Transcript Part 2

3.1 Introduction
• In this chapter, we learn:
– Some facts related to economic growth
that later chapters will seek to explain.
– How economic growth has dramatically
improved welfare around the world.
• this growth is actually a relatively recent
phenomenon
3.1 Introduction
• In this chapter, we learn:
– Some tools used to study economic
growth, including how to calculate growth
rates.
– Why a “ratio scale” makes plots of per
capita GDP easier to understand.
• The United States of a century ago could
be mistaken for Kenya or Bangladesh
today.
• Some countries have seen rapid economic
growth and improvements to health
quality, but many others have not.
3.2 Growth over the
Very Long Run
• Sustained increases in standards of
living are a recent phenomenon.
• Sustained economic growth emerges in
different places at different times.
– Thus, per capita GDP differs remarkably
around the world.
• The Great Divergence
– The recent era of increased difference in
standards of living across countries.
• Before 1700
– Per capita GPD in nations differed only by a
factor of two or three.
• Today
– Per capita GPD differs by a factor of 50 for
several countries.
3.3 Modern Economic Growth
• Timeline: from 1870 to 2000, United
States per capita GDP . . .
– . . . rose by nearly 15-fold.
• Implications for you?
– A typical college student today will earn a
lifetime income about twice his or her
parents.
3.4 Modern Growth around
the World
• After World War II, growth in Germany
and Japan accelerated.
• Convergence
– Poorer countries will grow faster to “catch
up” to the level of income in richer
countries.
• Brazil had accelerated growth until 1980
and then stagnated.
– China and India have had the reverse
pattern.
A Broad Sample of Countries
• Over the period 1960–2007
– Some countries have exhibited a negative
growth rate.
– Other countries have sustained nearly 6
percent growth.
– Most countries have sustained about 2
percent growth.
• Small differences in growth rates result in
large differences in standards of living.
Case Study: People versus
Countries
• Since 1960:
– The bulk of the world’s population is
substantially richer.
– The fraction of people living in poverty has
fallen.
• A major reason for changes
– Economic growth in China and India
– These are 40 percent of the world
population!
Case Study: Growth Rules in a Famous
Example, Yt = AtKt1/3Lt2/3
• Applying rules of growth rates
• Original output equation:
• Use multiplication rule to get
• Use exponent rule to get
3.6 The Costs of
Economic Growth
• The benefits of economic growth
– Improvements in health
– Higher incomes
– Increase in the variety of goods and services
• Costs of economic growth include:
– Environmental problems
– Income inequality across and within
countries
– Loss of certain types of jobs
• Economists generally have a consensus
that the benefits of economic growth
outweigh the costs.
3.7 A Long-Run Roadmap
• Are there certain policies that will allow
a country to grow faster?
• If not, what about a country’s “nature”
makes it grow at a slower rate?
Summary
• Sustained growth in standards of living
is a very recent phenomenon.
• If the 130,000 years of human history
were warped and collapsed into a single
year, modern economic growth would
have begun only at sunrise on the last
day of the year.
Summary
• Modern economic growth has taken hold in
different places at different times.
• Since several hundred years ago, when
standards of living across countries varied by
no more than a factor of 2 or 3, there has
been a “Great Divergence.”
• Standards of living across countries today
vary by more than a factor of 60.
• Since 1870
– Growth in per capita GDP has averaged
about 2 percent per year in the United States.
– Per capita GDP has risen from about $2,500
to more than $37,000.
• Growth rates throughout the world since
1960 show substantial variation
– Negative growth in many poor countries
– Rates as high as 6 percent per year in several
newly industrializing countries, most of which
are in Asia
• Growth rates typically change over time
• In Germany and Japan
– Growth picked up considerably after World
War II.
– Incomes converged to levels in the United
Kingdom.
– Growth rates have slowed down as this
convergence occurred.
• Brazil exhibited rapid growth in the 1950s
and 1960s and slow growth in the 1980s
and 1990s.
• China showed the opposite pattern.
• Economic growth, especially in India and
China, has dramatically reduced poverty in
the world.
• In 1960
– Two out of three people in the world lived on
less than $5 per day (in today’s prices).
• By 2000
– This number had fallen to only 1 in 10.
4.1 Introduction
• In this chapter, we learn:
– How to set up and solve a macroeconomic model.
– How a production function can help us understand
differences in per capita GDP across countries.
– The relative importance of capital per person
versus total factor productivity in accounting for
these differences.
– The relevance of “returns to scale” and
“diminishing marginal products.”
– How to look at economic data through the lens of
a macroeconomic model.
