Life-Cycles with Terminal Retirement

Abstract

This paper explores aspects of a model of the individual's optimal program of labor supply and human capital accumulation, and produces a number of unexpected results. The individual's allocation of time over his life between work and training has been modelled as an earnings-maximization problem, holding leisure fixed, and more recently as a utility-maximization problem, in which leisure is a choice variable for the individual, in the same way as work and train ing.2 The earnings maximization models have typically assumed that at any moment of time the rate of earnings and the rate of production of human capital are functions of the individual's human capital stock and the fraction of the day he devotes to work, and have the property that there is a diminishing marginal rate of substitution between earnings and human capital production. These models typically imply that any period of specialization in training occurs at the beginning of the individual's life cycle, and that thereafter the fraction of the day devoted to human capital accumulation falls towards zero which it reaches at or before the end of the life-cycle. They imply that actual earnings rise faster than and peak later than earning capacity or human capital stock. In utility maximizing models, the individual may balance gains in earnings, and thus consumption obtained through training and work, against the loss of leisure entailed. He maximizes lifetime utility, a function of consumption and leisure time, by choosing the optimal fraction of each day to spend at leisure, and the optimal division of the remainder of the day between work and training. The rate of earnings and the rate of production of human capital are functions of the stock of human capital, the fraction of the day taken up by leisure, and the division of the market time between training and work. Again, there is a diminishing marginal rate of substitution between human capital production and earnings, obtained by various choices of the division of the market time between training and work, holding the fraction of the day devoted to leisure constant. The individual faces a budget constraint over his lifetime as a whole, but can lend and