Written jointly with Andrew Kliman, this is a prepublication version of the entry on the falling rate of profit in O’Hara, Phillip A (1999) The Encyclopaedia of Political Economy, pp318-320. London and New York: Routledge. ISBN 0-415-15426-X. The terms in capital letters are references to other Encyclopedaedia entries

Although Karl MARX regarded his explanation of the FALLING RATE OF PROFIT TENDENCY as the most important law of modern POLITICAL ECONOMY, only since the GREAT DEPRESSION has it assumed a significant role in Marxist discussions of capital ACCUMULATION and economic CRISIS.  Both before and since, moreover, most Marxist and non-Marxist writers have argued that a falling profit rate tendency fails to result from a coherent, rigorous application of Marx’s value theory.  They thus deny that accumulation and crises can be legitimately theorized in terms of Marx’s law.

In the wake of Okishio’s (1961) work, this view has won near-universal acceptance.  Yet more recent research has shown that, when Marx’s value theory is interpreted in temporal terms, not by means of simultaneous equations, it does corroborate his law of the tendential fall in the profit rate.

Under rather general conditions, Okishio’s and subsequent research seemingly shows that, given profit rate equalization, technical changes which raise the innovating firm’s profit rate (calculated using current prices) cannot lower the economy-wide profit rate.   If real wages also rise, a falling profit rate may accompany the technical change, but the fall is actually caused by the wage increase, not labor-saving innovation itself, as Marx claimed in Capital, Vol. III, Part 3.

These demonstrations depend, however, on the “unobtrusive postulate” that input prices are determined simultaneously with i.e., constrained to equal output prices.  Ernst (1982) showed that, if commodities’ values fall continually, labor-saving innovation can lead to a falling uniform profit rate under conditions in which the “Okishio theorem” says it must rise.  Other researchers have arrived independently at the same result, and have also shown how a temporal interpretation of Marx’s value categories results in the falling path of commodity prices (or values) needed for the falling profit rate (see Kliman 1996; Freeman 1996).

When values (or the labor-time equivalents of money prices) decline, a falling profit rate is more likely when fixed capital is valued at historical cost, rather than current cost.  Yet the temporalist results do not depend on a particular method of fixed capital valuation or from any special set of assumptions, but stem from a completely different value calculation.  Even if one abstracts from fixed capital, as Okishio’s original contribution did, the temporalist profit rate may fall while the simultaneist rate rises.   We offer the following example as a substantiation of this claim (not as a model of the actual accumulation process).

In period t, Ait tons of iron and Lit labor-hours produce Xit tons of iron; and Awt tons of iron and Lwt labor-hours produce Xwt bushels of wheat.  Pit, Pwt and Pit+1, Pwt+1 are period t’s input and output prices, respectively, measured in *labor-hours* per unit of output (VALUE, PRICE OF PRODUCTION, MARKET PRICE discusses the conversion between monetary and labor-time magnitudes).  Assume a uniform real wage rate of bt bushels of wheat per labor-hour and a uniform profit rate, rt.   Each sector’s aggregate output price equals its “cost-price” (expenditures) times “1 plus the profit rate”:

(1)                  Pit+1Xit = (PitAit + PwtbtLit)(1+rt)

(2)           Pwt+1Xwt = (PitAwt + PwtbtLwt)(1+rt)

According to the “temporal single-system” interpretation of Marx’s theory, aggregate surplus-value (or profit), as measured in labor-time, equals living labor extracted (Lit + Lwt) minus the sum of value advanced as wages (PwtbtLit + PwtbtLwt).  Hence, although this interpretation has sometimes been thought to allow profit to arise independently of SURPLUS VALUE AND EXPLOITATION, it implies precisely that profit is positive only if workers supply more labor than the labor-time equivalent of their money wages.  The aggregate profit rate, surplus-value divided by capital advanced (here equal to aggregate cost-price), is thus

Assume that both sectors use 10% more iron input and produce 10% more output, each period, but extract only 1.2% more labor.  Thus, the technical COMPOSITION OF CAPITAL and labor productivity both rise continually.  Holding the real wage rate constant at b = 11/32, each innovation would increase profit rates at current prices.  Further assume that Ai0 = 44, Li0 = 11, Xi0 = 55, Aw0 = 6, Lw0 = 24, and Xw0 = 30, and that period 0’s input and output prices are equal (Pi0 = Pi1 = 2.2; Pw0 = Pw1 = 0.8).

