The fundamental questions of macroeconomics
The data of macroeconomics: production and
income
Macroeconomics
12 September 2018
Required readings
Topics for today
• Which are the main questions of macroeconomics? What
makes macroeconomics different form microeconomics?
What types of questions are macroeconomic questions?
• One of the main aggregates: GDP
Microeconomics versus Macroeconomics
• The prefix micro is derived from the Greek word mikros, which means ―small.‖
Microeconomics therefore studies the economic behaviour of individual
economic decision makers, such as a consumer, a worker, a firm, or a manager.
It also analyses the behaviour of individual households, industries, markets,
labour unions, or trade associations.
• The prefix macro comes from the Greek word makros, which means ―large.‖
Macroeconomics thus analyses how an entire national economy performs. A
course in macroeconomics examines aggregate levels of income and
employment, the levels of interest rates and prices, the rate of inflation, and
the nature of business cycles in a national economy.
Macroeconomics is built on microeconomics but new concepts and models will
have to be introduced.
Macro vs micro
Macroeconomics is the study of the economy as a whole  it models the
behaviour of aggregates that describe the economy.
• What causes recessions? What is ―government stimulus‖ and why might it
help?
• How can problems in the housing market spread to the rest of the economy?
• What is the government budget deficit? How does it affect workers,
consumers, businesses, and taxpayers?
• Why does the cost of living keep rising?
• Why are so many countries poor? What policies might help them grow out of
poverty?
• What is the trade deficit? How does it affect a country‘s well-being?
The US real GDP
(billions of 2012 chain-linked dollars)
The US real GDP
(percent change from quarter one year ago)
US real GDP per capita
Inflation in the US
Unemployment in the US
Economic models
In macroeconomics, too, we used models, which
…are simplified versions of a more complex
reality.
• irrelevant details are stripped away
…are used to:
• show relationships between variables
• explain the economy‘s behaviour
• devise policies to improve economic performance
Endogenous vs. exogenous variables
• The values of endogenous variables are determined in the
model.
• The values of exogenous variables are determined outside the
model: The model takes their values and behaviour as given.
• In the model of supply & demand for cars,
• endogenous: P, Qd, Qs
• exogenous: income, price of materials
There are various models
So we will learn different models for studying
different issues (e.g., unemployment, inflation, longrun growth).
For each new model, you should keep track of:
• its assumptions;
• which variables are endogenous;
• which are exogenous;
• the questions it can help us understand, and those it cannot.
Fundamental aggregates
Three fundamental aggregates
• GDP;
• measures of inflation;
• Unemployment (and other measures about the labour market)
Measuring GDP and inflation are strongly connected, and will be
discussed at the beginning of the course.
The discussion of the measures of unemployment is left to the
class in which the causes of unemployment will be dealt with.
0
Source: Penn World Table 9.1
2016
2014
2012
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
1958
1956
1954
1952
1950
GDP per capita in the US and Hungary
(in 2011 US dollars)
60000
50000
40000
30000
20000
10000
0
Source: KSH
2016
2014
2012
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
The quantity index of Hungarian GDP
(1960=100)
500
[ÉRTÉK]
450
400
350
300
250
200
150
100
50
GDP
• What is GDP and how to calculate it?
• What does it mean that „in 2011 US dollars‖? Why isn‘t it
enough to compare them just in dollars?
• What does it mean that „1960=100‖?
GDP
The total market value of all final goods and services produced within a
country in a given period of time.
(1) ―GDP is the Market Value . . .‖: Output is valued at market prices.
(2) ―. . . Of All Final . . .‖: It records only the value of final goods, not
intermediate goods (the value is counted only once).
(3) ―. . . Goods and Services . . . ―: It includes both tangible goods (food,
clothing, cars) and intangible services (haircuts, housecleaning, doctor
visits).
(4) ―. . . Produced . . .‖: It includes goods and services currently produced, not
transactions involving goods produced in the past.
(5) ― . . . Within a Country . . .‖: It measures the value of production within the
geographic confines of a country.
(6) ―. . . In a Given Period of Time.‖: It measures the value of production that
takes place within a specific interval of time, usually a year or a quarter
(three months).
