The variety of attempts to generate neoclassical results in a ‘Keynesian’ framework, and ‘Keynesian’ results in a neoclassical framework, together point to important failings in the General Theory. I will argue that the key failures are the inadequacy of Keynes’s critique of the neoclassical theory of output and the important ambiguities introduced into the analysis by his marginalist treatment of the labour market and by his portrayal of the marginal efficiency of capital as an elastic demand schedule for investment. Garegnani (1978, 1979) has argued that these failings may be remedied by application of the results of the debate on the neoclassical theory of capital derived from Sraffa’s Production of Commodities. I will illustrate this point by reference to the implications of the debate for Fisher’s analysis of investment and the rate of interest which Keynes identified with his own analysis.

Keynes defined the marginal efficiency of capital as follows:

  • If there is an increased investment in any given type of capital during any period of time, the marginal efficiency of that type of capital will diminish as the investment in it is increased, partly because the prospective yield will fall as the supply of that type of capital is increased, and partly because, as a rule, pressure on the facilities for producing that type of capital will cause its supply price to increase; the second of these factors being usually the more important in producing equilibrium in the short run, but the longer the period in view the more does the first factor takes its place. Thus, for each type of capital we can build up a schedule, showing by how much investment in it will have to increase within the period, in order that its marginal efficiency should fall to any given figure. We can then aggregate these schedules for all the types of capital, so as to provide a schedule relating the rate of aggregate investment to the corresponding marginal efficiency of capital in general which that rate of investment will establish. We shall call this the investment demand-schedule; or, alternatively, the schedule of the marginal efficiency of capital (Keynes 1936, p. 136).

  • Keynes’s argument is more complicated than may at first appear, involving as it does assumptions on both the supply and demand conditions for individual capital goods in both short and long run and, finally, at both individual and aggregate levels – the ultimate objective being the derivation of the relationship between the ‘rate of aggregate investment’ and ‘the corresponding marginal efficiency of capital in general’, or, to put it another way, the general rate of return.

Taking first the short-period aspect of the argument, Keynes’s assumption that increased investment in a given type of capital good will lead to higher cost of production – rising supply price – is quite unfounded. Any short-period situation, and particularly a short period in which capital capacity is widely underutilized, will be characterised by excess stocks of materials and machines in some (maybe all) sectors, with (perhaps) shortages in a few sectors too. In such a situation no definite hypothesis may be made as to the likely effect of increased output on cost, though in conditions of widespread excess capacity it seems reasonable to suppose that costs will tend to fall as fixed costs are averaged over higher output. ‘Pressure on the facilities’ for producing a given capital good will only tend to become significant as full employment is approached, and even then the consequences for the cost of production of an increase in supply of any one capital good cannot be predicted with confidence.

The short-run influence of the demands for capital goods on ‘prospective yield’ to be derived from further investment are likewise unpredictable, and as to the aggregate effect of all this – nothing can be said at all. Indeed, there is no short-run ‘marginal efficiency of capital in general’ to say anything about! The relationship which Keynes sought must be a long-run relationship, in the sense that it is sufficiently unambiguous and persistent to allow definite conclusions to be drawn concerning the influence of a given volume of investment on the rate of return.

Now, in the longer run Keynes himself suggested that increased output will not result in any increase in cost. Any diminution in return must, therefore, derive from the fall in prospective yield as more capital goods compete to sell their services. What then is the relationship between the volume of investment and the rate of return in the longer run, that is in a situation in which the cost minimising combination of factors is chosen? At the partial level Keynes first considers, the answer seems clear: if all other prices in the economy are taken as given, then ceteris paribus it may be argued that there is an inverse relationship between the rate of return and the quantity of capital invested in the production of a given output. But Keynes’s argument is on very shaky ground when he attempts to define the relationship for the economy as a whole by simple aggregation of these partial effects, for he can no longer use the ceteris paribus condition to keep at bay some fundamental problems.

These fundamental difficulties in Keynes’s characterization of the marginal efficiency of capital may be clarified by returning to Fisher’s analysis of the incremental rate of return on investment which Keynes tells us is ‘identical with my definition’ (Keynes 1936, p. 140).

