# Mises Daily Articles

## Sraffa's Production of Fallacies by Means of Fallacies

If you read up on the history of economic thought in the twentieth century, you are likely to encounter the work of Piero Sraffa, in particular his curious volume, *Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory* (Cambridge: Cambridge University Press, 1960). Although this book was instrumental in the so-called

In the present article I will try to summarize Sraffa's main themes and then offer criticism from an Austrian perspective. A critique of Sraffa has value in its own right but there is a serious ideological element at stake here. His work has long been cited by labor leaders and socialists of all stripes to show that labor unions can artificially increase real wages and the central bank can lower the interest rate and this would have no real effects on production; it would only redistribute ownership of the net output in each period. It turns out that Sraffa can only achieve such results by eliminating individuals and their subjective preferences from his model.

**MACRO VS. MARGINAL APPROACH**

As Sraffa's subtitle suggests, he intends his work to form the basis of an alternative to orthodox economic theory, as it has developed since the marginal revolution of the 1870s. As Sraffa explains in his Preface:

It is…a peculiar feature of the set of propositions now published that, although they do not enter into any discussion of the marginal theory of value and distribution, they have nevertheless been designed to serve as the basis for a critique of that theory. If the foundation holds, the critique may be attempted later, either by the writer or by someone younger and better equipped for the task. (vi)

As we shall see, Sraffa's book gives us an alternative way to derive the equilibrium prices, wages, and interest rates of hypothetical economies. Rather than, say, setting the equilibrium price of a machine equal to its marginal product, Sraffa instead will step back and view the entire economy as an interrelated system of various production processes. In Sraffa's view, the marginal approach is deficient because it encourages a myopic concentration on the particular good in question, when a better approach (in Sraffa's opinion) would recognize the truism that commodities are used, not only to satisfy consumer ends, but also to produce other commodities. To appreciate Sraffa's method, it's best to jump into some concrete examples.

**PRODUCTION FOR SUBSISTENCE**

In the simplest case, Sraffa imagines "an extremely simple society which produces just enough to sustain itself. Commodities are produced by separate industries and are exchanged for one another at a market held after the harvest" (3). Sraffa continues:

Suppose at first that only two commodities are produced, wheat and iron. Both are used, in part as sustenance for those who work, and for the rest as means of production—wheat as seed, and iron in the form of tools. Suppose that, all in all, and including the necessaries for the workers, 280 quarters of wheat and 12 tons of iron are used to produce 400 quarters of wheat; while 120 quarters of wheat and 8 tons of iron are used to produce 20 tons of iron. A year's operations can be tabulated as follows:

280 qr. wheat + 12 t. iron ---> 400 qr. wheat

120 qr. wheat + 8 t. iron ---> 20 t. iron

Notice that Sraffa has chosen his numbers so that every period, society produces just enough wheat and iron to replenish the quantities used up in production. Specifically, 280+120=400 quarters of wheat are used up in the production of wheat and iron, and 400 quarters of wheat is exactly what is produced in the first industry. Similarly, 12+8=20 tons of iron are used in the production of wheat and iron, and again, that is exactly the quantity produced in the second industry. Therefore, this society can continue indefinitely with this technology and endowments of resources, because every period it reproduces exactly what it uses up in production.

In such a world, Sraffa notes, "There is a unique set of exchange-values which if adopted by the market restores the original distribution of the products and makes it possible for the process to be repeated; such values spring directly from the methods of production" (3). It is here that Sraffa departs from marginal value theory. Even though we have focused purely on aggregate figures, rather than marginal utility or product, Sraffa can conclude, "In the particular example [of wheat and iron] we have taken, the exchange-value required is 10 qr. of wheat for 1 t. of iron" (3).

Before continuing, let us be clear on Sraffa's reasoning. So far, the technological facts have shown us that it is feasible from an engineering standpoint that this society continues to churn out 400 quarters of wheat and 20 tons of iron per period, indefinitely. But in order for this to be *economically* possible in a market setting, it is necessary that the individual(s) in charge of, say, wheat production can earn enough selling 400 quarters of wheat to buy (a) 280 quarters of wheat and (b) 12 tons of iron, since this is what the producer will need in order buy the appropriate inputs for next period's output. Of course, the wheat producer doesn't need to sell his entire gross output and then purchase 280 quarters as inputs for himself; he can simply divert the 280 quarters from his gross output and use it to replenish his reserves, and then sell the remaining 120 quarters of wheat on the market. Thus, in order for the wheat producer to stay in business, it must be the case that 120 quarters of wheat has an exchange value of at least 12 tons of iron.

But if we look at matters from the iron producer's point of view, we realize that in order for *him* to stay in business, his net product of 12 tons of iron must have an exchange value of at least 120 quarters of wheat (since that's how much wheat the iron producer needs to buy as inputs for next period). Putting the two conditions together, we conclude that the only way both producers can stay in business is if 120 quarters of wheat has an exchange value *exactly equal* to 12 tons of iron (which reflects the price of 10 qr. of wheat for 1 t. of iron in the Sraffa quotation above).

To reiterate, the point of this thought experiment is that (apparently) marginal considerations are not needed in order to compute market clearing prices, at least in a subsistence economy. The situation becomes more complicated in the case of a surplus.

**PRODUCTION WITH A SURPLUS**

In his second chapter, Sraffa deals with the more general case, where the amount of each commodity produced exceeds the total quantities used up in the various lines of production. For example, suppose we altered the technological facts from above and had the following relations:

280 qr. wheat + 12 t. iron ---> 575 qr. wheat

120 qr. wheat + 8 t. iron ---> 20 t. iron

In this scenario, we can't use the earlier technique to determine the equilibrium prices. In order for the entrepreneurs in each line to continue, they still must make enough from selling their output in order to replenish their supplies. But because of the surplus—i.e. because 575 quarters of wheat are being produced, while only 400 quarters of wheat are needed by the two industries—the two conditions are not enough to "pin down" the market prices of wheat and iron.