The circular flow diagram
MARKETS
FOR
GOODS AND SERVICES
•Firms sell
Goods
•Households buy
and services
sold
Revenue
Wages, rent,
and profit
Goods and
services
bought
HOUSEHOLDS
•Buy and consume
goods and services
•Own and sell factors
of production
FIRMS
•Produce and sell
goods and services
•Hire and use factors
of production
Factors of
production
Spending
MARKETS
FOR
FACTORS OF PRODUCTION
•Households sell
•Firms buy
Labor, land,
and capital
Income
= Flow of inputs
and outputs
= Flow of dollars
Copyright © 2004 South-Western
Three approaches of GDP accounting
Expenditure equals income because every dollar a
buyer spends becomes income to the seller 
• Total expenditure on domestically produced
final goods and services.
• Total income earned by domestically located
factors of production.
• Total value added: the sum of all the valuesadded in producing those goods and services.
• Value added: The value of output minus the value of the
Value added
Crude oil is tapped from a well and sold to a refiner for $1.00, who converts
it into plastic stock. The plastic stock is sold to a toy manufacturer for $2.00,
who makes a Frisbee and sells it at wholesale to a toy store for $7.15. The
toy store sells it at retail to the public for $9.99.
The value of the final good=9.99
Total values-added=(1.00-0.00)+(2.00-1.00)+(7.15-2.00)+(9.99-7.15)=9.99
Total income is not explicit in this example, but because of the simplicity of
the example the calculation must formally be the same as the calculation of
total income.
GDP accounting
Agriculture
Revenue: 25 000
Interest: 10 000
Wage 10 000
Industry
Revenue: 20 000
Intermediate product: 10 000
Wage: 8000
• GDP = total market value of final goods=
=20 000 + (25 000-10 000)=35 000
• GDP = total value added=25000+(20 000 -10 000)=35 000
• GDP= Total income=Interest+wage+profit= 10 000
+(10 000+8000)+(5 000+2000)=35 000
The expenditure components of GDP
• consumption, C
• investment, I
• government spending, G
• net exports, NX
The national income identity:
value
Y of= total
C + I + G + NX
output
aggregate expenditure
Consumption (C)
Consumption is the value of all goods and services bought
by households. It includes:
• durable goods : last a long time, e.g., cars, home appliances
• nondurable goods: last a short time, e.g., food, clothing
• services: work done for consumers, e.g., dry cleaning,
air travel
Investment (I)
• This is spending on goods bought for future use
(i.e., capital goods)
• It includes:
• Business fixed investment
Spending on plant and equipment and intellectual
property products
• Residential fixed investment
Spending by consumers and landlords on housing
units
• Inventory investment
The change in the value of all firms‘ inventories
Investment vs. Capital
Note: Investment is spending on new capital.
Example:
– 1/1/2009: economy has $500b worth of capital
– during 2009: investment = $60b
– 1/1/2010: economy will have $560b worth of capital
• assumes no depreciation
Stocks vs. Flows
Flow
A stock is a
quantity measured
at a point in time.
E.g.,
―The U.S. capital stock was
$26 trillion on January 1,
2009.‖
A flow is a quantity measured per unit of time.
E.g., ―U.S. investment was $2.5 trillion during 2009.‖
Stock
Stocks vs. Flows - examples
stock
flow
a person‘s wealth
a person‘s
annual saving
# of people with college
degrees
# of new college
graduates this year
the gov‘t debt
the gov‘t budget deficit
NOW YOU TRY:
Stock or Flow?
•
•
•
•
•
the balance on your credit card statement
how much you study economics outside of class
the size of your compact disc collection
the inflation rate
the unemployment rate
Government spending (G)
• G includes all government spending on goods and services.
• It excludes transfer payments (e.g., unemployment insurance
payments), because they do not represent spending on goods
and services.
Net Exports: NX = EX – IM
It is the value of total exports (EX) minus the value of total
imports (IM)
NOW YOU TRY:
An expenditure-output puzzle?
Suppose a firm:
• produces $10 million worth of final goods
• sells only $9 million worth
Does this violate the
expenditure = output identity?
Why output = expenditure
• Unsold output goes into inventory,
and is counted as ―inventory investment‖…
…whether or not the inventory buildup was
intentional.
• In effect, we are assuming that
firms purchase their unsold output.
