Monday, May 27, 2013

Kalecki And Sraffa: Compatible?

Two Great Economists
1.0 Introduction

Michal Kalecki set out macroeconomic models in which markup pricing was common. Economists in this tradition rarely explore the effect of inter-industry flows on prices. Sraffians, on the other hand, usually specify prices, at least, to a first approximation, in a model of full competition. Can work in the traditions of Michal Kalecki and of Piero Sraffa be usefully combined?

2.0 A Model

Consider an economy in which n commodities are produced by n (single-product) industries. Inter-industry flows are described by a nxn matrix A, where ai, j is the amount of the ith commodity used as input per unit output in the jth industry, at the given level of output of the jth industry. Labor inputs are described by the row vector a0, where a0, j is the quantity of labored hired in the jth industry per unit output, at the given level of output of the jth industry.

The positive constants m1, m2, ..., mn represent barriers to entry among the different industries. The going rate of profits is earned in industries in which mj is unity. Industries in which mj exceeds unity have high barriers to entry. Perhaps a large scale of production is needed to operate profitably in such an industry. Industries with mj less than unity are backwards, in some sense. At any rate, they earn less than the going rate of profits. These constants lie along the principal diagonal of the diagonal matrix M. That is, mi, j is mj, for i equal to j. And mi, j is zero, for i unequal to j.

The row vector p represents prices, where pj is the price of a unit quantity of the output of the jth industry. Suppose w represents the wage, and r represents The rate of profits.

The matrix A, the row vector a0, the diagonal matrix M, and one of the distributive variables (say, the rate of profits r) are the given data for this model. The prices p and the remaining distributive variable (for example, wages w) are the unknowns to be found. One can set out the (modified) Sraffa equations for prices:

(p A M + a0 w)(1 + r) = p

(I think models of full cost prices typically show markups being earned on both labor and material costs.) A numeraire should be specified. For example, one can set out the following normalization:

p1 + p2 + ... + pn = 1

Likewise, the markups are only specified by the model, so far, up to a scalar multiple. I suggest the following normalization condition for markups:

m1 x m2 x ... x mn = 1

Presumably this model can be extended, as in Sraffa (1960) to embrace fixed capital, land, joint production in general, and an analysis of the choice of technique.

3.0 Conclusion

The above has set out a model of prices of production. This model provides a framework for analyzing both the effects of inter-industry flows on prices and of markup pricing, arising from barriers to entry and other hindrances to full competition. The compatibility of some such model with both Kaleckian macroeconomics and the larger research agenda of Sraffa remains to be argued. Likewise, I have not shown the usefulness of this sort of model in empirical explanations of actual capitalist economies. One important issue in such discussions would probably be the applicability of models of prices of production to industries in which the planned operating level is less than full capacity.

This post should really have a bibliography, since the question of the compatibility of the economics of Kalecki and of Sraffa has been raised before. I gather that Paolo Sylos Labini, in some unpublished work in the 1960s, set out and analyzed a model rather like the above.


Magpie said...

Hi Robert,

Great topic. Maybe you should investigate this subject of a possible compatibility of Kalecki's approach to that of a Sraffian tradition.

Some months ago, in the comments section of Heteconomist, PeterC and I also discussed Kalecki's approach from a free market perspective (with competitive markets: no entry restrictions), in order to show that Kalecki's views are not incompatible with that situation, provided one considers profits are generated through Marx's exploitation mechanism, and not as an arbitrary markup.

We discuss a real-life situation.

The discussion is entirely "literary" and maybe you'll find my contribution a bit of a bore or amateurish.

In any case, for your amazement or amusement, I give you:

Wages, Materials, and the Markup

See the comments section.

If you have comments, please feel free (as I suspect Peter is too much of a gentle soul to provide criticism :-)).

I'm planning to elaborate that discussion further, although at the moment I'm busy studying the neoclassical theory of the firm and costs and its history.

Matias Vernengo said...

Ed Nell has a short paper on the topic in Mario Sebastiani's "Kalecki's Relevance Today" published in 1989.

Magpie said...

Thanks Matías. Do you know the exact title?

Robert Vienneau said...

Thanks for the suggestions. "Lord Keynes" recommends, rightly, a chapter in J. E. King's History of Post Keynesian Economics since 1936, a good reference. And another commentator recommends Fred Lee's work, where I too have read about markup pricing. I wonder if one wants to consider the markup on raw material costs, as well as wages, if it would be good to consider how to modify the Bidard and Erreygers corn-guano model, which has other controversies of its own.