## Thursday, November 17, 2016

### Labor theory of value: a primer

This is a different post from my normal posts. It is a primer and I must ask indulgence from many readers for whom this is all too well-known and obvious.  Why do I write it then? Because recently I was several times surprised by the casualness with which people talk of “labor theory of value” apparently implying thereby that it is some weird concoction where the price of a good should simply be proportional to the number of hours one has put in producing it. I have heard it from non-economists and it has not truly surprised me; but I have heard it from economists too and thought it was odd. So I decided to write this 1200-word primer.

According to Marx, in a non-capitalist market economy products are exchanged at the rate that corresponds to the “socially necessary labor” embodied in them, or differently put, labor necessity for their production. Start with a simplified situation where there is not capital.  Then, if, on average, product A requites 8 hours of labor and product B,  4 hours, the exchange rate will be 2B for 1A. Note that as products are exchanged at average (“socially necessary”) labor inputs, an inefficient producer that spends 10 hours of work to produce A will not be paid for 10 hours, but for 8. The reverse holds for a very efficient producer. So, producers are not just paid for their labor input regardless of how efficiently they work or organize production.

The introduction of capital, owned by the producers, brings us to Marx’s “petty commodity production”. Its key characteristic is that independent producers compete with each other but that each uses only his own labor (that is, there is no hired labor) and owns the means of production. It is very similar to the early American colonists. Capital, according to Marx (and also to Quesnay, Smith and Ricardo) simply contributes to the value through its depreciation, while only labor creates new value added. The equilibrium price is equal to w+d+s where w=wage, d=depreciation, and s=surplus value or profit. This is where labor theory of value and neoclassical theory of value part ways since according to the latter s is the marginal product of capital while for Marx it is simply part of labor contribution that is in excess of wage. It is the famous “surplus value”  produced by labor. It arises, Marx argued, from the unique feature possessed by labor, namely that its contribution to value is greater than the value embodied in goods that are necessary to compensate laborers fully for the expense of energy used in production of the goods. (Put very simply: you work 10 hours to produce goods worth \$10, but you need bread, wine, meat and olive oil worth only \$5 to be brought back to the same state of satisfaction that you were in before you started to work.) Of course, here in petty commodity production, where each producer owns his means of production, the distinction is immaterial because s belongs to him anyway. There is thus no exploitation which will appear only when hired labor is used, is paid w, and s remains in the hands of the capitalists.

Which indeed brings us to capitalism. Marx has noticed that the price structure of “petty commodity production” cannot be maintained in capitalism since different branches of production would earn different rates of return on their capital, and the feature of capitalism (as every neoclassical economist knows) is a tendency for profit rates to converge across lines of production so that the production of every type of good is, in equilibrium, equally profitable (obviously adjusted for risk).  However, with the pricing structure given in the previous paragraph, labor-intensive branches would produce lots of surplus value (since there are lots of people working there) and as the surplus value becomes capitalists’ profit, the ratio between s and total capital will be high. The opposite will hold in capital-intensive branches of production.

So, the equilibrium prices in capitalism must be different. These are, according to Marx, the “prices of production” that have the following structure: w+d+rK where r=economy-wide average rate of profit. Thus in equilibrium every branch of production earns the same rate of return on capital (K) employed there and of course each unit of labor is paid the same. Prices of production are exactly the same as the long-run Marshallian or Walrasian equilibrium price.

The conversion from the value-based prices under “petty commodity production” to the prices of production under capitalism has led to the famous “transformation problem” that has kept generations of Marxist economists busy. This was the problem quickly noted by Marx’s critics at the publication of the third volume of “Das Kapital”, starting with Achille Loria (whom few would have remembered today had he not been given the pride of place and opprobrium by  Engels in his Introduction to the Third volume) to Bohm Bawerk. Marx was criticized for inconsistency and for inability to show that prices are determined by value (=labor) under capitalism. The literature on the transformation problem is immense, but interested reader may consult the definition of the original problem by Bortkiewicz, and then classical solutions by Sraffa, Morishima etc.

Now, if Marx, Walras and Marshall agree on the equilibrium price in capitalism, where is the labor theory of value? For Marx, it emerges only at the aggregate level where Marx posits that the sum of values will be equal to the sum of production prices. The former is an unobservable quantity so Marx’s contention is not falsifiable. It is therefore an extra-scientific statement that we have to take on faith.

But there are, I think, three  important points to take away from this brief review of Marxian labor theory of value.

First, that Marx’s capitalist equilibrium prices are the same as Walrasian or Marshall’s long-run prices.

Second, that we are clearly very, very far from derisive statements that labor theory of value means that people are just paid for their labor input regardless of what is the “socially necessary labor” required to produce a good.

Third, and in my opinion the true contribution of Marx in this area, is to have insisted that the equilibrium price cannot be independent of the relations of production, that is, of who owns capital and in some cases (slavery) labor too. Two identical economies, but one composed of small-scale producers who own the means of production, and another capitalist, will have different relative prices. This, I think, is an important point for our understanding of pre-modern societies.

It is also important when we study the interaction of capitalist and pre-capitalist modes of production (as for example, during colonization) because the difference in equilibrium prices under different ownership structures means that even if the endowments of two societies (capitalist and pre-capitalist) are the same, relative prices will be different. Thus when India and England begin to trade (even had their endowments been the same), some Indian goods would have been cheaper, and others more expensive, than English. This, in turn, means that when we deal with societies whose ownership structures are different, opportunities for trade do not depend solely on the differences in endowments but also on the differences in the mode of production. This last point is nowadays often forgotten.