Okishio's theorem

The Okishio theorem (Japanese Okishio no teiri置塩 の 定理) states: If a company increases its rate of profit by introducing a new technique, which requires less labor input, but more use of material that then also the overall economy results in a higher rate of profit, if the new technology has been disseminated throughout the industry, have not increased under the condition that the real wages of the workers, so the purchasing power of wages measured in certain goods.

This theorem is contrary to the law of the tendential fall in the profit rate of Karl Marx, which assumes that after diffusion of the new technology on the entire industry to the overall economy follows a lower rate of profit. The capitalists were sitting as it were in a case of rationality.

The model of Sraffa

The reasoning by Nobuo Okishio, a Japanese economist, is based on a Sraffa model. The economy is composed of two Divisions I and II exist, where I is the capital goods ( means of production ) and II consumer goods for the workers - from the consumption of the capitalists is apart ("classical " consumption function ) - manufactures. The production coefficients indicate how much of the various inputs needed to produce a unit of a given output. In the local simple case there are only two outputs, the amount of capital goods, and the amount of consumer goods.

The production coefficients:

  • : To produce a capital good number of capital goods.
  • Number of working hours to produce a capital good.
  • Number of capital goods to produce a consumer good.
  • Number of working hours to produce a consumer product.

The workers get a certain wage for wage rate l per unit of labor, which is expressed in terms of consumer goods.

  • : Number of consumer goods which is necessary to produce a capital good.
  • : Number of the consumer, which is necessary to produce a consumer product.

Schematically, the economy will be represented as follows:

This can be represented in the following equations:

  • : Price of the capital good
  • : Price for the consumer
  • : General rate of profit. The described by Marx tends to balance the profit rates between industries (in this division) forms in the economy, a uniform rate of profit r out.

In the Division I this, expenditure on constant capital, spending on capital goods:

  • And for the variable capital:
  • .

In the Division II this, expenditure on constant capital:

  • And for the variable capital:
  • .

( You can not just add the constant and variable capitals of the two departments to a total economic size because you would have to know the size ratio between the two departments. To calculate this size ratio, see the memorandum calculations below.)

It now following assumptions are made:

  • The consumer should serve as numeraire, the price of the consumption good is therefore equal to 1
  • The real wage is.
  • The equation system is normalized by the outputs and each be set to 1.

In Marxism is usually assumed that the wage is equal to the value of labor power, so just so great that the workers can get their work force. Here is thus assumed that the workers per hour of work will need two consumer to obtain their labor.

One technique is in Sraffa defined by the size of the production coefficients. For example, a technique is given by:

  • : To produce a capital good number of capital goods.
  • Number of working hours to produce a capital good.
  • Number of capital goods to produce a consumer good.
  • Number of working hours to produce a consumer product.

Then we obtain the following equilibrium equation system, the missing values ​​for the price and for the rate of profit are already calculated and used:

Introduction of technical progress

You can now pick out of Division I, a company which has the same production technology as the department as a whole. Therefore applies to these things:

This company now introduces technical progress by reducing halved from about the necessary input of labor. This alone increased the technical composition of capital, because now needed to create a unit of capital goods is only half as much work, but just as much capital goods as before. In addition, however, it is assumed that the labor savings associated with a greater consumption of capital goods that will rise to.

For this a company that has introduced technological progress, resulting in the present prices and at the given wage rate - these quantities remain unchanged for yes, as long as a company changes its technique - the following equation:

The company could thus increase their rate of profit on. This corresponds to the extent that the very Marxist thinking, which holds that a company introduces a new technique only, if they increase their rate of profit.

Karl Marx, Volume III of Capital, MEW 25, p 275: " No capitalist ever voluntarily introduces a new mode of production, it may be even much more productive or even much increase the rate of surplus value, voluntarily as soon as it reduces the rate of profit. "

Marx, however, expected that when the new technology spreads throughout the department, the rate of profit not only for the " pioneer entrepreneur" drops again, but now that there is a lower rate of profit for the whole economy. The reason given is traditionally that only can create " living labor " added value - living labor but was saved - and that the constant capital, create spending on capital goods, no value, but only give their value to the final products.

