03 August 2012

Reading Sraffa (1)

In his book, Debunking Economics (2nd Ed), Steve Keen mentions Pierro Sraffa in connection to the dilemma of capital formation.

Capital formation is treated in [neoclassical] economics as occurring between static phases of production; capital itself is treated as if the financial meaning of "capital" were identical to the industrial sense of "capital." Economists seldom include any consideration of the industrial steps between financial "capital" (i.e., income diverted from present consumption into production, in the hopes of future income) and industrial capital (i.e., tools, buildings, fixtures, or inventories).1 They treat the provision of "spare" income as a hydraulic process, translating directly from money to productive instruments in a single step.

In the 1950s, a major preoccupation of economists was modeling simple economies using a set of equations. The idea was to simulate the behavior of a real economy with a virtual one. Obviously, a plausiblely complex economy complete with gas chromatographs and botts dots is not one that can be described with a manageable set of equations; so the economy was simplified immensely. Instead of acknowledging the existence of different modalities of capital, it was treated as a single fluid whole. Sraffa bucked this trend; he insisted on models of the economy that recognized the existence of physical objects used as capital.

The main historical impact of Sraffa was to attack the idea that a market economy can find a unique value of anything. A basic principle of neoclassical economics (and its successor, DGE) is that, in a free market, the share of economic surplus going to capital or labor will reach a socially optimum value.


Walrasian General Equilibrium

The pool of available commodities is represented as a matrix of n goods and m people. People are indicated as 1, 2, 3... and goods are represented as letters a, b, c...

Qa = qa, 1 + qa, 2 + qa, 3 . . .
Qb = qb, 1 + qb, 2 + qb, 3 . . .
Qc = qc, 1 + qc, 2 + qc, 3 . . .
. . . .
where Qa represents the total quantity of a, and qa, 2 represents the amount of a held by 1.

"Redistribution" takes place to meet the preferences of the original owners (who presumably made them in the first place). In this initial presentation of the problem, the prices of the commodities pb, pc,... are fixed (the price for commodity a is set to 1, and all other prices are in units of a).

Person (1) buys x'1, y'1, z'1,... of commodities a, b, c... (this is Walras' notation, and it wasn't thought out very well!) to wind up with
q'a, 1 + x'1 = qa, 1 + x'1,
q'b, 1 + x'1 = qb, 1 + x'1,
q'c, 1 + x'1 = qc, 1 + x'1,

. . . .

And Walras proceeds to demonstrate that markets will clear. Later he introduces the production process and utility functions, in a comprehensive effort to outline the system of equations the market must "solve."
Chart taken from Walras (1984), p.182-184
This is a loaded concept, and it's unlikely I'll explain it in a way that satisfies anyone. But neoclassical economics presupposes there is--at any given moment--an equilibrium value for prices and quantities of output that maximizes public welfare. If one had infinite knowledge of the production processes and utility functions, one could determine the amounts and prices of all the things the economy produced, such that everyone had the most satisfying mix of goods they could afford. An additional benefit is that the prices of goods would stimulate the correct amount of production, and cover the costs of inputs.

Lest anyone get the wrong idea, another crucial point of economics is that of course no one could possibly have remotely enough information to do this, but the free exchange of goods and productive inputs is constantly moving us closer to this equilibrium. Changing objective realities, such as shifting supplies of inputs, or changing preferences, pull us further away from it.

"Covering the costs of inputs" means--in this precise context--enough of a return to the supplier of each input that the supplier is motivated to provide enough to that particular goods producer to produce the market's demand for that particular good. So, for example, if the input is hours of productive labor, then there is a socially optimum wage that is best determined by the market.

The reason why I don't just say "Let the market decide!" is that, if economics is claiming to be a science instead of a religion, it has to claim there is some concrete social optimum out there to be discovered by the market, it has to explain what this social optimum will accomplish, and it has to explain why the market is likely to find it.


Sraffa's System

Superficially differs from Walras (above) in representing production rather than redistribution (though commerce), but mathematically the concept is similar: in Sraffa, redistribution occurs because producers of wheat, iron, and pigs are exchanging quantities of those commodities in order to produce another batch of each.

