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Summary Macroeconomics - N. Gregory Mankiw
Macroeconomics 1 (University of New South Wales)
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Summary
Macroeconomics
N. Gregory Mankiw
8th Edition
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Contents
Epilogue. What We Know, What We Don’t............................................................................................. 5
1. The Science of Macroeconomics......................................................................................................... 7
1.1. What Macroeconomists study ..................................................................................................... 7
1.2. How Economists Think ................................................................................................................. 8
1.3. How This Book Proceeds .............................................................................................................. 9
2. The Data of Macroeconomics ........................................................................................................... 10
2.1. Measuring the Value of Economic Activity: Gross Domestic Product........................................ 10
2.2. Measuring the Cost of Living: The Consumer Price Index.......................................................... 12
2.3. Measuring Joblessness: The Unemployment Rate..................................................................... 14
2.4. Conclusion: From Economic Statistics to Economic Models ...................................................... 15
3. National Income: Where it comes from and where it goes .............................................................. 16
3.1. What Determines the Total Production of Goods and Services?............................................... 17
3.2. How Is National Income Distributed to the Factors of Production? .......................................... 18
3.3. What Determines the Demand for Goods and Services?........................................................... 21
3.4. What Brings the Supply and Demand for Goods and Services Into Equilibrium?...................... 22
3.5. Conclusion .................................................................................................................................. 25
4. The Monetary System: What It Is and How It Works ........................................................................ 26
4.1. What Is Money? ......................................................................................................................... 26
4.2. The Role of Banks in the Monetary System ............................................................................... 27
4.3. How Central Banks Influence the Money Supply ....................................................................... 28
4.4. Conclusion .................................................................................................................................. 29
5. Inflation: Its Causes, Effects, and Social Costs................................................................................... 30
5.1. The Quantity Theory of Money .................................................................................................. 30
5.2. Seigniorage: The Revenue from Printing Money ....................................................................... 31
5.3. Inflation and Interest Rates........................................................................................................ 31
5.4. The Nominal Interest Rate and the Demand for Money............................................................ 32
5.5. The Social Costs of Inflation ....................................................................................................... 32
5.6. Hyperinflation............................................................................................................................. 34
5.7. Conclusion: The Classical Dichotomy ......................................................................................... 34
6. The Open Economy ........................................................................................................................... 35
6.1. The International Flows of Capital and Goods ........................................................................... 35
6.2. Saving and Investment in a Small Open Economy ..................................................................... 36
6.3. Exchange Rates........................................................................................................................... 37
6.4. Conclusion: The United States as a Large Open Economy ......................................................... 39
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7. Unemployment.................................................................................................................................. 41
7.1. Job Loss, Job Finding, and the Natural Rate of Unemployment ................................................ 41
7.2. Job Search and Frictional Unemployment ................................................................................. 42
7.3. Real-Wage Rigidity and Structural Unemployment ................................................................... 42
7.4. Labour-Market Experience: The United States .......................................................................... 43
7.5. Labour-Market Experience: Europe ........................................................................................... 43
7.6. Conclusion .................................................................................................................................. 44
8. Economic Growth I: Capital Accumulation and Population Growth ................................................. 45
8.1. The Accumulation of Capital ...................................................................................................... 45
8.2. The Golden Rule Level of Capital................................................................................................ 47
8.3. Population Growth ..................................................................................................................... 49
8.4. Conclusion .................................................................................................................................. 50
9. Economic Growth II: Technology, Empirics, and Policy..................................................................... 51
9.1. Technological Progress in the Solow Model .............................................................................. 51
9.2. From Growth Theory to Growth Empirics.................................................................................. 52
9.3. Policies to Promote Growth ....................................................................................................... 52
9.4. Beyond the Solow Model: Endogenous Growth Theory ............................................................ 54
10. Introduction to Economic Fluctuations........................................................................................... 56
10.1. The Facts about the Business Cycle.......................................................................................... 56
10.2. Time Horizons in Macroeconomics .......................................................................................... 58
10.3. Aggregate Demand................................................................................................................... 59
10.4. Aggregate Supply...................................................................................................................... 60
10.5. Stabilization Policy.................................................................................................................... 61
10.6. Conclusion ................................................................................................................................ 62
11. Aggregate Demand I: Building the IS–LM Model ............................................................................ 63
11.1. The Goods Market and the IS Curve ........................................................................................ 63
11.2. The Money Market and the LM Curve ..................................................................................... 66
11.3. Conclusion: The Short-Run Equilibrium ................................................................................... 68
12. Aggregate Demand II: Applying the IS–LM Model .......................................................................... 69
12.1. Explaining Fluctuations With the IS–LM Model ....................................................................... 69
12.2. IS–LM as a Theory of Aggregate Demand ................................................................................ 71
12.3. The Great Depression............................................................................................................... 73
12.4. Conclusion ................................................................................................................................ 74
13. The Open Economy Revisited: The Mundell–Fleming Model and the Exchange-Rate Regime ...... 75
13.1. The Mundell–Fleming Model ................................................................................................... 75
13.2. The Small Open Economy Under Floating Exchange Rates...................................................... 76
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13.3. The Small Open Economy Under Fixed Exchange Rates .......................................................... 76
13.4. Interest Rate Differentials ........................................................................................................ 77
13.5. Should Exchange Rates Be Floating or Fixed? .......................................................................... 78
13.6. From the Short Run to the Long Run: The Mundell–Fleming Model With a Changing Price
Level .................................................................................................................................................. 80
13.7. A Concluding Reminder ............................................................................................................ 80
14. Aggregate Supply and the Short- Run Trade-off between Inflation and Unemployment .............. 81
14.1. The Basic Theory of Aggregate Supply ..................................................................................... 81
14.2. Inflation, Unemployment, and the Phillips Curve .................................................................... 82
14.3. Conclusion ................................................................................................................................ 84
15. A Dynamic Model of Aggregate Demand and Aggregate Supply.................................................... 85
15.1. Elements of the Model ............................................................................................................. 85
15.2. Solving the Model..................................................................................................................... 87
15.3. Using the Model ....................................................................................................................... 88
15.4. Two Applications: Lessons for Monetary Policy....................................................................... 90
15.5. Conclusion: Toward DSGE Models ........................................................................................... 91
16. Understanding Consumer Behaviour .............................................................................................. 92
16.1. John Maynard Keynes and the Consumption Function ........................................................... 92
16.2. Irving Fisher and Intertemporal Choice.................................................................................... 92
16.3. Franco Modigliani and the Life-Cycle Hypothesis .................................................................... 95
16.4. Milton Friedman and the Permanent-Income Hypothesis ...................................................... 95
16.5. Robert Hall and the Random-Walk Hypothesis........................................................................ 96
16.6. David Laibson and the Pull of Instant Gratification.................................................................. 96
16.7. Conclusion ................................................................................................................................ 97
17. The Theory of Investment ............................................................................................................... 98
17.1. Business Fixed Investment ....................................................................................................... 98
17.2. Residential Investment........................................................................................................... 101
17.3. Inventory Investment ............................................................................................................. 101
17.4. Conclusion .............................................................................................................................. 102
18. Alternative Perspectives on Stabilization Policy ........................................................................... 103
18.1. Should Policy Be Active or Passive? ....................................................................................... 103
18.2. Should Policy Be Conducted by Rule or by Discretion?.......................................................... 104
18.3. Conclusion: Making Policy in an Uncertain World ................................................................. 106
19. Government Debt and Budget Deficits ......................................................................................... 107
19.1. The Size of the Government Debt .......................................................................................... 107
19.2. Problems in Measurement..................................................................................................... 107
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19.3. The Traditional View of Government Debt ............................................................................ 108
19.4. The Ricardian View of Government Debt............................................................................... 109
19.5. Other Perspectives on Government Debt.............................................................................. 110
19.6. Conclusion .............................................................................................................................. 111
20. The Financial System: Opportunities and Dangers ....................................................................... 112
20.1. What Does the Financial System Do?..................................................................................... 112
20.2. Financial Crises ....................................................................................................................... 114
20.3. Conclusion .............................................................................................................................. 116
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Epilogue. What We Know, What We
Don’t
There are things in economics that we know, but there are also unresolved questions
that are still heavily debated.
This book has given an introduction into the field of macroeconomics. There are some
important insights contained in the theories to which this book gives an introduction,
but the field of macroeconomics is far from complete. Here we outline the four most
important lessons of macroeconomics, and the four most important unanswered
questions.
