MACROECONOMICS
Chapter 8
Economic Growth II:
Technology, Empirics, and
Policy
Outline of the Chapter
1.
2.
3.
4.
Including technological change into
Solow Model.
Testing the model with data.
Discussing policy options to improve the
standard of living.
New growth theories.
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Including Technological Progress

Suppose technology is labor-augmenting.
It increases efficiency of labor.
 It increases the “effective” number of workers.
 Y = F(K,LE)


Example
Y = Kα(LE)1-α
 y = kα
where y = Y/LE and k = K/LE

3
What Does E Include?
Knowledge
 Health
 Education
 Institutions that promote growth of
production

4
Long Term Growth of E
If efficiency of labor (E) doubles in 35
years, E must be growing at annual rates
of 2%.
 If E doubles in 10 years, annual growth
rate is 7%.
 The growth rate of E, labeled g, will be
given outside of the system (exogenous)
in our analysis.

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Long Term Growth of LE

If E grows at rate g and population grows
at rate n, then LE must grow at rate g+n.


%Δ(LE) = %ΔL + %ΔE
If LE grows by n+g, then, once the
economy reaches the steady state (k*), K
must also grow by n+g to keep it at that
level.
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Steady State

Steady State k was the level of k, once reached,
remained there.

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

No increase or decrease of k takes place once that
equilibrium (k=k*) is reached.
Accumulation of k depends on investments
being larger than the depreciation plus n+g.
sf(k*) = (δ+n+g)k*
If savings (=investments) are larger than
(δ+n+g)k, k will increase; smaller: decrease.
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Steady State and Golden Rule
y
y= (Y/LE)
(δ+n+g)k
sy
k = (K/LE)
k
k*
k
8
Steady State and Golden Rule
y
y= (Y/LE)
(δ+n+g)k
sy
c*
s*y
k = (K/LE)
k*
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Growth Rates in Steady State
In steady state, k=k* and y=y*.
 k=K/LE implies that at steady state, in
order to keep k constant, K must increase
at rate n+g while k (capital per effective
worker) remains constant.
 y=Y/LE implies that to keep y=y*, Y must
grow at rate n+g.
 Per capita income must grow at g; capitaloutput ratio constant.

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Steady State and Golden Rule

Steady State:
sf(k*)=(δ+n+g)k*
 f(k*)-c*=sf(k*)
 c*=f(k*)-(δ+n+g)k*

But, the slope of f(k) at Golden Rule is
(δ+n+g) which is the definition of MPK.
 If the economy is at Golden Rule Steady
State, then MPK (=real rental price of
capital) must be equal to δ+n+g.

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Steady State
If long run growth of real GDP is 4% with
population growth of 1% and technology
growth of 3%, then we fulfill the
requirements of steady state.
 If Y grows at 8% with 2% population
growth and 3% technology growth we are
not at steady state. (See slide #8)

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Further Implications

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Constant returns to scale yields:
L(MPL)+K(MPK)=Y
Y growth is n+g
L growth is n
K growth is n+g
MPL growth must be g and MPK growth must be
zero.
US data show g=2% with MPL growth 2% and
MPK constant!
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Is U.S. at Golden Rule?
Given
n = 0.01
g = 0.02
δk = 0.1y
k = 2.5y
MPK(k) = 0.3y
( MPK )( k )

k
MPK 
0 .3 y
2 .5 y
0 .3
2 .5
k
k

0 .1 y
2 .5 y
  0 . 04
MPK  0 . 12
MPK    n  g
0 . 12  0 . 04  0 . 01  0 . 02
MPK will become smaller as k increases. In order for
k* to be a higher number, s has to increase.
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Endogenous Growth Models
Knowledge does not have diminishing
returns, and it has positive externalities.
 Once included in the production function, it
eliminates the k* steady-state property.
 Production function can be straight line
(Y=AK) or increasing slope (as E grows
fast in Y=F[K,(1-u)LE]).

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Endogenous Growth Models
As long as capital accumulation takes place, there is no
end to growth of income.
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Convergence or Divergence

Same production function, same s, g, n, δ.
Convergence, even if they start at different k.
 Production function might be connected to
urbanization.


Same production function, different s, g, n,
δ.
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Divergence
Different production functions: divergence
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Similarities

Production efficiency (E) and factor
accumulation (LE) and K seem to correlate
(go hand in hand).
Maybe an efficient economy promotes capital
accumulation.
 Maybe there are positive externalities to
capital: more savings, better production
function.
 Maybe better institutions and policies affect
both.

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http://www.economist.com/specialreports/
displayStory.cfm?story_id=14530093
The economy can grow faster than
normal for a period until it reaches the point where
it would have been without the crisis, when it
reaches its full potential again. (Friedman)
If the shortfall in demand persists it can
do lasting damage to supply, reducing the level of
potential output (scenario 2) or even its rate of
growth (scenario 3). If so, the economy will never
recoup its losses, even after spending picks up
again.
In a recession firms shed labor and
mothball capital. If workers are left on the shelf too
long, their skills will atrophy and their ties to the
world of work will weaken. When spending revives,
the recovery will leave them behind. Output per
worker may get back to normal, but the rate of
employment will not.
World Economic Outlook: cost of 88 banking crises over the past four decades. On
average, seven years after a bust an economy’s level of output was almost 10%
below where it would have been without the crisis.
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Does Free Trade Promote Growth?
Compare countries ranked according to
openness with growth.
 Study the impact of openness on growth.
 Instead of trade, look at geography. It is
an instrumental variable that correlates
with trade but does not correlate with other
variables that enhance growth.

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