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
*n*x*n* matrix **A**, where *a*_{i, 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 **a**_{0}, where
*a*_{0, 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 *m*_{1}, *m*_{2}, ...,
*m*_{n} represent barriers to entry among the
different industries. The going rate of profits is earned in industries
in which *m*_{j} is unity. Industries in
which *m*_{j} exceeds unity have high barriers
to entry. Perhaps a large scale of production is needed to operate
profitably in such an industry. Industries with
*m*_{j} 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, *m*_{i, j}
is *m*_{j}, for *i* equal to *j*.
And *m*_{i, j} is zero,
for *i* unequal to *j*.

The row vector **p** represents prices, where
*p*_{j} 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 **a**_{0},
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:

(pAM+a_{0}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:

p_{1}+p_{2}+ ... +p_{n}= 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:

m_{1}xm_{2}x ... xm_{n}= 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.

## 4 comments:

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

http://heteconomist.com/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.

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

Thanks MatÃas. Do you know the exact title?

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.Post a Comment