ECON 311 George Mason University Journal about a Current Economical Event Essay

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Intermediate Macroeconomics
ECON 311
Fall 2021
The purpose of the journal exercise is twofold: (1) to encourage you to follow current events and
(2) to provide you the opportunity to apply the concepts discussed in the readings and class.
The journals work as follows. Over the course of the semester students are responsible for
finding two separate current events related to the topics discussed in the class and readings.
Each journal is 3-4 pages typed, double spaced, 12 font, Times New Roman, 1-inch margins.
The first paragraph should summarize the event, while the rest of the journal should discuss how
the concepts in class readings/lectures/discussion can provide insight to the event being
discussed. The only reference needed is a link or reference to the source of the article(s). This is
not a research paper or analysis, but rather an exploratory exercise in order to become familiar
with applying economic concepts to current events. Your journal entry should sketch how the
class concepts relate to the event being considered and shed light on those events. Summaries of
the readings or current event, extensively paraphrasing or quoting others, etc. are not permitted.
DUE DATE:
The journal entry is due on October 27th
You will submit your journal entries on Blackboard.
Late journal submitted within 24 hours of the deadline will receive half credit as detailed in the
course syllabus. Students will be graded on the relevance of the topic selected as well as their
ability to express the connection between the event and macroeconomics in a clear and coherent
manner.
1
GRADING CRITERIA:
The following rubric will be applied in grading your journal entry and will provide you a guide
of the criteria for grading. Each category is worth up to 25 points:
1. The entry identifies a clear issue and offers a concise summary.
Excellent (25 pts)
Satisfactory (20 pts)
Unsatisfactory (10 pts)
Clearly identifies a current
Partially identifies a current
Fails to identify a clear
issue and provides a wellissue and has a partial
current issue and lacks a
defined summary of the key summary of the key themes
clear summary of the key
themes of the article.
of the article.
themes of the article.
2. The entry is written in a clear, engaging and logically structured manner free of
grammatical errors, typos, etc.
Excellent (25 pts)
Satisfactory (20 pts)
Unsatisfactory (10 pts)
The paper flows in a clear
Parts of the paper lack clarity The paper lacks a clear
and linear manner. The thesis due to a lack of structure.
structure and is therefore
is carried throughout the
Portions of the text are not
confusing and hard to follow.
paper. The text is free of
linked to the thesis. There are There are significant
grammatical errors and
some grammatical errors or
grammatical errors and
typos. The paper is written in typos. The paper is only
typos. The paper lacks
an engaging manner.
somewhat engaging.
engaging writing.
3. The entry incorporates and accurately engages relevant supporting data and evidence,
where necessary.
Excellent (25 pts)
Accurately and completely
engages the relevant data and
evidence related to the issue
being discussed.
Demonstrates the ability to
synthesize that data/evidence
into a broader analytical
discussion.
Satisfactory (20 pts)
Partially engages the relevant
data and evidence related to
the question, or makes minor
mistakes in discussing and
engaging the data/evidence.
Demonstrates a partial, above
average, ability to synthesize
data and evidence into a
broader analytical discussion.
Unsatisfactory (10 pts)
Fails to engage the relevant
data and evidence related to
the question, or makes major
mistakes in discussing and
engaging the data/evidence.
Demonstrates an inability to
synthesize data and evidence
into a broader analytical
discussion.
2
4. The entry clearly identifies the conclusions and implications of the analysis, where
necessary.
Excellent (25 pts)
Clearly and accurately
identifies conclusions and
implications resulting from
the analysis provided in the
paper. Shows a strong ability
to identify and communicate
the relationship between
theory, evidence, and
implications.
Satisfactory (20 pts)
Partially identifies
conclusions and implications
related to the argument
provided. Shows an above
average ability to identify the
relationship between theory,
evidence, and implications.
Unsatisfactory (10 pts)
Fails to identify conclusions
and implications related to
the argument provided. Fails
to identify the relationship
between theory, evidence,
and implications.