Assuming that the new production technique generally used in Division I and calculates the new steady-state growth ( and the new price ), then we obtain:

After generalization of the new production technique in the example Division I and after reaching a new equilibrium growth, although the rate of profit of the pioneering entrepreneur has become lower again, but overall is the new general rate of profit with higher than the original from.


Nobuo Okishio has this evidence out in a generic manner refutes the law of the tendential fall in the profit rate. However, there is in the above model only circulating capital, ie means of production which enter into the final products of the same in the same production period. Other studies have shown the results Okishios for the case of an economy with fixed capital, the means of production work for more than one production period extended. Labor -saving technical progress can therefore be rising and does not have to lead to lower overall rates of profit.

Marxist replies

1) A reaction of Marxists was that the criticism was adopted. The law of the tendential fall of the rate of profit does not amount to the central part of Marx's theory dar. There were plenty of other reasons against capitalism, so you should not rely on such a breakdown tendency.

A variant of this is that the law is accepted as an explanation for the recurring cyclical changes ( crises ), but not as a long -term trend.

Michael Heinrich challenges both a breakdown crisis and towards an understanding of the crisis as cyclical compensatory movement and concludes: " However, by the conditions of production of profit repeatedly collide with the elementary vital interests of the majority of the population will also again and again the Ask question about the legitimacy of this social system and the possibility of a social alternative " or". Whether it increases or decreases the capitalist accounting moderate expression of capitalist exploitation, does not change the principle, narrow-minded character of the capitalist mode of production. "

2) A second response was, was sought within the Sraffa model for ways to invalidate the Okishio argument by the example - but Marx unknown - law of constant wage share was introduced - whether that unions operate productivity-oriented wage policy it that companies pass on part of the increased productivity in the form of lower prices in the competitive struggle, and thus enhancing the purchasing power of wages, real wages had. With a constant wage rate, the rationality case provides for the companies this way: The individual company that introduces technical progress, first makes an extra profit. However, in generalization of technical progress, the real wages adjust so that the original, higher wage rate is restored. However, the company stay on the increased cost of the increased use of capital goods sit. The rate of profit has fallen.

Against this argument is an objection to the assumption of a constant labor share is problematic. The rate of profit it could always be stabilized when the wage rate would be adjusted downward. Thus, in the numerical example, the increase in the profit rate is associated with a fall in the wage share of 58.6 % to 41.9 %, see the detailed statement below.

3) The third type reaction is to reject the Sraffa model as a framework, especially the comparative static method. In capitalism, it does not wait until a new equilibrium is reached, but the introduction of new technical methods is an ongoing process. The law of the tendential fall in the profit rate is used if an increasing proportion of the production is invested per job and not in additional jobs. Such ongoing development can not be detected by the comparative statics of Sraffa models.

When Alfred Müller and Stephan Krueger is a prerequisite for the falling rate of profit (as well as the cyclical fluctuations ) that production is carried out industrially using machinery. The capitalist enterprises seek their profits independently own responsibility to increase, there is no central planning authority of the national economy. Okishio abstracted, however, in his model of fixed capital, there is only circulating capital. This admissibility of this abstraction is controversial.

After Alfred Müller Okishio the theorem does not take into account the special features of capitalist society. "If there was a macroeconomic coordination body and would be the capitalist private ownership of the means of production waived would balanced in control of the control means and for solving the problem of information supply and demand, and the economy was moving on a steady equilibrium path. The difficulties arise when the capital ratio comes in and the production process is only a means for the recovery process of capital. " This is done by the individual capitalist without macroeconomic coordination.

Similarly, in Stephan Kruger, here make the company " autonomous ", ie the instantaneous profit or cost position independent investment depending on the location. During the crisis, rationalization investments are made, the increase in both labor productivity and to get the technical composition of capital so out of the crisis. The momentary advantage for the individual company is long-term of the fall of the general rate of profit over because of so rising composition of capital.