GDP:
An important and versatile concept
We have now seen that GDP measures:
• total income
• total output
• total expenditure
• the sum of value-added at all stages
in the production of final goods
Some multiple choice questions about GDP
If the price of a hot dog is $2 and the price of a hamburger is
$4, then 30 hot dogs contribute as much to GDP as _________
hamburgers.
a) 5
b) 15
c) 30
d) 60
Answer: b
Some multiple choice questions about GDP
Angus the sheep farmer sells wool to Barnaby the knitter for
$20. Barnaby makes two sweaters, each of which has a
market price of $40. Collette buys one of them, while the
other remains on the shelf of Barnaby‘s store to be sold later.
What is GDP here?
a) $40
b) $60
c) $80
d) $100
Answer: c)
Some multiple choice questions about GDP
Which of the following does NOT add to U.S. GDP?
a) Air France buys a plane from Boeing, the U.S. aircraft
manufacturer.
b) General Motors builds a new auto factory in North Carolina.
c) The city of New York pays a salary to a policeman.
d) The federal government sends a Social Security check to
your grandmother.
Answer: d)
Some multiple choice questions about GDP
An American buys a pair of shoes manufactured in Italy. How do
the U.S. national income accounts treat the transaction?
a) Net exports and GDP both rise.
b) Net exports and GDP both fall.
c) Net exports fall, while GDP is unchanged.
d) Net exports are unchanged, while GDP rises.
Answer: c)
Some multiple choice questions about GDP
Which is the largest component of GDP?
a) consumption
b) investment
c) government purchases
d) net exports
Answer: a)
GNI vs. GDP
• Gross National Income (GNI):
Total income earned by the nation‘s factors of
production, regardless of where located
• Gross Domestic Product (GDP):
Total income earned by domestically-located
factors of production, regardless of nationality
•
GNI – GDP = factor payments from
abroad
minus factor payments to abroad
• Examples of factor payments: wages, profits,
NOW YOU TRY:
Discussion Question
In your country, which would you want to be bigger,
GDP or GNI? Why?
Real and Nominal GDP
• GDP is the market value of all final goods and
services produced.
• nominal GDP measures these values using
current prices.
• Current prices are the prices that prevailed at the
time of production
• real GDP measure these values using constant
prices (the prices during the base year).
Nominal versus real GDP
(Supposing that there are two goods for final use, A and B)
NGDPt  P Q  P Q
A
t
A
t
B
t
RGDPt  P Q  P Q
A
b
A
t
B
b
B
t
B
t
NOW YOU TRY:
Real and Nominal GDP
2016
2017
2018
P
Q
P
Q
P
Q
good A
$30
900
$31
1,000
$36
1,050
good B
$100
192
$102
200
$100
205
Nominal GDP
Real GDP
 Compute nominal GDP in each year.
 Compute real GDP in each year using 2016 as the base year.
NOW YOU TRY:
Real and Nominal GDP
2016
2017
2018
P
Q
P
Q
P
Q
good A
$30
900
$31
1,000
$36
1,050
good B
$100
192
$102
200
$100
205
Nominal
GDP
(30×900) +
(100×192) =
$46,200
(31×1000) +
(102×200) =
$51,400
(36×1,050) +
(100×205) =
$58,300
Real
GDP
(30×900) +
(100×192) =
$46,200
(30×1000) +
(100×200) =
$50,000
(30×1,050) +
(100×205) =
$52,000
Growth Rate: computation
Value for the year  value for previous year
Growth Rate 
100
value for previous year
Nomina
l GDP
2016
2017
2018
$46,200
$51,400
$58,300
$46,200
$50,000
$52,000
NOW YOU TRY:
Real and Nominal GDP
Growth
Rate %
Real
GDP
Growth
Rate %
Value for the year  value for previous year
Growth Rate 
100
value for previous year
Nominal
GDP
2016
2017
2018
$46,200
$51,400
$58,300
11.26
13.42
$50,000
$52,000
8.23
4.00
Growth
Rate %
Real
GDP
Growth
Rate %
$46,200
NOW YOU TRY:
Real and Nominal GDP
[(51,400 – 46,200) /
46,200] ✕ 100 = 11.26
Value for the year  value for previous year
Growth Rate 
100
value for previous year
Chain-Weighted Real GDP
• Over time, relative prices change, so the base year should be
updated periodically.
• In essence, chain-weighted real GDP
updates the base year every year,
so it is more accurate than constant-price GDP.
• Your textbook uses constant-price real GDP, because:
• the two measures are highly correlated
• constant-price real GDP is easier to compute.