Grading Process:
journal entry will be read in the context of the four criteria in the rubric above and graded on a
100-point scale, adding up the points from each category. Examples:
An “A+” (100/100) journal entry is one that earns scores of “Excellent” in the four
categories of criteria. It provides a clear, has a clear summary of the key issues. The text
is well-structured and demonstrates the student’s ability to independently evaluate the
ideas presented in the course. The entry is free of grammatical or spelling errors and
awkward language.
A “B” (80/100) journal entry is one that earns “Satisfactory” scores in the four categories
above. It contains a partial summary of the event. The structure is somewhat confusing
and/or does not provide creative, independent analysis. There are some grammatical or
spelling errors and awkward language.
A “C” (70/100) journal entry is one that earns two “Unsatisfactory” scores and two
“Excellent” scores in the four categories above. The entry presents information relevant
to the current event without any clear organizing principle, or contains significant
weaknesses in expression.
An entry that earns three or more “Unsatisfactory” scores will earn a failing grade, “F”
(at most, 55/100). The entry generally fails to address the thrust of the assignment,
contains numerous grammatical errors, and generally lacks coherence.
3
Chapter 1
Introduction to
Macroeconomics
1.1 Introduction
In this chapter, we learn
• the definition of macroeconomics and important
questions to consider.
• foundations of macroeconomic models and
modeling.
• the three-part structure of the text:
• the long run
• the short run
• issues for the future.
Subfields in Economics
• Macroeconomics
• The study of how the interactions of people
and firms through markets affect overall
economic activity
• Microeconomics
• The study of individual people, firms, or
market behavior
Important Macroeconomic Questions to Consider
Why is today’s average American
• more than 10 times richer than 100 years ago?
• 50 times richer than the average Ethiopian?
Do we understand and know the causes of the recent
global financial crisis?
What role do stock markets play in the economy?
How did the 2008 Affordable Care Act impact the price
of healthcare, economic growth, and government
expenditures?
Per Capita GDP in Seven Countries
Inflation Rate in Certain Rich Countries
Inflation
It is obvious that (most) unemployment is bad.
But, what are the costs of inflation to society?
• Unexpected and symmetric inflation
• Unexpected and asymmetric inflation
• Deflation
• Sticky prices
The Unemployment Rate in the United States, Europe, and Japan
1.2 How Macroeconomics Studies Key Questions
Macroeconomists have a general approach to study
questions of interest:
• Document the facts.
• Develop a model.
• Compare predictions of the model with original facts.
• Use the model to make other predictions that will
eventually be tested.
Models
• Models simplify the complicated real world into its most
relevant elements.
• A model is useful if it has good predictive power.
• Economic models often involve systems of multiple
equations.
Parts of an Economic Model—1
Parameter
• An input that is fixed over time, except when the
model builder changes it for an experiment
Exogenous variable
• An input that can change over time, but determined
ahead of time by the model builder
• Exogenous = “outside of the model”
Endogenous variable
• An outcome of the model—something that is
explained by the model
• Endogenous = “within the model”
Parts of an Economic Model—2
Suppose We Have a Working Model…
How can we use it?
• Change parameters and exogenous variables to see
how they affect endogenous variables.
• Predict costs and benefits of new government
policies.
Model Example—1
Labor supply and demand
Variables:
• ???? = number of hours laborers want to work
• ???? = number of labor hours firms want to hire
• ?? = wage
Parameters:
Model Example—2
Supply function
•
•
•
Demand function
•
•
•
Model Example—3
Supply function
•
Demand function
•
Equilibrium
•
Model Example—4
• Increase in income taxes
• Increase in an input price
1.3 An Overview of the Book
Economics
Macroeconomics
Microeconomics
Long run
Short run
International
Economic growth
Business cycles
Open economy
Standards of
living
Inflation
Unemployment
Monetary/Fiscal
policy
Currency crises
Exchange rates
An Overview
More divisions
• Theoretical
• Mathematical models
• Empirical
• Data
• Theoretical and empirical methods are not
independent.
The Long Run
Income per person in the United States:
• $2,800 in 1870
• $44,000 in 2008
• Many countries have not experienced similar
increases in living standards.
