Production Without a Surplus
Sraffa would begin by positing a subsistence economy with only two commodities: iron and wheat. Those commodities would be utilized in further production, thus producing more of the same, but only enough to make up for the “capital” (iron and wheat) expended in the process. Thus, Sraffa begins with two simple production rules:
(1) 280 qr. wheat + 12 t. iron → 400 qr. wheat
(2) 120 qr. wheat + 8 t. iron → 20 t. iron
Notice that the “wheat industry” produces 400 qr. of wheat, precisely enough for the needs of both industries and the “iron industry” produces 20 t. of iron, again precisely enough for another cycle of production.
However the gaps in Sraffa’s theory should be obvious in what it does not tell us. He does not give us “production functions” of different industries, instead he limits his analysis to one given point for each industry. In the real world, one might assume that if the wheat industry had been given more inputs, say 350 qr. wheat and 20 t. iron, it might produce much more wheat and thus enable more iron production. However having been limited to only one possible point of production for each industry, we can’t actually posit any kind of marginal or dynamic changes.
Why is this important? It’s is important because once Sraffa has asserted these immutable processes of production, he then asserts that an equilibrium must occur such that goods exchange perfectly as to redistribute the outputs into the industries they originally were employed as inputs. Therefore, to redistribute the factors into the industries required at the level required, 120 qr. wheat must be exchanged for 12 t. iron resulting in a “price level” of 10 qr. wheat for 1 t. iron. On the obvious level, this is precisely the reverse of what marginalists claim about equilibrium; Sraffa sets a price independent of human behavior.
Of course in reality, there might be a totally different exchange rate of iron and wheat and thus the inputs to the two different firms might be entirely different than before. In reality then, both industries would produce a different number of goods as a function of their production functions. However because Sraffa does not give us production functions, he sentences the analyst the assuming that the goods somehow will redistribute such that the given production processes will be satisfied, because he has absolutely nothing else to work with!
Quite simply, we have no reason to think that Sraffa’s supposed exchange rate of wheat and iron is the only possible equilibrium, but he forces us to do so by limiting us to one possible production equation. There’s no reason even to assume that this economy is subsistent given other distributions of inputs. For example, if we say that the wheat industry has greater marginal returns to wheat and less to iron, we might see that a price at which wheat is dearer compared to Sraffa’s equilibrium might well produce an overabundance of wheat within several iterations. Even if the iron industry receives less inputs than in Sraffa’s equilibrium, if the wheat industry can make up the difference we might see a non-subsistence level of industry. Sraffa leaves out the possibility of other price levels that might as well produce more or less than the subsistence level.
Production with a Surplus
Sraffa then proposes an economy with slight revision of rule (1) such that there is a surplus:
(1*) 280 qr. wheat + 12 t. iron → 575 qr. wheat
Sraffa then says that the ratio of exchange that evens the profit rate between the wheat and iron industry is 15 qr. wheat : 1 t. iron. Again without any particular reasoning, he asserts this new level to be a kind of equilibrium price. Again, this can only escape the casual reader as not being fallacious because Sraffa does not allow for any other inputs to production. What’s worse is that there is no particular reason in the situation of a surplus for the wheat industry to put its surplus on the market, which only serves to reduce the market price of its product. An individually rational wheat magnate (given the other market assumptions of Sraffa) would have no reason to put the “extra” 175 qr. wheat on the market at all.
What’s also important is that Sraffa doesn’t set any developmental dynamics to his system. As I alluded to before, a normal industry, in theory and practice, could use a “surplus” to increase production in the future and thus further increase their own future surplus further or the social surplus as a whole; Sraffa however simply refers to the extra 175 qr. wheat as “‘luxury’ produts which are not used, whether as instruments of production or as articles of subsistence, in the production of others” and that they “have no part in the determination of the system. Their role is purely passive.” Sraffa compares the surplus wheat to “ostrich-eggs” and “racehouses” which he addresses as luxury goods that could not conceivably influence production of other commodities (!) (that is even though we have posited industries that use wheat as an input, because Sraffa has straight-jacketed his analysis to using one and only one point of production, any increase in production is simply redundant).
Production with Explicit Labor
Sraffa then sets up a model in which labor exists as well as a necessary prerequisite for production. This is where is potential innovation of Sraffa’s method ends. Had all of the other disjoints I have mentioned been solved, Sraffa still commits a quintessentially classical error in using labor as a discrete quantity.
