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.