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Date:
Fri Mar 31 17:19:18 2006
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[log in to unmask] (Ross B. Emmett)
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Surplus and classical distribution theory 
 
Anthony Brewer 
Department of Economics 
University of Bristol 
 
It is often said that the classical economists had a 'surplus' theory  
of distribution. I will argue that although there is some truth to this  
claim, it is one that must be rather carefully qualified. I have become  
increasingly convinced that the vague and imprecise way the word  
'surplus' is used is a hindrance to clear thinking. 
 
What is a surplus theory? If x + y = z, and if x and z are fixed  
independently of each other and of y, then one can say that y is the  
surplus of z over x. For example, if my brother and I get a cake and if  
he first takes what he wants, regardless of the size of the cake, then  
my share is a residual or surplus. What he takes might depend, say, on  
how he feels, provided it does not depend on the total to be divided.  
But if we split the cake equally, or by any other rule that makes his  
share depend on mine or on the size of the cake, then my share is not a  
pure surplus. 
 
In the surplus interpretation, classical distribution theory looks like  
this: (a) wages are fixed at a given level, (b) wage plus non-wage  
income equals (the value of) total output, so (c) non-wage incomes are  
determined by the surplus of output over wages. Valuation of output  
poses well-known problems, but my concern here is with the problems  
which would remain even if output were homogeneous. Note in particular  
that proposition (a) is the key to the surplus theory, since (b) is  
really quite trivial. A surplus theory with any substance to it must do  
more than assert proposition (a) - it must offer some coherent  
mechanism to bring it about. 
 
The classical wage theory of wages was directly based on population  
theory - (a) if wages are above subsistence, population and hence  
labour supply grows, and (b) wages are governed by demand and supply,  
in that rising labour supply, ceteris paribus, lowers wages (e.g. 
Ricardo, p. 94). In a static model it would follow that wages tend to  
subsistence. 
 
There are other ways in which wages could be fixed prior to everything  
else, but they cannot plausibly be attributed to the classics. Wages  
could be fixed by law or binding custom, but the classics did not think  
so since they discussed variations in wages in response to changing 
economic conditions. Employers could conspire to fix wages at  
subsistence. Smith did mention conspiracy, but his texts as a whole  
cannot plausibly be interpreted in those terms. Employers might  
voluntarily pay subsistence (but no more) because workers cannot work 
efficiently if they are paid less. This would be a sensible story, but  
I cannot find it in the the classics. Bargaining theories of wages are  
sometimes mentioned in this context, but any sensible bargaining theory  
makes the outcome depend on the total to be divided. Smith did discuss  
bargaining power, implying that employers could force wages down to  
subsistence, but immediately added that it did not apply to a growing  
economy. 
 
What of the claim that wages are determined by social or historical  
factors, over and above physical subsistence? A legal or customary wage  
could include elements other than physical subsistence, but that is not  
relevant to classical economics. If there is a social element in 
classical wage theory it must be built into the population theory. If  
people will starve (or allow their children to starve) rather than be  
'indecently' dressed, then clothes to a socially determined standard of  
decency are necessary. If, as Cantillon suggested, people will not 
marry unless they can be sure of an adequate standard of life for the  
resulting children, then the equilibrium wage will adjust accordingly.  
It is not enough to utter the words 'historical and moral element' like  
a mantra. The mechanism has to be explained, and demonstrated in the  
texts. 
 
Did the classics have a surplus theory as defined? For reasons of  
space, I shall consider only Smith and Ricardo. First Smith. His main  
theory of wages is very clear from the bulk of the Wealth of Nations,  
despite the rather confusing alternatives considered at the start of the 
chapter on wages. He was concerned with growing economies, where wages  
must be above subsistence to allow the labour force to grow in line  
with the demand for labour, so wages depend on the growth rate (Smith  
I.viii.16-27). That could still be counted as a surplus theory in the  
sense defined above if growth, and hence wages, were independent of  
output and profits, but they are not. In colonies, for example, high  
per-capita output on the best land and low rents (or land prices) lead  
to rapid accumulation and high wages. In countries which have reached  
their 'full complement of riches', investment opportunities are low,  
profits are low, and so are wages. Smith had not worked out all the  
details of these interactions, but it is clear that he had advanced  
substantially beyond a crude surplus theory. 
 