The purpose of Sraffa’s critique of marginalist capital theory was to take the fallacious concept of “capital” as some sort of amorphous blob concept and cogently divide it into the many different kinds of capital products that make it up (and that actually exist). After this, one could see clearly the disjuncts between capital the real thing and “capital” the aggregate element which doesn’t necessarily reflect the facts of individual markets for capital goods.
But Sraffa doesn’t seem to realize that the precise same thing could and should be done in an analysis of labor as well. The classical problem of labor is exactly the same as that of capital: both entities do not correspond to groups of products that have the set prices or markets, rather they represent a large continuum of goods and services that can’t necessarily be quantified in one number. Labor is actually probably less aggregatable for the simple purpose that even simple and repetitive tasks involve convoluted methods that, for virtue of being performed by humans, can’t easily be done by a computer algorithm or machine.
“Reduction to Dated Labor”
Then when Sraffa looks for a way to compute market values of already created products, he evokes effectively a labor theory of value to explain the values of commodities.
A labor theory of value seems mistakenly plausible in Sraffa’s method because there is no market mechanism whatsoever: again, market prices are erroneously computed by the immutable production equations that Sraffa gives, thus in reality, human utility-maximizing behavior isn’t the genesis of emergent market prices, rather they are set by a seemingly apperated desire within the commodities themselves to find themselves within the market they are needed to continue production at the given level.
Since there is, in economic terms, no real market at all, the only option is to base market pricing on some objective value, in Sraffa’s case, the only thing he never disaggregated: labor. To this point, we can unleash all of the typical arguments against computing price or value from labor, all of them circulating over the fact that to an agent in the market, it makes no difference how much labor was present in the production of a good he might wish to buy.
Of course Sraffa’s “reduction to dated labor” is really only one side of the coin, in the market-less economy that Sraffa proposes, everything not determinable by labor must somehow be a function of other objective factors, specifically capital. Of course since capital also comes to have labor-imputed value, the only difference in price is the interest/wage rate of the economy, which seems to have no market determination whatsoever (which is partially the point of Sraffa’s analysis).
The Rate of Interest
In Sraffa’s model, he adds in the interest and wage rates which are to be mechanisms by which the surplus of any iteration of production are distributed. His goal of course is to revive the Ricardian theory of distribution (or any theory of distribution) seeing that anything except for some kind of marginal concept would mean a non-market (or institutional) determination of wage/profit rates.
With some sardony, I will repeat myself in saying that Sraffa has done this in his model by throwing out the market altogether: there are no rudimentarily rational economic agents or economic dynamics, instead he posits a static economy where there cannot be any marginal concepts whatsoever because there can be no unilateral changes in the production function because there are no production functions. Instead Sraffa simply says that products must move from industry to industry at a certain exchange rate because he obliges the firms to produce at his given production level, an absolute reversal of all economic decision-making.
That said, one should ask himself why precisely Sraffa should propose one uniform interest rate. He has already established in his model that there is no uniform substance “capital” and that presumably all the commodities one generally thinks of as capital goods are different market items which have no market equilibrating rate as one. Why then does he establish one profit/interest rate for all goods? For his algebra, it does indeed make little difference seeing that all capital quantities are (ironically) aggregated and indexed by the rate afterwards, but it would seem important to analyze the differences between rates in each product and how they interact.
That of course would be a lot more circumlocution to be able to divide returns to capital between all industries; Sraffa would have to find some kind of market-like mechanism to distributed the profit rate.
The Cambridge Capital Controversy
In case it isn't obvious, I find Commodities to be a severe let-down. The methods are mostly baseless and all of Sraffa's conclusions can be implied in what he leaves out or assumes away in his original formulation. Of course the work does deserve some praise for its role in the Cambridge Capital Controversy, because in the thick web of confusion that Sraffa weaves, there is at least one nugget of insight: that capital and its marginal returns is not cogently non-aggregatable. Thus, one cannot compute interest or profit rates of an economy as a whole on the basis of marginal productivity because that marginal productivity is a function of how we aggregate capital, which again is defined in terms of marginal productivity. Sraffa may trip on every possible obstacle in working to show this (including trying to aggregate capital in terms of labor) but we have to acknowledge that it triggered at least some movement to a viable criticism of an ongoing error in neoclassical theory.