Why Sraffa’s Theory Does Not Contain a Labour Theory of Value

August 12th, 2017
in history, macroeconomics

by Philip Pilkington

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In my last post I tried to argue that, for a number of reason, once we make additions to Sraffa’s theory to make it comprehensive enough to confront the real world any potential interpretation of the theory in line with the labour theory of value falls apart. In that post, however, I never dealt with why some people have sought out a labour theory of value in Sraffa’s work.

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The reason for this seems to start in chapter III of Productions of Commodities By Means of Commodities. In this chapter Sraffa considers what impact variations in wage-profit distributions will have on the prices of goods in any given economy. I will first try to lay out the basic argument in as simple terms as I can.

Assume that all income goes to wages in a given economy. Now assume that different industries have different or heterogeneous inputs. Thus, while some need quite a lot of labour relative to other inputs, some need very little labour relative to other inputs. Now assume that we lower the wage rate by increasing the profit share. We must also, for simplicity’s sake, assume that the profit share is homogenous between industries. (I argued against this for other reasons in the last post but I am happy to concede on this assumption here for the sake of argument; note however that my criticisms in the last post with regard to the idea that firms that undertake superior innovations in marketing can add a higher mark-up does away with the labour theory of value anyway).

So, what happens when the wage rate is lowered to accommodate profits? Quite simply that those industries that have more labour intensive production will have a greater ‘saving’ than those industries that have less labour intensive production. This is a very intuitively simple argument. If Industry A has ten times the labour inputs that Industry B has then it will accrue ten times the cost-savings relative to Industry B from any reduction in wages. What’s more we have assumed a homogenous profit-rate so both Industry A and Industry B will have to pay the same profit-costs (in Post-Keynesian language, they will have to add the same mark-up). These two movements put pressure on Industry B to raise its prices relative to Industry A.

But the story doesn’t end there. In order to understand how relative prices are affected, we also have to conceptualise what might be referred to as ‘knock-on effects’. You see, in Sraffa’s system, inputs are the product of other inputs. So, we have to take into account the fact that as relative prices change in line with different labour intensities these prices will be passed on to other industries. To conceptualise this imagine that there is an industry, call it Industry L, that has nothing but labour costs. Industry L will obviously see the greatest relative price decreases if wage rates are brought down. But it follows that those industries that more heavily use the inputs of Industry L will see more substantial reductions in their relative prices through this channel than industries that use these inputs less heavily. As the reader can appreciate, this all gets rather complicated rather quickly. The sharp-eyed reader will also note that at its essence this is the basis of Sraffa’s famous ‘reswitching’ argument.

Implicit in this argument is that labour is the variable input. This, I think, is why some people interpret Sraffa’s theory as a labour theory of value. They assume that since in Sraffa’s argument, changes in the wage-profit distribution is that which causes relative price changes, then what we are talking about is a labour theory of value proper. This is simply incorrect.

Although Sraffa does use the example of wage-profit distribution changes to discuss price changes we could equally discuss any number of other inputs. A good example might be energy. Since we must assume that almost all modern industries use energy this makes energy just as important as labour. So, we could equally explore the effects that changes in the price of energy due to, say, geological scarcity, have on prices.

A labour theory of value adherent might counter this by saying:

“No, you misunderstand. The labour theory of value is concerned with distribution between human beings. When we change the distribution between wages and profits we change the relative amount that different classes of human beings receive of the social product. When we discuss energy price increases we are not discussing distribution in the sense that it is absurd to say that more income is distributed to ‘energy’ — a non-conscious, non-social entity.”

But this is a fallacious argument and is based on the nonrecognition of the demand side of the problem; one which is not dealt with in Sraffa’s book. In fact, we must assume that the different social classes consume commodities that contain different degrees of each input. In the case of energy (or food!) wage-earners will consume more of the energy-intensive commodities (heating oil, petrol etc.) out of their relative income share than their capitalist counterparts (for some empirical justification of this see the following post). Thus, as a price increase in energy inputs makes its way through the system, an effective redistribution is effected between wage earners and profiteers.

Clearly then, changes in any input price will affect the distribution of income (sharp-eyed readers will note here the essence of the Sonnenschein-Mantel-Debreu theorem). Once we take the Sraffian theory out of its vacuum and add a demand-side wherein different income groups consume different ‘baskets’ of goods (note, we need make no silly marginalist assumptions when doing this) then a change in any input cost will have redistributionary effects. This clearly shows that not only is the wage-profit relationship not the exclusive determinate of prices in a simple Sraffian economy, but it also shows that the wage-profit relationship is not the exclusive determination of income in that economy once we add a demand side — one which is implicit in Sraffa’s work anyway, which is clear when he discusses luxury goods in the second chapter.

So, even without taking into account the criticisms of the labour theory of value that I put forward in the last post — criticisms that rely on adding assumptions to the Sraffa model that generate greater realism — we can still say that the labour theory of value is false. Wages are just an input like any other — they are simply the price of labour. When the price of labour changes it affects relative prices and the distribution of income; but the same is true if the price of any other input changes.

This is not to say that wages are not probably the most important variable to consider when trying to understand income distribution. They probably are. But that has all of nothing to do with the labour theory of value.

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