: Faculty of Arts and Social Sciences, Sabancı University, 34956, Orhanlı, Tuzla, I ̇stanbul, Turkey. Tel: +90-216-483-9267. Fax: +90-216-483-9250. E-mail: ozgur@sabanciuniv.edu.
‡ D i v i s i o n o f t h e H u m a n i t i e s a n d S o c i a l S c i e n c e s , C a l i f o r n i a I n s t i t u t e o f Te c h n o l o g y, e - m a i l : serkan@hss.caltech.edu
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1 Introduction
We analyze markets in which the price of a traded commodity is fixed at a level where the supply and the demand are unequal. This phenomenon is observed in many markets, either because the price adjustment process is slow, such as in the labor market, or because the prices are controlled from outside the market (e.g. by the state), such as in health, education, or agricultural markets. These observations are conceptualized in the idea of market disequilibrium which has been particularly central in Keynesian economics after Clower (1965) and Leijonhufvud (1968). For more on this, see Benassy (1982).
For markets in inequilibrium, it is important to understand how trade takes place and how the current practice can be improved upon through the design of “good” rules that regulate it. In this paper, we propose such “trade rules” and evaluate them on the basis of some standard properties in the literature.
In our model, a set of producers face demand from a set of consumers (who might be individuals as well as other producers that use the traded commodity as input). We assume that the individuals have convex preferences on consumption bundles. They thus have single-peaked preferences on the boundary of their budget sets, and therefore, on their consumption of the commodity in question. Similarly, we assume that the producers have convex production sets. Their profits are thus single-peaked in their output or input. Due to these observations, our paper is related to earlier studies on single-peaked preferences.1
A trade rule, in our model, takes in the preferences of the buyers and the sellers and in turn, delivers (i) the volume of trade (i.e. the total trade that will be carried out between the buyers and the sellers) and (ii) how the volume of trade will be allocated among the agents on either side of the market. We introduce a class of Uniform Trade rules each of which, in step (i), determines the volume of trade as the median of total demand, total supply, and an exogenous constant and in step (ii), allocates this volume “uniformly” among agents in either side of the market.
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