Consumption and Wage Humps in a Life-Cycle Model with Education

The empirically observed hump-shaped pattern in individuals' consumption over their life cycle cannot be explained by the classical consumption-savings model. We explicitly solve an extended model with utility depending on both consumption and leisure and with endogenous educational decisions affecting future wages. We show that optimal consumption has the observed hump shape, and we pin down the peak age. The hump results from consumption and leisure being substitutes and from the endogenously determined implicit price of leisure being decreasing over time; more leisure means less education, which negatively affects all future wages, and the present value of foregone wages decreases with age. In contrast to earlier related work, the presence of the consumption hump does not require the wage rate to be hump shaped, but also occurs when the wage rate is increasing over life as found in empirical studies