The four most important lessons of Macroeconomics
1. In the long run, a country’s capacity to produce goods and services determines the
standard of living of its citizens. The most important question policymakers can
answer is what promotes long run economic growth.
2. In the short run, aggregate demand influences the amount of goods and services
that a country produces. Supply may be the sole determinant of GDP in the long
run, in the short run it is demand that determines the level of GDP.
3. In the long run, the rate of money growth determines the rate of inflation, but it
does not affect the rate of unemployment. There is no such trade-off in the long
run between inflation and unemployment, as is consistent with the classical
dichotomy.
4. In the short run, policymakers who control monetary and fiscal policy face a trade-
off between inflation and unemployment. Although this trade-off does not exist
in the long run, it does exist in the short run.
The four most important unresolved questions in Macroeconomics
1. How should policymakers try to promote growth in the economy’s natural level of
output? Should the government only focus on a high savings rate? Or focus on
stimulating technological progress? Or leave everything to the market? How
should it do these things?
2. Should policymakers try to stabilize the economy? If so, how? Is it possible for
policymakers to predict economic fluctuations and respond accordingly? Do
current policymakers have the necessary tools to do so? Even if they could, do
the benefits outweigh the costs?
3. How costly is inflation, and how costly is reducing inflation? When policymakers
are faced with a situation of rising inflation, they are faced with a choice.
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Should they try to reduce inflation, or is the resulting unemployment not worth
it? How quickly should they try to reduce it?
4. How big a problem are government budget deficits? Will budget deficits be
balanced by consumer saving, as Ricardian equivalence suggests? Or will it
cause a skyrocketing public debt that puts the burdens of today’s consumption
in the hands of future generations?
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1. The Science of Macroeconomics
Macroeconomics is the branch of economics that studies the economy as a whole.
1.1. What Macroeconomists study
Macroeconomics is the study of the economy as a whole. Macroeconomists attempt
to explain the macro-variables that affect the lives of all individuals in an economy,
most importantly, Real GDP, the inflation rate, and the unemployment rate. They are
different from micro economists and from economic policymakers.
Most people are casually introduced to the subject of macroeconomics through
political debates, news events and debates. They are thereby informed of the large-
scale economic events and processes that influence every individual in the economy.
Everyone has some understanding, even if it is vague and rudimentary, of the
questions that are related to the economy as a whole, and it is the discipline of
macroeconomics in which these questions are rigorously studied: What explains the
vast differences in wealth between rich and poor countries? What explains the
periodic recessions and depressions that all countries are affected by? What explains
inflation? And what can the government do to improve these issues?
Macroeconomics is the systematic study of these phenomena, of everything related
to the economy as a whole. It is contrasted to microeconomics, which is the study of
individual firms and markets within the larger economy. It is also contrasted with
economic policy, which is the job of politicians, not necessarily of macroeconomists.
The difference is that macroeconomists try to explain and understand the economy,
but they do not necessarily have the political power to form policies.
On the one hand, macroeconomists use models to attempt to understand and predict
the economy. These models are simplified mathematical “simulations” of the real
economy that try to capture the ‘essence’ of particular macroeconomic processes. On
the other hand, macroeconomists also study actual historical events and processes in
all their complexity, using these models. For example, macroeconomists are still trying
to understand the causes of the economic crisis of 2008, a historical event, by using
various macroeconomic models.
There are many macroeconomic variables, too many to name them, but they all
revolve around the three most important variables: Real GDP, The total level of
income in an economy, the inflation rate, the rate at which prices are rising on
average, and the unemployment rate, the amount of workers that don’t have a job as
a percentage of the amount of workers (also called the labour force). Most of
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macroeconomics is about explaining the long-term and short-term movement of these
variables.
1.2. How Economists Think
Macroeconomists attempt to explain the economy objectively. The predominant
approach to economic theory is the building of models. Models are collections of
endogenous and exogenous variables and relations between them that attempt to
explain aspects of the complex economy in a simplified manner.
Economists address issues that are often politically and ideologically charged, but
attempt to do so in an objective way. The predominant way that economists build
theories of the economy, is by building models. A model is a collection of endogenous
variables and exogenous variables, and a relationship between them. Endogenous
variables are the variables that an economists tries to explain, for example the short
term fluctuation of GDP during an economic crisis. Exogenous variables are the
variables that are thought to explain the changes in the endogenous variables, for
example consumer confidence. In other words, changes in the exogenous variables
are assumed to be the causes of changes in the endogenous variables. In this example
model, a change in consumer confidence is assumed to result in a change in GDP, but
not the other way around. A simpler way of putting it is: Exogenous variables go into
the model, and endogenous variables come out.
The most famous economic model is the supply-demand model. The supply function
of a good is given by the equation
Qs = S(P,Pm).
Where P is the price of the good, and Pm is the price of the materials used to make the
good. The demand function is given by the equation
Qd = D(P, Y)
Where Y is the aggregate/national income. The final part of the model is the
assumption of market clearing: that the price of the good adjusts so that supply equals
demand:
Q = Qs = Qd
Where Q is the amount of that good produced after the market clears. This is called
the equilibrium quantity, and the price at which the market clears is the equilibrium
price. In this model, Q and P are the endogenous variables, and Y and Pm are the
exogenous variables.
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However, there is most often not one model that completely explains a
macroeconomic phenomenon, so economists usually use multiple models. The models
then differ in the assumptions that they make about the relationships between the
variables. For example, some models assume that markets do not always clear
because prices are sticky, meaning that prices tend to change only slowly after a
change in an exogenous variable (a change in an exogenous variable is also called a
shock), whereas other models assume continuous market clearing and flexible prices.
1.3. How This Book Proceeds
An overview of the structure of the book.
The outline of this book is as follows:
Part one: Introduction
Chapter 1 and 2
Part Two: Classical Theory: The Economy in the Long Run
Chapters 3 to 7
Part Three: Growth Theory: The Economy in the Very Long Run
Chapters 8 and 9
Part Four: Business Cycle Theory: The Economy in the Short Run
Chapters 10 to 14
Part Five: Topics in Macroeconomic Theory.
Chapters 15 to 17
Part Six: Topics in Macroeconomic Policy
Chapters 18 to 20
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2. The Data of Macroeconomics
The three most important statistics in macroeconomics are GDP, the inflation rate,
and the unemployment rate.
2.1. Measuring the Value of Economic Activity: Gross Domestic Product
Gross Domestic Product (GDP) is the measure of the total income in the economy, or
equivalently, the total expenditures on goods in the economy. It is derived from the
circular flow of economic activity and measured within the framework of the
national income accounts. We make the distinction between Real- and Nominal
GDP, and the GDP-Deflator, a measure of inflation, is derived from the two. The
components of GDP are consumption, investment, government expenditure and net
exports. GDP is always adjusted for seasonal cycles.
Economists use economic theories to explain and understand the economy, but a
theory that is not based on empirical data is likely not valid. Data is used to 1) build
theories, and 2) test their validity. In other words, data is the evidence used to test
theories. Economists have become better and better over time at systematically
collecting data relating to the economy. This chapter focuses on the three most
important macroeconomic statistics on which data is being collected: GDP, the
inflation rate, and the unemployment rate
Income, Expenditure and the Circular Flow
GDP is measured by combining a large amount of “primary data sources”:
administrative data such as data of tax collection, data from government programs,
regulatory programs, and statistical surveys of firms. These are then used to estimate
the value of GDP.
There are two interpretations of the GDP statistic: 1) The total income of everyone in
the economy, and 2) the total expenditure of goods and services in the economy.
These quantities are the same, because every time a good is purchased, the
expenditure on that good by the buyer is exactly the same as the income provided by
that good for the seller.
The system that is built to categorize and relate all the components of GDP is called
national income accounting, and is based on the “circular flow model” of the economy.
The circular flow model consists of two actors: Firms, and Households. There are two
flows in this model: 1) the flow of goods and services. Households provide labour to
firms that are used to produce goods. And firms provide these goods to households.
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2) The flow of currency (e.g. Dollars/euros). Firms provide income payments to
households in exchange for their labour, and households provide expenditure
payments to firms in exchange for their produced goods. The two measurements of
GDP correspond to the total income and total expenditure respectively.
The values of goods measured in the national income accounts come from the market
price of that good. If there is no market for a good, an estimate is made of its value
(called its imputed value). The underground economy, or black market, is not included
in GDP.