Chain-Weighted Real GDP
RGDP3 RGDP1 RGDP2 RGDP3



RGDP0 RGDP0 RGDP1 RGDP2
at prices of year 0 and 1
at prices year 1 and 2
at prices year 2 and 3
A multiple choice question about GDP
If all quantities produced rise by 10 percent and all prices
fall by 10 percent, which of the following occurs?
a) Real GDP rises by 10 percent, while nominal GDP falls
by 10 percent.
b) Real GDP rises by 10 percent, while nominal GDP is
unchanged.
c) Real GDP is unchanged, while nominal GDP rises by 10
percent.
d) Real GDP is unchanged, while nominal GDP falls by 10
percent.
Answer: b)
Hungarian GDP at current prices
(million HUF)
45.000.000
42.072.786
40.000.000
35.000.000
30.000.000
27.193.630
25.000.000
20.000.000
15.000.000
5.835.633
10.000.000
5.000.000
Source: KSH
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
0
Hungarian GDP at current prices and at average
2005 prices (million HUF)
45.000.000
42.072.786
40.000.000
35.000.000
30.000.000
22.559.880
25.000.000
20.000.000
27.468.843
15.000.000
10.000.000
5.000.000
RGDP
NGDP
Forrás: KSH
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
0
„Economic growth”=growth of real GDP
quantity index of GDP
Seasonally adjusted
(same quarter of the previous year=100,0)
106
104
102
100
98
96
94
92
I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I. III. I.
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Source: KSH
Values added by sector in Hungary, 2018
(taxes on production excluded)
Mezőgazdaság,
erdőgazdálkodás, halászat
4,39%
Feldolgozóipar
23,72%
Szolgáltatások összesen
66,40%
Építőipar
5,48%
Sources: KSH
The expenditure side of GDP in Hungary, 2018
(million HUF)
25.000.000
20.000.000
15.000.000
10.000.000
5.000.000
0
Fogyasztás
(49,07%)
Beruházás
(27,06%)
Sources: KSH
Kormányzati vásárlás
(19,09%)
Nettó export
(4,78%)
Something we will not consider
(export + import as percentage of GDP in Hungary and the US)
180
160
140
120
100
80
60
40
20
Source: WDI
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
0
GDP and GNI in Hungary
(current prices, million HUF)
45.000.000
38.355.115
40.000.000
36.823.641
35.000.000
30.000.000
25.000.000
20.000.000
15.000.000
10.000.000
5.000.000
GNI
Source: KSH
GDP
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
0
GDP and „happiness”
GDP and „human development”
Source: Kulhamn et al. (2011, p. 10)
Problems (at the end of chapter 2 of your
textbook)
A farmer grows a bushel of wheat and sells it to a
miller for $1. The miller turns the wheat into flour
and then sells the flour to a baker for $3. The
baker uses the flour to make bread and sells the
bread to an engineer for $6. The engineer eats the
bread. What is the value added by each person?
What is the bread‘s contribution to GDP?
Problems (at the end of chapter 2 of your
textbook)
Suppose a woman marries her butler. After they
are married, her husband continues to wait on her
as before, and she continues to support him as
before (but as a husband rather than as an
employee). How does the marriage affect GDP?
How do you think it should affect GDP?
Problems (end of chapter 2 of your textbook)
Place each of the following transactions in one of
the four components of expenditure:
consumption, investment, government purchases,
and net exports.
a. Boeing sells an airplane to the U.S. Air Force.
b. Boeing sells an airplane to American Airlines.
c. Boeing sells an airplane to Air France.
d. Boeing sells an airplane to Amelia Earhart.
e. Boeing builds an airplane to be sold next year.
The data of macroeconomics:
inflation
Macroeconomics
19 September 2019
Real GDP is inflation-adjusted
• Changes in nominal GDP can be due to:
– changes in prices, and
– changes in quantities of output produced.
• Changes in real GDP can only be due to
changes in quantities,
– because real GDP is computed using
constant base-year prices.
GDP Deflator
• Inflation rate: the percentage increase in the overall level of
prices
• One measure of the price level: GDP deflator
Definition:
Nominal GDP
GDP deflator = 100 
Real GDP
NOW YOU TRY:
GDP deflator and inflation rate
NGDP
GDP
deflator Inflation
RGDP
(2016=10 rate (%)
0)
2016 $46,200 $46,200
2017 51,400
n.a.
