The Optimum Lifetime Distribution of Consumption Expenditures: Comment
In a recent article in this Review, Lester C. Thurow (p. 326) argued that . . . individuals will continue to dissave as their income rises until current income equals desired current Thus if it were possible to estimate the income at which an individual becomes a zero saver for each year of his life, it would be possible to determine his optimum life distribution of consumption. To implement this idea, he suggested two alternative definitions of zero saving. Based on these definitions, two optimum lifetime distributions of consumption expenditures were estimated for individuals between the ages of 20 and 80 (see Figure 2 on p. 328). The idea appears to be quite ingenious. Its usefulness is appealing because the estimation procedure is relatively simple. The procedure involves merely plotting a graph of zero-saving income levels for various age groups of individuals. Thurow was quick to warn us that his idea may have several limitations. Aside from limitations of technical nature, he pointed out that his procedure assumes that the lifetime utility function has annual utility levels as its sole arguments. In addition, the annual utilities are assumed to be independent and additive. Despite these limitations, the suggested procedure for the estimation of the optimum lifetime distribution of consumption expenditures may be very useful if it does not involve other limitations of a more serious nature. This note attempts to explore the possibility of developing an alternative estimation procedure and to examine the validity of the suggested procedure. The fact that the suggested procedure uses only those observations with zero saving at each year of age and discards all other observations with positive or negative saving is somewhat disturbing. This implies that the lifetime distributions of consumption expenditures of those individuals with positive or negative savings are not optimum. One can argue, as Thurow did, that their distributions of lifetime consumption expenditures, particularly those with negative savings, are subject to institutional constraints. We must realize, however, that those people with zero saving are also subject to the same constraints. For example, if the interest rate were higher (or lower) than the actual level, their savings may be positive (or negative) instead of zero. In any event, it seems desirable to develop an estimation procedure which uses all available observations instead of only some of the observations. In general, we can suppose that the average propensity to consume (which is equal to the marginal propensity to consume, if we assume a constant average propensity) is determined by both age and the relative income position of a particular individual. This proposition is consistent with both the permanent income and the relative income hypotheses.' For convenience of discussion, let us suppose that individual consumption functions may be reasonably approximated by
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