Fisher’s analysis is based on the substitution of capital for labour in a full-employment equilibrium, and throughout his discussion of the theory of saving, investment and interest, he imposes a major limitation on his argument – he assumes that all prices, wages and rents are fixed, and do not vary with variations in the rate of interest (Fisher 1930, p. 131n). This ‘fixedprice’ assumption allows Fisher to express all magnitudes in terms of ‘money’, and to move between discussion of individual behaviour and that of the economy as a whole without considering the inter-relationship between the rate of interest and prices.

An attempt to generalize Fisher’s analysis to a many-commodity model, and hence to relate the determination of prices to the determination of the rate of interest, has been made by Solow (1963, 1967). I have analysed Solow’s model and the debate it provoked elsewhere (Eatwell 1976); for our purposes we need only summarize my main conclusions.

It is assumed by Solow that the economy is in a stationary state, producing a consumption good, corn, by means of many reproducible inputs and labour. To enable the definition of limits we may further assume that the technical possibilities of the economy are characterised by a wage-profit frontier which is an envelope to an infinity of wage-profit curves, such that techniques are arrayed continuously along the frontier. Furthermore, consumption and value of capital per head associated with the variation in technique may be described by differentiable functions.

Since the techniques used in the production of corn require inputs of commodities other than corn, the wage-profit line for each technique may assume any negatively sloped curvature. But consumption good output per capita, c, (ie net output per head) and the value of produced inputs per capita, k, are continuous differentiable functions of the rate of interest (rate of profit), r, even though the technique in use varies continuously with r:

$$ c=z(r)\, k=\frac{\mathrm{net}\, \mathrm{output}-\mathrm{wages}}{\mathrm{rate}\, \mathrm{of}\, \mathrm{profit}}=\left[z(r)-g(r)\right]/r $$
(1)

where g(r) = w is the equation of the wage-profit frontier.

The rate of return over cost of a transition between the technique in use at r and the ‘adjacent’ technique at r + h is the ratio of the value of the difference in the perpetual consumption streams to the value of the difference in the capital stocks (i.e. the sacrifice required to effect the transition):

$$ {\displaystyle \begin{array}{l}\left[z\left(r+h\right)-z(r)\right]/\hfill \\ {}\left[\frac{z\left(r+h\right)-g\left(r+h\right)}{r+h}-\frac{z(r)-g(r)}{r}\right]\hfill \end{array}} $$
(2)

‘In the limit, as the number of techniques grows denser’, h → 0 and expression (2) becomes:

$$ {z}^{\prime }(r)\frac{r^2}{r\left[{z}^{\prime }(r)-{g}^{\prime }(r)\right]-z(r)+g(r)}\ne r; $$
(3)

the marginal rate of return over cost is not equal to the rate of profit. The equality would hold iff:

$$ z(r)=g(r)-r{g}^{\prime }(r) $$
(4)

This would be the case of an economy having the properties of Samuelson’s (1962) surrogate production function, and would indicate that, to all intents and purposes, the economy under consideration was set in a one-commodity world. The inequality does not depend on the presence of reswitching or even perversity. So long as the economy contains more than one produced input the rate of profit is not equal to the rate of return over cost. Or, more generally, no demand schedule for investment as a function of the rate of interest may be constructed.

The lack of any logical foundation for the construction of an elastic demand schedule for investment as a function of the rate of interest is simultaneously a critique of the neoclassical theory of output and of Keynes’s concept of the marginal efficiency of capital – which was itself derived from the neoclassical schedule. Moreover, the fact that the neoclassical theory of output is synonymous with the neoclassical theory of value means that an effective critique of the latter necessarily constitutes an effective critique of the former. There is no logically consistent foundation to the idea that variation in relative prices, or in the rate of interest, or in money wages, will cause the system to tend to a full-employment level of output. Keynes’s utilisation of the notion of a demand schedule for investment may perhaps be explained by the pioneering nature of the General Theory, in which the main propositions of a new theory of output are combined with vestiges of the old theory; by the need to present an apparently ‘complete’ theory; and by the pragmatic ambiguity with which many neoclassical propositions were presented in the then dominant Marshallian formulation.

However, once the corrosive influence of the presence of a marginal efficiency of capital schedule is removed, not only is the neoclassical synthesis seen to be without logical foundation (as in any other version of pseudo-Keynesian theory, such as that of Leijonhufvud (1968) or Malinvaud (1977), which assumes a monotonic inverse relationship between the rate of interest and the volume of investment), but also Keynes’s positive contribution, the principle of effective demand, is thrown into more dramatic relief.

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