If we let P_{w} be the price of wheat, and P_{i} be the price of iron, all we can now say is that 280P_{w} + 12P_{i} <= 575P_{w}, and 120P_{w} + 8P_{i} <= 20P_{i}. Unlike the previous case of subsistence, these two inequalities do not allow us to solve for unique values of P_{w} and P_{i}.

Sraffa comes to the rescue by introducing the "rate of profits," which he denotes by *r*. (This of course is what the Austrian would call the real net rate of interest.) Because of competition among capitalists, when there is a physical surplus in any one industry, there must be a uniform appreciation on invested capital in *all* industries. Therefore, in order to solve for the equilibrium prices of wheat and iron in the above scenario, we must introduce another variable, the rate of profits, so that the following equations hold:

(280P_{w} + 12P_{i}) x (1+*r*) = 575P_{w}

(120P_{w} + 8P_{i}) x (1+*r*) = 20P_{i}

Solving these equations, we conclude that 15 quarters of wheat exchange for 1 ton of iron, and the "rate of profits" is 25 percent. Even in the case of surplus production, Sraffa has apparently determined the equilibrium prices and interest rate without reference to marginal values.

**THE IDEOLOGICAL ELEMENT**

Now that we understand the basic Sraffian approach, we are in a position to understand some of his results, and why they were seized with such enthusiasm by leftist academics and Italian labor leaders. In subsequent sections, Sraffa derives results that depict a tradeoff between the real wage and rate of profits. In particular, Sraffa's analysis suggests that in a developed economy, the proportion of the "surplus" that goes to the workers versus the capitalists is arbitrary, and not at all "determined" by technological or economic facts. In Sraffa's models, for example, labor unions could increase real wages and lower interest rates, and this would have no real effects on production but would merely redistribute ownership of the net output in each period.

**THE FLAW IN SRAFFA'S APPROACH**

Despite his interesting approach and clever results, Sraffa does not succeed in overthrowing marginal value theory. Rather than replacing the modern focus on subjective decisions made on the margin, Sraffa simply assumes them away. For example, in the simplest case of a subsistence economy, Sraffa just takes it for granted that the people in this economy will continue to produce 400 quarters of wheat and 20 tons of iron every period, forever. But *why* should they do this? Suppose the people don't *like* iron or wheat! Or, more to the point, suppose the people discover a better use for their stocks of iron and wheat than to simply make more iron and wheat. How are the people supposed to break out of their subsistence mode in Sraffa's world?

Naturally, the Sraffian would respond that, if we wished to model such a scenario, we should use the more general case of production with a surplus. Then, if the members of our hypothetical economy wish to produce something besides wheat and iron, we simply need to include the relevant line in our list of technological recipes.

But this misses the point. Sraffa's method of determining equilibrium prices in a surplus economy already assumes that the system *has settled down at the optimum level of production in all possible lines*. Sraffa's techniques leave no room for the individual members of society to influence the methods of production that end up being used (whether or not there is a surplus), ultimately because there *are no individuals* in Sraffa's models.

This objection is strongest when it comes to the allegedly most important of Sraffa's results. Sraffa has shown that the rate of profits is "a free variable" (i.e. indeterminate and subject to external influence, in particular *downward*) only by excluding intertemporal optimization from his models. Yes, if the only function served by interest rates is to indicate the common rate of appreciation on invested capital, then there might be a range of values that will be consistent with general equilibrium.

However, if we also require that the market rate of interest reflects the subjective premium placed by consumers on present versus future consumption—a feature lacking in Sraffa's aggregate models—then this will eliminate the multiplicity of equilibrium rates of interest. Because it too is a "price" subject to supply and demand, there is nothing more nor less arbitrary in the determination of the interest rate than there is in the price of televisions.

**CONCLUSION**

Thus we see that Sraffa's techniques suffer from a very common problem, even among professional economists. Although most people understand that market forces lead to a unique (given the circumstances), "correct" price for radios or Big Macs, for some reason the rate of interest is considered malleable. Sraffa achieves results to the contrary only by eliminating individuals (and their subjective preferences) from the outset.

Having said this, I still urge the serious student of Austrian capital and interest theory to peruse Sraffa's work. Sraffa's 2neo-Ricardian disciples were not completely misguided in their attacks on the neoclassical mainstream in the

…in general the use of the term 'cost of production' has been avoided in this work, as well as the term 'capital' in its quantitative connotation, at the cost of tiresome circumlocution. This is because these terms have come to be inseparably linked with the supposition that they stand for quantities that can be measured independently of, and prior to, the determination of the prices of the products. (Witness the 'real costs' of

and the 'quantity of capital' which is implied in the marginal productivity theory.) Since to achieve freedom from such presuppositions has been one of the aims of this work, avoidance of the terms seemed the only way of not prejudicing the issue. (9) Marshall

Although he was wrong to condemn interest as an unnecessary and exploitive institution, Sraffa was perfectly correct to criticize the conventional, mainstream justification of the capitalists' income. To offer a proper defense of interest payments, one must turn to a theory of interest (such as the theories offered by Austrian economists) that does not view interest as the marginal product of capital.

- 1. On the Cambridge capital controversy, and its relevance to the Austrian school, see my earlier article.
- 2. Because of the similarity between his methods and the (verbal) general equilibrium models of David Ricardo, Sraffa and his followers are often called
*neo-Ricardians*. This is somewhat confusing, since their opponents are the*neo-classicals*; David Ricardo was a classical economist, after all.