Balanced Stochastic Growth at the Maximum Rate

Abstract

The von Neumann model of balanced growth is extended to the case of uncertainty by defining balanced stochastic growth as a stochastic process of output vectors Z (t) such that the sequence Z (t)lw' Z (t-1) is a stationary process, where w is a fixed strictly positive vector; i.e. growth is balanced if the relative proportions of the different commodities are stationary. Conditions are given under which: (1) the long-run growth. 1 w'Z(T) rate R = hm T log w' Z (O) and the expected growth rate r = E log w!' i ~ ~ 1) are well defined, and r = E R; (2) r attains a finite maximum r* on the set of all balanced growth processes that are feasible for a given technology, and r* is the same for all strictly positive w; (3) for any balanced growth process, R::; r* with probability one, and if r = r* then R = r* with probability one.