Figure 1: Household Decisions on Investments in Human Capital
Note: LTU = Lifetime utility. Source: Prepared by the author.
resources to human capital and consumption so as to maximize utility. Note that with a binding budget restriction, consumption equals remaining resources after investment in education. Therefore C = R − M . Let δ denote the subjective discount factor. Then the household problem is max{M } U (R − M ) + δY (M, B),
(1)
subject to the borrowing constraint R ≥ 0 and non-negativity conditions, M ≥ 0, C ≥ 0. The first-order condition for the solution to the problem described in equation 1 implies that the marginal returns to lifetime utility through consumption must equal the marginal returns to lifetime utility through investment in human capital after the schooling period is over: U 0 (R − M ∗ ) = δY 0 (M ∗ , B),
(2)
Note that the optimal level of household investment M ∗ is a function of the parameter B. Therefore, one would expect household investment to adjust to other inputs. Figure 1 is a graphic representation of equation 2. The horizontal axis represents the amount of resources available to the household. The optimal amount of investment in human capital will be such that the marginal contribution to utility through education is equal to the marginal utility of those resources for alternative uses. Intuitively, this means that the last dollar invested in education should provide as much additional expected utility as the last dollar invested in alternative uses. This is point A in the figure. 5