50,000
2018 58,300 52,000
• Use your previous answers to compute the GDP
deflator in each year.
• Use GDP deflator to compute the inflation rate
from 2016 to 2017, and from 2017 to 2018.
NOW YOU TRY:
Answers
NGDP
GDP
deflator Inflation
RGDP
(2016=10 rate (%)
0)
2006 $46,200 $46,200
100.0
n.a.
2007
51,400
50,000
102.8
2.8
2008
58,300
52,000
112.1
9.1
GDP Deflator: overall price level
2016
2017
2018
GDP
Deflat
good
or
A
P 100×Q
P 100×Q
51,400/50,0 58,300/52,0
100
$30 900 $31
1,000 00
$36= 112.1
1,050
00 = 102.8
good
B
12.1%
Same192 $102
2.8% higher
$100
200 $100
205
higher
Average
prices
compared
to base year
P
Q
Nomin (30×900) + (31×1000) + (36×1,500)
al
(100×192) (102×200) = + (100×205)
GDP = $46,200
$51,400
= $58,300
Real
GDP
(30×900) + (30×1000) + (30×1,500)
(100×192) (100×200) = + (100×205)
= $46,200
$50,000
= $52,000
2016
2017
2018
NOW YOU TRY:
Real and Nominal
Nomin
GDP
$46,20 $51,40 $58,30
al
0
0
0
GDP
Growt
h Rate
%
11.26 13.42
GDP Deflator =
Nominal GDP /
Real GDP
It is a measure of
the overall price
Real $46,20 $50,00 $52,00
level
Its growth rate is a
GDP
0
0
0
measure of the
rate of inflation
Growt
h Rate
%
GDP
Deflat
or
8.23
1.00
4.00
1.028 1.121
As an
approximation, the
GDP Deflator’s
growth rate =
growth rate of
Nominal GDP –
Understanding the GDP deflator
Example with 3 goods
For good i = 1, 2, 3
Pit = the market price of good i in month t
Qit = the quantity of good i produced in
month t
NGDPt = Nominal GDP in month t
RGDPt = Real GDP in month t
Understanding the GDP deflator
NGDPt P1tQ1t  P2tQ2t  P3tQ3t
GDP deflatort 

RGDPt
RGDPt
 Q1t 

 P1t
 RGDPt 
 Q2t 

 P2t
 RGDPt 
 Q3t 

 P3t
 RGDPt 
The GDP deflator is a weighted average of prices.
The weight on each price reflects
that good‘s relative importance in GDP.
Note that the weights change over time.
International Comparisons
• When the GDP numbers for various countries‘
are being compared, the same currency units
must be used
• There are two ways of converting from national
countries to a common currency, such as the US
dollar
– Use market exchange rates
– Use a common set of prices (PPP)
GDP per capita, in US dollars
Source: World Development Indicators,
Country Name
Singapore
Switzerland
United States
Netherlands
Austria
Germany
United Kingdom
Japan
Italy
Hungary
Russian Federation
Iran, Islamic Rep.
Botswana
China
Jordan
Jamaica
India
Nigeria
Cameroon
GDP2017
at PPP
exhange
rates
93 905.42
65 006.53
59 531.66
52 941.12
52 557.48
50 715.55
43 876.60
43 875.75
39 817.15
28 375.37
25 533.00
20 949.94
17 354.20
16 806.74
9 153.35
8 995.35
7 055.55
5 860.85
3 694.20
GDP2017
at market
exchange
rates
57 714.30
80 189.70
59 531.66
48 223.16
47 290.91
44 469.91
39 720.44
38 428.10
31 952.98
14 224.85
10 743.10
5 415.21
7 595.60
8 826.99
4 129.75
5 109.55
1 939.61
1 968.56
1 446.70
Chain-Weighted Real GDP
• Over time, relative prices change, so the base
year should be updated periodically.
• In essence, chain-weighted real GDP
updates the base year every year,
so it is more accurate than constant-price GDP.
• Your textbook uses constant-price real GDP,
because:
– the two measures are highly correlated
– constant-price real GDP is easier to compute.
CONSUMER PRICE INDEX
(CPI)
Consumer Price Index (CPI)
• It is a measure of the overall level of
prices
• It is published by national and
international statistical offices.