Real GDP versus Nominal GDP
There are two different measurements of GDP: Real GDP and Nominal GDP. The
Nominal GDP of year 2012 is measure by using the amounts produced of all goods
and services and their prices in the year 2012. The problem with this measurement, is
that because the price level changes over time, sometimes to a very great extent
(inflation), this makes the comparison of nominal GDP in year 2000 with nominal GDP
in year 2010 rather meaningless. It could be possible that the economy did not
produce any more goods in 2010 than in 2000, but if prices have risen, there will
nevertheless be a growth in nominal GDP. To correct for inflation, the Real GDP
statistic was created. It measures the GDP using constant prices for all years. The
value of this constant price level is the price level in the so called base-year. For
example, if the base year is 2000, then the real GDP of 2012 is formed from the
amount of goods produced in 2012 and the price level from the year 2000:
Real GDP in year 2012 = (2000-price of apples X 2012 quantity of apples) +)
2000-price of oranges X 2012 Quantity of oranges)
One measure of the inflation rate, the rate at which prices are increasing, is called the
GDP deflator, and can be calculated from real and nominal GDP:
GDP Deflator = Nominal GDP/Real GDP
It is the price of output in a year relative to its price in the base-year.
The Components of Expenditure
GDP is divided into four broad categories within the national income accounts:
Consumption. The goods and services bought by consumers/households for
immediate use.
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Investment. The goods and services bought for future use. They include
business fixed investment, residential fixed investment, and inventory
investment. This generally refers to expenditure on goods that can be used in
future production.
Government Purchases. Goods and services purchased by all levels of
government (e.g. federal, national, local, etc..)
Net exports. The export of goods and services to other countries minus the
imports from other countries. This accounts for trade between countries.
The national income accounts identity summarizes these components of expenditure:
Y = C + I + G + NX
Besides GDP, there are a number of other very similar but subtly different measures
of income. Gross national product (GNP), which corrects for cross-border factor
payments, net national product (NNP) which accounts of the tearing down of goods
over time (depreciation), and a number of other measure.
Seasonal Adjustment
GDP is always measured over a time interval. This is equivalent to saying that it is a
”flow” variable, and not a” stock” variable. A stock variable is measured at a specific
point in time. An analogy for this is the example of a river that moves to a lake. The
river consists of a flow variable, because it consists of a certain amount of water that
moves into the lake over a certain time interval (for example 1000 litres per second),
but the lake consists of a stock variable, because it contains a certain amount of water
at a certain point in time. So GDP is always income per year/month/day (usually
measured as per year). However, the actual GDP changes vastly at different parts of
the year. During the summer holidays, GDP is relatively low. Economists are much
more interested in the “average” GDP over the whole year, than in the predictable but
un-interesting seasonal differences. This is why GDP is usually seasonally adjusted,
which means that that the GDP measured during a quarter of a year is not the actual
income during that time interval, but what that income would be on average over the
entire year. In this way, GDP over time is “smoothed”. GDP statistics are almost
always seasonally adjusted.
2.2. Measuring the Cost of Living: The Consumer Price Index
Inflation is the gradual increase in the price level of an economy, the
weighted average level of prices of all goods in an economy. There are multiple
measures of the inflation rate, of which the CPI is the most commonly used, and it is
a Laspeyres index. Another is the GDP deflator, which is a Paasche index. Neither of
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these measures are perfect estimates of inflation, and all measures either understate
or overstate inflation.
Inflation is the process that the price level rises over time. The price level is a kind of
“average” of all the prices of all the goods in the economy. There are multiple
measures of the price level, and the most commonly used measure is the Consumer
Price Index (CPI), that measures the price level of a large number of consumer goods.
Another example is the GDP deflator (explained in the preceding subchapter). The CPI
and other price indexes are always measured with respect to some base-year.
If the base year is 2000, then the CPI in year 2012 is:
CPI = (2012-quantity of apples X 2012-price of apples) + (2012-quantity of
oranges X 2012- price of oranges)/ (2012 quantity of apples 2000 price of
apples) + (2012 quantity of oranges 2000price of oranges)
There are a number of key differences between CPI and GDP-deflator measures of
inflation.
1. The GDP-deflator measures the prices of all goods, whereas the CPI measures
the prices only of consumer goods.
2. 2. The GDP deflator includes only domestically produced goods, whereas the
CPI includes also imported goods. For example, an increase in the price of oil
has no impact on the GDP deflator of a non-oil producing country, but it will
likely strongly influence the CPI.
3. GDP-deflator is a Paasche index, whereas the CPI is a Laspeyres index. A
Paasche index is an index with a changing basket of goods (quantities of the
good are different in the base year than in the year being measured), whereas a
Laspeyres index is an index with a fixed basket of goods. The significance of
this is that a Laspeyres index overstates inflation, whereas a Paasche index
understates inflation. The actual level of inflation is not directly measurable,
but for this reason, economists sometimes take the average of a Laspeyres and
Paasche index to more accurately estimate the level of inflation.
Besides the inherent bias of Laspeyres indexes to overstate inflation, there are other
reasons why the CPI allegedly overstates inflation:
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1. The introduction of new goods. This will increase the purchasing power of
consumers, because new goods are often also better, yet it is not reflected in a
lower CPI
2. Unmeasured increases in quality. Goods are often improved in subtle ways.
(E.g. computers have become better over the last decades), but these
improvements are not measured into the CPI. Therefore, if the price of a
computer rises over time, the CPI will consider this to contribute to inflation,
even if this rise in price might be a reflection of an increase in its technological
qualities.
2.3. Measuring Joblessness: The Unemployment Rate
The unemployment rate is the fraction of unemployed workers as a percentage of
the labour force. It is related to but distinct from the labour-force participation rate,
the number of people willing and able to work as a percentage of the adult
population in a country. The unemployment rate is measured using a household
survey.
The unemployment rate is an important economic measure because a high
unemployment rate suggests that the economy is not using its resources to its fullest
extent, and because high unemployment means a large number of people who are
unsatisfied.
The unemployment rate is estimated by a government agency (e.g. the U.S. Bureau of
Labour Statistics), using a large survey of households. People are categorized into one
of three categories:
Employed
Unemployed
Not in the Labor Force
The labour force equals the amount of employed workers plus the amount of
unemployed workers (L = E + U), and it refers to the number of people that are able
and willing to work. People not in the labour force include those who would want a
job but have given up looking for one, or those who cannot work or do not want to
because they are disabled retired, or students.
The unemployment rate is the number of unemployed as a percentage of the labour
force (u = U/L). Similar but distinct statistic is the labour force participation rate, the
number of people in the labour force as a percentage of the adult population.
In most western economies the labour force participation rates among men have
decreased slightly, whereas that of women has increased steeply over the last 60
years.
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2.4. Conclusion: From Economic Statistics to Economic Models
The three statistics of GDP, inflation rate, and unemployment rate are quantified
measures of the performance of the economy. They are used as policy information
by practical decision makers, but also as empirical data for economic scientists, who
use them to build and test their models. One key lesson learnt from this chapter is
that all macroeconomic statistics are only imperfect estimates.
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3. National Income: Where it comes from
and where it goes
GDP is the measure of national income. This chapter addresses where GDP comes
from, how income and output are distributed, and what determines the supply and
demand for goods and services.
The circular flow model introduced in chapter 2, consisting of firms and households, is
a bit too simple. A more expanded version of the circular flow model also includes the
government, and three key markets: The markets for goods and services, the markets
for the factors of production, and the financial markets.
This chapter will develop a basic classical model that explains the interactions depicted
in this figure, thereby answering four basic questions about GDP:
What determines a nation’s total income (GDP)?
How is this income distributed among workers and owners of capital?
How is the output of production distributed among households and firms?
How is equilibrium between demand and supply of goods and services
achieved?
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3.1. What Determines the Total Production of Goods and Services?
The production function and factors of production together determine the level of
output.
In the classical theory, GDP is determined by two things:
1) The factors of production of an economy
2) The production function of an economy
The current consensus of economists is that the classical theory is a theory of the long
run, and therefore does not explain short run fluctuations in GDP, nor the very long
run development of the economy. For this, see chapter 10 and 8 respectively.
Factors of production
Factors of production are inputs used by firms to produce goods and services. There
are two main factors of production, Labour (L) and Capital (K). Sometimes Land is also
included as a factor of production, but it is omitted in this book.
