Introduction to Modern Economic Growth competencies in the same way as firms invest in their physical capital–to increase their productivity The seminal work by Ted Schultz, Jacob Mincer and Gary Becker brought the notion of human capital to the forefront of economics For now, all we need to know is that labor hours supplied by different individuals not contain the same efficiency units; a highly trained carpenter can produce a chair in a few hours, while an amateur would spend many more hours to perform the same task We capture this notion by thinking that the trained carpenter has more efficiency units of labor embedded in the labor hours he supplies, or alternatively he has more human capital The theory of human capital is very rich and some of the important notions will be discussed in Chapter 10 For now, our objective is more modest, to investigate how including human capital makes the Solow model a better fit to the data The inclusion of human capital will enable us to embed all three of the main proximate sources of income differences; physical capital, human capital and technology For the purposes of this section, let us focus on the continuous time economy and suppose that the aggregate production function of the economy is given by a variant of equation (2.1): (3.13) Y = F (K, H, AL) , where H denotes “human capital” How this is measured in the data will be discussed below As usual, we assume throughout (often implicitly) that A > Let us also modify Assumption as follows Assumption 1’: The production function F : R3+ → R+ in (3.13) is twice continuously differentiable in K, H and L, and satisfies ∂F (K, H, AL) ∂F (K, H, AL) ∂F (K, H, AL) > 0, > 0, >0 ∂K ∂H ∂L ∂ F (K, H, AL) ∂ F (K, H, AL) ∂ F (K, H, AL) < 0, < 0, < 0, ∂K ∂H ∂L2 Moreover, F exhibits constant returns to scale in its three arguments We also replace Assumption with the following: 118