The Market

Equilibrium, Stability, Mythology

Sydney N. Afriat

• Publisher: Taylor & Francis
• Year: 2006
• eBook ISBN: 9781134420032
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

This punchy book unites mainline mathematical economics and sometimes idiosyncratic political economy. Freshness is brought to the market concept giving general equilibrium theory a new lease of life, and an opening of thought on such matters as free trade, globalization and the environment.
Where most theories of general equilibrium have been based on utility maximizing traders, Afriat here maintains the view that the topic essentially is concerned with aggregates and that anything to do with utility is at best secondary if not spurious. The book goes on to discuss political economy, in particular the idea of 'optimum', and its abuses, especially in doctrine related to the market.
This novel book will be of equal appeal to mathematical thinkers, those interested in the theory of market and political economists.

Part I

The market phenomenon

The market is a distinct phenomenon present in all kinds of circumstances. To understand it as such, and as being unconditioned by very special circumstances, it should in some way be cut off for a separate treatment. Though one may then be in an imaginary world, demonstrating the market phenomenon in a well-defined, abstract world – one we know well because we invented it – should go some way towards providing an explanation of the phenomenon.

The occurrence of markets is commonplace, it is outstanding, no planning committee or other agency is required to take part, they just happen, almost anywhere. The conditions to be considered therefore should be quite primitive, and for developing a theory some such conditions have to be explored.

The possibility of a market cannot be isolated from the process of original realization. An existing possible arrangement is tantalizing in the absence of a way of getting to it, from some, and perhaps any position. The tâtonnement or tentative groping process of Walras, or something like it, is therefore an essential part of the matter. The pure existence possibility has to be joined with some operational finding process. That requires a kind of roughness, overriding disturbances, so as to embody the stability of the self-regulated system without which it could not, in practice, exist.

The considerations are necessarily abstract, intended only to reflect something of the form of common experience. A simplest representation therefore could be of adequate value. This is not micro-economic theory that pretends to offer a picture of the system built from ultimate parts, but more on the surface.

That a good has a price P is demonstrated when a transaction takes place, in which it has that price. There is no real alternative sense in which a good can have a price. It means nothing that cabbages are $1 per pound if no one, or rather no two, are buying and selling at that price. Goods left on the shelf with a price tag on them, like many a house for sale, do not have a price until they are sold. Those tags are at most offers, or just factors in the tâtonnement. There are countless other goods on the shelf, some of them not yet invented.

In the transaction there is a buyer and a seller, and, even though two are present, what is bought and what is sold are the same thing. There seems to be no escape from that. In other words, supply S equals demand D: S = D. This is not an equation with content. It just connects two names that have been given to the same thing. But why give the same object two different names? It would be more logical to give it one, say the transaction quantity Q.

We have a transaction price P and quantity Q for a good. Both are observable, and they are observed together. But it is very popular to give Q two different names, S and D, and then talk about S and D separately as if they were distinct entities, which could, moreover, exist apart. There is a puzzle here, or some confusion – possibly on the part of this writer.

It could be wondered (from limitless curiosity) why any price should be just P and not higher or lower. Since the market is central to economics, it is in some way understandable that there should be an attempt to give an explanation of price, even a complete one. But what kind of explanation can there be? To explain a change in a price is a more modest endeavour than explaining a price. The same is true with regard to the neck of the giraffe, the elongation is well understood in terms of evolutionary mechanisms (despite some debate about that) but no biologist attempts a complete explanation of the giraffe. Economists, of the fundamentalist kind, have greater courage. They offer an explanation of price, of all prices; or, rather, a form for an explanation has been proposed (perhaps more than one). But carrying out a realization of the form is a further matter having much less attention. One may ask what content there could be just in the proposal about form, and whether there is anything in it that can be known to be true or false, or neither.

A main doctrine about a price in settled times was that it should be settled. A price was part of the order of things like fowls of the air and beasts of the field; there was such a thing as a proper chicken and it had a proper price. The price could be known and counted on; it could enter into plans for a dinner or the allocation of a budget. This is a rational position, and practical, but it is not one that can always be enjoyed, because unsettled times produce changes also in prices. The interest then is still practical; not why prices should all be absolutely what they are, but how they might change. This is as with the giraffe. There can still be the question of why there should be any offer to explain all prices, and even whether there really is an explanation.

It has been said “Teach a parrot to say “Supply and Demand” and there you have an economist” (Stephen Leacock, Literary Lapses). Whether or not this statement deserves approval it suggests a pleonasm, since we decided that, to the extent of anything visible, supply and demand are the same thing. They are not equal, but are indistinguishable. That is a matter of inescapable logic, since what means buying something to a buyer means selling something to a seller, and these two things happen to be identical. All the same, though the two things are one, it is outstanding that the same cannot be said of the buyer and the seller. These are two separate individuals. In fact, since the transaction is voluntary on both sides, it seems something of a coincidence that they got together. For theory, here is not just the chance but the matter to be explained.

This apparent chance has an extension to the aggregate, where it looks as if an unlikely coincidence must occur in order to have a price at all, because those willing to buy must be exactly matched by those willing to sell. It seems implausible that everyday economic life, where the price phenomenon is a commonplace, should be based on such a precarious balance. Theory should deal with the possibility of the fine arrangement; and, since feasibility is of incomplete interest without an idea of how it is realized, it should deal also with the process for arriving at it. Just now, however, the concern is with elements rather than aggregates.

The encounter between buyer and seller might in reality have some significant effect on each. If this is of a special and individual kind it must be ignored, and for purposes of theory we should deal with simple automata. A simplicity in the encounter is assured if the only recognizable interface between buyer and seller is the price. For a start, it is supposed that the buyer and the seller in their separateness each have a definite potentiality for their part in the transaction which takes place, already existing and then realized from the encounter. A shape for such assumptions is provided by the following:

i Anyone willing to buy a unit of a good at some price would be willing to buy it also at any lower price.

ii Anyone willing to sell a unit of a good at some price would be willing to sell it also at any higher price.

