What is the Okishio theorem?

It is a theorem by the Japanese Marxian economist Okishio:

If you have

An economy with equalized rates of profit Constant real wages The opportunity for balanced growth

Then any cost-saving technical change for a capitalist will raise the rate of profit in the economy as a whole.

(See Wikipedia for an adequate popularization.)

It was seen as contradicting a generally accepted presentation of Marx’s theory of a falling profit rate:

As an individual capitalist invests in more capital-intensive techniques, this would give him more profit. But once generalised, the process would raise the capital-to-labour ratio and lower the average rate of profit in the economy

What about the empirical data?

The graph shows the actual rate of profit in Japan over 40 years after his paper. Average rate rate clearly falls.

It falls a great deal.

What gives?

What assumptions did he make?

An economy with equalized rates of profit between industries Constant real wages The opportunity for balanced growth

It is important to note that Okishio was constructing a theory about rational choices of techniques by individual firms subject to the above assumptions. If it turns out that the assumptions are wrong, or that the rate of profit is not fundamentally and issue of rational choice of technique the theory falls. You need a paradigm shift away from the paradigm of rational choice which dominated economics when he was originally writing.

1. Equalized rates of profit? No!

Actual rates of profit are not equalized. Capital-intensive industries systematically experience lower rates of profit. See diagram below reproduced from (https://www.researchgate.net/publication/5208399_A_note_on_the_organic_composition_of_capital_and_profit_rates):

So one key assumption of the Okishio theorem is false.

Okishio himself admits this :

“the theorem is a form of comparative statics, a comparison between an old equilibrium and a new equilibrium. This does not have much meaning if the new equilibrium is not established.”



“Whether it is or not depends on whether competition among capitalists leads to the situation where profit rates are equalised in every sector. Many people have tried unsuccessfully to prove the convergence on production prices thus implied” (Okishio, N. “Competition and production prices.” Cambridge Journal of Economics 25.4 (2001): 493-501)

Investment implications

Lacking equalized profit rates, capitalists cannot use the average profit rate to make investment decisions.



The interest rate is the only general rate available for calculation.

In addition, capitalists only know what their own firm makes, and perhaps the profit rate foreseen in another line of production they are invited to invest in.

The current Bank of Japan base interest rate is –0.1%

Thus any business that offers even a slight positive profit rate would be preferable to leaving money in the bank.

Suppose a capitalist’s current capital stock earns 4% per annum. Investing in a new line of production at 1% per annum would still be a rational choice over saving the money in the bank. In contrast to Okishio’s assumptions, investment could then also flow into sectors with lower-than-average profit rates!

2. Constant real wage? No!

In actual fact real wages rose in Japan from 1961 to 2001.

In his 2001 paper, Okishio says that if you have competition between capitalists to employ labour, the rate of profit will decline to zero. He illustrates this with the following diagram:

So Okishio accepts that a second key assumption is false.

3. Balanced growth? No!

What is balanced growth?

This goes back to the von Neumann theory of growth (Von Neumann, J. “A model of general economic equilibrium.” Readings in the Theory of Growth. Palgrave Macmillan, London, 1971. 1-9.). The key points are:

Equal expansion rate across all industries

Equal growth rates of capital stock and of employment.

But this is not met in practice in Japan since Japan has almost no immigration, and a declining birth rate.

In consequence balanced growth is impossible, due to the limit to labour supply and an aging population.

Japanese population is shrinking by about half a million a year now.

Okishio and population growth

Okishio showed that if the rate of growth of the population is 1%, then the rate of profit will converge to 1%. He illustrates this process with another diagram:

see how in this case the equilibrium profit rate levels off at the growth rate of propulation.

Zachariah and Cockshott arrive at a similar result but this time using a model based on actual statistics not a mere simulation like Okishios. Below we reproduce the trajectory of the rate of profit that comes from our model (the solid line ) with the actual trajectory of of profit rates for Japan. As you can see the actual trajectory almost exactly follows the equilibrium rate from our equation. ( for detailed working and more diagrams see Classical Econophysics by Cockshott, Cottrell et al).

Using a stochastic labour theory of value, we derived a more general formula for the trajectory of the average rate of profit:

r* = (g+p+d)/a



where

g = growth of workforce

p = growth of labour productivity

d= depreciation rate,

a = share of surplus being reinvested

Lessons for Scientific Socialists

Always look at the assumptions of a theory. Check against empirical reality. See what corrections the author herself introduces for different assumptions. The falling average rate of profit is not an issue of choice of technique It is an issue of accumulation at the level of society as a whole Is the capital stock rising faster than the population? If so, the profit rate will fall If the reverse, profit rate will tend to rise You can not separate historical materialism from human reproduction and demography