Labour is not homogeneous. The structure of wages clearly affects  
profits and other variables. To assert, as some do, that the structure  
of relative wages can simply be treated as given prior to everything  
else is an evasion, not a solution to the problem. Smith at least  
tackled the question seriously. 
 
Could it be said that although Smith did not hold a subsistence wage  
theory there is an asymmetry between his treatment of wages and profits  
which justifies treating his theory as in some way surplus-like? I have  
some sympathy with this view, but it is difficult to sustain. Labour  
supply depends on population (inter alia), which grows because of  
natural human desires. But the accumulation of stock (capital) also  
depends on a natural human desire, the desire to better oneself.  
Population growth is checked when the wage falls to subsistence, and 
accumulation is also checked when profits fall to a minimum set by the  
risk of loss. This does not amount to perfect symmetry between wages  
and profits (why should it?), but it is hard to see either as prior to  
the other. 
 
Ricardo, by contrast, did state a crude surplus theory, with wages  
reduced to subsistence by the demographic mechanism and non-wage  
incomes as the residual. The problem is that he also understood and  
accepted Smith's more sophisticated wage theory. The crude subsistence  
wage theory, with or without social elements in subsistence, is valid  
in a non-stationary state if and only if demographic changes work  
through much faster (strictly, infinitely faster) than changes in the  
demand for labour caused by capital accumulation. It would be 
absurd to believe that they do (as Marx, for example, pointed out). The  
simple subsistence wage, and hence the simple surplus element in  
Ricardo's theory, is its weak point, not its strength. One can  
reasonably debate whether he thought of it simply as a heuristic 
simplification  or whether there is a real inconsistency (c.f.  
Hollander, 195-6, Peach, 130-1). In any case, to attribute an  
unqualified surplus theory of distribution to either Smith or Ricardo  
is to undervalue and oversimplify their writings. 
 
Finally, a very brief word on Marx (who I do not count as a classical  
economist). He explicitly rejected the Malthusian theory of wages, and  
could not therefore take over the classical version of surplus theory  
as it stood. His main statement of the theory of surplus value in Vol. I 
of Capital depends on a definition of the 'value of labour power' in  
terms of subsistence requirements (with a 'historical and moral  
element'). It offers no reason why wages should be at this level and  
therefore has no substantive content. However, Chapter 25 contains a 
different story, in which accumulation raises the demand for labour  
power and drives up wages but rising wages in turn check accumulation,  
while labour-saving technical change tends to bring wages down again.  
This incomplete sketch of dynamic interaction between wages, profits,  
and growth clearly does not meet the conditions for a surplus theory as  
defined above.  
 
I conclude: (1) the substance of a surplus theory of distribution has  
to derive from the wage theory on which it is based. (2) To the extent  
that there was a classical surplus theory, it was based on 'Malthusian'  
population theory and stands or falls with it. Any claim that such a 
theory can be used in modern conditions is clearly untenable. (3) Even  
a Malthusian population theory only yields a pure surplus theory of  
distribution in a static economy. As Smith and Ricardo both knew, in a  
growing economy distribution and growth interact to produce wages above  
subsistence, invalidating a simple surplus theory. 
 
Hollander, S. Classical Economics, 1987, Blackwell 
Peach, T. Interpreting Ricardo, 1993, CUP 
Ricardo, D. Principles (Works, vol I), ed P. Sraffa, 1951, CUP 
Smith, A. Wealth of Nations (Glasgow Edition), 1976, CUP. 
 
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