Education and the Family: Some Notes

where H and L are, respectively, the amount of skill and the amount of unskilled labor used in production, and α is a parameter describing the nature of the technology. We assume that the production function exhibits constant returns with respect to the two inputs together but diminishing returns with respect to each individual input. This formulation also imposes the restriction that all levels of human capital are perfect substitutes–one of the insights of the paper by Mookherjee and Ray, cited above, is that relaxing this assumption introduces an additional source of persistent inequality. Labor Supply: Each person in the economy is assumed to own one unit of unskilled labor. In addition they own a certain number of units of skills, which correspond to the amounts they invested in human capital. The Life Cycle: Agents in this economy live for three periods. In the first period of their lives there is no consumption or work: all they do is acquire skills. The second period is when people work and earn an income. We assume that labor has no disutility associated with it. This income can be spent on current consumption or saved and invested for consumption in the next period, when they no longer have wage income. In the second period of their lives they also give birth to exactly one child. The population therefore stays unchanged over time and each cohort is assumed to be size one. Human Capital: Human capital is produced using a combination of human capital and unskilled labor. The cost of acquiring h units of human capital is γs(h, h−) units of human capital and (1 − γ)s(h, h−) units of unskilled labor, where 0 ≤ γ ≤ 1 and h− is the level of human capital of the parent of the