Endogenous Determination of FDI Growth and Economic Growth:The OECD Case

Y=F(K^*,N)
where Y is output, K ^* is total physical stock available in the domestic economy, and N is
labor stock. The optimization conditions for the representative firm entail equality between
the marginal products and the factor prices:

f '( k *) = r

f ( k *) - k * f ′( k *) = w

In (4), k ^* is capital per person that exists in a domestic country at a particular time, w is the
real wage rate, and r is the world’s real rate of interest. Capital accumulation function for the
domestic resident is

(5)

where k is capital per person owned by domestic residents, n is the population growth rate,
c is the consumption. If we substitute for w from equation (4b) and for r from equation (4a)
into equation (1), the change in assets per capita can be determined as

k^& = f (k^*)-r(k^* -k) -nk -c

k ^* - k represents the sum of foreign investments per capita in the domestic country and
without loss of generality, we assume that k^* -k > 0. Note from equation (6) that it would
become the standard equation of motion of Ramsey if the economy were closed, k^* -k = 0.
The difference between equation (6) and the macroeconomic budget constraint of Ramsey
model is that the domestic economy is incurring rental cost for the total foreign capital that
t

came in until time t . By definition, it must be true that k^* - k = ∫ FDIdt , where FDI is the
0

physical capital inflow from abroad at time t . If we take time derivative of this identity, we
obtain that k^{& *} - k^& = FDI . Hence, we may alternatively express equation (6) as follows:

k^&* = f(k^*)-r(k^*-k)-nk-c+FDI

* . ʃz,^ ɪ,             ɪ У y y .   _ У   f '( k ɔ k * ^    ₁ ,ʌʌɪ-

Given that y = f (k ), the growth rate of output is g = — =   —*--*. Substituting

y                     f(k^*) k^*

_k&^*

respective value of — from (7), we may express growth rate of output as
k^*

= f '(^k∙)^k∙ Γfτ.__r (k*-k) _-nk_- c_ ₊ fd_l

^gy        Z∕J*∖        7*      '      7* n 7* 7*      7*

f ( k )    k k k k k

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