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A close look at labour markets, Keynes and effective demand shows that low demand is very bad for equality

A simple idea from game theory could yet upset the sacred tenants of neoclassical economics. This articles explores the implications for the theory of distribution and Keynes's theory of effective demand.
Tim Bending
10 January 2011

Practical men, as Keynes famously said, are usually the slaves of some defunct economist. Today's practical men are slaves of a few simple ideas from the 1870s and 1890s. But the discipline of economics has moved on. It has become more heterdox; less coherent.

Take the idea of equilibrium. The general equilibrium theory of Walras (1874) imagines the economy as one great, inter-connected market in which unhindered competition brings all demands and supplies into balance. General equilibrium is seen as an optimal state of affairs (Pareto, 1896) in which no one can benefit except at the expense of another. Walrasian general equilibrium became a paradigmatic image for neoclassical economics; it purports to tell us what we could achieve through the promotion of unhindered competition.

But then there is game theory. John Nash (in 1950) suggested a different kind of equilibrium. A Nash equilibrium exists when all players in a game, knowing the strategies employed by the others, opt to maintain their own strategies unchanged. Such an equilibrium is compatible with perfect competition, but the result does not have to be Pareto optimal.

Game theory has been applied to a great range of microeconomic problems. It's not controversial. So does this mean that the policy orthodoxy is based on an objective consideration of when the one equilibrium is more fitting than the other? Not at all. It remains a slave of the late 19th Century. The idea that free markets give Pareto optimal results is still paradigmatic.

It is also deeply questionable. I have previously argued that the huge pay differentials that afflict modern market economies can be attributed to a form of rent, to an unearned and unproductive distribution of income. This is, in fact, an example of a Nash equilibrium at work. I wish to use the present article to discuss the wider macroeconomic implications of this idea.

The marginal productivity theory of distribution

The marginalist revolution of the 1870s brought new theories of employment and investment. Firms keep on employing more and more labour and capital, said the marginalists, so long as adding an extra unit of either creates an increment of product larger than the respective increment of wages or interest. This seemed to offer a fruitful way to explain wages and interest, but it took another two decades before a general neoclassical theory of distribution emerged.

The breakthrough was proposed by J. B. Clark in 1889 and proven mathematically by Wicksteed in 1894. It was the realisation that if all factors of production are paid in this way – at their marginal rate of productivity – then the total product of the economy is necessarily used up. This is the marginal productivity theory of distribution (MPTD). It places the determination of wages and interest firmly within the general equilibrium vision of the economy.

The MPTD matters because of the messages it sends, namely:

  • Free competition promotes a Pareto optimal distribution of income.

  • In free markets, people are paid roughly according to their productivity.

  • Free markets lead to full employment. If you can't find work, you're asking for more wealth than you would produce.

  • Free trade will gradually equalise global returns on labour and capital; poor countries will catch up with the rich.

Clearly, if the marginal productivity theory of distribution is wrong, then economic policy has been driving in the wrong direction. Indeed, Marxian and Neo-Ricardian schools offer completely different methodological approaches. Yet it was perhaps Keynes who, unwittingly, came closest to an effective challenge.

Keynes's partial revolution

Keynes accepted the MPTD. His target was narrower: the neoclassical theory of employment. According to the latter, both the level of employment and the level of wages are determined by the intersection of the marginal product and marginal disutility of labour, thus:

But Keynes's theory of effective demand asserts the possibility of “involuntary unemployment”. It suggests that employment can fall to levels at which marginal product exceeds marginal disutility. So what happens to wages? Taking the MPTD as given, Keynes is forced to say that wages always equal marginal productivity, as in Figure 2. Were wages to fall below marginal productivity – say to b – then the marginal products of the factors of production would not add up to the total product; there would be product left over. Within the neoclassical framework, this is not compatible with Keynes's assumption of “a perfectly working economy” and his desire to show an “unemployment equilibrium”.

But this brought big problems. If wages are above the disutility of labour, then won't money wages be bid down by unemployed workers? Since real wages = marginal productivity (under the MPTD), falling money wages should imply a corresponding fall in prices. Keynes's critics and neoclassical interpreters were quick to pounce one of Keynes's own observations, that such deflation would effectively increase the money supply. This, in turn, should lower interest rates, raise investment, and raise aggregate demand, and so constitute a mechanism by which an economy might return itself to full-employment, just as the pure neoclassicals always insisted it would. Keynes's ideas were incorporated into a “neoclassical-Keynesian synthesis”. In it, Keynes's theory of unemployment became no more than a special case of the neoclassical theory, applicable in the context of “sticky wages”.

The neoclassical-Keynesian synthesis is challenged by post-Keynesians on grounds such as the adverse effects of deflation and theory of endogenous money. Post-Keynesians have also variously embraced neo-Ricardianism and institutional economics as approaches that call the basic assumptions of neoclassical economics into question. They may have a point. But in all this, the simple, charismatic clarity of Keynes's original thesis is lost.

