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CLASS #18: THE SOLOW GROWTH MODEL
- Modeling growth: the Solow growth model.
- Convergence toward the steady state in the Solow growth model ... or
``the last will be first''.
- The Solow growth model with population growth.
Mechanics of the Solow growth model.
Assumptions:
- Closed economy:
- Cobb Douglas production function
- Saving (hence Investment) is a constant fraction s of output:
It=sYt
- Total factor productivity (A) is constant.
- For the time being, population is constant:
Nt=N
.
From the definition of investment:
Divide both sides by N and obtain:
or
kt+1=f(kt).
This is a non-linear difference equation: strange object! Let us study the
function
:
1) f(0)=0
2)
3)
,
4)
,
5)
- Steady state per capita level of capital k*.
- Convergence to k* from any level of capital.
- A steady state per capita level of capital implies a steady state
level of output
:
the economy eventually stops growing.
- What does the steady state depend upon?
- How fast do you reach the steady state?
Consider population growth at a rate
:
divide both sides of
by Nt and obtain:
or
- The steady state per capita level of capital is lower:
- because of population growth, you have
to provide capital for the newborn, and that capital depreciates.
- Again, convergence to k* from any level of capital;
and again, a steady state per capita level of capital implies a steady state
level of output
:
the economy eventually stops growing.
- The new steady state is:
and depends:
- positively on the saving rate s, and A;
- negatively on depreciation and population growth (remember the
empirical regularities about growth);
This model does not explain sustained growth - in the next class we will introduce technological progress.
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Marco Del Negro
2000-02-28