Macroeconomics - The Solow growth model

The central question in economics of development: why this country have developed more than the others. what thing need to growth in country?

With resources in economy, how do we exploit to fast growth and sustainable growth ?

The first, we consider the solow model. It's a basic and fundamental model for almost all analyst of growth.

Assumptions of model:

---- the economy is big enough that the gains form specialization have been exhausted. That mean when we change factors multiply c them then output will rise c. F(cK,cAL)= cF(K,AL)

---- Only 3 important factors: Capital (K), Labor (L), Knowledge (A).

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The static model :

we have a function of output: Y = F ( K, AL ). That's call : labor-augmenting or Harrod-neutral. ( we have 2 other models. The Capital augmenting model Y= F(KA,L) and the Hicks-neutral model Y=A.F(K,L) )

This model is sastify 2 assumptions above. We will consider what happen with this model.

Use Cobb-Douglass function:

F(K,AL) = K^alpha . (AL)^ (1-alpha)

The dynamic model :

We consider what happen if factors change ???

with X`(t) is shorthand for derivative of X or dX(t)/d(t)

Labor and Knowledge is exogenuous variables

We have:

finally

Or:

 k'(t) = s.f(k(t)) - (g+n+@).k(t)

That's key equation of the Solow model

We consider the growth rate of economy:

Come back with key equation of model:

when k converge k* ( k* is condition s.f(k(t)) = (g+n+@)k(t)). 

==> f'(k*) = 0. k is constant require K'/K = A'/A + L'/L = g+n 

==> the growth rate equal (g+n)

If we consider the growth per labor rate: (Y/L)'/(Y/L) = alpha. (K/L)'/(K/L) + (1-alpha). A'/A = g