Geography, Health, and Demo-Economic Development

5. Firms and the Macro-Economy

A large number of firms produces with a constant returns to scale technology using capital K ,
human capital, and land, X . Human capital is given by the number of young adults, L, times
their human capital endowment, h. Supply of land is fixed, technological progress is exogenous,
and the production function is of Cobb-Douglas type and the same as in Galor and Weil (1998).

Yt = At K (L_ih t)^α(^1-β)X(1^-α)(1^-β) ,  0 <α ≤ 1,0 <β< 1 ,            (12)

where A denotes the level of general productivity. The parameter α measures the importance of
arable land. If α = 1, land plays no role in production. According with the empirical evidence we
assume that arable land per capita is of limited supply (particularly in geographically unfavorable
regions) and decreases with population growth (see the evidence cited in Sachs et al., 2004).

Factors are paid according to their marginal product. The interest rate is given by the world
market. Substituting (12) into r = βY∕K, solving for K, and re- substituting into (12), provides
Y_t = A_t(L_th_t)^αX^1-α where A_t ≡ A1^/(1^—β) (в/г)^в/(1—β). Labor income per adult is obtained as
y_t = α(1 — β)Y_t∕L_t, or after substituting Y_t and normalizing land to one as

yt = α(1 — β)AtLα^-1hα .                                (13)

Assume now that human capital endowment of the current work force depends positively on
child expenditure of their parents, h_t+₁ = f (h_t). Because the number of workers depends on
fertility of their parents (and child survival rates at that time), and both fertility and child
expenditure depend on income, equation (13) provides the link between generational income
levels. Next generation’s income is given by

yt+1 = α(1 — β)(1+ gA)At [(1 + gL(yt)) ∙ Lt]^α- 1 ∙ [f (h(∏(yt)))]^α   .

Justified by the focus of analysis on developing economies we assume that productivity grows at
an exogenously given rate gA. Let xt ≡ At∕L_t^1-α define a labor supply adjusted measure of pro-
ductivity and let us for notational convenience assume that human capital expenditure of parents
relates one-to-one to human capital endowment of their children, ht+1 = h_t. Macroeconomic

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