Introduction to Modern Economic Growth be equal to −(1−α)/α wj = α (1 − α)(1−α)/α Aj Rj Consequently, a worker with human capital hi will receive a wage income of wj hi Once again, this is a more general result; with aggregate constant returns to scale production technology, wage earnings are linear in the effective human capital of the worker, so that a worker with twice as much effective human capital as another should earn twice as much as this other worker (see Exercise 3.9) Next, substituting for capital from (3.25), we have total income in country j as −(1−α)/α Yj = (1 − α)(1−α)/α Rj Aj Hj , where Hj is the total efficiency units of labor in country j This equation implies that ceteris paribus (in particular, holding constant capital intensity corresponding to Rj and technology, Aj ), a doubling of human capital will translate into a doubling of total income Notice that in this exercise we are keeping not only Aj , but also Rj constant While it may be reasonable to keep technology, Aj , constant, one may wonder whether Rj will change systematically in response to a change in Hj While this is a possibility, any changes likely to be second-order First, international capital flows may work towards equalizing the rates of returns across countries Second, when capital-output ratio is constant, which Proposition 2.11 established as a requirement for a balanced growth path, then Rj will indeed be constant (irrespective of the exact form of the production function, see Exercise 3.10) Therefore, under constant returns and perfectly competitive factor markets, a doubling of human capital (efficiency units of labor) has the same effects on the earnings of an individual as the effect of a doubling of aggregate human capital has on total output This analysis implies that the estimated Mincerian rates of return to schooling can be used to calculate differences in the stock of human capital across countries So in the absence of human capital externalities, a country with 12 more years of average schooling should have a stock of human capital somewhere between exp (0.10 × 12) ' 3.3 and exp (0.06 × 12) ' 2.05 times the stock of human capital of a county with fewer years of schooling This implies that, holding other factors constant, this country should be about 2-3 times as rich as the country with zero 134