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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 students 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 todays 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 Model1

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 modelsomething that is

explained by the model

Endogenous = within the model

Parts of an Economic Model2

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 Example1

Labor supply and demand

Variables:

???? = number of hours laborers want to work

???? = number of labor hours firms want to hire

?? = wage

Parameters:

Model Example2

Supply function

Demand function

Model Example3

Supply function

Demand function

Equilibrium

Model Example4

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, 18702015

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 Markets1

Complete and competitive markets

Deviations:

Market power

Externalities

Public goods

Asymmetric (imperfect) information

Pareto Efficiency and Free Markets2

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 Economy1

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 Economy2

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.)

Labors share of GDP has remained approximately

constant over time.

Share of GDP to capital

One-third (approx.)

Labors 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 nations

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 years prices.

Real GDP will be measured in a certain years 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 GDP1

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 GDP2

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, 20182020

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 Weighting1

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 Weighting2

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 200300 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 Growth1

Population growth evolves the same way:

Intuitively, tomorrows population in time period t+1 depends on

todays population in period t.

If equation (1) is true in time t, it also applies to time t+1. It follows

that

Population Growth2

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 19602017:

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 worlds 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 Equilibrium1
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 Equilibrium2
Solution1
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
Solution2
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.
Labors 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 Models Prediction for Per Capita GDP (United States = 1)
Predicted Per Capita GDP in the Production Model
The Models 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