Everything Old Is New Again

An orthodox response to the Cambridge Capital Controversy (CCC) is to assert that mainstream price theory is centered around General Equilibrium theory. Very short run models of intertemporal and temporary equilibrium are, it is claimed, unaffected by the CCC. I think that capital reversing is manifested in such models by dynamic equilibrium paths with counter-intuitive behavior.

For example, suppose the labor supply increases along such a path in that later generations increasingly prefer to consume commodities, not leisure. A dynamic equilibrium path can be constructed in which this increasing labor supply is associated with an increasing wage. Likewise, suppose instead that the supply of capital increases in that later consumers increasingly prefer to defer present consumption in favor of future consumption. Here, too, such increased savings can be associated with an increasing interest rate.

I have expressed this view before. I have decided that I am not going to develop concrete numerical examples any time soon. So I have put up what I have so far as a paper over on the Social Sciences Research Network (SSRN).

If I were to continue, the next step in the analysis is conceptually straightforward, although tedious. One would linearize the stationary state solutions around limit points for the dynamic equilibrium points. An examination of eigenvalues of the resulting matrix reveals local stability properties. I expect at least some equilibria will have, at best, the stability of saddle points. But multiple equilibria arise, and perhaps the desired dynamic equilibrium paths can be constructed. One might consider other forms of the utility maximization problem, if different stability properties are desired.