For information: the material side

The dual system of equations

For the above considerations, it was sufficient to consider only the monetary terms. Should further investigations be carried out to about the size of constant capital c, variable capital v and value ( or profit ) m for the economy as a whole to calculate or ratios between these variables as the rate of surplus value s / v or the value composition of capital c / v to calculate, then the size ratio between the departments I ( capital goods ) and II (consumer goods ) must be determined. This is done by representing the steady growth of the material side.

In the previous equations was calculated as under certain technical conditions, which were represented by the production coefficients, and under a certain given real wage, which was represented as the amount of consumer goods per hour worked, a uniform rate of profit r is emerging, while still a price was set. Here the price of the consumption good equal to 1 was set ( numeraire ) and the price of the capital goods calculated. Thus the conditions for a steady growth were determined in monetary terms expressed.

The general formula

This steady growth is materially possible, the following must apply:

So there must be now an additional quantity K can be calculated that reflects the size ratio between Divisions I and II, where the Division I weight 1 and the Division II is then assigned the weight K.

If it is assumed in such growth models that total profits are used in the next period to to produce the same technical basis in accordance with the rate of profit r more, then it follows that the growth rate of material considered ( g) is equal to the rate of profit r.

The concrete numerical examples

For the first numerical example with the rate of profit results in:

The weight of Division II. For the second numerical example with the rate of profit results in:

The weight of Division II is now. The respective growth rates g are equal to the profit rate r.

On the left side of the equations are in the respective first inputs to the equation and the second equation is to the left in each case, the amount of which is required as an input. On the right side of the equations is in the front as output an estate of and in the second equation of K goods.

An assessment of the input of the price, then we obtain the constant capital c. An assessment of the input with the set price, then we obtain the variable capital v. Reviewed you. The output of a Guts and K goods from the current prices and, you get the entire revenue of the economy c v m

If we subtract this turnover the amount for the constant and variable capital (c v) from, is obtained as the residual profit m.

It can then be the value composition of capital c / v, the rate of surplus value s / v and the " wage rate " v / calculate (m v).

For the wage rate is calculated in the first case and the second case. This corresponds to rates of surplus value of 0.706 or 1.389. For the value composition of capital c / v is obtained in the first case and 6.34 in the second case 12,49. According to the formula

Rate of profit calculate again the two rates of profit and.

Comparative static method

In this example, note that the comparative static method is based, that is, there are different economies, which are located on a balanced growth path compared. Assuming an equilibrium consideration to imbalance models over, can set up quite different results. If the capitalists increase the technical composition of capital, because this gives them increased the rate of profit, it may also under the pressure of competition is a continuous process, which means that the economy no longer has the time to ease in to a new balanced growth path but continued labor-saving rationalization investments lead to stagnation tendency. The law of the tendential fall in the profit rate is nowadays understood under the impression the Okoshio - criticism, as an imbalance model.


  • In the abstract, can at the fall of the price of the individual commodity as a result of increased productive power, and therefore a simultaneous increase in the number of these well feilern goods, the rate of profit remain the same, ... climbing could be the rate of profit even if the increase in the rate of surplus value, a significant reduction in value of would involve elements of constant and especially of fixed capital. But in reality, the rate of profit, as already seen, fall in the long run. Karl Marx, MEW 25, The Capital III, pp. 239f. The last sentence, however, as we now know, a supplement of Friedrich Engels.
  • No capitalist ever voluntarily introduces a new mode of production, it may be even much more productive or to reproduce as much nor the rate of surplus value, voluntarily as soon as it reduces the rate of profit. But any such new mode of production cheapens the goods. He therefore sold originally on their price of production, perhaps above their value. He pockets the difference that exists between its cost of production and the market price of the other, produced to higher production costs of goods. He can do this because the average of the socially erheischten for the production of these goods is greater than the work with the new mode of production, labor-time required. Its production procedure is above the average of the society. But the competition generalizing and subjects them to the general law. Then the fall of the profit rate occurs - perhaps first in this sphere of production, and resembles afterwards with the Andren from - so that is entirely independent of the will of the capitalists. Karl Marx, Capital, Volume III, MEW 25, p 275