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IV. Long run analysis
Chap 10-12
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What to read for
– What determines long-run growth?
– What is the role of capital accumulation?
– What is the role of technological progress?
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IV.a Growth – stylized facts (chap 10)
• Focus on growth, not short-run output fluctuations
• Growth = steady increase in per capita income
• Why care about growth? – Because it is indispensable for
increasing the
population’s living standards (reducing poverty)
• Historical trends: there has been a large increase in living
standards over the last decades. – Note, however, that income is
related but not
identical to ‘happiness’
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Long-term growth in the US
(Logarithmic scale on the vertical axis).
Aggregate U.S. output has
increased by a factor of 42
since 1890.
U.S. GDP Since 1890
Figure 10 - 1
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10000
20000
30000
40000
50000
1940 1950 1960 1970 1980 1990 2000 2010 2020
US GDP per capita (constant 2005 $)
0
2000
4000
6000
8000
10000
12000
14000
16000
1940 1960 1980 2000 2020
US GDP $ billionnominal
US GDP billion,constant 2005 $
From 1950-2010 - Nominal GDP increased
by a factor of 49 - Real GDP increased by a
factor of 6.5 (due to inflation)
From 1950-2010, - Real per capita GDP
increased by a factor of 3.2
Note: - Inflation increase: 7.58 - Population increase: 2.04 -
So nominal GDP increase =
3.2*2.04*7.58 = 49
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-4
-2
0
2
4
6
8
10
12
1947-01-01 1960-09-09 1974-05-19 1988-01-26 2001-10-04
Inflation (GDP deflator), quarterly (year-on-year % change)
Source:
http://research.stlouisfed.org/fred2/series/GDPDEF/downloaddata?cid=21
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
1960 1970 1980 1990 2000 2010
CPI inflation, annual (%)
Source: U.S. Dept. of Labor, Bureau of Labor Statistics.
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Growth and Happiness
Happiness and Income per Person across Countries Figure 1
Low income – high happiness
High income – high happiness
Low income – low happiness
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Convergence…
• There has been convergence of incomes among rich
countries;
• Also some convergence among Asian countries;
• but little convergence among other developing countries.
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Cross-country growth – conditional convergence
There is no clear relation
between the growth rate of per
person output since 1960 and
the level of output per person in
1960.
Growth Rate of GDP per Person since 1960 versus GDP per Person
in 1960 (2000 dollars) for 70 Countries
Figure 10 - 3
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Sources of growth:
– From increase in factors of production
– But there are diminishing returns to scale
– Long-run growth requires technological progress and increase
in productivity;
• capital accumulation alone cannot sustain growth in the long
run
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•The aggregate production function depends on the state of
technology. The higher the state of technology, the higher the
output for a given level of K and N.
Y F K N ( , )
The Aggregate Production Function
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•Decreasing returns to capital: increases in capital, given
labor, lead to smaller and smaller increases in output.
•Decreasing returns to labor: increases in labor, given capital,
lead to smaller and smaller increases in output.
Returns to Scale and Returns to Factors
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•Constant returns to scale imply that we can rewrite the
aggregate production function as:
Output per Worker and Capital per Worker
Y
NF
K
N
N
NF
K
N
, ,1
The amount of output per worker, Y/N, depends on the amount of
capital per worker, K/N.
As capital per worker increases, so does output per worker; but
output per worker increases at a decreasing rate: diminishing
returns to capital.
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Output per Worker and Capital per Worker
Increases in capital per worker
lead to smaller and smaller
increases in output per worker.
Output and Capital per Worker
Figure 10 - 4
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Suggested practice exercises
• Chapter 10: 3, 4, 7