The analysis of economic growth helps explain the long
run.
Per Capita GDP in the United States, 1870–2015
The Short Run
Potential output
• Measure of how per capita GDP would evolve with
completely flexible prices and fully employed
resources
• In 1982, actual output was 5 percent less than
potential output.
• Deviations in actual and potential output usually
last only a short time.
Long-term growth dominates short-run fluctuations.
Welfare
Welfare: Variable used to determine preferable policies and
rank outcomes
Measuring welfare is highly subjective.
• More GDP (consumption) increases welfare.
Are there variables other than GDP that we should
consider?
Examples:
• Leisure
• Equality
• Life expectancy
• Environmental quality
• Individual freedom
Pareto Efficiency and Free Markets—1
Complete and competitive markets
Deviations:
• Market power
• Externalities
• Public goods
• Asymmetric (imperfect) information
Pareto Efficiency and Free Markets—2
Why do economists disagree?
• Nature of market failures (magnitude)
• Theory of complete and competitive markets breaks
down.
• Which Pareto efficient outcome is best?
Chapter 2
Measuring the
Macroeconomy
2.1 Introduction
In this chapter, we learn
• the importance of gross domestic product (GDP).
• the composition of GDP, and how it has changed
over time.
• how to use GDP to examine
• the evolution of living standards.
• differences in living standards across countries.
Introduction
National income accounting:
• Method of aggregating the production of diverse
goods into a single measure of overall economic
activity
National accounting:
• State of an economy at a given time
• Changes to an economy over time
• Differences across countries
2.2 Measuring the State of the Economy
Gross domestic product (GDP):
• The market value of the final goods and services
produced in an economy over a certain period
• http://www.bea.gov/
United States GDP:
• $12.5 trillion in 2005
• $14.4 trillion in 2008 ($47,000 per person)
• $20.5 trillion in 2018 ($62,00 per person)
Measuring the State of the Economy—1
U.S. GDP
2005 2006 2007 2008
GDP
12.6 13.4 14.0 14.3
(in trillions
of $)
Growth
rate GDP
6.3% 4.5% 2.1%
14.4
14.2
14
13.8
13.6
13.4
13.2
13
12.8
12.6
12.4
2005
7%
6%
5%
4%
3%
2%
1%
2006
GDP (in trillions of $)
2007
Growth rate GDP
0%
2008
Measuring the State of the Economy—2
Production measure of GDP:
• The number of goods produced in the economy
Expenditure measure of GDP:
• The total purchases in the economy
Income measure of GDP:
• All the income earned in the economy
All three approaches give identical measures of GDP:
Production
Expenditures
Income
The Expenditure Approach to GDP
The national income accounting identity states:
where:
• ?? = GDP (in dollars)
• ?? = Consumption
• ?? = Investment
• ?? = Government purchases
• ???? = X – M = Exports – Imports
Investment
Business fixed investment (nonresidential)
• Spending by firms on plants, machinery and
equipment
Residential investment
• Construction of new houses and apartment
buildings
Inventory investment
• Changes in inventories (of final or intermediate
goods)
Variables
Gross Domestic Product
Personal Consumption Expenditures
Goods
Durable Goods
Nondurable goods
Services
Gross Private Domestic Investment
Fixed Investment
Nonresidential
Structures
Equipment
Intellectual Property Products
Residential
Change in private inventories
Net Exports of Goods and Services
Exports
Goods
Services
Imports
Goods
Services
Government Consumption Expenditures and Gross
Investment
Federal
National Defense
Nondefense
State and Local
2018
20,580.20
13,998.70
4,364.80
1,475.60
2,889.20
9,633.90
3,628.30
3,573.60
2,786.90
633.2
1,222.60
931.1
786.7
54.7
-638.2
2,510.30
1,661.30
848.9
3,148.50
2,570.60
577.9
% of GDP
100.00
68.02
21.21
7.17
14.04
46.81
17.63
17.36
13.54
3.08
5.94
4.52
3.82
0.27
-3.10
12.20
8.07
4.12
15.30
12.49
2.81
Per Capita
62,794.60
42,713.03
13,317.94
4,502.37
8,815.57
29,395.09
11,070.72
10,903.82
8,503.43
1,932.03
3,730.41
2,840.99
2,400.39
166.90
-1,947.28
7,659.46
5,068.98
2,590.18
9,606.75
7,843.45
1,763.30
3,591.50
1,347.30
793.6
553.7
2,244.20
17.45
6.55
3.86
2.69
10.90
10,958.44
4,110.90
2,421.44
1,689.46
6,847.54
Source: Bureau of Economic Analysis
Notes: Billions of Dollars (per capita in dollars): Last Revised on: September 30, 2019
Expenditure Shares of U.S. GDP
The Income Approach to GDP
The income approach
• Measures the sum of all income earned in the
economy
Capital
• Inputs into production other than labor that are not
used up in the production process
• Increased by firms through investment
Depreciation
• The deterioration of the capital stock due to wear
and tear
•
The Income Approach to U.S. GDP in 2018
Total Share of GDP to Inputs
Share of GDP to labor
• Two-thirds (approx.)
