Intermediate Macroeconomics
Lecture 6
Economic Growth
Goal
? Develop the Solow Growth Model
--- How much of the economy’s output
should be consumed today and how much
should be saved for the future?
? Static analysis (Ch,3) ? Dynamic
The Accumulation of Capital
1,The supply for goods
Production function,
Characteristics,CRS
Per Capita ---
(,)Y F K L?
(,)a Y F a K a L?
(,1 )YKFLL?
()y f k?
The Accumulation of Capital
? The production function
y
k
y=f(k)
y?
k?
y M PK
k
? ?
?
The Accumulation of Capital
2,The demand for goods
--- Solow model assumes that the demand for
goods comes from consumption and investment
only,
y c i??
(1 )c s y?? ? ()i s y s f k??
The Accumulation of Capital
3,The steady-state level of capital
y
k
y=f(k)
i=sf(k) y
c
i
The Accumulation of Capital
? Change in capital stock
k i k?? ? ?
y=f(k)
y
k
i=sf(k)
k?
k*
The Accumulation of Capital
? Steady-state
?
?
?
0k i k?? ? ? ?
**ik ??
( * ) *s f k k??
The Accumulation of Capital
? Example,Cobb-Douglas function
Steady state,
1 / 2 1 / 2Y K L?
yk?
**s k k??
2
2*
s
k
?
?
The Accumulation of Capital
? s=0.15,=0.05,k=1 ? k*=9 ?
k y c i n v, de p,c h a n g e i n k
1 1 1 0.85 0.15 0.05 0.1
2 1.1 1.05 0.89 0.16 0.055 0.1023213
3 1.202 1.1 0.93 0.16 0.06 0.1043596
4 1.307 1.14 0.97 0.17 0.065 0.1061312
…
50 5.76 2.4 2.04 0.36 0.288 0.0719967
100 7.987 2.83 2.4 0.42 0.399 0.0245709
…
9 3 2.55 0.45 0.45 0
The Accumulation of Capital
? s=0.15,=0.05,k=16 ? k*=9
?
k y c i n v, de p,c h a n g e i n k
1 16 4 3.4 0.6 0.8 -0.2
2 15.8 3.97 3.38 0.6 0.79 -0.193762
3 15.61 3.95 3.36 0.59 0.78 -0.187741
4 15.42 3.93 3.34 0.59 0.771 -0.181929
…
50 10.86 3.3 2.8 0.49 0.543 -0.048763
100 9.52 3.09 2.62 0.46 0.476 -0.013192
…
9 3 2.55 0.45 0.45 0
The Accumulation of Capital
? Steady-state level of capital has nothing
to do with the starting level of capital,
Things that matter are,
--- the savings rate (s)
--- the depreciation rate
--- the technology (production function f)
The Accumulation of Capital
? Explain why Japan has a higher standard of
living (output level per capita) comparing to
similar countries?
? Try to explain high growth periods after
World War II in Japan and Germany,as well
as after 1978 in China,
? If there is no change in s,or,or f,new
steady state level of y and k are the same as
before
?
The Accumulation of Capital
? Increase in the savings rate (s)
y
k
i=sf(k)
k?
y=f(k)
The Accumulation of Capital
? Increase in depreciation rate ( )
y
k
i=sf(k)
k?
y=f(k)
?
The Golden Rule Level of
Capital
? Higher s ? higher k ? higher y
? However,individuals do NOT care about k or
y but the amount of goods/services they can
consume,
? The steady state with the highest
consumption is called,the golden rule
level of capital accumulation.”
The Golden Rule Level of
Capital
? From the Solow model
?
? At the steady state,
? Choose k* to maximize c*
y c i?? c y i??
* * *c y i??
* ( * ) *c f k k???
'( * * )fk ??
The Golden Rule Level of
Capital
? What if k* < k**?
y
k
i=sf(k)
k?
y=f(k)
k** k*
Policy makers increase s in order to increase k*
The Golden Rule Level of
Capital
? The transition path
c
i
y
Increase s
The Golden Rule Level of
Capital
? What if k* > k**? y
k
i=sf(k)
k?
y=f(k)
k**
Policy makers increase s in order to increase k*
k*
The Golden Rule Level of
Capital
? The transition path
c
i
y
Decrease s
Summary
? Solow growth model
1,Supply for goods and production fn,
2,Demand for goods and consumption fn,
3,The steady-state level of k
4,The Golden Rule level of k
5,Transition path from one steady state to
the Golden Rule steady state