We make the simplifying assumption in this chapter that the factors of production are
fixed, i.e. they do not change over time. This is depicted symbolically by an overbar as
follows:
K =K, L = L
We also make the simplifying assumption that all factors are fully utilized in
production at all times, which effectively means zero unemployment, and zero idle
capital.
Production function
the production function is a function of form:
Y = F (K, L)
It reflects, among other things, the available technology in an economy that allows it
to use the factors of production to produce goods and services. This means for
example that an economy with a very highly educated and skilled labour force will
have a different production function than a country with a lowly educated and
unskilled labour force. The former country will produce more with the same amount
of labour and capital than the latter, which is represented by a higher value of the
production function given the same K and L.
One possible property of a production function is constant returns to scale. This
means that increasing the amount of labour and capital by 10% will also increase
production, and therefore GDP, by 10%. This is depicted mathematically as follows:
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zY = F(zK,zL)
Production functions can also have increasing and decreasing returns to scale.
We also assume that the production function is fixed over time.
The supply of goods and services
the production function and the factors of production together determine the supply
of goods and services in the classical model. Because both the factors and the
production function are fixed, GDP is also fixed in the classical theory:
Y = F(K,L) = Y (WITH OVERBARS)
Growth in GDP is addressed in chapters 8 and 9
3.2. How Is National Income Distributed to the Factors of Production?
National income is distributed among the different factors of production, labour and
capital. This chapter addresses how this distribution arises.
This subchapter explains the so called neoclassical theory of distribution, a neoclassical
theory that predicts how the income is distributed among the factors of production.
The theory is a synthesis between classical (18th century) theory of supply and
demand, and the 19th century theory of marginal productivity.
Factor prices
Factor prices are the amounts paid to the factors of production per time interval (it is
therefore a flow-variable). The factor price of labour is the hourly, daily, weekly,
monthly, or yearly wage. The factor price of capital is the hourly, weekly, monthly, or
yearly rental price of that capital good (for example the monthly rental price of renting
an office building, or of a factory machine).
In the classical (long term) theory, the factor price is determined by the equilibrium
between the supply and demand of that factor.
The Decisions Facing a Competitive Firm 18
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The classical theory assumes that all firms are competitive firms. A competitive firm is
so small that it has negligible influence on the market prices in which it trades. This is
equivalent to the assumption of perfect competition.
We assume that the goal of all firms is to maximize profit. Profit is determined as
follows:
Profit = Revenue – Costs.
Where Costs = Labour Costs – Capital Costs.
And Revenue = Good price * F(K,L)
Where F(K,L) is the individual production function of the firm, and gives the amount
of its good produced.
Therefore:
Profit = P*F(K,L) – WL – RK
Where W is the wage rate of labour, and R is the rental rate of capital.
A firm must decide how much Labour and Capital to employ in order to maximize
profit.
The Firm’s Demand for Factors
the demand for the factors of production is the amount that all firms would like to
employ of those factors. Firms will want to employ such an amount that they
maximize their profits. According to the classical theory, they will employ such that
the Marginal product of that factor equals the price of that factor, and this can be
explained as follows.
The marginal product of labour (or capital) is the extra production created by
employing an extra unit of that factor.
So MPL = F(K,L+1)-F(K,L)
the marginal product of a factor can also be calculated by taking the mathematical
derivative of the production function with respect to that factor.
Most production functions have a property called diminishing marginal product. This
means that, while keeping all other factors constant, increasing the amount of a factor
will yield less and less results per unit. E.g. employing 1 worker instead of 0 workers
will yield far greater results for a firm than employing 101 workers instead of 100.
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Because firms maximize profits, they keep employing a factor of production until
doing so would no longer increase profits. In other words, they stop employing it as
soon as marginal revenue equals marginal cost (i.e. until the extra revenue of
employing 1 unit of a factor equals the extra cost of employing it):
ΔProfit = ΔRevenue – Δcost = 0
For Labour this is
P * MPL – W = 0
And for Capital it is
P * MPK – R = 0
From this we can derive the wage rate and the rental rate of capital:
W = P * MPL
R = P * MPK
Alternatively we can write the real wage and real rental rate instead of their nominal
values (just like deriving real GDP from nominal GDP):
W/P = MPL
R/P = MPK
So the firms demand each factor of production until marginal product falls to their real
factor price.
The Division of National Income
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The income is distributed between the owners of the firm, the owners of capital and
the workers (labour). However the economic profit of the firms in the neoclassical
theory, is zero. This is because the neoclassical theory assumes a production function
with constant returns to scale, and therefore when marginal products equal the real
price of the factors, revenue equals costs, and profit is zero.
Here we must distinguish between economic profit and accounting profit. In the real
world, the owners of the firm are usually also the owners of capital, and accounting
profit therefore also equals the return to capital. Economic profit only equals the
profit that remains after having paid the owners of capital.
We conclude that total income is distributed among labour according to the marginal
productivity of labour, and to capital according to the marginal productivity of capital.
The Cobb-Douglas production function
one commonly used production function is the cob-douglas production function.
It has the following form:
F(K,L) = AKαL1-α, Where 0<α<1
It has two important characteristics:
1. It has constant returns to scale
2. A constant percentage of economic output is distributed to the factors of
production, namely its power.
The second means that a share of α goes to the owners of capital, and a share of 1-α
goes to labour. The cob-douglas function is often used, because it has been shown
empirically that the share of income that goes to labour and capital is indeed very
constant.
3.3. What Determines the Demand for Goods and Services?
Demand for goods and services is determined by those who are willing to purchase
its output: consumers, investors and the government.
The previous subchapter explains the distribution of income (GDP). This subchapter
explains the distribution of expenditures on the goods produced (also GDP).
WE make the simplifying assumption of a closed economy meaning that there is no
trade with other countries, so that net exports are zero. This means that GDP
becomes:
Y=C+I+G
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Consumption
Consumption is done by households, and is thus based on the income of households,
Y. However, households have to pay taxes T to the government, so the amount that
they consume is not based on income, but on disposable income Y –T:
C = C(Y-T)
This function is called the consumption function, and its derivative is the Marginal
propensity to consume.
Investment
Investment is expenditure on goods used for the future. The interest rate is the major
determinant of the quantity of investment goods demanded. The interest rate is the
cost of funds used to finance investment. However, just as there is real and nominal
GDP, there is a real and a nominal interest rate. The real interest rate (r) is the nominal
interest rate (i) corrected for the effect of inflation (π):
r=i–π
Investment is a function of the real interest rate:
I = I(r)
Note: there are in fact an enormous number of different interest rates, but since they
are all strongly related, we simplify this by speaking of “the interest rate”.
Government purchases
Government purchases or government expenditures are all expenditures by all layers
of government (local, state, federal/national).
Government purchases are not the same as government spending. Government
spending also includes income transfers, such as social security programs, and
retirement programs, but this is not included in government purchases.
If government expenditures equal taxes, then the government is running a balanced
budget. If G is less than T, it runs a surplus, and if T is less than G it runs a deficit. Both
T and G are fixed variables in the classical theory.
3.4. What Brings the Supply and Demand for Goods and Services Into
Equilibrium?
In the classical model, equilibrium between supply and demand of goods and services
is determined by the interest rate, which is determined by the market for loanable
funds.
In this model, the exogenous variables are Taxes and Government expenditure, and
the endogenous variables are consumption, investment and the interest rate. The
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question is, what brings supply and demand for output in equilibrium?
Equilibrium in the supply and demand for goods and services
the supply of the goods and services in the economy is determined by the production
function
Supply of Y = F(K,L) = Y- WITH OVERBARS
the demand for goods and services is
Y = C+I+G, Where C = C(Y-T)
I = I(r)
G=G
T=T
So because the economy is in equilibrium:
Y = C(Y-T) + I(r)+G
The interest rate r is the only variable that is not determined. It is the interest rate
that changes in order to equilibrate supply and demand for goods and services. When
supply equals demand, we speak of the “equilibrium interest rate”.
Equilibrium in the financial markets
Why is it the interest rate that equilibrates the supply and demand of goods and
services? To understand this we turn to the financial market, and its role in the
circular flow.
Households do not spend all their disposable income. They allocate their disposable
income to consumption and private saving. The government also does not necessarily
spend all their tax revenue, or more than it. The budget surplus is equal to public
saving. National saving is the sum of public and private saving, and is fixed because all
its constituent elements are fixed:
S = Y-T-C(Y-T) + T-G
Saving is equal to the supply of loanable funds in the financial markets. The financial
markets serve the function of redirecting national saving to investment. Loanable
funds can be seen as just another good, where the interest rate equilibrates the two:
S = I(r)
The interest rate adjusts until the amount that firms want to invest equals the amount
that households and the government want to save, so that the quantity of loanable
funds supplied and demanded are equal.
