Introduction to Modern Economic Growth which defines mi (t) as the current income of individual i at time t consisting of labor earnings, w (t) hi (t), and asset income, R (t) bi (t − 1) (we use m rather than y, since y will have a different meaning below) The production side of the economy is given by an aggregate production function Y (t) = F (K (t) , H (t)) , that satisfies Assumptions and 2, where H (t) is “effective units of labor” or alternatively the total stock of human capital given by, Z hi (t) di, H (t) = while K (t), the stock of physical capital, is given by Z K (t) = bi (t − 1) di Note also that this specification ensures that capital and skill (K and H) are comple- ments This is because a production function with two factors and constant returns to scale necessarily implies that the two factors are complements (see Exercise 10.7), that is, ∂ F (K, H) ≥ ∂K∂H Furthermore, we again simplify the notation by assuming capital depreciates fully (10.29) after use, that is, δ = (see Exercise 10.8) Since the amount of human capital per worker is an endogenous variable in this economy, it is more useful to define a normalized production function expressing output per unit of human capital rather than the usual per capita production function In particular, let κ ≡ K/H be the capital to human capital ratio (or the “effective capital-labor ratio”), and Y (t) H (t) ả K (t) = F ,1 H (t) = f (κ (t)) , y (t) ≡ where the second line uses the linear homogeneity of F (·, ·), while the last line uses the definition of κ Here we use κ instead of the more usual k, in order to preserve 482