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Lecture 15
Solow Growth Model
Last Time
This Time
Contributions to GDP Growth
∆Y/Y = ∆A/ A + α·(∆ K/K) + β·(∆ L/L)

OR:

The growth rate of real GDP, ∆Y/Y, equals
the growth rate of technology, ∆ A/A, plus the
contributions from the growth of capital,
α·(∆K/K), and Labour, β ·(∆L/L).
Solow Growth Model

 Each household divides up its real income in a fixed
 proportion s to saving and 1 − s to consumption
 ( C ).
 Capital depreciate at the same constant rate δ
δ K is the amount of capital that depreciates each
year

                         5
Solow Growth Model
Labour force, L = ( Labour force/ population)
· population

Labour-force participation rate

Assume Labour force participation rate is constant.

Labour force growth rate is the population growth
rate: n.
Solow Growth Model
Model ignores:
Government
No taxes, public expenditures, debt, or money
International Trade
No trade in goods or financial assets
Solow Growth Model
Assume ∆A/A = 0

∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L)

The growth rate of real GDP is a weighted
average of the growth rates of capital and
Labour.
Solow Growth Model
Y=C+I
Real GDP = consumption + gross investment

Y− δ K = C + ( I − δ K)
Real NDP = consumption + net investment
Solow Growth Model
• Real saving =        s                       ·       (Y − δK)

• Real saving = (saving rate) · (real income)




                  Macroeconomics - Barro   Chapter 3         10
Solow Growth Model

• Y− δ K     =               C                + s· ( Y− δ K)

• Real income = consumption + real saving




                 Macroeconomics - Barro   Chapter 3      11
Solow Growth Model
 C+ s· ( Y− δ K) = C+ I − δ K

             or

   s· ( Y− δ K) = I − δ K
Real saving = net investment
Solow Growth Model
∆k/k = s·(y/k) − sδ − n

∆y/y = α·(∆k/k)

∆y/y = α·[ s·( y/k) − sδ − n]
Solow Growth Model
steady state.
When k = k∗, ∆k/k equals zero.
∆k/k = 0, k stays fixed at the value k∗.


                    y* = f(k*)
Solow Growth Model
In the steady state, ∆ k/k equals zero.
s· ( y*/ k*) − sδ − n= 0

s·( y* − δ k*) = nk*

Steady-state saving per worker = steady-
state capital provided for each new worker
Example
Mathematica
Beatriz Orestra’s Story
Ec4004 2008 Lecture15 Ss
––Beatriz Orresta
quot;You know, we're not used to this, not
having enough food,quot; said Orresta, with a
hint of embarrassment in her voice.
She paused, and began to weep.
quot;You can't know what it's like to see your
children hungry and feel helpless to stop
it,quot; she said.
quot;The food is there, in the grocery store,
but you just can't afford to buy it
anymore. My husband keeps working, but
he keeps bringing home less and less. We
never had much, but we always had food,
no matter how bad things got. But these
are not normal times.quot;
                    ––Beatriz Orresta
Next Time
Read Barro, chapters 4 and 5

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Ec4004 2008 Lecture15 Ss

  • 4. Contributions to GDP Growth ∆Y/Y = ∆A/ A + α·(∆ K/K) + β·(∆ L/L) OR: The growth rate of real GDP, ∆Y/Y, equals the growth rate of technology, ∆ A/A, plus the contributions from the growth of capital, α·(∆K/K), and Labour, β ·(∆L/L).
  • 5. Solow Growth Model Each household divides up its real income in a fixed proportion s to saving and 1 − s to consumption ( C ). Capital depreciate at the same constant rate δ δ K is the amount of capital that depreciates each year 5
  • 6. Solow Growth Model Labour force, L = ( Labour force/ population) · population Labour-force participation rate Assume Labour force participation rate is constant. Labour force growth rate is the population growth rate: n.
  • 7. Solow Growth Model Model ignores: Government No taxes, public expenditures, debt, or money International Trade No trade in goods or financial assets
  • 8. Solow Growth Model Assume ∆A/A = 0 ∆Y/Y= α·(∆K/K) + (1−α)·(∆L/L) The growth rate of real GDP is a weighted average of the growth rates of capital and Labour.
  • 9. Solow Growth Model Y=C+I Real GDP = consumption + gross investment Y− δ K = C + ( I − δ K) Real NDP = consumption + net investment
  • 10. Solow Growth Model • Real saving = s · (Y − δK) • Real saving = (saving rate) · (real income) Macroeconomics - Barro Chapter 3 10
  • 11. Solow Growth Model • Y− δ K = C + s· ( Y− δ K) • Real income = consumption + real saving Macroeconomics - Barro Chapter 3 11
  • 12. Solow Growth Model C+ s· ( Y− δ K) = C+ I − δ K or s· ( Y− δ K) = I − δ K Real saving = net investment
  • 13. Solow Growth Model ∆k/k = s·(y/k) − sδ − n ∆y/y = α·(∆k/k) ∆y/y = α·[ s·( y/k) − sδ − n]
  • 14. Solow Growth Model steady state. When k = k∗, ∆k/k equals zero. ∆k/k = 0, k stays fixed at the value k∗. y* = f(k*)
  • 15. Solow Growth Model In the steady state, ∆ k/k equals zero. s· ( y*/ k*) − sδ − n= 0 s·( y* − δ k*) = nk* Steady-state saving per worker = steady- state capital provided for each new worker
  • 20. ––Beatriz Orresta quot;You know, we're not used to this, not having enough food,quot; said Orresta, with a hint of embarrassment in her voice. She paused, and began to weep. quot;You can't know what it's like to see your children hungry and feel helpless to stop it,quot; she said.
  • 21. quot;The food is there, in the grocery store, but you just can't afford to buy it anymore. My husband keeps working, but he keeps bringing home less and less. We never had much, but we always had food, no matter how bad things got. But these are not normal times.quot; ––Beatriz Orresta
  • 22. Next Time Read Barro, chapters 4 and 5