Saturday, December 11, 2021

A Mistake In Kurz And Salvdori (1995)?

On page 299 of Kurz and Salvadori (1995), they write:

System (10.10) is identical with system (8.13).

The above statement is correct only if the steady state rate of growth is zero. The analysis presented around system 8.13 applies to any rate of growth lower than the rate of profits.

Chapter 8 is about joint production in general. Equations 8.13a through 8.13e specify a long-period position for joint production. Equation 8.13c specifies quantity relations and is:

zT ( B - (1 + g) A) ≥ cT

Equation 8.13d is a duality condition known as the rule of free goods. It is:

zT ( B - (1 + g) A) y = cT y

A full exposition would explain the notation above.

Chapter 10 is about land rent. Equations 10.10a, 10.10b 10.10c, 10.10f, and 10.10g specify a long-period position with land being cultivated. Equation 10.10a specifies quantity relationships and, more or less, is:

xT ( B - A) ≥ dT

Equation 10.10b is the rule of free goods for models with rent. It is:

xT ( B - A) p = dT p

If the rate of growth were positive in models of rent, a steady state could not be maintained. Eventually, a less efficient technique (at the given rate of profits) must be adopted, and the rate of growth must be lower.

I find I often may explain the dual quantity system for Sraffa's price equation in a confused manner. I often want to consider the trade-off between a steady state rate of growth and consumption per worker, with a given composition of the consumption basket. Given the technique, this trade-off is identical to the wage curve for the technique. On the other hand, one could present the quantity relations for a given level and composition of net output, that is, for given requirements for use. In an exposition, one must choose one of these approached.

Kurz and Salvadori (1995) is comprehensive. Of the mathematics I understand, this is as close as I found to a mathematical mistake. After publication, some argued about what I think are matters of history and judgement in the critique of neoclassical theory in Chapter 14. I think it was demonstrated about half a century ago that most of what most mainstream economists teach in North America is, at best, incorrect. From twitter, I have learned that economics is astrology for white men.

• Heinz D. Kurz and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge University Press.

1 comment:

Anonymous said...

“Medawar could say that scientists narrow down to focus on tractable problems”