Reproduction schemes
재생산 표식
The numerical models Marx built in Part III of Volume II of Capital to show how society's annual product is exchanged so as to recreate the conditions of the next year's production. He divides the economy into Department I, producing means of production, and Department II, producing means of consumption, and splits each department's product into constant capital (c), variable capital (v) and surplus-value (s). In simple reproduction, where all surplus-value is consumed, I(v + s) must equal IIc; in expanded reproduction, where part of it is accumulated, I(v + s) must exceed IIc. The schemes became the arena for the debate among Lenin, Tugan-Baranovsky, Luxemburg, Bukharin and Grossman over whether market demand limits capitalist growth, and they fed into Leontief's input–output analysis.
In depth
How does society's product become the condition of production again?
Volume I of Capital follows a single capitalist who buys labour-power and extracts surplus-value. But for a society to go on producing year after year, what it makes in a year has to flow to the right places. Factories must replace the materials they used and the machines that wore out, and workers and capitalists must buy food and clothing. For an individual capitalist it is enough to turn his commodities into money; for society as a whole, the quantities of means of production and means of consumption produced must match the quantities needed.
Marx stressed that this movement "is not only a replacement of value, but a replacement in material": the sums must balance, but machines must also reach the places that need machines and bread the places that need bread. He took his cue from the Tableau économique of the eighteenth-century French physiocrat François Quesnay.
What are the two departments?
Marx divides the total production of society in two: "I. Means of Production, commodities having a form in which they must, or at least may, pass into productive consumption. II. Articles of Consumption, commodities having a form in which they pass into the individual consumption of the capitalist and the working-class." Machines and steel belong to Department I, bread and clothing to Department II. The value of each department's product splits again into constant capital c, variable capital v and surplus-value s.
How do the figures balance in simple reproduction?
Marx's example runs as follows (the figures are illustrative, with a rate of surplus-value of 100 percent). Department I produces 4,000c + 1,000v + 1,000s = 6,000 of means of production, Department II 2,000c + 500v + 500s = 3,000 of articles of consumption, a total value of 9,000. When the capitalists consume all the surplus-value and production stays at the same scale, Marx speaks of simple reproduction.
Follow the exchanges. Department I's 4,000c exists as means of production and is traded within Department I to replace its machines and materials. Department II's 500v + 500s exists as consumer goods and is consumed directly by its own workers and capitalists. Two blocks remain. The workers and capitalists of Department I need 1,000v + 1,000s worth of food and clothing but hold means of production; Department II must replace 2,000c of worn-out machines and used materials but holds consumer goods. If they swap, everything falls into place, but only if the two blocks are equal. In Marx's formula, I(v + s) = IIc.
What changes in expanded reproduction?
Under capitalism the capitalists do not spend all their surplus-value but invest part of it in new machines and new workers. The means of production that Department I turns out in a year must then more than replace what both departments have used up, so I(v + s) must exceed IIc. Marx's initial scheme for expanded reproduction is Department I 4,000c + 1,000v + 1,000s and Department II 1,500c + 750v + 750s, in which I(v + s) = 2,000 exceeds IIc = 1,500 by 500. Marx assumes that Department I accumulates half its surplus-value, 500. The part to be exchanged with Department II is then 1,000v + 500s = 1,500, matching IIc, and the remaining 500 becomes additional constant and variable capital in Department I. The next year both departments begin on a larger scale.
What debates did the schemes provoke?
The schemes led straight to a political question: can capitalism grow at all, given the limits of market demand? In the 1890s the Russian Narodnik economists Vasily Vorontsov and Nikolai Danielson argued in underconsumptionist terms that the poverty of the peasants left the home market too narrow for capitalism to develop in Russia. Lenin answered with the schemes, in "On the So-Called Market Question" (1893) and The Development of Capitalism in Russia (1899): capitalism creates its own market through demand for means of production rather than consumer goods, and "in capitalist society, the production of means of production increases faster than the production of means of consumption."
The Legal Marxist Mikhail Tugan-Baranovsky went further with the same schemes, arguing that so long as proportions are kept, accumulation can continue indefinitely independent of consumption, and that crises arise from disproportions between branches. Rosa Luxemburg drew the opposite conclusion in The Accumulation of Capital (1913): in a closed system of capitalists and workers there is no identifiable source of demand for the accumulated surplus-value, so capitalism expands by devouring non-capitalist "outside" markets, and that is imperialism. Otto Bauer, Nikolai Bukharin and Lenin criticised her; Bukharin replied that additional constant capital is demand for means of production and additional variable capital demand for consumer goods, so demand comes from the investment process itself.
In 1929 Henryk Grossman faulted Luxemburg for mistaking an abstraction, meant only to show that value and material conditions can be reconciled, for a picture of real history, and, extending a scheme of Bauer's, argued that a rising organic composition of capital eventually brings accumulation to a halt. Ernest Mandel and Roman Rosdolsky held instead that the schemes state not the conditions of balanced growth but the minimum requirements for reproduction; Mandel added the notion of "contracted reproduction", production on a shrinking scale. The schemes' links between sectors were developed further in Wassily Leontief's input–output analysis, with one difference: by treating gross profit as an input, Leontief makes input and output values always equal, while in Marx's model output value is normally higher than input value.