Download Facts of Growth

Growth: the steady increase in aggregate
output over time.
U.S. GDP Since 1890
Aggregate U.S. output has
increased by a factor of 42
since 1890.
The logarithmic scale on the vertical axis allows for the
same proportional increase in a variable to be represented
by the same distance.
Measuring Standard of Living: Per capita Purchasing
Power Parity GDP in “International Dollar Prices”
 Each country’s outputs in US prices
Translating a country’s GDP into dollars at the current exchange
rate of its currency does not work for two reasons:
 Exchange rates can vary a lot
•
The country will seem affluent one year, destitute in another year
 The lower a country’s output per capita, the lower the prices of
food and basic services in that country
•
•
You don’t need that many dollars to live well in Ecuador
The price of a Big Mac is low in Quito because Ecuadoran
hamburger flippers aren’t paid much
Income and Happiness: Stay tuned for Carol Graham
Happiness and Income per Person across Countries
3 of 26
The Facts of Growth – The
Very Long Run
On the scale of human history, the growth of output per capita is a
recent phenomenon.
Looking across two millennia
• From the end of the Roman Empire to 1500, no output per
capita growth in Europe
• 1500-1700 -- Small growth in output per capita (0.1%/year and
0.2%/year 1700 to 1820)
• 1820-1950 -- Modest growth (U.S. = 1.5%)
• The high-growth of the 1950s and 1960s is unusual
• Leaders in output/capita change over the centuries:
Italy  Netherlands  U.K.  US
Growth in Rich Countries since 1950
The Convergence of Output per Person since 1950
Growth Rate of GDP per
Person since 1950
versus GDP per Person
in 1950, OECD Countries
Countries with initially lower levels of
output per person have typically grown
faster.
• Turkey, Greece, New Zealand are off
of the frontier
Looking at Growth Across Many Countries
Growth Rate of GDP per
Person since 1960
versus GDP per Person
in 1960 (2000 dollars) for
70 Countries
There is no clear relation between
per person the growth rate of
output since 1960 and the level of
output per person in 1960.
• Torture the data and you’ll find
“conditional convergence,” e.g.,
conditional on initial educational
attainment
The Aggregate Production Function
The aggregate production function is the relation between aggregate output
and the inputs in production.
Y  F ( K, N )
Y = aggregate output.
K = capital—the sum of all the machines, plants, and office buildings
in the economy.
N = labor—the number of workers in the economy.
The aggregate production function F: how much output is produced
for given quantities of capital and labor
The aggregate production function depends on the state of technology.
The higher the state of technology, the more output for a given inputs of
K and N.
Returns to Scale and Returns to Factors
Constant returns to scale: if the quantities of capital and labor are doubled—
then output will also double. You can replicate what you’re doing well.
2Y  F (2 K ,2 N )
Or more generally, for any number
x,
xY  F ( xK , xN )
Decreasing returns to capital: increases in capital, given labor, lead to
smaller and smaller increases in output as the level of capital increases.
• The same worker using bigger and bigger shovels will dig deeper and
faster... but the hole won’t increase in proportion to the increased sizes of
shovels.
Decreasing returns to labor: increases in labor, given capital, lead to smaller
and smaller increases in output as the level of labor increases.
• More and more workers staffing the same hotel front desk will process
increasing numbers of guests...but not in proportion to the increase in
workforce.
Output per Worker and Capital per Worker
Constant returns to scale implies that we can rewrite
the aggregate production function as:
Y
 K N
K 
 F  ,   F  ,1
 N N
N 
N
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 with decreasing returns to capital, output won’t increase in
proportion to the increase in capital.
Output per Worker and Capital per Worker
 Increases in output per
worker (Y/N) can come
from increases in capital
per worker (K/N).
 Accumulation of capital
depends on saving
exceeding depreciation.
 Or increases in Y/N can
come from improvements
in technology that shift
the production function,
F, and lead to more
output per worker given
capital per worker.
 Because of decreasing
returns to capital, capital
accumulation by itself
cannot sustain growth.
Increases in capital per worker
lead to smaller and smaller
increases in output per worker.
The Effects of an
Improvement in the
State of Technology
 Sustained growth
requires sustained
technological progress.
The economy’s rate of
growth of output per
person is eventually
determined by the
economy’s rate of
technological progress.
An improvement in technology shifts the
production function up, leading to an
increase in output per worker for a given
level of capital per worker.
Key Terms
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growth
logarithmic scale
standard of living
output per person
purchasing power, purchasing
power parity (PPP)
convergence
Malthusian trap
four tigers
emerging economies
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aggregate production function
state of technology
constant returns to scale
decreasing returns to capital
decreasing returns to labor
capital accumulation
technological progress
saving rate