Given these assumptions, were (1) and (2) converted into simultaneous equations by replacing the input prices on the right-hand sides with output prices (which would render (3) both redundant and wrong), the profit rate would rise monotonically from 21.21% to 25%.  Yet equations (1) through (3) imply that prices in both sectors fall continually, and the profit rate, initially equal to 21.21%, falls monotonically to 15%.  Since this conclusion contradicts the Okishio theorem without violating any of its stated premises, it refutes the theorem.

Because this example is not a model of capital accumulation, its monotonically declining profit rate is not a prediction that the actual profit rate is incapable of rebounding.  If, in response to falling profitability, technical change slackens, the temporalist interpretation suggests that the profit rate will rise.  Crises also restore profitability by devaluing and destroying old capital no longer able to be employed profitably, as do collapsing prices that eliminate the over-valuation of capital which arises in “boom” times.  These additional results are consonant with Marx’s theory that crises are the mechanism by which the tendential fall in the profit rate is periodically overcome (see Capital, Vol. III, Ch. 15).

Not only do simultaneist and temporalist profit rates diverge systematically even when fixed capital is disregarded, but the divergence does not depend on particular assumptions concerning rates of growth or technical change, number of sectors, profit and wage rate differentials, etc.  Although temporalist results have been challenged on the ground that “unrealistic” examples are used to illustrate the divergence, such criticisms overlook the fact that systems such as (1)-(3) express a different theory of economic relations than do their simultaneous determination counterparts, and therefore yield different results under almost every set of assumptions.  If input and output prices are determined simultaneously, the profit rate is a function of use-values (technical and real wage coefficients) alone, not the extraction of surplus-labor in production.  In system (1)-(3), however, the level of the profit rate depends crucially on surplus-labor extraction.

We suggest that simultaneist conclusions correspond to a theory in which use-value, not labor-time, is the substance of value, and the profit rate measures the expansion of use-value, not the expansion of capital-value through the extraction of surplus-labor.  Because prior research has employed comparative static methods, which prevent value magnitudes from moving in opposition to use-value magnitudes, the elemental difference between the two theories has been obscured until recently, but historical-time examples reveal it clearly.

Consider a corn model, in which wages equal zero, all corn output is reinvested as seed-corn, and extraction of living labor is constant each year.  Since the value of last year’s output equals the constant capital invested plus the value added by living labor and, since all output is reinvested, this year’s constant capital likewise equals last year’s constant capital plus the value added.  It thus follows trivially from Marx’s theory that constant capital (equal here to total capital) increases continually and, since the value added by living labor (equal here to surplus-value) is constant, the profit rate, surplus-value divided by total capital, declines continually.

Yet if each year’s corn output is 25% greater than corn input, the simultaneist profit rate is a constant 25%.  This conception of profitability thus seems to resemble both the neoclassical capital-productivity theory of the interest rate and Ricardo’s explanation of profit rate movements in terms of physical productivity, which, in Marx’s (1957-58, p. 754) view, “flees from economics to seek refuge in organic chemistry.”

Selected References

Ernst, John R.  (1982)  “Simultaneous Valuation Extirpated:  A Contribution to the Critique of the Neo-Ricardian Concept of Value”, Review of Radical Political Economics, vol 14, no 2, pp. 85-94.

Freeman,  Alan.  (1996)  “Price, Value and Profit – a continuous, general treatment”, in Alan Freeman and Guglielmo Carchedi (Editors) Marx and Non-Equilibrium Economics Cheltenham, U.K.:  Edward Elgar.

Kliman, Andrew.  (1996)  “A Value-Theoretic Critique of the Okishio Theorem”, in Alan Freeman and Guglielmo Carchedi (Editors) Marx and Non-Equilibrium Economics Cheltenham, U.K.:  Edward Elgar.

Marx, Karl.  (1857-58)  Grundrisse:  Foundations of the Critique of Political Economy.  New York:  Vintage, 1973.

Okishio, Nobuo.  (1961)  “Technical Changes and the Rate of Profit’, Kobe University Economic Review, no 7, pp. 85-99.

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