Wealth and Optimal Consumption of Retired Consumer: Two-Phase Life Cycle Model

In testing the life cycle theory of saving, the question whether the bequest motive is a significant determinant of saving has become a controversial issue. Someone argue that if the wealth of the retired consumers declines at a slow rate, it is an indication of existence of a significant bequest motive or it is because of uncertainty of expected life span. In this paper, optimal consumption path is calculated, and some simulated results are presented on the time path of wealth for retired consumers. It is shown that if wealth is measured in nominal values, the wealth curve can take increasing and decreasing shapes depending upon the expected life span, the rate of interest, and the growth rate of consumption, irrespective of significance of the bequest motive. Thus, the rate of decumulation of nominal wealth alone cannot be used as evidence for significance or insignificance of the bequest motive.