For this reason the theorem, first proposed in 1961, excited great interest and controversy because, according to Okishio, it contradicts Marx's law of the tendency of the rate of profit to fall.
[citation needed] Marx had claimed that the new general rate of profit, after a new technique has spread throughout the branch where it has been introduced, would be lower than before.
This result was widely understood, including by Marx himself, as establishing that capitalism contained inherent limits to its own success.
Okishio's theorem was therefore received in the West as establishing that Marx's proof of this fundamental result was inconsistent.
More precisely, the theorem says that the general rate of profit in the economy as a whole will be higher if a new technique of production is introduced in which, at the prices prevailing at the time that the change is introduced, the unit cost of output in one industry is less than the pre-change unit cost.
See below for the relative magnitudes of the two departments which serve as weights for summing up constant and variable capitals.)
Now the following assumptions are made: Okishio, following some Marxist tradition, assumes a constant real wage rate equal to the value of labour power, that is the wage rate must allow to buy a basket of consumption goods necessary for workers to reproduce their labour power.
For a technique, for example, might be numerically specified by the following coefficients of production: From this an equilibrium growth path can be computed.
So, the technique of production of this firm is described by the following: Now this firm introduces technical progress by introducing a technique, in which less working hours are needed to produce one unit of output, the respective production coefficient is reduced, say, by half from
This accords with Marx's argument that firms introduce new techniques only if this raises the rate of profit.
The traditional reasoning is that only "living labour" can produce value, whereas constant capital, the expenses for investment goods, do not create value.
Because the new technique is labour-saving on the one hand, outlays for investment goods have been increased on the other, the rate of profit must finally be lower.
Let us assume, the new technique spreads through all of department I. Computing the new equilibrium rate of growth and the new price
Nobuo Okishio proved this generally, which can be interpreted as a refutation of Marx's law of the tendency of the rate of profit to fall.
Mechanisation, defined as increased inputs of machinery per unit of output combined with the same or reduced amount of labour-input, necessarily lowers the maximum rate of profit.
[2] Some Marxists simply dropped the law of the tendency of the rate of profit to fall, claiming that there are enough other reasons to criticise capitalism, that the tendency for crises can be established without the law, so that it is not an essential feature of Marx's economic theory.
Then, the prisoner's dilemma works like this: The first firm to introduce technical progress by increasing its outlay for constant capital achieves an extra profit.
But as soon as this new technique has spread through the branch and all firms have increased their outlays for constant capital also, workers adjust wages in proportion to the higher productivity of labour.
Such an ongoing process cannot be described by the comparative static method of the Sraffa models.
In the equations above a general, for all branches, equal rate of profit was computed given whereby a price had to be arbitrarily determined as numéraire.
To establish this steady growth also in terms of the material level, the following must hold: Thus, an additional magnitude K must be determined, which describes the relative size of the two branches I and II whereby I has a weight of 1 and department II has the weight of K. If it is assumed that total profits are used for investment in order to produce more in the next period of production on the given technical level, then the rate of profit r is equal to the rate of growth g. In the first numerical example with rate of profit
On the right hand side of the first equations of the two numerical examples, respectively, is the output of one unit of
There is a continuing process of increasing the technical composition of capital to the detriment of job creation resulting at least on the labour market in stagnation.
The law of the tendency of the rate of profit to fall nowadays usually is interpreted in terms of disequilibrium analysis, not the least in reaction to the Okishio critique.
Between 1999 and 2004, David Laibman, a Marxist economist, published at least nine pieces dealing with the Temporal single-system interpretation (TSSI) of Marx's value theory.
In his lead paper in a symposium carried in Research in Political Economy in 1999,[6] Laibman's key argument was that the falling rate of profit exhibited in Kliman (1996)[7] depended crucially on the paper's assumption that there is fixed capital which lasts forever.
These and other arguments were answered in Alan Freeman and Andrew Kliman's (2000) lead paper in a second symposium,[8] published the following year in the same journal.
[12] In other words, proponents of the Okishio theorem have always been talking about how the rate of profit would behave only in the case in which input and output prices happened to be equal.
Kliman and Freeman suggested that this statement of Laibman's was simply "an effort to absolve the physicalist tradition of error.
"[13] Okishio's theorem, they argued, has always been understood as a disproof of Marx's law of the tendential fall in the rate of profit, and Marx's law does not pertain to an imaginary special case in which input and output prices happen for some reason to be equal.