240 qr wheat + 12 ton iron + 18 pigs = 450 qr wheat
90 qr wheat + 6 ton iron + 12 pigs = 21 ton iron
120 qr wheat + 3 ton iron + 30 pigs = 60 ton pigs

In this example, the output is equal to the inputs, and exchange must take place again afterwards so that the same amount of everything (as before) can be produced. Subsequently, Sraffa switches to scalable matrix algebra to allow for many different commodities.

Here he shows the arrangement of identities required to ensure continuous production. The term Ba prefers to the amount of commodity b used in the production of a. The amounts used in the production of each commodity are fixed by available methods and the amount of each commodity "required" by Sraffa's "economy."

Aapa + Bapb + . . . + Kapk = Apa
Abpa + Bbpb + . . . + Kbpk = Bpb
. . . . .
Akpa + Bkpb + . . . + Kkpk = Kpk

When solved, the values of p ensure that the producers of each commodity will be able to buy the inputs they need in order to reproduce the output of the previous cycle.

Subsequently, Sraffa develops his imaginary economy to include wages and economic surplus.

Taken from Sraffa (1960), p.4
When Sraffa published his book, it triggered a major controversy over the question of general equilibrium in economics. With respect to mainstream economics in the USA, neoclassical economics had never really been displaced.2 In effect, Sraffa was writing a treatise on general equilibrium in a world that was still Walrasian; he had written a rough draft in 1926, then dusted off the manuscript, and published it in 1960--still in a Walrasian world.

The book is puzzling to most readers. It's not obvious if Sraffa is trying to carry a torch for his beloved David Ricardo, or if he really is making a pointed gesture for the benefit of Walrasians. Rather than construct a model economy with indifference curves and household endowments of capital/labor, Sraffa uses merely production functions and abstract commodities. The capital contribution to production represents all inputs besides labor. The commodities must be end products of production as well as inputs of production. Over successive chapters, Sraffa builds up his analysis to include a richer and more detailed model of the economy. But to what purpose?

In subsequent posts, I will attempt to explain what this purpose could be.

(Part 2)


  1. Classical economists, such as David Ricardo, made a major distinction between "circulating capital" and "fixed capital." Inventories, whether of merchandise or raw materials, are "circulating capital"; firm revenue is directly related to inventory moving out the door. Machinery, buildings, and fixtures are "fixed capital"; firm revenue may increase if the firm buys more of it, but the object is to keep it in working condition as long as possible before it is used up.

    Neoclassicals like Lionel Robbins noted that this was actually an ambiguous distinction, since the difference between f- and c-capital was really the time period of production one was looking at. Inventory of finished goods one hopes to sell is clearly circulating, but what about drill bits used in the process of recovering petroleum? The exploration company would like to conserve them, but over the long run, the more bits used, the more petroleum recovered (and sold to refineries).

  2. I actually discovered this when I was compelled to read Paul Samuelson (Foundations of Economic Analysis, Harvard University Press (1947). Subsequently, I noticed the persistence of neoclassical assumptions and methods all through the 1960s and 1970s. For readers shocked by my claim, this will seem like a weak defense. However, my posts on Steve Keen and Hyman Minsky will treat this in greater detail.

    For an account of the Cambridge Capital Controversy "provoked" by Sraffa's book, please see Eckhard Hein & Engelbert Stockhammer (2011), pp.3-4.
economic surplus: excess of output over input; not to be confused with "surplus value," a concept from Marxian economics.

Sources & Additional Reading

Piero Sraffa, Production of Commodities by Means of Commodities, Cambridge University Press (1960): link goes to complete text online.

Léon Walras (trans. William Jaffé), Elements of Pure Economics, Orion Editions (1984/1954); translation based on 4th Edition (1900).

"Debunking Economics, Part V: The Holy War Over Capital," Unlearning Economics (26 July 2012): for a summary of Steve Keen's account of the Cambridge Capital Controversy

Eckhard Hein & Engelbert Stockhammer, A Modern Guide to Keynesian Macroeconomics and Economic Policies, Edward Elgar Publishing (2011). Hein & Stockhammer's account of the Cambridge Capital Controversy includes a plausible explanation of why Joan Robinson's victory over Samuelson and Solow was ignored by the economics profession.

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