Economic growth and economic development 496

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 necessari

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 1 and 2, where H (t) is “effective units of labor” or alternatively the total stock of human capital given by,

H (t) =

Z 1 0

hi(t) di, while K (t), the stock of physical capital, is given by

K (t) =

Z 1 0

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,

2F (K, H)

Furthermore, we again simplify the notation by assuming capital depreciates fully after use, that is, δ = 1 (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 func-tion In particular, let κ ≡ K/H be the capital to human capital ratio (or the

“effective capital-labor ratio”), and

y (t) ≡ H (t)Y (t)

= F

µ

K (t)

H (t), 1

¶

= f (κ (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

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