• A model:
– Is a mathematical representation of a
hypothetical world that we use to study
economic phenomena.
– Consists of equations and unknowns with real
world interpretations.
• Macroeconomists:
– Document facts.
– Build a model to understand the facts.
– Examine the model to see how effective it is.
4.2 A Model of Production
• Vast oversimplifications of the real world
in a model can still allow it to provide
important insights.
• Consider the following model
– Single, closed economy
– One consumption good
Setting Up the Model
• A certain number of inputs are used in
the production of the good
• Inputs
– Labor (L)
– Capital (K)
• Production function
– Shows how much output (Y) can be
produced given any number of inputs
• Others variables with a bar are parameters.
• Production function:
Output
Productivity
parameter
Inputs
• The Cobb-Douglas production function is
the particular production function that
takes the form of
Assumed to be 1/3.
Explained later.
• A production function exhibits constant
returns to scale if doubling each input
exactly doubles output.
Returns to Scale Comparison
Find the sum of
exponents on the inputs
Result
• sum to 1
• the function has constant
returns to scale
• sum to more than 1
• the function has
increasing returns to
scale
• sum to less than 1
• the function has
decreasing returns to
scale
• Standard replication argument
– A firm can build an identical factory, hire
identical workers, double production stocks,
and can exactly double production.
– Implies constant returns to scale.
Allocating Resources
Firm chooses inputs
to maximize profit
Rental rate
of capital
Wage rate
• The rental rate and wage rate are taken as
given under perfect competition.
• For simplicity, the price of the output is
normalized to one.
• The marginal product of labor (MPL)
– The additional output that is produced when
one unit of labor is added, holding all other
inputs constant.
• The marginal product of capital (MPK)
– The additional output that is produced when
one unit of capital is added, holding all other
inputs constant.
• The solution is to use the following hiring
rules:
– Hire capital until the MPK = r
– Hire labor until MPL = w
• If the production function has constant
returns to scale in capital and labor, it will
exhibit decreasing returns to scale in
capital alone.
Solving the Model:
General Equilibrium
• The model has five endogenous
variables:
– Output (Y)
– the amount of capital (K)
– the amount of labor (L)
– the wage (w)
– the rental price of capital (r)
• The model has five equations:
– The production function
– The rule for hiring capital
– The rule for hiring labor
– Supply equals the demand for capital
– Supply equals the demand for labor
• The parameters in the model:
– The productivity parameter
– The exogenous supplies of capital and labor
• A solution to the model
– A new set of equations that express the five
unknowns in terms of the parameters and
exogenous variables
– Called an equilibrium
• General equilibrium
– Solution to the model when more than a
single market clears
• In this model
– The solution implies firms employ all the
supplied capital and labor in the economy.
– The production function is evaluated with the
given supply of inputs.
– The wage rate is the MPL evaluated at the
equilibrium values of Y, K, and L.
– The rental rate is the MPK evaluated at the
equilibrium values of Y, K, and L.
Interpreting the Solution
• If an economy is endowed with more
machines or people, it will produce
more.
• The equilibrium wage is proportional to
output per worker.
• Output per worker = (Y/L)
• The equilibrium rental rate is
proportional to output per capital.
• Output per capital = (Y/K)
• In the United States, empirical evidence
shows:
– Two-thirds of production is paid to labor.
– One-third of production is paid to capital.
– The factor shares of the payments are equal
to the exponents on the inputs in the CobbDouglas function.
• All income is paid to capital or labor.
– Results in zero profit in the economy
– This verifies the assumption of perfect
competition.
– Also verifies that production equals spending
equals income.
Case Study: What Is the Stock Market?
• Economic profit
– Total payments from total revenues
• Accounting profit
– Total revenues minus payments to all
inputs other than capital.
• The stock market value of a firm
– Total value of its future and current
accounting profits
– The stock market as a whole is the value of
the economy’s capital stock.
4.3 Analyzing the Production
Model
• Per capita = per person
• Per worker = per member of the labor
force.
– In this model, the two are equal.
• We can perform a change of variables
to define output per capita (y) and
capital per person (k).
• Output per person equals the productivity
parameter times capital per person raised to
the one-third power.
Output per person
Productivity
parameter
Capital per person
• What makes a country rich or poor?
• Output per person is higher if the
productivity parameter is higher or if the
amount of capital per person is higher.
– What can you infer about the value of the
productivity parameter or the amount of
capital in poor countries?
Comparing Models with Data
• The model is a simplification of reality,
so we must verify whether it models the
data correctly.
