Endogenous growth mode
why were they created ?
They were developed to overcome the failures of solow which are:
1- failure to generate long-run growth
the DMR of K is a key factor that limits the ability of the model to explsin long-run growth & cross country income diffrences
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2- Modest differences in predicted income levels even with large s differences
3- Large differences in implied returns to capital
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AK model
Production fn: Y=AK => y=Ak y grows at the same rate of k => sA-(d+n) / 1+n
Learning-by-doing
Human Capital
R&D
International technology transfer
k'-k= sAk-(d+n)k / (1+n)
- This model has no steady-state hence no intersection between lines
- straight-line reflecting constant returns to scale implying constant growth
- A change in s will have a permeant effect on growth rates faster growth through higher s level
- countries that share the same TFP have the same MRk which is why there is no flow of K from R to P as there is no abundance of K
A higher s > leads to a fall in c in the short-run > more investments & capital accumulation > increase in Y & y > c will always increase once again in the long-run more than the previous level (graph)
Convergence or divergence
if the fundamentals are the same
if the fundamentals are different
AK implies that both will have the same growth rate regardless of their starting point yet they won't meet, will stay parallel
if small but persistent differences in s can explain large gaps in y compounded overtime can later create very large gaps in income (unlinke solow it explains the differnces in income)
when skills / knowledge is accumulated as by-product of the production process
the production fn of AK is problematic since that it ignores N completely
as worker use new K they gain knowledge, developing more efficient ways and improving productivity
when workers learn-by-doing they contribute to a a larger stock of knowldge "poistive spill over" as benfits go beyond firms
Ideas and knowledge are non-rivals can be used without diminishing its value
the model assumes abscence of IP rights over ideas
Production fn: Yi= F(Ki, ANi) DMR to K Y=F(K,λKN)
however,
The spillover cancels out the effect of dimindhing
If K increases by 1% and A by less than this it would imply a diminishing returns & no long-run growth
If K increases by 1% and A by more than 1% this would imply increasing returns to scale which implies endogenous growth
the case of stable is unrealistic and unsupported