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Changes in Saving: The Effect of fiscal policy
From the equation of the market for loanable funds, it can be seen that if government
purchases increases, saving decreases. So the interest rate must increase, and
therefore investment decreases.
Because the level of income is assumed to be constant in the classical model, the
increase in government purchases is offset exactly by a decrease in investment.
Therefore we say that government purchases crowd out investment.
A decrease in taxes has a similar effect, but also influences saving by increasing
disposable income, so the effect of a decrease in taxes on saving is smaller than an
equal increase in government expenditures.
Changes in investment Demand
It is possible that investment demand increases, because for example there is
technological innovation, or because the government encourages investment through
its tax or regulatory laws. In this case the investment function I(r) shifts to the right.
However because saving is fixed, this has no effect on investment, only on the
interest rate.
There are also models that assume that saving and consumption depends on the
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interest rate, so that saving is not fixed. However we do not address such models in
this book.
3.5. Conclusion
This chapter has explained the classical model, but this model only described the
economy in the long run. It neglects the short run and very long.
This chapter has explained the classical long run model that assumes that prices adjust
to equilibrate supply and demand. We will address more expanded models in later
chapters by focusing on different aspects of the economy:
This model does not address the role of money. This is addressed in chapters 4
and 5
It does not address trade. This is addressed in chapter 6
It does not address unemployment, which is addressed in chapter 7
It assumes that the capital stock, labour force and production technology is
fixed. This assumption is dropped in chapter 8 and 9 which addresses the very
long run, the growth of an economy.
It does not address the fact that in the short run, prices are sticky. Chapters 10
to 14 explain the short run business cycle.
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4. The Monetary System: What It Is and
How It Works
The two main types of macroeconomic policy are fiscal policy and monetary policy,
and this chapter discusses the basics needed to understand monetary policy,
inflation and the banking system. It discusses the role of money, banks and the
central bank in the economy.
4.1. What Is Money?
The way economists use the word money is different from the way it is used in
everyday life. There are different types of money, and this chapter introduces the
concept of the money supply.
The word money has a specific meaning in the field of economics that is different
than its meaning in everyday use. It is the stock of assets that can be readily used to
make transactions. It does not refer to the wealth of an individual. It nevertheless
includes certain instruments not usually regarded as money, such as money market
assets.
Functions of Money
There are three functions of money
A store of Value. It allows people to transfer purchasing power from the
present to the future
Unit of account. It allows us to compare the value of different items, such as
cars and apples, which would otherwise be very difficult to compare
Medium of exchange. It allows us to exchange goods and services with each
other without having to find a set of individuals who happen to have exactly
what the others want.
Types of Money
Over history there have been different types of money. Today the most commonplace
form of money is fiat money, money that has no intrinsic value as a good. Another
type is commodity money. In this case a certain commodity that also has an intrinsic
value is used as money, such as copper which is much used in industries. Using gold as
money, or paper money that is officially backed by gold, is called a gold standard. Fiat
money is generally considered efficient because it is lightweight (lower transaction
costs). The value in money is not actually in the intrinsic value of the item, but in the
fact that it is a social convention.
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How the Quantity of Money is controlled.
The quantity of money of a certain currency is called the money supply. Monetary
policy is the control of the government over the money supply. Monetary policy is
delegated to a central bank in most countries. The central bank of the United States is
called the Federal Reserve. Central banks control the money supply primarily by open-
market operations, which is the purchasing and sale of government bonds. A sale of a
bond in exchange for money reduces the money supply (because the money used to
purchase the bond from the central bank, is now no longer in the economy but in the
central bank’s vaults), and the purchase of a bond increases the money supply.
How the Quantity of Money is measured.
There is not just one measure of the money supply, because what counts as money is
somewhat vague. What is always included is currency, the total paper money and
coins in an economy. Also included are demand deposits. In another measure, savings
deposits are also included. M1 equals Currency + demand deposits. M2 equals M1 +
money market mutual fund balances + savings deposits.
4.2. The Role of Banks in the Monetary System
The role of the banking system in the monetary system is that in fractional-reserve
banking, the money supply is in part determined by banks.
The central bank does not actually directly control the money supply, because the
money supply is not just currency. The money supply is determined by both the
central bank, and the banking system, and in order to understand the money supply
we must understand fractional reserve banking. Throughout the book we assume that
M = M1.
100-percent-reserve banking
In a world with 100-percent-reserve banking, banks do not lend out the money that
people deposit. This means that if one puts money on the bank, the deposits on that
bank will increase just as much as the currency will decrease (because the currency is
now in the bank’s vaults, and no longer in the economy).
The balance sheet of a bank thus looks like this
In this type of banking system the banking system does not affect the money supply.
Fractional Reserve banking
For the last centuries, the banking system has been a fractional-reserve
banking system. This means that banks only keep a fraction of their deposits as
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reserves and give out the rest as loans. The balance sheet of the bank now looks like
this:
The amount that is loaned out is now held either as currency or it is put back into a
bank. Therefore “the same dollar is counted twice”, because it is counted as a deposit
by the person who went to the bank, but also as a deposit by the person who loaned
from the bank. This in turn is again lent out, and so forth. We say that banks create
money. They do this by transferring funds from savers to borrowers, and this process
is called financial intermediation.
Bank Capital, Leverage and Capital Requirements
In the previous examples, a bank only has bank deposits, but in reality, banks also
have their own capital. The fact that banks use deposited funds besides their capital
to invest is called leverage. The leverage ratio is the ratio of the bank’s total assets to
its capital (owner’s equity). One of the regulatory restrictions on banks is capital
requirement. This means that the leverage ratio is not allowed to be higher than a
certain amount (i.e. the capital to asset ratio must be higher than a certain amount).
4.3. How Central Banks Influence the Money Supply
The central bank determines the monetary base, and the banking system determines
the money multiplier. Together they determine the money supply.
We now combine the model of the banking system and the central bank to build a
model of the money supply.
A Model of the money supply
The model has three exogenous variables:
Monetary base B. The total number of Currency C and Reserves R. B = C + R.
Reserve-deposit ratio rr. The fraction of deposits held by banks in reserve. It is
determined by bank policy and regulatory laws. Rr = R/D
Currency-deposit ratio cr. The ratio of currency C that people hold to the
demand deposits D. cr = C/D.
We use M = M1, which is C + D.
Dividing the money supply by Monetary Base gives
M/B = (C+D)/(C+R)
Dividing top and bottom of the fraction by D gives
M/B = (C/D + 1)/(C/D + R/D) = (cr +1)/(cr + rr)
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We call m = (cr +1)/(cr + rr), the money multiplier.
Therefore, M = m * B
The monetary base is for this reason sometimes called high powered money,
The Instruments of Monetary Policy
The Central bank has multiple ways to change the monetary base. The main one as
described earlier is open market operations. The CB can also lend directly to banks at
the so called discount rate (the interest rate on these loans).
The Central bank can also influence the reserve-deposit ratio by multiple means. The
main instrument of doing so is the reserve requirements, a regulation that imposes a
minimum on the reserve-deposit ration of each bank. This tool has become less
effective because banks have started to hold excess reserves. Another tool is that the
CB can pay interest on reserves at the CB. This means that if banks hold reserves, the
CB pays those banks an interest on them.
Although the CB has multiple instruments by which it can effectively change the
money supply, it is not straightforward for the CB to actually control the money
supply, because it often does not have the necessary information to predict how the
money multiplier will change. One example where this went wrong is the banking
crisis during the 1930’s; the Federal Reserve is often blamed here for not increasing
the money supply.
4.4. Conclusion
We have now seen how the central bank can control the money supply, but this is
only interesting if we know how the money supply influences the economy, which is
the subject of the next chapter.
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5. Inflation: Its Causes, Effects, and Social
Costs
This chapter addresses the causes, effects, and social costs of inflation and its
relation to the money supply within the classical theory. Inflation is the overall
increases in prices.
Inflation can sometimes take such proportions that we speak of hyperinflation,
periods of extraordinarily high inflation, such as the 500 percent inflation per month
in Germany in 1923. “Normal” levels of inflation are between 2 and 20 percent.
5.1. The Quantity Theory of Money
The quantity theory of money describes the effect of the money supply on inflation
in the long run.