• The CPI is used to:
– track changes in the typical household‘s
cost of living
– adjust many contracts for inflation (COLA,
cost of living adjustment)
– allow comparisons of dollar amounts over
time
How CPI is constructed
1. Survey consumers to determine composition
of the typical consumer‘s ―basket‖ of goods
2. Every month, collect data on prices of all items
in the basket; compute cost of basket
3. CPI in any month equals
Cost of basket in that month
100 
Cost of basket in base period
The composition of the CPI’s “basket” in the
US
Other goods and
services; 3,179
Transportation;
17,107
Housing; 41,649
Medical care;
8,631
Apparel;
3,069
Food and
beverages; 14,159
Recreation(5);
5,651
Education and
communication(5);
6,556
NOW YOU TRY:
Compute the CPI
Typical consumer‘s basket: 20 pizzas, 10
compact discs
prices:
For each year,
compute
pizza
CDs
 the cost of the
basket
2012
$10
$15
 the CPI (use 2002 as
2013
$11
the base year)
$15
 the inflation rate
2014
$12
from the preceding
$16
year
2015
$13
NOW YOU TRY:
Compute the CPI and Inflation Rate
Typical consumer’s basket: 20 pizzas, 10
compact discs
pizza CDs cost
CPI inflation
201
$10
$15
2
201
$11
$15
3
201
$12
$16
4 Cost of typical consumer' s basket in current period
CPI 
100
201 Cost of typical consumer' s basket in base period
$13
$15
5
NOW YOU TRY:
Compute the CPI and Inflation Rate
Typical consumer‘s basket: 20 pizzas, 10
compact discs
pizza CDs cost
CPI inflation
201
$10
$15
2
$350
201
$11
$15
3
$370
201
$12
$16
s basket in current period
4 Cost of typical consumer'$400
CPI 
100
201 Cost of typical consumer' s basket in base period
$13
$15
5
$410
NOW YOU TRY:
Compute the CPI and Inflation Rate
Typical consumer‘s basket: 20 pizzas, 10
compact discs
pizza CDs cost
CPI inflation
201
$10
$15
2
$350
100
201
$11
$15
3
$370
105.71
201
$12
$16
s basket in114.29
current period
4 Cost of typical consumer'$400
CPI 
100
201 Cost of typical consumer' s basket in base period
$13
$15
5
$410
117.14
NOW YOU TRY:
Compute the CPI and Inflation Rate
Typical consumer‘s basket: 20 pizzas, 10
compact discs
pizza
CDs
cost
CPI
inflation
201
$10
$15
2
$350
100
201
$11
$15
3
$370
105.71
5.71
201
$12
$16
s basket in114.29
current period8.11
4 Cost of typical consumer'$400
CPI 
100
201 Cost of typical consumer' s basket in base period
$13
$15
5
$410
117.14
2.50
CPI in current period  CPI in preceding period
Inflation 
100
CPI in preceding period
US inflation
-1
01/01/1999
01/07/1999
01/01/2000
01/07/2000
01/01/2001
01/07/2001
01/01/2002
01/07/2002
01/01/2003
01/07/2003
01/01/2004
01/07/2004
01/01/2005
01/07/2005
01/01/2006
01/07/2006
01/01/2007
01/07/2007
01/01/2008
01/07/2008
01/01/2009
01/07/2009
01/01/2010
01/07/2010
01/01/2011
01/07/2011
01/01/2012
01/07/2012
01/01/2013
01/07/2013
01/01/2014
01/07/2014
01/01/2015
01/07/2015
01/01/2016
01/07/2016
01/01/2017
01/07/2017
01/01/2018
01/07/2018
01/01/2019
01/07/2019
Eurozone inflation
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
-0,5
Source: Eurostat
0
-5
1993/ Jan/
1993/ Sep/
1994/ May/
1995/ Jan/
1995/ Sep/
1996/ May/
1997/ Jan/
1997/ Sep/
1998/ May/
1999/ Jan/
1999/ Sep/
2000/ May/
2001/ Jan/
2001/ Sep/
2002/ May/
2003/ Jan/
2003/ Sep/
2004/ May/
2005/ Jan/
2005/ Sep/
2006/ May/
2007/ Jan/
2007/ Sep/
2008/ May/
2009/ Jan/
2009/ Sep/
2010/ May/
2011/ Jan/
2011/ Sep/
2012/ May/
2013/ Jan/
2013/ Sep/
2014/ May/
2015/ Jan/
2015/ Sep/
2016/ May/
2017/ Jan/
2017/ Sep/
2018/ May/
2019/ Jan/
Hungarian inflation (12 months)
35
30
25
20
15
10
5
Source: MNB
Understanding the CPI
Example with 3 goods
For good i = 1, 2, 3
Ci = the amount of good i in the CPI‘s
basket
Pit = the price of good i in month t
Et = the cost of the CPI basket in
month t
Eb = the cost of the basket in the base
period
Understanding the CPI
Et P1tC1 + P2tC2 + P3tC3
CPI in month t 

Eb
Eb
 C1 
 C2 
 C3 
   P1t    P2t    P3t
 Eb 
 Eb 
 Eb 
The CPI is a weighted average of prices.