• Labor’s share of GDP has remained approximately
constant over time.
Share of GDP to capital
• One-third (approx.)
Labor’s Share of GDP
The Production Approach to GDP
No “double counting” in GDP
• Only the final sale of goods and services count.
Value added
• The amount each producer contributes to GDP
• The revenue generated by each producer minus the
value of intermediate products
Only new production of goods and services counts
toward GDP.
What Is Included in GDP and What Is Not?—1
GDP considers only final goods and services.
Intermediate goods are not included in GDP
calculations.
• For example, if Alcoa sells aluminum to Ford to
make a Focus ST, the sale of the car is included in
GDP, but not the sale of the aluminum.
What Is Included in GDP and What Is Not?—2
• Included:
• Government spending on
goods/services
• Factory production
• Healthcare expenditures
• Ingredients and food
purchased
• Kids in day care
• Not included:
• Government transfer
payments
• Environmental conditions
• A measure of a nation’s
health
• Time spent cooking at home
• Babysitter
Measures of Well-Being
GDP is used by economists as a proxy for standards of
living.
Differences in GDP Over Time
http://www.gapminder.org/videos/200-years-thatchanged-the-world-bbc/
2.3 Measuring Changes Over Time
When examining GDP over time, we need to take into
account changes in prices.
Nominal GDP:
• A measure of GDP when prices and quantities have not
been separated, using current year prices
•
Real GDP:
• Actual quantity of goods and services, using base year
prices
•
Measuring Changes Over Time
To compute GDP across time, we must use a certain year’s prices.
• Real GDP will be measured in a certain year’s dollars.
• Nominal GDP is measured in current dollars.
Nominal GDP:
• where N is the total number of goods and services in the
economy, and
are prices in year t.
Real GDP:
prices
• where N is the total number of goods and services in the
economy and
are prices in year t-1.
An Example of Changes in Nominal GDP—1
Consider an economy that produces two goods: steak
(s) and basketballs (b).
Nominal GDP in 2014:
If the quantity of goods and services produced does not
change, but prices do change:
• Nominal GDP will change.
• Real GDP will not change.
An Example of Changes in Nominal GDP—2
Suppose:
Year
2014
2015
Price of Quantity
Price of
Steak of Steak Basketballs
$10
$12
Nominal GDP in 2014:
Nominal GDP in 2015:
50
50
$25
$28
Quantity of
Basketballs
100
100
Real and Nominal GDP in a Simple Economy, 2018–2020
Another Example
Now suppose:
Year
Price of
Steak
Quantity
of Steak
Price of
Basketballs
Quantity of
Basketballs
2014
2015
$10
$12
50
60
$25
$28
100
105
Nominal GDP in 2015:
Real GDP in 2015 (in 2014 prices):
Quantity Indexes
Calculating real GDP changes over time:
• The Laspeyres index
• Calculates changes in real GDP using the initial
prices
• The Paasche index
• Calculates changes in real GDP using the final year
prices
Over long-time intervals the two indexes can result in
substantial differences.