This subchapter explains the Quantity theory of money, the dominant (classical)
theory of the effect of the money supply on the economy (in the long run).
The theory consists of the quantity equation:
Money X Velocity = Price X Transactions
MXV=PXT
Where V is the transactions velocity of money, the number of times a
dollar/euro/yen changes owner during a given period of time. T is the total amount of
transactions done during that period of time. The quantity equation is an identity (it is
by definition true, due to how the variables are defined).
However, the amount of transactions is hard to measure and not very meaningful, so
therefore we change the equation to
M X V = PXY
Where Y is output, or income (GDP). Output is not the same as the amount of
transactions, but they are roughly proportional, so that the equation still reasonably
holds. Within this equation, V becomes the income velocity of money.
The money demand function and the quantity equation.
We can express the money supply in terms of how much goods and services it can
purchase. This gives us the real money balances, M/P. We can then write the money
demand function, the demand for real money balances:
(M/P)d = kY
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By assuming that money demand must equal money supply, we can rewrite this to
M(1/k) = PY, so that we see that V = 1/k. We conclude that the money demand and
money velocity are two sides of the same coin.
Using these definitions, we now formulate the quantity theory of money by assuming
that money velocity remains constant: MVUPBAR = PY. Since Y is fixed in the
classical theory, there is a direct linear relation between the money supply and the
price level.
According to this theory therefore, the central bank has ultimate control over
inflation. Again, this classical theory works well in the long run, but not so well in the
short run.
5.2. Seigniorage: The Revenue from Printing Money
Seignorage is government revenue caused by increasing the money supply.
Inflation is not the only direct consequence of increasing the money supply. The most
important motivator for the government to increase the money supply is to earn
revenue that is received by printing money. This source of government revenue is
called seignorage. This is effectively a hidden inflation tax, because printing money
causes inflation over time, while households’ income stays the same, thereby
decreasing real household income. In history, wars have often been financed by
seignorage revenue, and are often accompanied by higher inflation. An example is the
American Revolution.
5.3. Inflation and Interest Rates
The real interest rate can be derived from the nominal interest rate and the rate of
inflation.
There is an important relation between inflation and the interest rate. Just like many
economic variables, there is both a nominal interest rate and a real interest rate. The
nominal interest rate is the actual interest rate paid (e.g. by government bonds). The
real interest rate is corrected for inflation:
r=i–π
Thus the real interest rate is a theoretical variable not actually observed, but derived
from the nominal interest rate and inflation. However, if we write it in its opposite
form, and assume that the real interest rate remains relatively constant, we get the
Fisher equation:
i=r+π
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We can see that the nominal interest rate can change either because the real interest
rate changes, or because the inflation rate changes. The one for one relation between
the nominal interest rate and the inflation rate is called the fisher effect.
Two Real interest rates: Ex Ante and Ex Post
We distinguish between two types of real interest rate:
Ex Ante r = i – Eπ, where Eπ is the expected level of inflation at the time that
the contract of a loan is signed. It is the real interest rate expected beforehand.
Ex Post r = i – π. It is the real interest rate actually realized afterwards.
Because the nominal interest rate does not actually adjust to inflation after the
contract is signed, the more precise version of the fisher equation is
i = r – Eπ.
5.4. The Nominal Interest Rate and the Demand for Money
There is a relation between the interest rate and the demand for money.
The money demand function in the quantity theory is based on the assumption that
money demand is proportional to income (addressed in 5.1). However in reality
money demand is also dependent on the nominal interest rate. The nominal interest
rate is effectively the price of holding money, because it is an opportunity cost of
foregoing the income of saving. Therefore we introduce the more complete money
demand function:
(M/P)d = L(i, Y)
This can also be written as
(M/P)d = L(r + Eπ, Y)
This shows us that the current money demand depends on the expected future price
level. Therefore the demand for money depends on the money supply growth, which
complicates the earlier quantity theory of money.
5.5. The Social Costs of Inflation
Economists point to specific costs associated with inflation that are different than
what laymen tend to consider. There is also a possible benefit of inflation.
Most non-economists believe that there are certain social costs associated with
inflation. Economists certainly agree that such costs exist, but the layman’s view of
the costs of inflation is different from the costs of inflation described by the classical
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view.
Layman’s view: Inflation is bad because it diminishes the real purchasing power of
people’s income.
The classical response to this is that nominal incomes also rise with inflation, so that
inflation does not cause a diminishing real purchasing power.
The actual costs of inflation according to the classical view can be put in two
categories: expected and unexpected inflation.
The Costs of Expected Inflation
There are a number of costs associated with inflation that people “saw coming”.
It being an inflation tax has a distorting effect on the amount of money people
hold. This creates so called shoeleather costs, costs that are created by having
to go to the bank more often.
Firms have to change their prices more often. This creates so called menu
costs, because changing a price often has a cost.
High levels of inflation mean that there is higher variability in relative prices in
cases where prices haven’t changed yet due to menu costs.
Many provisions in the tax codes do not take inflation into account, causing
microeconomic inefficiencies if inflation is high.
An always changing price level is inconvenient for people, because it makes it
harder to use money to compare the value of things.
The Costs of Unexpected inflation
Economists generally think that unexpected inflation, inflation that the public didn’t
see coming, is more harmful than expected inflation.
It arbitrarily reallocates wealth from creditors to debtors
It diminishes the incomes of individuals on fixed pensions
Therefore highly variable inflation, which has a larger element of unexpected inflation,
is relatively damaging. It is an empirical regularity that higher inflation is also
associated with higher variability of inflation.
One Benefit of Inflation
An inflation of 2 to 3 percent is a good thing according to some economists.
According to this argument, nominal wage cuts don’t happen often, and inflation is a
way of allowing a reduction of real wages in case this is necessary to equilibrate the
labour market.
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5.6. Hyperinflation
Hyperinflation is an extreme level of inflation.
Hyperinflation is “extraordinarily high” inflation and this is usually defined as inflation
larger than 50 % per month. The costs of hyperinflation are the same as the costs of
expected inflation, but these costs rise to extreme and unmaintainable levels.
The causes of hyperinflation boil down to an extreme growth in the money supply.
Most often this growth is necessary to finance government spending. The
government doesn’t have enough other sources of revenue, so uses seignorage
revenue. However due to the costs of high inflation, this is a downward spiral, so that
the government is eventually “trapped” in a policy of hyperinflation. A famous
example of this is Germany from 1922 to 1924, where inflation reached 100 percent
per month, until a new central bank was installed that was banned from buying
government bonds. This hyperinflation started because of Germany’s fiscal problems
after WWI, leading it to turn to seignorage revenue. Another famous example is
Zimbabwe, where in 2008 inflation reached 231 million percent.
5.7. Conclusion: The Classical Dichotomy
The classical dichotomy is one of the fundamental theoretical propositions in
classical theory.
One important conclusion of the classical theory is that although inflation has certain
effects by itself, in the long run money is “neutral”. This gave rise to the classical
dichotomy, the distinction that has already been made earlier, between real and
nominal variables. Real variables correct for the price level and inflation, because in
the long run, inflation has approximately no effect on economic activity (e.g. doubling
the price level will double nominal GDP, but it will not double actual physical
production). This phenomenon is called monetary neutrality, and it is approximately
correct in the long run. In chapter 10 we study how monetary neutrality breaks down
in the short run.
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6. The Open Economy
Previous chapters have discussed a closed economy. This chapter introduces the
open economy, an economy that conducts international trade.
6.1. The International Flows of Capital and Goods
International capital flows and the flows of goods and services always balance out.
When we include international trade in our analysis the national income accounts
identity of an open economy needs to be expanded:
Y = C + I + G + X – IM
Where X is exports and IM is imports. Imports need to be subtracted from GDP,
because imports are not produced in the domestic economy, but they are included in
consumption, investment and government expenditures. Equivalently, they have to be
subtracted because people expend income on imports but nobody in the domestic
economy earns income from those expenditures. We define net exports as exports
minus imports: NX = X- IM. Now the identity becomes:
Y= C + I +G + NX
International capital flows and the Trade Balance.
In chapter 3 we derived the equation S = I for a closed economy, but in an open
economy we have to take into account net exports. Saving S is still equal to Y – C – G,
and rewriting the open economy income identity now gives: S = I + NX. This can be
rewritten as S-I = NX.
