This post presents another anomaly for neoclassical economics established in Sraffa's framework. It does not present a numeric example, but only outlines the possibility of one. Maybe Kurz and Salvadori (1995) or Woods (1990) contain specific numeric values in which a process can recur along the so-called factor price frontier without the reswitching or recurrence of techniques also arising. Han and Schefold found process recurrence empirically to be more common than reswitching. They say:
"In fact, it is often observed that returns of processes are connected with reverse capital deepening within the scope of our investigation (but it can easily be seen that either phenomenon can also occur without the other)." - Han and Schefold (2006)2.0 The Model
Consider a simple economy in which workers produce two commodities, apples and bananas from inputs, also composed of apples and bananas. Two processes are known for producing apples, and these processes are labeled IA and IIA. Two processes, IB and IIB are also known for producing bananas. This a circulating capital model; all inputs are used up in each production in producing the outputs.
A technique consists of two processes, one for producing apples and one for producing bananas. The claim is that processes can be such that techniques are cost-minimizing at the rates of profits indicated in Table 1. Notice that in this table, each technique is cost-minimizing only in one interval for the rate of profits. Techniques do not reswitch or recur. Yet the first process for producing apples does recur. That process is part of the cost-minimizing technique in both the first and the last interval for the rate of profits. The reswitching of techniques is sufficient for processes to recur, but is not necessary.
|Rate of Profit||Technique|
|0 ≤ r ≤ r1||IA, IB|
|r1 ≤ r ≤ r2||IIA, IB|
|r3 ≤ r ≤ r1||IIA, IIB|
|r3 ≤ r ≤ rmax||IA, IIB|
Process recurrence is also paradoxical from the exploded neoclassical perspective. An ill-trained neoclassical economist might expect the principle of substitution to hold for individual industries, as well as at the level of the entire economy. In the simple sort of model from which the outlined example is drawn, a higher rate of profits is associated with a lower wage. The specification of a process includes the specification of the how many person-years of labor is needed per unit output in the given industry. Figure 1 shows this normalized direct labor input as a function of the wage. Process recurrence is incompatible with the supposed neoclassical principle of substitution.
|Figure 1: Labor Intensity Versus Wage In A Single Industry|
- Z. Han and B. Schefold (2006) "An Empirical Investigation of Paradoxes: Reswitching and Reverse Capital Deepening in Capital Theory", Cambridge Journal of Economics, V. 30
- Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis, Cambridge University Press
- J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press