Introduction to Modern Economic Growth where the instantaneous utility function u (·) satisfies Assumption and ρ > We ignore technological progress and population growth to simplify the discussion Labor is again supplied inelastically We follow the specification in Chapter and assume that the aggregate production possibilities frontier of the economy is represented by the following aggregate production function: Y (t) = F (K (t) , H (t) , L (t)) , where K (t) is the stock of physical capital, L (t) is total employment, and H (t) represents human capital Since there is no population growth and labor is supplied inelastically, L (t) = L for all t This production function is assumed to satisfy Assumptions 1’ and 2’ in Chapter 3, which generalize Assumptions and to this production function with three inputs As already discussed in that chapter, a production function in which “raw” labor and human capital are separate factors of production may be less natural than one in which human capital increases the effective units of labor of workers (as in the analysis of the previous two sections) Nevertheless, this production function allows a simple analysis of neoclassical growth with physical and human capital As usual, it is more convenient to express all objects in per capita units, thus we write Y (t) L = f (k (t) , h (t)) , y (t) ≡ where K (t) H (t) and h (t) ≡ L L are the physical and human capital levels per capita In view of Assumptions 1’ k (t) ≡ and 2’, f (k, h) is strictly increasing, continuously differentiable and jointly strictly concave in both of its arguments We denote its derivatives by fk , fh , fkh , etc Throughout, we assume that physical and human capital are complementary, that is, fkh (k, h) > for all k, h > We assume that physical and human capital per capita evolve according to the following two differential equations (10.20) k˙ (t) = ik (t) − δ k k (t) , 475