Introduction to Modern Economic Growth (and the earnings capacity) of each individual is a function of his or her years of schooling For example, ignoring other determinants of wage earnings, we can write ˜ (Si ) the wage earnings of individual i is a function of his or her schooling as wi = φ ˜ function is identical across countries and can The first key assumption is that this φ ˜ (Si ) ≈ exp (φSi ) so that be approximated by an exponential function of the form φ we obtain equation (3.24) The reasons why this may be a reasonable assumption will be further discussed in Chapter 10 Second, we need to assume that there are no human capital externalities– meaning that the human capital of a worker does not directly increase the productivity of other workers There are reasons for why human capital externalities may exist and some economists believe that they are important This issue will also be discussed in Chapter 10, where we will see that human capital externalities are unlikely to be very large Thus it is reasonable to start without them The key result which will enable us to go from the microeconometric wage regressions to cross-country differences is that, with constant returns to scale, perfectly competitive markets and no human capital externalities, differences in worker productivity directly translate into differences in income per capita To see this, suppose that each firm f in country j has access to the production function yf j = Kf1−α (Aj Hf )α , where Aj is the productivity of all the firms in the country, Kf is the capital stock and Hf is effective units of human capital employed by firm f Here the CobbDouglas production function is chosen for simplicity and does not affect the argument Suppose also that firms in this country face a cost of capital equal to Rj With perfectly competitive factor markets, profit maximization implies that the cost of capital must equal its marginal product, ả Kf (3.25) Rj = (1 − α) Aj Hf This implies that all firms ought to function at the same physical to human capital ratio, and consequently, all workers, irrespective of their level of schooling, ought to work at the same physical to human capital ratio Another direct implication of competitive labor markets is that in country j, wages per unit of human capital will 133