Friday, May 03, 2013

A Near-Term Goal

I would like to develop a numeric example with:

  • Smooth production functions, and
  • Properties analogous to the ones highlighted in this example.

One of the parameters of the utility functions in this example expresses the willingness of consumers to defer consumption. A greater willingness to defer consumption supposedly represents a greater supply of "capital", in some sense. In a "perverse" case, this greater supply, all else the same, is associated with a long run equilibrium with a higher equilibrium interest rate.

I do not think that the "perversity" I am trying to illustrate depends on the distinction between discrete technologies and smooth production functions. I am aware, however, of a theorem that applies to a technology with smooth production functions, but not to discrete technology:

Theorem: Consider an economy in which all produced commodities are basic, in the sense of Sraffa, for all feasible techniques. And suppose the production of one commodity can be described by a continuously differentiable production function. Then this economy cannot exhibit reswitching of techniques.

The relevance of this theorem to my goal is not clear. I am willing to consider examples with non-basic goods. So examples should be possible to construct with smooth production functions and reswitching. But I do not even need reswitching. I am merely looking for capital-reversing. And I do not even insist that real Wicksell effects be positive. I will be content with positive price-Wicksell effects swamping negative real Wicksell effects.

Maybe the kind of example I am seeking is set out in a end-of-the-chapter problem in Heinz D. Kurz and Neri Salvadori's 1997 book, Theory of Production: A Long-Period Analysis (Cambridge University Press).

By looking at the convexity of the wage-rate of profits curves on the frontier, one can read off the direction of price Wicksell effects. And I have already shown that an example can be created with Cobb-Douglas production functions and positive price Wicksell effects. I have yet to examine the relative sizes of price and real Wicksell effects in the example, derive conditions on their directions and sizes, or create a numeric example satisfying those conditions.

Eventually, I would like to explore the dynamics of non-stationary equilibrium paths in such a model built on unarguably neoclassical premises. The point is to continue an internal critique of neoclassical microeconomics, not to describe actually existing capitalist economies.


windwheel said...

I don't see any perversity. If the marginal efficiency of capital goes up so does the interest rate.
I expect to see a subsistence economy whose savings rate suddenly goes up to experience an outward shift of the p.p.f simply because, if people are saving more, then to continue to subsist they most be working longer hours in which case the marginal efficiency of capital will probably rise faster simply because people are now thinking of ways to make it more productive.
What is perverse is if there is an Entrepreneurial class which can extract a rent such that the interest rate falls though marginal capital efficiency rises.
This could happen if there is a class/caste/gender/age or nomenklatura/Credentialized elite type barrier to entry to Entrepreneurship or else if it is a repugnancy market.

Robert Vienneau said...

I do not see how the marginal efficiency of capital alters in the model I hope to develop. Technology is taken as given. And I also intend, at first anyways, to assume a constant number of hours worked.

windwheel said...

O.k, so in the first period, people consume less out of their income leaving a surplus. If this surplus is instantaneously invested the m.e.C goes down so the interest rate goes down so the share of Capital in total factor income goes down assuming diminishing returns. But this means the share of Labor/ Land must have gone up unless there is a separate Entreprenurial class which has engrossed the gain. If there are no barriers to entry into that class and agents are identical in appetency and ability for that function than the total reward to Saving has increased and assuming a sort of Wicksell effect things which were previously consumption goods have been repackaged as either capital or a store of value and their prices have gone up thus over-all the 'interest rate' has risen.