SAVING AND THE RATE OF RETURN*

THE PRINCIPAL OBJECTIVE of this study is to investigate theoretically and empirically the relation between saving in the private sector of the United States and the rate of return on capital. A model of household behavior is developed in which the supply of labor is simultaneously determined with consumption and saving in a utility-maximizing framework. Previous studies have assumed that individuals could adjust their consumption time-path but not the pattern of labor services offered; the implicit assumption is that a labor-leisure decision precedes the consumption-saving decision. Allowing these decisions to be made simultaneously is more realistic. This is accomplished by introducing leisure into the household utility function. The utility function thus depends on consumption and leisure in the present and all future time periods. The functional forms that are used to represent the utility function have separability properties which allow the maximization of utility to be partitioned into a two-stage process. In the first stage total wealth is allocated between the present and all future periods, while the second stage distributes each period's allocation to the individual commodities, consumption and leisure. The time constraint combines with this result to yield the supply of labor and hence current wage income. A simple but restrictive specification for the welfare function is the nested CobbDouglas, where each single-period utility index is a Cobb-Douglas function of consumption and leisure, and the overall index is a Cobb-Douglas function of all the single-period indices. The allocation of wealth resulting from such a function is independent of the relative prices of consumption and leisure and of the rate of return. The Cobb-Douglas function has two well-known generalizations which can be used to relax the implied proportionality. The first is the Stone-Geary utility function which introduces nonhomogeneity parameters into the single-period utility indices. These are usually interpreted as committed amounts of consumption and (in this case) leisure. Allocation is still proportional at the margin but not proportional overall. The price level, the wage rate, and the rate of interest, however, still do not affect the allocation. The second generalization of the Cobb-Douglas function is the constant-elasticity-of-substitution (CES) function. In this case prices and the rate of return have a role to play in the allocation provided the elasticities of substitution are different from unity. Of course, both generalizations could be made simultaneously, yielding a nested CES function with nonhomogeneity parameters. Demand functions for consumption and leisure are derived for the various utilityfunction specifications. The demand functions corresponding to the generalized utility functions all have proportionality (Cobb-Douglas) as special cases. Thus with appropriate econometric specifications and time-series data the empirical relevance of the generalizations can be assessed. Even though the behavioral relations of the household sector are of primary interest, the observed variables entering these relations are jointly determined with other macro-variables in the economy. Feedback from the rest of the economy raises the possibility of stimultaneous-equations bias. Thus a complete, though simplified