This gives us the relation between capital flows and the trade balance. The trade
balance is simply another word for net exports (because it shows the balance of
inward and outward trade). Net capital outflow is the outflow of loanable funds minus
the inflow, and since saving is the total domestic amount of loanable funds available,
and these funds are expended on investment, S-I is the net capital outflow. So the
trade balance must by definition equal net capital outflow. If NX and S-I are positive,
the domestic economy is in a trade surplus, if they are negative it is in a trade deficit,
and if they are zero, it is running balanced trade.
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In summary:
6.2. Saving and Investment in a Small Open Economy
Saving and investment in a small open economy do not determine the interest rate as
they did in a closed economy. Instead, they determine net exports and net outflow of
capital.
We now use this identity (an equation that is by definition true and therefore is not a
theory, because it has no empirical content), and build a theory for a small open
economy with perfect capital mobility. A small open economy is an open economy
whose GDP is so small that it has no effect on the world interest rate r*. Perfect
capital mobility means that there are no barriers between the financial markets of the
domestic economy and the world economy. Because of this assumption, the domestic
interest rate must equal the world interest rate:
r = r*
r* is determined by global demand and supply of loanable funds, but since we describe
a small open economy, the domestic economy has no influence on r*. We assume a
small open economy because it simplifies the analysis.
The Model
We use three assumptions from the model for a closed economy:
Y = Y = F(K,L)
C = C(Y-T)
I = I(r)
We can now write the accounting identity as NX = S – I(r*).
Therefore, Net exports are determined solely by saving, and investment at the world
interest rate.
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How Policies influence the Trade Balance.
Domestic fiscal policy.
Increasing G reduces S, shifting the Savings curve to the left, thereby
decreasing net exports.
Fiscal policy abroad.
Foreign fiscal expansion (increasing G or decreasing T) decreases global saving,
and this increases r*
Shifts in Investment Demand.
This shifts the investment curve to the right, and since r* stays the same, net
exports decreases.
Evaluating Economic Policy
The difference between an open and a closed economy is that in a closed economy,
reducing saving will reduce investment, whereas in a small open economy, reducing
saving will reduce net exports, increase capital inflow and thereby increase the
nation’s debt to foreigners. This is usually seen as a bad thing, but it is not necessarily.
Some countries, such as South Korea, have ran large trade deficits for an extended
period of time, but this capital inflow went into investment, allowing its economy to
grow very rapidly.
6.3. Exchange Rates
The exchange rate is the rate at which two currencies can be traded. It determines
the level of net exports.
This section introduces a new key variable in macroeconomics, one specific to open
economies, namely the exchange rate. The nominal exchange rate e is the rate at
which two currencies can be exchanged. In this book the exchange rate is always
expressed as units of foreign currency per unit of domestic currency. So if the
domestic currency is the Euro, and 1 euro can be exchanged for 2 dollars then the
exchange rate between euro and dollar is 2.
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The real exchange rate ε is the relative price of goods of the two economies. It is the
nominal exchange rate adjusted for the price levels:
ε = e * P/P*
Where P is the domestic-, and P* the foreign price level.
Because people’s willingness to trade with a country depends on the real exchange
rate, we write Net exports as a function of the real exchange rate:
NX = NX(ε)
The determinants of the real exchange rate.
We know two things about net exports:
It must equal saving minus investment
It is related to the real exchange rate
This model combines the two by saying that the real exchange rate is determined by
both these things being true. In other words, the equilibrium real exchange rate is the
rate at which the supply of domestic currency from net capital outflow is equal to the
demand of domestic currency for net exports.
How Policies Inflience the Real Exchange Rate.
Fiscal Policy at Home. Increasing G or lowering T shifts the S-I curve to the left,
thereby increasing the real exchange rate.
Fiscal Policy abroad. Foreign countries increasing G or lowering T increases the
world interest rate. This decreases investment so shifts S – I to the right.
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Shifts in investment demand. If investment demand increases, investment also
increases because r* stays the same. This shifts S-I to the left, and increases the
real exchange rate.
Effects of trade policies. Trade policies try to increase net exports by increasing
export supply or decreasing import demand. However we see from the figure
that this will not actually increase net exports, as this is determined by S-I. It
will only increase the real exchange rate.
The Determinants of the Nominal Exchange Rate.
We can rewrite the relation between real and nominal exchange rate as follows:
e = ε *(P*/P)
And we can now derive what would be the change in e given a change in one of the
other three variables:
% change in e = % change in ε + % change in P* - % change in P
This can be rewritten as
% change in e = % change in ε + (π*-π)
Where π* is foreign inflation and π is domestic inflation.
So we see that the nominal exchange rate over time changes due to 1) a change in the
real exchange rate 2) differences in levels of inflation.
The Special Case of Purchasing-Power Parity.
There is an important hypothesis in economics called the law of one price. This entails
that two identical goods in different locations must have the same price, because if
one were cheaper than the other, buyers would flock to that good instead of the more
expensive one. This law applied to the international marketplace is called purchasing-
power parity (PPP). It refers to the situation where all goods in the economy have the
same real price in each country. In our model it is described by the situation where the
Net Exports curve is very sensitive to changes in the real exchange rate, so that the
real exchange rate maintains purchasing-power parity. This entails that 1) changes in
saving or investment do not change the real exchange rate, and 2) the nominal
exchange rate is only changed by changes in the price levels.
There is some evidence that PPP works as an approximation in the long run, but it is
not a perfect description of exchange rates.
6.4. Conclusion: The United States as a Large Open Economy
The assumption of a small open economy is only a simplification in most cases.
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The assumption of a small open economy is not realistic for large countries such as
the United States. The United States should be seen as a large open economy. It is
important to realize that this simplifying assumption is not realistic, and that countries
like the United States actually behave in a way that is a little bit in between a closed
economy and a small open economy.
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7. Unemployment
Unemployment in the long term is determined by the rate of job separation and job
finding, and policies aimed at reducing long term unemployment should target those
variables.
There is always some unemployment in all market economies. Economists distinguish
between long term unemployment and short term fluctuations in unemployment.
Short term fluctuations are only addressed in the theories of the Business cycle,
chapter 10 to 14. In this chapter we discuss the natural rate of unemployment, the
average rate of unemployment around which it fluctuates.
7.1. Job Loss, Job Finding, and the Natural Rate of Unemployment
A basic model of unemployment is introduced.
We introduce here a model of labour-force dynamics that shows the determinants of
the natural rate of unemployment. We start with the definition of the rate of
unemployment
L=E+U
Where L is the labour force, E is the employed labour force, and U is the unemployed
labour force. The unemployment rate here is U/L
We assume that the labour force is fixed, and that a fraction of the employed E loses
their job each month, and that a fraction of the unemployed find a job. We denote the
rate of job separation (the rate at which employed people lose their job each month)
as s, and the rate of job finding (the rate at which unemployed find a job each month)
as f.
We now find the condition of steady state to determine the natural rate of
unemployment. In the steady state, the amount of people that lose a job must equal
the amount of people that find a job so that
fU = sE
Substituting L –U for E, and rewriting, we find
U/L = s/(s+f) or equivalently, U/L = 1/(1+f/s)
This shows how the natural rate of unemployment depends on the rate of job
separation and the rate of job finding, and that a policy aimed at reducing the natural
rate of unemployment must either make it easier for people to find jobs, or decrease
the rate at which people lose their job. There are underlying reasons for why the rate
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of job separation and the rate of job finding are the way they are, and the next two
sections discuss two of them.
7.2. Job Search and Frictional Unemployment
Frictional unemployment is one of the two main categories of natural
unemployment.
One important element of natural unemployment is frictional unemployment. This is
unemployment that is caused by the fact that it takes time for workers to find a new
job. Workers are not all the same, so it usually takes time and effort to match a
worker to the job that suits him or her.
Frictional unemployment is inevitable, because there are always shifts in demand and
shifts in production technologies for goods. If such a shift occurs, there is also a shift
in the demand for labour needed to produce those goods, so certain jobs will
disappear and new jobs will be created. Such a shift is called a sectoral shift, and they
will cause both job separation and job finding. Another cause of frictional
unemployment is the failure and creation of firms.
Public Policy and Frictional Unemployment
The government often tries to decrease frictional unemployment using for example
employment agencies to match workers and jobs more quickly. However they
inadvertently also create frictional unemployment sometimes, for example
with unemployment insurance. This is insurance by the government to unemployed
workers, which tends to increase the time spent unemployed. However this need not
necessarily be a bad thing, because the longer time spent unemployed may result in a
more efficient allocation of workers to jobs.