These are norms consistent with price being an incentive to sell and a disincentive to buy, and not necessarily absolute laws. We know from Veblen about ostentatious expenditure, and ostentatious charity or any other dispositions that might be imagined could be an addition to that. The situation is not different from Newton's when he made uniform motion a norm; so non-uniform motion causes attention to forces, if any can be found, and here ostentation is to Veblen something like what gravitation was to Newton. These assumptions express free disposal: the buyer who pays less is free to dispose of the difference leaving a situation which is the same and therefore as acceptable as when more had been paid, and similarly on the side of a seller.

If P_b is the upper limit to prices at which the buyer would be willing to buy a unit and P_s is the lower limit at which the seller would sell, then simultaneous willingness on both sides requires

P_s < P < P_d.

Hence

P_s < P_d.

for simultaneous consent to a transaction quantity at some price P, which then can be anywhere between P_s and P_d. Otherwise, at least one refuses and there is no transaction.

When successive further units are brought in we get declining and rising step functions, and if the units are small and numerous these become general monotonic curves, the supply and demand curves for buyer and seller. This line can be taken further by bringing in notions about a market and these individuals being in one.

Important data of the sensible world of economics concern form, not hard to get but evident from experience. No measurements are needed to know it, or read it. Also, things on paper are a part of economics because they affect behaviour and events; they are a real part of the real world. There is a voluminous recording and manipulation of data, but nothing of what in the main passes for economic theory really depends on it; in part of its nature it is near to ritual, in some form indispensable to social decision making as from time immemorial. The empiricism of natural scientists is different from so-called ‘empirical work’ in economics.

These possible views are entertained in connection with price theory based on supply and demand, in order to evaluate rather than object to it. The theory relies on ideas of the kind already described that have obvious reference to experience and we know what they mean. But there is a transition at some point, and there can be questions about the result. For instance, if the final theory were true there would be no way of knowing it, and so there can be question about the sense of offering it as true, or even as possibly true. As for its being false, in particular economies we know that it is, at least to some extent, because for instance prices are subject to various regulations. Also, time is a complication that makes the theory even more difficult to interpret. Nonetheless, and perhaps rightly so, the theory of prices and their equilibrium (in an unknown and unknowable framework) is given an important place in economic theory. Whether or not there should be a complaint exactly here, there can be one of another order about the ‘welfare’ appendages to this theory.

The matters up to now have a local and individual reference, but dealing with an economy signifies a global framework of information and competition. Stephen Leacock brings that out in ‘Boarding House Geometry’, another of his Literary Lapses. He sets out the argument in the manner of Euclid, a few Postulates and then Propositions. The former go something like this:

Postulates

A landlady is an angular figure equal to anything.

Boarding house sheets produced however far each way will not meet.

A pie is produced any number of times

...

and so forth. Then comes the first Proposition, and its Proof:

Proposition All boarding house rents are equal.

Proof is by the method of reduction ad absurdum by which an hypothesis is impossible if it has impossible consequences:

Proof Suppose, if possible, that the rents are not equal. Then one is greater than the other. Then the other is less than it might have been, which is absurd, &c.

The absurdity is from the landlady's side and it could have gone just as well from the tenant's side – that is, the other is greater than it might have been ... Leacock takes for granted our stated assumptions about buyers and sellers. While there are transactions in a good at price P no seller will sell at a lower price and no buyer will buy at a higher one. Since joint consent is needed, there will be no transactions at a price above or below P, and the good has a single price P. There is a global equalization, a global information situation having been presupposed.

Should buyers willing to buy at the price be exhausted before sellers willing to sell, then if further transactions take place they will be at a price that brings in more buyers and thereby a lower price, though not one so low as to cut out all sellers. Those sellers who are within their threshold and prepared to sell at a lower price will take part, and those others who were at or beyond it will not. In going to a lower price demand rises and supply falls; similarly with the reverse situation, in which further transactions would take place, if at all, at a higher price. At any point the price is what it is because all who would be buyers at that price find sellers and all sellers, buyers. There might be none of either. But it makes no sense to say cabbages are £1 per kilo if there is a would-be buyer at the price who cannot find a seller, or a seller who cannot find a buyer. The price being P depends on the balance S = D. If both sides of this equation are zero, as when buyers and sellers are far apart and there are none for a range of prices, it would not be precarious; otherwise it is, and there are movements. This is a dynamic picture giving sense to movements. It does not depend on a knowledge of the total numbers that would buy or sell at whatever price; whatever these might be, should it make sense even to refer to them, they can be recognized to be continually changing. At any moment one can in principle know the prevai...

Table of contents

• Cover Page
• Half Title page
• Series Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Foreword
• Preface
• Acknowledgements
• Part I The market phenomenon
• Part II Market equilibrium and stability
• I Sperner's lemma
• II The Kkm Lemma
• III Distribution Matrices
• Bibliography
• Part III The linear market model
• Part IV Market & Myth
• Part V On trade, and self-sufficiency
• 1 An introduction to economics
• 2 The ‘Optimism' of market doctrine
• 3 Keynes on “National self-sufficiency”
• 4 In Adelaide (or anywhere)
• Part VI In the economic context: concerning ‘efficiency'
• 1 Aristotle's Value Problem and General Equilibrium
• 2 Theorems of the Market “The First and Second Theorems of Welfare Economics”
• 3 Hypothetical traders for the linear market
• 4 Historical note on “Data Envelope Analysis” frontier and stochastic-frontier production functions
• Index