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Recent empirical research (Flavin [I981], Hayashi [1982]) has rejected the certainty-equivalent formulation of permanent income hypothesis (Hall [l978]). These findings are often attributed to households’ inability to borrow completely against expected future labor income. This paper is a theoretical investigation of optimal consumption behavior under risk aversion, random income fluctuations, and borrowing restrictions. The principle objective is to establish the existence and to investigate the properties of the stationary probability distribution which characterizes the behavior of consumption under these conditions. Schechtman [1976] proves that optimal consumption converges almost surely to mean income if the rate of interest on savings is zero, the (infinitely lived) household does not discount future utility, borrowing is prohibited, and income is an iid random variable. Bewley [1976] generalizes Schechtman’s …