Generic Indeterminacy of Steady-State Competitive Equilibria in Walras-von Neumann Production Economies

This paper studies the structure of the set of steady-state equilibria defined in quite generalized von Neumann economic models. First, it shows that in any von Neumann production economy, there is an admissible domain of non-negative interest rates such that for any interest rate within the domain, there exists an associated steady-state equilibrium. Second, for almost all interest rates within the domain, the associated steady-state equilibrium is indeterminate. Thus, in summary, for any von Neumann production economy, there is a dense subset of the admissible domain over which the set of steady-state equilibria consists of a finite number of one-dimensional continuums of those equilibria. This feature is observed regardless of whether the underlying economy is regular or not, which is a sharp contrast with the finite and discrete features of the other types of Walrasian equilibria in static as well as intertemporal regular economies. These main results suggest, as a new, future research agenda, the necessity of studying an appropriate equilibrium selection mechanism that should be applied before market competition.