Chain Weighting—1
The Fisher index (chain weighting) is the preferred
approach to calculating real GDP.
• Average of the Laspeyres and Paasche index
• Can be applied on a year-by-year basis if we
compute real GDP each year
Recall:
• which is the GDP deflator rearranged:
•
Chain Weighting—2
We can make the following transformation:
Using Chain-Weighted Data
Main reason for using chain-weighted data:
• Prices of computers rapidly changed in the 1990s
Main disadvantage:
• The sum of real C, I, G, NX will not equal real chainweighted GDP because the prices used in
constructing the components are different.
General rule to follow:
• For particular components of GDP, we look at the
ratio of nominal variables.
• When you want real rates of economic growth, use
the chain-weighted real measures.
2.4 Comparing Economic Performance across Countries
The exchange rate:
• Price at which different currencies are traded
To make comparisons of GDP across countries:
• GDP must be expressed in a common currency by
first adjusting it by the exchange rate.
• This value of nominal GDP must be multiplied by the
ratio of prices in the countries.
An Example of Comparisons of Economies
Suppose we are trying to compare GDP in China and
the United States.
1. Use the exchange rate to turn Chinese yuan into U.S.
dollars:
$1
26.4 ???????????????? ???????? ×
7.6 ????????
2. Adjust for relative price level of goods:
= $3.5 ????????????????
Comparison of Countries
• In general, rich countries tend to have higher price
levels than poor countries.
• This is mainly because poor countries have lower
wages.
Chapter 3
An Overview of Long-Run
Economic Growth
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,
• how this growth is a relatively recent phenomenon,
• 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.
Motivation: Why Is Economic Growth Important?
A 1 percent change in annual
growth appears small, but it may
lead to large differences in the
levels of output over time.
Consider a 100-year period:
• Country A and B begin at the
same level of GDP ($100 billion).
• Country A grows at 1 percent
each year.
• Country B grows at 0.25 percent
each year.
Hypothetical GDP Values
(in billions of dollars)
280
260
240
220
200
180
160
140
120
100
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Country A
Country B
3.2 Growth Over the Very Long Run
Sustained increases in standards of living are a recent phenomenon:
• The first agricultural revolution was about 10,000 years ago.
• Yet, only in the last 200–300 years has modern economic
growth appeared.
Economic growth emerges in different places at different times for
many reasons. Some results of this are:
• Standards of living have diverged dramatically.
• Per capita GDP differs remarkably around the world.
Growth Over the Very Long Run
3.3 Modern Economic Growth
Looking over the past 150 years: from 1870 to 2018, United States
real per capita GDP rose by more than 15-fold.
Assuming this rate of growth continues, a typical college student
today will earn a lifetime income about twice that of his or her
parents.
Modern Economic Growth
The Definition of Economic Growth
Growth of per capita GDP
• The exact rate of change of per capita GDP
A percentage change
• The change between two periods divided by the value of the
variable in the initial period
Percentage change in GDP between period t and t+1:
where g bar (??)? is the associated constant growth rate.
Example: Population Growth—1
Population growth evolves the same way:
Intuitively, tomorrow’s population in time period t+1 depends on
today’s population in period t.
If equation (1) is true in time t, it also applies to time t+1. It follows
that
Population Growth—2
But, equation (1) gives us the value for
So, we can plug (1) into (2) to get
And, we could continue this process for any number of time periods,
until we recognize the pattern:
The Constant Growth Rule
The constant growth rule states that
(6)
•
where
•
?? is the time period,
•
???? is the value of variable ?? in time ??,
•
???? is the initial value of variable ?? in period 0,
•
is the constant growth rate.
Population over Time
The Rule of 70
The Rule of 70:
• If y grows at a rate of g percent per year, then the number of
years it takes y to double is approximately equal to 70/g.
Notes:
• Small differences in growth rates result in large differences over
time.
• The time it takes to double only depends on the growth rate and
not on the initial value.
The Ratio (Logarithmic) Scale
A plot where equally spaced tick marks on the vertical axis are
labeled consecutively with numbers that exhibit a constant ratio:
• When doubling, we want this constant ratio to be “2.”
