A theory of age-dependent value of life and time

A model is constructed to examine how the utility and dollar values of life and time change as one ages, encompassing several previous studies as special cases. If the interest rate is no higher than the depreciation rate (in deriving utility) and also no larger than the sum of the depreciation rate and the growth rate of wage (allowed to be negative) at any age, then the dollar value of life monotonically declines as one ages. The dollar value of life increases first and then declines as one ages, i.e., the dollar value of life over age exhibits an inverted-U shape, if the interest rate is higher than the depreciation rate by a sufficient margin. While the utility value of time may decrease with age (time is more precious for the young), the dollar value of time increases with age if the interest rate is sufficiently higher than the depreciation rate. A distinction is also made between a shift from work to leisure and the value of time (which may not equal to the wage rate) as such with conceptual and policy implications.