Malthusian regime: The Basic Structure of the Model 3

Budget Constraint: Quantity-Quality of Children Vs. Consumption

Following the standard model of household fertility behavior (Becker, 1960) it is assumed that the household chooses the number of children and their quality in the face of a constraint on the total amount of time that can be devoted to child-raising and labor market activities. We further assume that the only input required to produce both child quantity and child quality is time. Since all members of a generation are identical in their endowments, the budget constraint is not affected if child quality is produced by professional educators rather than by parents.

Let rq + ree/+i be the time cost for a member of generation t of raising a child with an education level e^+1. That is. rq is the fraction of the individual’s unit time endowment that is required in order to raise a child, regardless of quality, and re is the fraction of the individual’s (or of an equally educated teacher’s) unit time endowment that is required per each unit of education of each child.

Consider members of generation t who are endowed with ht efficiency units of labor at time t. Define potential income, zt, as the amount that they would earn if they devoted their entire time endowment to labor force participation: zt = wtht. Since individuals do not generate utility from consumption at time i, their potential income is divided between expenditure on child rearing (quantity as well as quality), at an opportunity cost of wtht{rq + reet+i] per child, and savings for future consumption, sL. Hence, in the second period of life (parenthood), the individual faces the budget constraint:

Hence, the individual’s level of human capital is an increasing, strictly concave function of the quality (education), and a decreasing strictly convex function of the rate of technological progress. Furthermore, education lessens the adverse effect of technological progress. That is, technology complements skills in the production of human capital. The higher the rate of technological progress the higher the relative return to quality. fast payday loans online

Moreover, although the number of efficiency units of labor per- worker is diminished during the transition from one technological state to another – the ‘erosion effect’ – the effective number of the efficiency units of labor per worker, which is the product of the workers’ level of human capital and the economy’s technological state (reflected in the wage per efficiency unit of labor). is presumably higher as a result of technological progress. That is, the overall effect of technological progress from period t to period t-hi on the potential income of members of generation t H- 1 may be positive. Furthermore, once technology returns to a stationary state, the ‘erosion effect’ is eliminated, whereas the positive ‘productivity effect5 is still in place.