• So, on the y-axis, instead of “1, 2, 3, 4” we have “1, 2, 4, 8”, or in
our case, “6, 12, 24, 48.”
When plotted on a ratio scale, a variable that grows at a constant
rate will be a straight line.
Population over Time, Revisited
U.S. GDP on a Ratio Scale
On a ratio scale; if growth rates are rising, the slope will be
increasing; if the growth rate is constant, it will be a straight line.
Per capita GDP in the United States has grown at approximately 2
percent per year over the past 150 years.
• This outcome is easy to see using a ratio scale,
• Approximately linear.
Per Capita GDP in the United States, Ratio Scale
Calculating Growth Rates
?
Begin with the constant growth rule:
?
Now, solve for .
Divide both sides by ??0:
?
Raise both sides to the 1/?? power:
?
Subtract 1 from both sides:
?
The Ratio Scale in Action: Per Capita GDP since 1870
3.4 Modern Growth around the World
After World War II, growth in Germany and Japan were similar, in
that they both accelerated.
• As we see in Figure 3.6, over time, the acceleration slows.
Convergence:
• Poorer countries will grow faster to “catch up” to the level of
income in richer countries.
Argentina had accelerated growth until 1980 and then slowed
considerably.
• China and India have had the reverse pattern.
A Broad Sample of Countries
Over the period 1960–2017:
• Some countries have exhibited a negative growth rate.
• Other countries have sustained nearly 7% growth rates.
• Most countries have sustained about 2% growth rates.
Small differences in growth rates result in large differences in
standards of living.
Levels and Growth Rates of Per Capita GDP
Case Study: People versus Countries
• A major reason for changes:
• The bulk of the world’s population is • Economic growth in China and
India
substantially richer.
• These two countries account for 40
• The fraction of people living in
percent of the world population.
poverty has fallen.
• Since 1960:
3.5 Some Useful Properties of Growth Rates
Growth rates of ratios, products, and powers follow several simple
rules.
Growth rates obey mathematical operations that are a level simpler
than the operation on the original variable.
• Variables divided ? growth rates subtracted
• Variables multiplied ? growth rates added
• Variable taken to a power number? growth rate multiplied by
that number
Some Useful Properties of Growth Rates
Suppose two variables ?? and ?? have average annual growth rates of
???? and ????, respectively.
Assume also that gz is the average annual growth rate of ??.
Then the following rules apply:
Examples of Growth Rate Calculations
U.S. Population, GDP, and Per Capita GDP
Growth Rules in a Famous Example
?
Applying rules of growth rates to a Cobb
Douglas production function:
Original output equation:
?
Use multiplication rule to get:
?
Use exponent rule to get:
?
3.6 The Benefits and 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
The next few chapters examine the following:
• Chapter 4: How can we measure differences in income levels
across countries?
• Chapter 5: Develops the Solow growth model
• Chapter 6: Is human capital a driver of economic growth?
Also part of the long-run discussion is:
• Chapter 7: The labor market, wages, and unemployment in the
long run
• Chapter 8: Determinants of long-run inflation
3.8 Additional Resources
Additional Resources of interest:
• Google Scholar: www.scholar.google.com
• Robert E. Lucas Jr., “Some Macroeconomics for the 21st
Century.”
• The Maddison Project:
https://www.rug.nl/ggdc/historicaldevelopment/maddison/
• CIA World Factbook:
https://www.cia.gov/library/publications/the-worldfactbook/
Chapter 4
A Model of Production
4.1 Introduction
In this chapter, we learn
• how to set up and solve a macroeconomic model.
• the purpose of a production function and its use for
understanding differences in GDP per capita across
countries.
• the role of capital per person and technology in
explaining differences in economic growth.
• the relevance of “returns to scale” and “diminishing
marginal products.”
• how to look at economic data through the lens of a
macroeconomic model.
Introduction
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
Inputs in the production process:
• Labor
• Capital
Production function:
• Shows how much output (Y) can be produced given
any number of inputs
Setting Up the Model – Production Function
Model
Output growth corresponds to changes in ??.