A labour market Nash equilibrium

The MPTD tells us that “wages” will equal the marginal productivity of labour prevailing at a given level of employment. Keynes accepted this, and it was the undoing of his theory. But in reality, something slightly more complicated is happening.

The disutility of labour is essentially an opportunity cost. It is the cost of doing what an employer wants you to do, instead of what you want to do. It is, therefore, the price of our time. The marginal disutility of labour is the supply price of a quantity of labour. Offer less that this, and no one will work for you.

But firms do not just need quantities of labour. They also need different qualities. The need skills, knowledge and experience. Market conditions for obtaining labour qualities and quantity are very different. Firms need absolute quantities of labour. They can hire too much. And they can always get enough, as long as they pay its marginal cost. By contrast, the qualities a firm needs are not absolute but relative. Specifically, they need skills, knowledge and experience as good as, or better, than those obtained by their competitors. Employees can be too many, but they can never be too good at what they do. While the supply of labour-time is fairly elastic, therefore (raise wages and more is forthcoming), the supply of a relative quality is, by definition, perfectly inelastic. Only one employee can be “the best”, no matter how much employers pay.

Now, let us suppose, following Keynes, that weak effective demand causes a degree of involuntary unemployment, as in Fig. 2. The marginal disutility of labour (b) is below its marginal productivity (a). Under these circumstances, firms can obtain the quantity of labour-time that they need at the price b. But this leaves a residual (a – b), and has done nothing to ensure that firms get the qualities of labour that they need.

Imperfect competition might allow the owners of these firms to keep this residual as excess profits. But assuming competitive circumstances, firms must use this residual to compete for the workers who best offer the qualities they require. Practically speaking, firms have no choice. If they do not match the pay offered to experienced and skilled workers by their competitors they risk being driven out of business. They are participants in a prisoners' dilemma game which can be represented as follows:

In this game, which assumes perfect competition, the behaviour of firms will tend towards a Nash equilibrium (represented by the outcome “survive; survive”) in which they employ the entire residual product available to them in competition for workers who are relatively qualified.

It must be added that this residual product is not actually distributed to workers according to their quality or competence. As I have described previously, the importance to a firm of obtaining quality labour varies according to the job being filled. Specifically, it depends on the degree that the worker in that job will be able to influence, for better or worse, the productivity of the whole firm. Heavily supervised manual labourers have negligible influence. Employees who manage large numbers of other employees, or large quantities of money, have vastly more influence. A rational firm will concentrate its resources in competing for skilled and experienced employees in proportion to the influence entailed by different jobs. Thus manual labourers will be paid little more than the marginal disutility of labour time; executives vastly more. The most incompetent banker will be better paid than the most skilled manual labourer. The degree of pay inequality, meanwhile, is a function of the size of the residual product, and thus of the degree of unemployment.

A marginal cost theory of distribution

According to the above, the distribution of national income has two principle determinants: the marginal disutility of labour at a given level of employment, and the rate of interest (itself determined by the marginal disutility of forgoing liquidity at a given money supply). The residual is distributed by firms to employees, in proportion to job influence, in a competition for relatively qualified labour.

It is possible to sketch out some implications of this theory:

  • Keynes' theory of effective demand is upheld as the explanation of employment and output. The “Keynes” and “real balance” effects, used to suggest self-regulatory mechanisms for regaining full-employment, do not apply. This because unemployment is not, by itself, deflationary. By themselves, changes in the level of employment only result in changes to the composition of wages and thus the distribution of wage income.

  • Lowered wage demands do not create employment, but only lead to further skewing of income distribution, or to deflation.

  • Expanding output may lead to inflation, as has often been observed (the “Philips curve”, etc.), but only where above average rates of pay are “downwards sticky”.

  • Full-employment can be defined as the point at which labour's marginal cost equals its marginal disutility, with the distribution of residual to employees in proportion to job influence reduced to zero. Full employment has never been reached in capitalist economies. They consistently perform below their potential output, leaving people involuntarily unemployed.

  • The residual is a form of pure rent. Payments of the residual are not necessary to bring forth labour and do not correspond to productivity. There are therefore no grounds for defending the pay inequality created by the distribution of the residual in terms of “just rewards”. Distribution is not Pareto optimal, but inefficient.

  • Free trade and the pursuit of comparative advantage will not necessarily lead to the global equalisation of returns to labour, so long as there is a global deficiency of effective demand. Where one country specialises in low influence professions (e.g. agriculture, contract manufacturing) and another specialises in high influence professions (research and development, management of global processes, finance), the former will lock itself into wage rates dominated by the local marginal disutility of labour, while the latter will benefit from pay dominated by the residual of globalised production processes.

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