7.3. Real-Wage Rigidity and Structural Unemployment
Structural unemployment is one of the two main categories of natural
unemployment.
Wage rigidity is a second reason for natural unemployment. It is the tendency that
wages do not adjust to a level that equilibrates supply and demand. Unemployment
that results from wage rigidity is called structural unemployment.
This book describes three main causes of wage rigidity:
Minimum wage laws. The government forbids firms to hire workers for a lower
wage than the minimum wage. If there are workers that want to work but are
not skilled enough to be hired for minimum wage, they will remain unemployed
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Unions and collective bargaining. Unions bargain with firms for a wage that
suits the insiders of the union: the workers that are already employed by the
firm. The outsiders, the workers that would like to work for the firm, but are
unemployed, are not at the bargaining table, so that the wage is set higher than
they would like (because the high wage stops them from being
employed).Unions do not necessarily cause wage rigidity, and countries in
which outsiders have more influence in unions tend to have lower
unemployment
Efficiency wages. According to efficiency wage theories, increasing the wage
of workers also increases their efficiency, for example because they are more
motivated, or in underdeveloped economies, because it allows them to be
more healthy. Another reason is that it reduces the incentive for workers to
leave the firm. Another reason is that it attracts better skilled workers.
Efficiency wages cause the firm to employ less workers than the labour supply.
7.4. Labour-Market Experience: The United States
The U.S. labour market is used as a case study of unemployment.
Using the U.S. labour market we now discuss some additional facts about
unemployment
The Duration of Unemployment
Not all unemployed workers are unemployed for an equal amount of time. If workers
are employed for a long time, this is a signal that the worker may be part of the
structurally unemployed, rather than the frictionally unemployed. Information about
the distribution of unemployment duration among the unemployed is an important
indicator for policymakers, as frictional unemployment and structural unemployment
require very different policy solutions. It is a matter of contention in the United States
what the causes are of long term unemployment. Some say the government
unemployment insurance is the problem, others say it has to do with the economic
downturn of the beginning of the 21st century.
Another fact that becomes clear by looking at the U.S. situation is that the labour
force, unlike in the model of this chapter, is not fixed. The crisis of 2008 has caused
many people to become discouraged workers, workers who have given up looking for
a job. They are not counted in the labour force.
7.5. Labour-Market Experience: Europe
Europe is used as a casy study of unemployment.
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Looking at Europe, we see that unemployment has risen steadily since 1960. There
has during the same period also been a pattern that workers are working less and less
hours per week. Europeans now work a smaller amount of hours per week on average
than Americans, and there are multiply hypotheses for this difference
Europeans have more taste for leisure than Americans.
The tax systems of Europe discourage work more than those of the U.S.
because they are higher
Unions push for shorter work weeks, and unions are more important in Europe
than in the U.S.
7.6. Conclusion
Natural unemployment is unemployment in the long run.
Natural unemployment is a permanent phenomenon that cannot be completely
removed. The government can try to reduce structural unemployment, but some
causes of structural unemployment, such as minimum wage laws, are desired.
Frictional unemployment can also be tried to be reduced, but it is a normal part of the
economy that results from the job matching process, which is necessary for a well-
functioning economy.
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8. Economic Growth I: Capital
Accumulation and Population Growth
The Solow Growth model is the basic model that describes long run growth of GDP.
Part II, Chapters 3 to 7, explained the classical theory of macroeconomics. It is a
theory that is now thought to apply to the Long Run of an economy. Part III, chapters
8 and 9 address growth theory, the theory of the Very Long Run. In this theory, GDP
is no longer assumed to be constant. Instead it tries to explain economic growth over
time. This is usually a slow process, 2 to 4% per year, and changes over one year are
not very noticeable, but over decades and centuries has enormous effects on the
productive power and standards of living in an economy.
The model introduced in chapter 8 and 9 is the Solow Growth Model, the basic
standard model used for economic growth in macroeconomics.
8.1. The Accumulation of Capital
The basic elements of the Solow growth model are savings, investment, and the level
of capital.
We introduce the fundamentals of the Solow Growth model
Supply of goods and the production function
The Solow model uses a basic production function for the economy, the same as is
used in the classical model in part II:
Y = F(K,L)
And just as in part II, it is a constant returns to scale production function:
zY = F(zK,zL)
However, in the Solow model, we rewrite the production function into a different
form. Instead of using the standard production function, we use the production per
labour function, and we write quantities per worker in lower letters, so that y = Y/L, k
= K/L, and the production function becomes
Y/L = F(K/L,1) = y = f(k).
We can now derive the marginal product of capital:
MPK = f(k+1)-f(k), or equivalently, MPK = f’(k)
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Note that this is not the absolute marginal product of capital, but the marginal product
of capital per labour.
The demand for goods and the consumption function.
We ignore the government and trade in this simplified model, so that the demand for
goods and services is given by
y=c+i
Where c is consumption per worker, and i is investment per worker.
A fraction of the income is saved by households and this is given by s. this means that
a fraction 1 – s is consumed. Therefore the consumption function is:
c = (1-s)y
W can plug this into the goods market demand function to obtain investment
y = (1-s)y + i => i = sy
Which is again equivalent to saying that investment equals savings.
These two ingredients, the production function and the consumption function are the
basis of the Solow growth model.
Growth in the Capital Stock and the Steady State.
The purpose of the Solow model is to explain long term growth, and it does so by
analysing the effect of investment on the capital stock k (capital per worker). Besides
investment, the building of new capital equipment, the second force that influences
the capital stock is depreciation, the tearing down of existing capital equipment.
The rate of deprecation each year is given by δ. So the change in the capital stock is
given by
Δk = i – δk, which is written as
Δk = sf(k) – δk.
The depreciation of capital goods increases linearly with respect to capital per labour,
but since the production function has constant returns to scale, investment increases
at a decreasing rate with respect to capital per labour. This means that there is a point
at which there is a steady-state, a level of capital per labour that makes that new
production of capital goods equals depreciation of old capital goods. We denote the
steady state level of capital by k*. So the steady state level of capital is defined by the
following equation:
sf(k*) = δk*, so that Δk = 0
For this reason δk can also be called the break-even level of investment here.
Two examples of the process of moving towards the steady state level of capital are
Japan and Germany after the war. The war destroyed a very large part of the factories
and other productive machinery in those countries, while the labour force was still
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able to produce the pre-war level of production. This caused investment to be much
bigger than depreciation, so that there was a period of fast capital accumulation.
How Saving Affects Growth
The Solow model predicts that an increase in the savings rate should also increase the
level of capital per labour. A higher saving rate means higher capital stock and
therefore a higher level of output in the steady-state. However a higher saving rate
does not mean higher long term growth. It only means a higher level of output at the
steady-state. Factors that influence the level of long term growth are addressed in
chapter 9.
8.2. The Golden Rule Level of Capital
The golden rule level of capital is the level of capital that maximizes consumption in
the long run.
The previous subchapter addresses the relation between the saving rate and the level
of output, but it does not address the relation to consumption. If the saving rate is 1,
then the highest output is maintained in the steady-state, but none of this output
goes to consumption, so this high level of output does not increase the standard of
living. The question arises, what is the “optimal” level of capital? I.e. what level of
capital maximizes consumption in the steady state? This level of capital is called
the Golden Rule level of capital, and is denoted by k*gold.
To find it, we can rewrite the demand for goods and services as:
c = y- i
Because in the steady state, investment equals depreciation, and y = f(k*), we rewrite
this as follows
c* = f(k*) – δk*
Where c* is steady-state consumption, and the golden rule level of capital is the level
of capital that maximizes c*.
Using the First Order Conditions (FOC), of maximization of a function using
derivatives, we conclude that the derivative of f(k*) must equal that of δk* (if you do
not understand this, consult a calculus textbook, or simply rote learn the result). This
is written as:
MPK = δ
When this equation holds, we have reached the golden rule level of capital. For
example if
MPK = 1/(2sqrt(k)),
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We derive that k*gold = 1/(4 δ2). This is summarized in the following graph:
We can also derive the necessary saving rate to achieve this golden rule level of
capital by equating the steady state level of capital to 1/(4 δ2) and solving for s.
The Transition to the Golden Rule Steady State
Policymakers can influence the saving rate, so the policymaker’s problem is to set the
saving rate such, that the golden rule level of capital is achieved. Here are two
graphical depictions of what happens if a policymaker corrects for a situation of
higher than golden rule level and lower level of capital respectively:
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