• The best models:
– Are insightful about how the world works
– Predict accurately
The Empirical Fit of the Production Model
• Development accounting:
– The use of a model to explain differences
in incomes across countries.
Set productivity
parameter = 1
• Diminishing returns to capital implies that:
– Countries with low K will have a high MPK
– Countries with a lot of K will have a low MPK,
and cannot raise GDP per capita by much
through more capital accumulation
• If the productivity parameter is 1, the
model overpredicts GDP per capita.
Case Study: Why Doesn’t Capital Flow
from Rich to Poor Countries?
• If MPK is higher in poor countries with
low K, why doesn’t capital flow to those
countries?
– Short Answer: Simple production model
with no difference in productivity across
countries is misguided.
– We must also consider the productivity
parameter.
Productivity Differences: Improving
the Fit of the Model
• The productivity parameter measures
how efficiently countries are using their
factor inputs.
• Often called total factor productivity
(TFP)
• If TFP is no longer equal to 1, we can
obtain a better fit of the model.
• However, data on TFP is not collected.
– It can be calculated because we have data on
output and capital per person.
– TFP is referred to as the “residual.”
• A lower level of TFP
– Implies that workers produce less output for
any given level of capital per person
4.4 Understanding TFP
Differences
• Why are some countries more efficient
at using capital and labor?
Human Capital
• Human capital
– Stock of skills that individuals accumulate
to make them more productive
– Education, training, etc.
• Returns to education
– Value of the increase in wages from
additional schooling
• Accounting for human capital reduces
the residual from a factor of 11 to a
factor of 6.
Technology
• Richer countries may use more modern
and efficient technologies than poor
countries.
– Increases productivity parameter
Institutions
• Even if human capital and technologies
are better in rich countries, why do they
have these advantages?
• Institutions are in place to foster human
capital and technological growth.
– Property rights
– The rule of law
– Government systems
– Contract enforcement
Misallocation
• Misallocation
– Resources not being put to their best use
• Examples
– Inefficiency of state-run resources
– Political interference
Case Study: A “Big Bang” or
Gradualism? Economic Reforms in
Russia and China
• When transitioning from a planned to a
market economy, the change can be
sudden or gradual.
– A “big bang” approach is one where all old
institutions are replaced quickly by
democracy and markets.
– A “gradual” approach is one where the
transition to a market economy occurs
slowly over time.
• Russia followed a “big bang” approach,
yet GDP per capita has declined since the
transition.
• China has seen accelerated economic
growth using the “gradual” approach.
4.5 Evaluating the Production
Model
• Per capita GDP is higher if capital per
person is higher and if factors are used
more efficiently.
• Constant returns to scale imply that
output per person can be written as a
function of capital per person.
• Capital per person is subject to strong
diminishing returns because the
exponent is much less than one.
• Weaknesses of the model:
– In the absence of TFP, the production
model incorrectly predicts differences in
income.
– The model does not provide an answer
as to why countries have different TFP
levels.
Summary
• Per capita GDP varies by a factor of 50 between
the richest and poorest countries of the world.
• The key equation in our production model is the
Cobb-Douglas production function:
Output
Productivity
parameter
Inputs
• The exponents in this production
function:
– One-third of GDP is paid out to capital.
– Two-thirds is paid to labor.
– Exponents sum to 1, implying constant
returns to scale in capital and labor.
• The complete production model consists
of five equations and five unknowns:
-
Output Y
Capital K
Labor L
Wage rate w
Rental rate r
• The solution to this model is called an
equilibrium.
• The prices w and r are determined by
the clearing of labor and capital
markets.
• The quantities of K and L are
determined by the exogenous factor
supplies.
• Y is determined by the production
function.
• The production model implies that
output per person in equilibrium is the
product of two key forces:
– Total factor productivity (TFP)
– Capital per person
• Assuming the TFP is the same across
countries, the model predicts that
income differences should be
substantially smaller than we observe.
• Capital per person actually varies
enormously across countries, but the
sharp diminishing returns to capital per
person in the production model
overwhelm these differences.
• Making the production model fit the
data requires large differences in TFP
across countries.
• Economists also refer to TFP as the
residual, or a measure of our
ignorance.
• Understanding why TFP differs so much
across countries is an important question
at the frontier of current economic
research.
• Differences in human capital (such as
education) are one reason, as are
differences in technologies.
• These differences in turn can be partly
explained by a lack of institutions and
property rights in poorer countries.
This concludes the Lecture
Slide Set for Chapter 4
Macroeconomics
Second Edition
by
Charles I. Jones
W. W. Norton & Company
Independent Publishers Since 1923