Karl Marx (1818-1883)
https://www.marxists.org/archive/marx/works/1867-c1/p1.htm
What was Marx’s transformation problem? In Volume I of Das Kapital, Marx starts his dissection of capitalism with the concept of value and builds on it his theory of surplus value. Marx declared that capitalism’s secret is the commodification of labor power. Labor power is the only commodity that creates surplus value, the value in excess of labor power’s exchange value–that is, the workers’ wage rate. In that same volume of his magnum opus, Marx explained the profits of capital as resulting from surplus value. He left open the problem of explaining how capitalists with differing ratios of labor to machinery can have similar profits, a contradiction to be resolved in further works. Marx, in Capital Vol III, takes up the matter again, but according to Eugen von Böhm-Bawerk’s essay, does not resolve the issue logically.
Marx’s transformation problem exists simply because of another problem he noted with capitalism–the so-called realization problem. Workers might create surplus value in the realm of production but unless goods are sold (in the realm of commerce), profits cannot be realized by the capitalists and surplus value remains just potential profit. In the realm of commerce where prices are important, the price level of commodities are important to the extent that they define the size of the profit rate that will be enjoyed by particular capitalists which will in turn serve as a signal to other capitalists if a particular industry is an attractive investment site. Capitalist competition brings profit rates down, However, Marxist political economy also points out that an increasing capital/labor ratio or what Marx called organic composition of capital (the ratio between living and dead labor) will lower profit rates since only living labor can create surplus value. Dead labor simply transfers its exchange value to the total price of the commodities. Dead labor (like capital goods and raw materials) cannot create surplus value.
If Marx had to transform value into prices, the marginals had to transform their ‘utils’–a measure of utility to explain why consumers demanded or liked to consume commodities–to exchange values or market prices. Second generation marginalists like Alfred Marshall worked on theories of marginal physical productivity as the explanation for product costs/prices while third generation marginalists like Francis Ysidro Edgeworth and Eugen Slutsky, while believing that utility represents some quantity, developed the concept of indifference curves which did away with the need to quantify utility.
Alfred Marshall (1842-1924)
In a work published in 1907, the Russian economist and statistician Ladislaus Bortkiewicz identified the transformation problem in Marx’s work. He proved that the data used by Marx was sufficient to calculate the general profit rate and relative prices. Though Marx’s transformation procedure was not correct—because it did not calculate prices and profit rate simultaneously, but sequentially—Bortkiewicz has shown that it is possible to get the correct results using the Marxian framework, i.e. by using the marxian variables constant capital and variable capital, it is possible to obtain the profit rate and the relative prices in a three-sector model. His “correction of the Marxian system” has been the great contribution of Bortkiewicz to classical and Marxian economics but it was completely unnoticed until Paul Sweezy’s 1942 book “Theory of Capitalist Development”. Piero Sraffa’s Production of Commodities by Means of Commodities (1960) has provided the complete generalization of the simultaneous method for classical and Marxian analysis.
Ladislaus Bortciewicz (1868-1931)
What was the transformation problem of the first generation theoreticians of the Marginal school of economics? The marginalists (marginal analysts) sought to resolve a conundrum that flummoxed Adam Smith: the so-called diamond-water paradox. How come diamonds, which humans do not need to live, are most costly than water, without which humans will die? Menger figured this out at about the same time as Jevons and Walras. He said that the first pail of water satisfied the strongest want (thirst), while succeeding pails satisfied lesser wants, such as cleaning. In a small village next to a large river, all of the people’s uses of water would be filled, making the value of one additional pail of water zero. This is the essence of marginal analysis: look at the value or cost of the last additional unit, the unit “at the margin”.
Francis Ysidro Edgeworth (1845-1926)
This theoretical innovation moved economic theory away from Adam Smith’s supply-side “cost-of-production” theory of commodity prices. The marginalists argued that commodities are valuable more because of their ability to satisfy consumers’ demand (to make them happy, in other words) rather than the costs incurred in producing them. And why and how do commodities satisfy consumers or make them happy? They satisfy because they are useful. For this reason, first generation marginals valorized utility to explain commodity prices–marginal utility however rather than total utility.
Eugen (Evgeny) Slutsky (1880-1948)
Utility, while difficult to measure, was conceived by the first marginalists as a quantity. Happiness or usefulness, of course, cannot be quantified. But there are methods and assumptions in microeconomics for calculating a reasonable approximation of this elusive concept. In microeconomics, happiness is measured by a concept called utility. The standard unit of measurement that microeconomics uses to measure utility is called the util. The util has no concrete numerical value like an inch or a centimeter. Instead, it’s an arbitrary and subjective – yet convenient – way to assign value to consumer choices and to measure the consumer utility of one choice against another. A number of the first generation marginals were quite bothered by the inability to measure utility. Subsequent marginal analysts innovated theoretically to move from using (marginal) utility to explain commodity price determination. This was the marginal school’s transformation problem.
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