General Equilibrium and People Production Factories

This post began as an examination of the weak definition of General Equilibrium in Wikipedia but has evolved into a examining the foundational assumptions of what ‘General Equilibrium’ is in particular in terms of dominant DGSE models. The purpose is not to attack ‘Equilibrium’ theory itself but to think carefully about under what circumstances it can approach generality if ever.

The Wikipedia definition

a set of prices exists that will result in an overall equilibrium, hence general equilibrium

Wikipedia General Equilibrium Entry

Bu what is ‘equilibrium’ we have to rely on the entry for Economic Equilibrium

Wikipedia Economic Equilibrium Entry

This begs a question what do we mean by ‘supply equals demand’. A more pithy definition you will often find relates to market clearing.

General equilibrium is the situation where all markets clear.
Politique Francias Lecture Notes 2012

But all market can clear through short side rule selling even when at disequilibrium. Agents may be forced to sell at less than equilibrium prices because of binding budget constraints, such as the need to pay debts, pay rents etc. The fact that this occurs in some markets does not imply that this is balanced by other markets not clearing. The only constraint is that excess supplies = excess demands and short side selling might occur in all such markets.

A better definition I think is that All good and asset markets clear at the cost price and rate of profit anticipated by economic agents.

This is more helpful I think in that it directly links the classical notion of real cost with the principal of rational expectations of prices as first set out in Chapter 7 of Gerard Debreu’s Theory of Value. I do not assume for a moment that this is an optimal, stable or unique condition or that prices are not moving at equilibrium. Nor do I make any assumption about the competitive nature of an economy or make any prior assumption of non-existence of profits. Rather and simply that this is a point of attraction for prices. As Walras himself said.

Such is the continuous market, which is perpetually tending towards equilibrium without ever actually attaining it, because the market has no other way of approaching equilibrium except by groping, and, before the goal is reached, it has to renew its efforts and start over again, all the basic data of the problem, e.g. the initial quantities possessed, the utilities of goods and services, the technical coefficients, the excess of income over consumption, the working capital requirements, etc., having changed in the meantime. (Walras 1954: 380–381).

Here we can see the connection between the classical notion of the ‘long run’ and the attempt by thinkers such as Marshall and Walras to formalise this ‘equilibrium’ condition.

However the reason I underline good and asset markets is that the labour market is different – people are not produced. As a result unemployment exists and is not simply a result of the unemployed having higher utility than the employed.

The core ‘long run’ mechanism in classical economics of course was the tendency for equilibration of rates of profit across investments. I do not believe that supposed other equilibriating mechanisms (Says Law, interest rates clearing loanable funds) exist, rather they are misunderstandings of how the equilibration mechanism operates when money itself is a produced commodity. Understood in this way general equilibrium operates when all there is no more profitable investment of factors of production that can be undertaken by capitalists with their existing information and knowledge. Even if this purely hypothetical state were reached there may be disequilibrium trading of goods already produced and in existing inventories before these are run down. Here I think is the core common point of agreement between Ricardo, Marx even, Marshall and Walras.

The problem is labour is not produced by a capitalist process. Of course it could be. Pregnant women could be owned by companies. The education could be run by the company based on the anticipated demand for labour and various skills years ahead. When there was a surplus of any particular type of skilled or unskilled labour the company could pay for them to be transported or simply culled. When there was a shortage of anticipated labour young women of childbearing age could be kidnapped and forcibly impregnated. Of course labour is not produced in this manner. But crucially because it is not, we do not have people production factories, we do not have a complete market for labour as a commodity.

The existence of a ‘complete’ market is crucial for the existence of a single pareto optimal equilibrium under the Arrow-Debrau proof (understanding of course that the pareto optimal; condition was invented to justify the inequality of wealth under fascism). A complete market treats each differentiable good as a separate commodity, such as skill on a lathe or cooking. Indeed it is not meaningful to talk of unemployment overall only as an aggregate of segmented markets of different levels of skill and experience. As the labour market is not ‘complete’ there can be multiple non optimum equilibriums including equilibriums with high levels of unemployment.

One of Ricardo’s great advances over Adam Smith was to treat labour as a commodity. The adjustment process however was not the transfer of equity investments but the Malthusian reproduction process. Labour was at its costs price, the price of reproduction. If there was a shortage of labour people would reproduce, a surplus they would starve. Where he disagreed with Malthus was in seeing that the price of food was not a given but depended on factor inputs. Labour would be in shortage when the rate of increase of capital formation was greater than the rate of increase of the working age population, in suplus when the opposite was the case. However it might take many many years for this equilibriation forces to operate. Because labour in shortage or surplus is not (in the large part) subject to complete markets to rectify it can be treated as medium term fixed in quantity and subject to the laws of rent. When labour in in shortage it can effectively charge an absolute rent as there is no rent free margin. This rent comes straight off profits and increase housing rents. It is in capitals interest to minimise this loss of surplus to landowners hence the need to maintain a ‘standing army’ of the unemployed to minimise loss of profits.

We now come to Keynes notion of a unemployment equilibrium. Of course ‘in the long run we are all dead’ was his pithy view of the population/wage equilibration process. In the forward of the general theory he posits that his theory is general whilst the classical theory is a special case limited only to ‘a limiting point of the possible points of equilibria’. I don’t hold to the ‘disequilibria’ interpretation of Keynes that unemployment is only possible due to price friction/stickiness. This is sloppy thinking confusing price stickiness with non-completeness of markets. I read Keynes as describing a non-complete market with multiple non pareto optimal points of equilibrium which include high unemployment equilibrium.

Modern DGSE theory rather dodges the non-completeness of the labour market by subsuming it within the preferences of a single representative agent. Hence we have the perversity of a theory which proposes that unemployment is primarily a matter of choice. Search theory is bolted on to try to explain unemployment through frictions. There are many useful insights in search theory, which seems to get ever more complex, but it is built on foundations of sand, the problem is not one of frictions (the absence of which might simply speed a business cycle into a high unemployment position) but market completeness.  Sympotomatic of the confusion this sows is the thought often posted on Neo-classical and Austrian blogs is why the unemployed don’t work for nothing.  The answer of course is they would lose the time spent searching for better paid work, applying for paying jobs, growing food, helping with low margin family businesses, even where there is no welfare begging or stealing, and where there is losing welfare necessary to eat.  Work time is survival time and the opportunity cost of working for nothing means starving.  Indeed in most of the world most of the unemployed are for most of the time gainfully occupied in these activities.

The absence of a complete labour market in a form which might be acceptable in a non-slave society is the reason the state intervenes, providing welfare, education etc. In the past and in more authoritarian settings it did undertake transportation, culling and forcible pregnancies as we know. This is not a non-grounded extreme example for effect.

Finally I would agree with Roger Farmer

The problem with classical models is not the equilibrium assumption; it is the optimality implication. The idea that the current state of affairs is socially optimal is so obviously at odds with the existence of mass unemployment that it has given equilibrium theory a bad name. In very simple models, equilibrium and optimality are the same thing. But that conclusion is a very special implication of some equilibrium models. It does not hold in general. That idea is key to reconciling Keynesian economics with equilibrium theory…. To understand the persistence of high unemployment, we do not need to assume that prices are sticky or that markets are in disequilibrium. Mass unemployment does not occur because markets are in disequilibrium: Mass unemployment occurs because the market equilibrium is not socially optimal.

I would only partially agree with the final part however as unemployment has multiple causes. Disequilibrium and disproportionality can be a cause of employment, but high mass unemployment is caused by non complete labour and money markets leading to none-optimality.


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