Monday, January 16, 2017

A Story Of Technical Innovation

Figure 1: The Choice of Technique in a Model with Four Techniques
1.0 Introduction

I often present examples of the choice of technique as an internal critique of neoclassical economics. The example in this post, however, is closer to how I think techniques evolve in actually existing capitalist economies. Managers of firms know a limited number of processes in each industry, sometimes only the one in use. Accounting techniques specify a set of prices. An innovation provides a new process in a given industry. The first firm to adopt that process may obtain supernormal profits, whatever the wage or normal rate of profits. Other firms will strive to move into the industry with supernormal profits and to use the new process. Prices associated with the new technique result in the wage-rate of profits frontier being moved outward, perhaps along its full extent.

This example was introduced by Fujimoto (1983). I know it most recently from problem 22 in Woods (1990: p. 126). It is also a problem in Kurz and Salvadori (1995). Fujimoto probably labels it a curiosum because of details more specific than the above overview of how Sraffians might treat technical change.

2.0 Technology

This example is a two-commodity model, in which both commodities, called iron and corn, are basic. Suppose iron is used exclusively as a capital good, and corn is used for both consumption and as a capital good. Consider the processes shown in Table 1. Each process exhibits Constant Returns to Scale. The coefficients in each column show required inputs, per unit output, in each industry for each process. Each process requires a year to complete, and outputs become available at the end of the year. This is a circulating capital model. All commodity inputs are totally used up in the year by providing their services during the course of the year.

Table 1: The Technology

For this economy to be reproduced, both iron and corn must be (re)produced. A technique consists of an iron-producing and a corn-producing process. Table 2 lists the four techniques that can be formed from the processes listed in Table 1. In this example, not all processes or techniques are known at the start of the dynamic process under consideration.

Table 2: Techniques
Alphaa, c
Betaa, d
Gammab, c
Deltab, d

3.0 Price Systems

A system of prices of production characterize smooth reproduction with a given technique. Suppose a unit of corn is the numeraire. Let w be the wage, r be the (normal) rate of profits, and p be the price of a unit of iron. Suppose labor is advanced, and wages are paid out of the surplus. If the Alpha technique is in use, prices of production satisfy the following system of two equations in three unknowns:

(2/5)(1 + r) + (1/2) w = p
(2/5) p (1 + r) + (1/2) w = 1

A non-negative price of iron and wage can be found for all rates of profit between zero and a maximum associated with the technique. Figure 1 illustrates one way of depicting this single degree of freedom, for each technique.

4.0 Innovations

I use the above model to tell a story of technological progress. Suppose at the start, managers of firms only know one process for producing iron and one process for producing corn. Let these be the processes comprising the Alpha technique. In this story, the rate of profits is exogenous, at a level below the rate of profits associated with the switch point between the Gamma and Delta technique, not that that switch point is relevant at the start of this story.

Somehow or other, prices of production provide a reference for market prices. For such prices, the economy is on the wage-rate of profits curve for the Alpha technique in Figure 1. This curve is closest to the origin in the figure.

Suppose researchers in the corn industry discover a new process for producing corn, namely process (d). A choice of technique arises. Corn producers see that they can earn extra profits by adopting this technique at Alpha prices. The Beta technique becomes dominant. Eventually, the extra profits are competed away, and the economy lies on the wage-rate of profits curve for the Beta technique. Under the assumption of an externally specified rate of profits, the wage has increased.

Next, an innovation occurs in the iron industry. Firms discover process (b). At Beta prices, it pays for iron-producing firms to adopt this new process. The wage-rate of profits curve for the Delta technique lies outside the wage-rate of profits curve for the Beta technique. Thus, the Delta technique dominates the Beta technique. But prices of production associated with the Delta technique cannot rule. If the Delta technique were prevailing, corn-producing firms would find they can earn extra profits by discarding process (d) and reverting to process (c). The Gamma technique is dominant at the given rate of profits, and workers will end up earning a still higher wage.

I guess this story does not apply to the United States these days. In the struggle over the increased surplus provided by technological innovation, workers do not seem to be gaining much. At any rate, Table 3 summarizes the temporal sequence of the dominant technique in this story.

Table 3: A Temporal Series of Innovations
in Use
Processes (a) and (c) knownAlphaa, c
Processes (d) introducedBetaa, d
Process (b) introducedGammab, c

I do not see why one could not create an example with a single switch point between the Gamma and Delta techniques, where that switch point is at a wage below the maximum wage for the Alpha technique. For such a postulated example, one could tell story, like the above, with a given wage. The capitalists would end up with all the benefits from technological progress.

5.0 Conclusion

This example illustrates that innovation in one industry (that is, the production of iron) can result in the managers of firms in another industry (corn-production) discarding a previously introduced innovation and reverting to an old process of production.

  • T. Fujimoto 1983. Inventions and Technical Change: A Curiosum, Manchester School, V. 51: pp. 16-20.
  • 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 International.

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