The purpose of this paper is to prove the existence of a steady state for a simple decentralized growth model which is subject to random shocks. The model has the following elements. The population is composed of an endless sequence of overlapping cohorts of two-period households; each cohort is the same size; and, there is an aggregate production function and one output good. Because the labor supply is fixed, the production function relates output in each period t to the total saving of all young families in period t 1 and to the current realization zt of a random variable Z: The random variable has an exogenous, unchanging, and known distribution. Futures markets are imperfect: young families can save at time t only by investing in physical capital, which will pay a return at time t + 1. The return depends on the size of the time-(t + 1) capital stock, k,, and on zl+ r. Let y, = y(k,1, zt) be the vector of incomes of young families at time t. Then such families use a function g( vf) = k, to predict k, (note that g is nonstochastic). The families adjust their saving to maximize their expected utility, where the latter is computed using g and the distribution function for 5. We call resulting aggregate savings by young families y(y,, g). We use a fixed-point argument to prove the existence of sets K and Y and an expectation function g such that if all realizations of 5 fall within Z, (i) Y(K x Z) c K (ii) g(y) = K and (iii) g(y) = y(y, g) all y E Y. The resulting g determines (in a very simple context) what Grandmont [7] would call “ ‘rational’ expectations” and what Radner [ 17, 181 would call an “equilibrium of plans and expectations.” We use this g to generate a transition function v for k,. We then show v has a finite invariant set K* (which includes all feasible states except one trivial one); there are a finite number of ergodic sets EL,..., EN c K* for V; and there is a unique stationary distribution function Di associated with each Ei. Each pair (Di, Ei) constitutes a “steady state” (corresponding to Green and Majumdar’s [9] concept of an “equilibrium distribution” and to Grandmont’s (71 “long-run equilibrium”): Once the evolution of the economy carries it into Ei some