1. Serge Coulombe, ECO 6120 1 – The Solow Model: theoretical analysis
Textbook: Economic Growth second edition by Robert J. Barro and Xavier Sala-i-Martin, MIT Press, 2004.
1 – The Solow Model: theoretical analysis
Macro and economic growth
Endogenous growth
`Growth empirics
Economic development
Basic model of economic growth
Model of capital accumulation
`One good model

2. Key exogenous variables: s, x, n, δ
The Solow (1956) Model
Key exogenous variables: s, x, n, δ
Saving (investment) is a fixed proportion of output sY
Population (labour force) growing at rate n: L(t)=L(0)ent
Exogenous technological progress: A(t)=A(0)ext
Focus on the dynamics of capital accumulation:

3. A concave production function

4. Inada conditions

5. The production function
y=f(k)
f(k)
The production function k
Decreasing slope

7. Cobb-Douglas

8. The evolution of the Capital/Labour ratio

9. The dynamics of capital accumulation
Since:

10. (n+x+δ)k
sf(k) k k1 k* k2
If k=k1, sf(k1) > (n+x+δ)k1, Δk > 0
If k=k2, sf(k2) < (n+x+δ)k2, Δk < 0

12. Phase diagram in the Solow modelk* k

13. The steady-state k*: sf(k*)=(n+x+δ)k*
Investment per unit of effective worker
(n+x+δ)k
sf(k) k k*
The steady-state k*: sf(k*)=(n+x+δ)k*

14. Effect of an increase in the savings rate, s(1)>s(0)
Investment per unit of effective worker
(n+x+δ)k
s(1)f(k)
s(0)f(k) k
k(0)
k(1)
Effect of an increase in the savings rate, s(1)>s(0)

15. s t t k t
t(0)

16. ln(Y/L) t c t
t(0)

17. Since On steady state: Δk* = 0
The golden rule
Since On steady state: Δk* = 0
C* is maximized at dc*/dk*=0, then:

18. Golden rule in the Solow Model
f(k*)
f’(k*)
(n+x+δ)k*
c*max k*
k*gold

21. Effect of a decrease in population growth, n(1) < n(0)
Investment per unit of effective worker
(n(0)+x+δ)k
(n(1)+x+δ)k
sf(k) k
k(0)
k(1)
Effect of a decrease in population growth, n(1) < n(0)