There are three ways that ?? can change:
• Capital stock (K) changes.
• Labor force (L) changes.
• Ability to produce goods with given resources (K, L)
changes.
• Technological advances occur (changes in A).
• TFP is assumed to be exogenous in the Solow
model.
Cobb-Douglas Production Function
The Cobb-Douglas production function is a particular
production function that takes the form of
where ? is assumed to be 1/3.
F(K,L) is increasing in both K and L.
• More inputs yield more output.
•
A production function exhibits constant returns to
scale if doubling each input exactly doubles output.
Constant Returns to Scale (CRS)
If ?? and ?? increase by x%,
• ? ?? also increases by x%
Mathematically,
•
• Homogeneous function (of degree 1)
Standard replication argument
Output per Person (Intensive Form)
Divide output by the number of workers
• Per capita = per person = per worker
• Lowercase letters denote per capita.
We can rewrite output per person as
where
and
Typical Production Function
Graph of
Note: If ?? = 0 then ?? = ??(??) = 0.
10
8
6
y
4
k
2
0
0
200 400 600 800 1000
k
Returns to Scale Comparison
• Sum of exponents
• Sum to 1
• Sum to > 1
• Sum to < 1 • Result • Constant returns to scale • Increasing returns to scale • Decreasing returns to scale Allocating Resources • ?: profits • r: rental rate of capital • w: wage rate The rental rate and wage rate are taken as given under perfect competition. • Hire capital until MPK = r. • Hire labor until MPL = w. For simplicity, the price of the output is normalized to one. Marginal Products The marginal product of labor (MPL) is the additional output that is produced when one unit of labor is added, holding all other inputs constant: The marginal product of capital (MPK) is the additional output that is produced when one unit of capital is added, holding all other inputs constant: Diminishing Marginal Product of Capital in Production Diminishing Returns Formally: Suppose we have one unit of K and one unit of L. Assume this results in one unit of Y. • Add a second unit of L. • Previously, each unit of L had one unit of K to work with. • Now, each unit of L has ½ unit of K to work with. • We are assuming that this will make each unit of L less productive, and output will increase, but not double. Solving the Model: General Equilibrium—1 • Five endogenous variables • Output (Y) • The amount of capital (K) • The amount of labor (L) • The wage (w) • The rental price of capital (r) • Five equations • The production function • The rule for hiring capital • The rule for hiring labor • Supply equals the demand for labor. • Supply equals the demand for capital. Solving the Model: General Equilibrium—2 Solution—1 A solution to the model • A new set of equations that express the five unknowns in terms of the parameters and exogenous variables General equilibrium • Solution to the model when more than a single market clears Supply and Demand in the Capital and Labor Markets Solution—2 In This Model… The solution implies that • firms employ all the supplied capital and labor in the economy. • the production function is evaluated with the given supply of inputs: • ?? = ?????? evaluated at the equilibrium values of Y, K, and L. • ?? = ??????evaluated at the equilibrium values of Y, K, and L. Interpreting the Solution 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: • of production is paid to labor • of production is paid to capital • The factor shares of the payments are equal to the exponents on the inputs in the Cobb-Douglas function. Labor’s Share of Income Equilibrium All income is paid to capital or labor. • Results in zero profit in the economy • Verifies the assumption of perfect competition • Also verifies that production equals spending equals income • Income = production 4.3 Analyzing the Production Model Development accounting: • The use of a model to explain differences in incomes across countries • Setting the productivity parameter = 1 Comparing Models with Data Our example uses only one good, but countries produce far more than one good. • How can our model help to understand per capita GDP across widely different countries? Models are simplified versions of reality. The best models are those that tend to be very close to true, despite the simplicity. • If the gap between the model and the world is too large, we will see this failure when we use data. The Empirical Fit of the Production Function If the productivity parameter is 1, the model overpredicts GDP per capita. 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. The Model’s Prediction for Per Capita GDP (United States = 1) Predicted Per Capita GDP in the Production Model The Model’s Prediction for Per Capita GDP 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 countrie