Friday, April 28, 2006

Learning More About Capital-Reversing

David Skarbek asks me:

I can't find a good explanation of what capital reversing is and why it matters. The link in your last post is typical: "neoclassical thinking is wrong because of XXXXXXXX and it's a shame they don't get it right". What is XXXXX? The post mentions aggregate production function, what does that have to do with the microeconomics of a firms hiring practices? Why would they pay people more than their productivity?

I'm genuinely interested in this concept. Would you mind explaining it?

Nobody is claiming in this argument that workers are paid more than the value of "their [marginal] productivity".

Reswitching, capital reversing, and price Wicksell effects can be used to critique aggregate production functions, the explanation of wages and employment by the supply and demand of labor, and much more. But I cited Mathew Forstater not for his second paragraph, but his third. I find it a non-sequitur to reject a demonstration of the logical invalidity of an argument on empirical grounds. Furthermore, by looking at the thread on which Forstater is commenting, one can see a range of views.

I think of capital-reversing as a matter of correctly applying arithmetic. I recognize many teachers of economics in the United States train their students in outdated and exploded intuition.

One way to learn about capital reversing is to consider Sections 1, 2, and 6 in my draft paper, Creating Two-Good Reswitching Examples. Consider wages in Figures 1 and 2 around the switch point at the higher rate of profits (also known, at least for introductory explanations, as the rate of interest). Suppose net output (after replacing used-up means of production) for each technique under consideration consists of one unit of the first commodity. How much labor is required as an input to each technique? Which technique is adopted at a higher wage around this switch point? If you can figure out the answer to these questions, you will be well on your way.

The examples mentioned above consist of a choice between two techniques. Garegnani published an example in 1970 of the analysis of the choice among an uncountably infinite number of techniques.

Or you can take a look at this textbook (Garegnani's example is Exercise 5.8.23):
  • Kurz, H. D. and Salvadori, N. (1995). Theory of Production: A Long-Period Analysis, Cambridge University Press


Anonymous said...

I am sorry, but your comments are at best opaque. There is no elucidation at all. We do not want to read a million lines of example.
Please what is capital reversing?

Anonymous said...

I posted that post about u not answering the question. Fortunately i found it out. I leave it as an exercise for you where I found this out ..

In the Cambridge controversies, the problems created for the neoclassical
parables by Wicksell effects were termed reswitching and capital-reversing. Re-
switching occurs when the same technique—a particular physical capital/labor
ratio—is preferred at two or more rates of interest while other techniques are
preferred at intermediate rates. At lower values of the interest rate, the cost-
minimizing technique “switches” from a to b and then (“reswitches”) back to a. The
same physical technique is associated with two different interest rates, violating
parables 1 and 2.