Monday, September 19, 2016

Nine Spades Are a Lump of Leets

The section on capital from Joan Robinson's 1970 review of Charles Ferguson's The Neoclassical Theory of Production and Distribution employs the "lump of leets" motif to highlight a key issue in the Cambridge critique of neoclassical capital theory. Robinson's substantive lump-of-leets critique offers an instructive contrast to the abject flimsiness of the proverbial lump-of-labor fallacy claims.

For some years they remained cooped up in this position, repelling all attacks with blank misunderstanding. Then, growing bold, they descended to the plains and tried to prove Sraffa wrong. ...

Capital

The neo-neoclassicals' concept of capital is derived from Walras, but they have transformed it into something quite different. In a Walrasian market, when dealing begins, there are particular supplies of factors already in existence each measured in physical terms - man-hours, acres, tons, pints, and yards. In the neo-neoclassical concept of capital all the man-made factors are boiled into one, which we may call leets in honour of Professor Meade's steel.* But leets, though all made of one physical substance, is endowed with the capacity to embody various techniques of production - different ratios of leets to labour - and a change of technique can be made simply by squeezing up or spreading out leets, instantaneously and without cost. A higher output per man requires a larger amount of leets per man employed. In Walrasian competitive equilibrium there can never be increasing returns from one factor applied to a given quantity of another. This rule is observed by leets. There is a well-behaved production function in leets and labour for each kind of output, including leets. 
Moreover, leets can absorb technical progress, without losing its physical identity, again instantaneously and without cost. Then to simplify still further, output is also taken to be made of leets; the whole Walrasian system is reduced to a "one-commodity world." 
This is the conception in which Professor Ferguson has re-affirmed his faith. Many economists, nowadays, who are interested in practical questions are impatient of doctrinal disputes. What does it matter, they are inclined to say, let him have his leets, what harm does it do? But the harm that the neo-neoclassicals have done is, precisely, to block off economic theory from any discussion of practical questions. 
When equipment is made of leets, there is no distinction between long and short-period problems. The answer to Dennis Robertson's question is simply fudged. Nine spades are a lump of leets; when the tenth man turns up it is squeezed out to provide him with a share of equipment nine-tenths of what each man had before. 
There is no such thing as a degree of utilisation of given equipment rising or falling with the level of effective demand. (Professor Solow pretends that his production functions are drawn in terms of concrete capital goods, but the fact that the short-period utilisation function is identical witli the long-period pseudo-production function gives him away.) 
There is no room for imperfect competition. There is no possibility of disappointed expectations - indeed, there is no difference between the past and the future, for the past can always be undone and readjusted to a change in the present situation. 
There is no problem of unemployment. The wage bargain is made in terms of product and there is perfect competition both between workers for jobs and between employers for hands. Unemployed workers would bid down wages and the pre-existing quantity of leets would be spread out to accommodate them. The neo-neoclassicals have reconstructed the vague doctrines of the neoclassicals from which was derived the dogma which Keynes had to attack in the great slump of the 'thirties, that unemployment can be caused only by wages being too high. 
In long-period analysis, the neo-neoclassics are prone to confuse a comparison of positions of equilibrium (as in a pseudo-production function) with a "Wicksell process" of accumulation without technical progress. "A given state of technical knowledge" consists simply of a production function in terms of leets and labour. Accumulation consists of adding some leets to the pre-existing stock and squeezing it into a new quantity per man employed. This entails raising the wage rate and reducing the return per ton of leets. Thus a process of raising the capital-labour ratio means creeping along the production function, moving step by step from lower to higher ratios of leets to labour. (It is notable that when Professor Samuelson conceded defeat in the "reswitching controversy, he did so in this form. He seemed to suppose that if the process of accumulation hit a backward switch, where a lower rate of profit is associated with a lower value of capital per man, the economy would suddenly find itself able to consume part of its capital without reducing its productive capacity.) 
This brings into play the other aspect of pre-Keynesian theory. Saving consists in a decision not to consume a part of the current output and this causes investment to make a corresponding addition to the stock of "capital." The neo-neoclassicals have succeeded in tying themselves up again in habits of thought from which Keynes had had "a long struggle to escape." (However, when it comes to offering advice on questions of national policy many of them propounded quite simple-minded Keynesian views.**)

* J. E. Meade, A Neoclassical Theory of Economic Growth (London 1961). 
** Cf. R. M. Solow, The Nature and Sources of Unemployment in the United States (Wicksell Lectures, 1964).  

Stanley Bober commented on Robinson's critique [highlighted in italics] in "Classical Economic Fashion Redux: Growth Economics to the Forefront" Eastern Economic Journal, Vol. 17, No. 1 (Jan. - Mar., 1991), pp. 122-129:
The neoclassical explanation of the distribution of income is based on the idea of supply and demand operating in competitive markets; with the demand for the resource being derived ultimately from its contribution to output at the margin, i.e. its marginal productivity. The supply of the factor being determined by the disutility associated with its use. Now Sraffa was able to show that a system of equilibrium prices could be derived independently of any notion of marginal change and without any direct relation to the role played by the demand for factor services. There was simply no need to rely on the ideas of marginal disutility or marginal productivity to determine equilibrium prices. We should mention that Keynes, early on, denied that demand for labor services depends on its marginal productivity; he rejected the notion that labor income or, indeed, the amount of employment could be determined by marginalists principles at the micro level in the labor market. 
Yet there is a more telling point specifically regarding the capital input. Once we accept the reality of the heterogeneous commodity that constitutes capital (we get away from the notions ectoplasm or lump of leets representations), then, as we mentioned, there is no way to measure the quantity of capital except by calculating these quantities in value terms. This brings us to the obvious problem that the marginal product of the value of the physical capital as a determinant of the rate of profit is itself not possible in the absence of knowing what the rate of profit is. The values of the stock of capital depends on prices, and the prices in turn will depend on the distribution of income (on the rate of profit). There is a circularity of reasoning to talk in terms of placing quantities of "capital" into an aggregate production function, and then to take its marginal productivity to determine the rate of profit. The valuation placed on the input capital is not independent of the distribution of income which the "quantity" of capital is meant to explain - and there is no way to get hold of an aggregate measure called capital independent of the rate of profit that it is supposed to determine.