Savings, Investment and Capital in a System of General Intertemporal Equilibrium — an Extended Comment on Garegnani with a Note on Parrinello

Is intertemporal general equilibrium concerned by the Cambridge critique of the theory of capital? Many thought, and for a long time, that it was not the case, since there is no aggregate of capital in general equilibrium theory, at least not in a form which would be visible immediately in the Arrow-Debreu model with a finite horizon (Debreu, 1959). Others suspected that the problems of capital theory would affect all versions of neoclassical theory, without being able to indicate the consequences for general equilibrium. Burmeister (1980, p. 122) introduced the assumption of regularity, i.e. essentially the postulate that the total change in the values of capital goods employed falls whenever a rise of the rate of interest causes a switch of technique/A variant of this assumption was used by Epstein (1987) to demonstrate the convergence of an intertemporal equilibrium with an infinite horizon towards a steady state in which the rates of return on all assets became equal among themselves and equal to the (variable) rates of time preference of the consumers. Here, the relationship with the Cambridge debate was made explicit and it was remarked (see also Burmeister, 1980, p. 125; Schefold, 1997, chapter 18.1) that the absence of reswitching and reverse capital deepening were necessary conditions in neoclassical theory to exclude the specific instability discussed in Schefold (2005a, 2005b) which might prevent the economy from reaching a terminal state with a uniform rate of profit after starting from arbitrary initial endowments of capital goods.