Growth with Externalities (Romer
(1986a) Model)
In this model Romer has
introduced the technological spillover as the engine of economic growth.
Preferences and Technology
Consider an economy with zero
population growth. Also assume that the production side of the economy consists
of a set [0,1] of firms.
The production function of
each firm is
Where K and L denote the capital and
labour rented by a firm i.
Labour augmenting technology
A(t) is common to all the firms and does not vary with i.
Also
for all t, where L is constant level of labour.
Firms are competitive in all markets and
factor price are given by the marginal products.
The key assumption of Romer (1986a) is
that although firms take A(t) as given, this stock of technology (knowledge)
advances endogenously for the economy as a whole. This takes place because of
physical capital spillover across firms.
Romer assumes that A(t) grows
continuously as
A(t) = BK(t) ………….(2)
So that knowledge stock of the economy
in proportion to its capital stock.
Substituting the value of equation 2 In
1 we get.
Y(t) = F(K(t), BK(t)L)
As the above equation is homogeneous of
degree 1 we get,
Where k(t) = K(t)/L is the capital
labour ratio in the economy.
So, marginal products and factor price
can be expressed as
Equilibrium
A competitive equilibrium is defined
similarly to that in the neoclassical growth model. But in this model knowledge
spillover (equation 2) is external to each firm. Equilibrium factor prices are
given by equation 3 and 4.
Since the market rate of return r(t) = R(t)-
δ is also constant.
Then the consumption must grow at the
given rate of
This also clears that that capital and
output grows at the same rate of consumption.
Hi. I’m Vivek Sharma. I do write Blog on different issues and topics related to Economy, Exams and Political issues. Inspired to make things looks better.
Well elaborated thank you very much.
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