The weight on each price reflects
that good’s relative importance in the CPI’s basket.
Note that the weights remain fixed over time.
Why the CPI may overstate inflation
• Substitution bias:
The CPI uses fixed weights, so it cannot reflect
consumers‘ ability to substitute toward goods whose
relative prices have fallen.
• Introduction of new goods:
The introduction of new goods makes consumers
better off and, in effect, increases the real value of
the dollar. But it does not reduce the CPI, because
the CPI uses fixed weights.
• Unmeasured changes in quality:
Quality improvements increase the value of the
dollar, but are often not fully measured.
The size of the CPI’s bias
• In 1995, a Senate-appointed panel of experts
estimated that the CPI overstates inflation by
about 1.1% per year.
• So the BLS made adjustments to reduce the bias.
• Now, the CPI‘s bias is probably under 1% per
year.
NOW YOU TRY:
Discussion Questions
1. If your grandmother receives Social Security,
how is she affected by the CPI‘s bias?
2. Where does the government get the money to pay
COLAs to Social Security recipients?
3. If you pay income and Social Security taxes,
how does the CPI‘s bias affect you?
4. Is the government giving your grandmother
too much of a COLA?
5. How does your grandmother‘s ―basket‖ differ
from the CPI‘s? Does this affect your answer to
Q4?
CPI vs. GDP Deflator
• Prices of non-consumer goods:
– included in GDP deflator (if produced
domestically)
– excluded from CPI
• Prices of imported consumer goods:
– included in CPI
– excluded from GDP deflator
• The basket of goods:
– CPI: fixed
– GDP deflator: changes every year
Two measures of inflation in the U.S.
Percentage change
from 12 months earlier
15%
C
PI
10%
5%
GDP
deflator
0%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Problems (end of chapter 2 of your
textbook)
Consider an economy that produces and
consumes hot dogs and hamburgers. In
the following table are data for two
different years.
•
•
•
Using 2010 as the base year, compute the following statistics
for each year: nominal GDP, real GDP, the implicit price
deflator for GDP, and a fixed-weight price index such as the
CPI.
By what percentage did prices rise between 2010 and 2015?
Give the answer for each good and also for the two measures
of the overall price level. Compare the answers given by the
Laspeyres and Paasche price indexes.
Explain the difference.
End-of-chapter problems
End-of-chapter problems
GROWTH RATE MATH
Two arithmetic tricks for
working with percentage changes
1. For any variables X and Y,
percentage change in (X  Y )
 percentage change in X
+ percentage change in Y
Example: If your hourly wage rises 5%
and you work 7% more hours,
then your wage income rises
approximately 12%.
Two arithmetic tricks for
working with percentage changes
2. percentage change in (X/Y )
 percentage change in X
 percentage change in Y
Example:
GDP deflator = 100 
NGDP/RGDP.
If NGDP rises 9% and RGDP rises 4%,
then the inflation rate is approximately 5%.
• The growth rate of the ratio of two
variables equals the difference of
their growth rates.
• The growth rate of the product of
two variables equals the sum of
their growth rates.
• The growth rate of a variable raised
to an exponent, is the growth rate
of the variable times the exponent.
If Z = X × Y then gz = gx + g y
znew  zold znew
gz 

1
zold
zold
znew xnew ynew
1 gz 


zold xold yold
1  g z  (1  g x )(1  g y )
1 gz  1 gx  g y  gx  g y
gz  gx  g y  gx  g y
gz  gx  g y
The growth rates here are in
decimal form: for example, if
X grows at the rate of 5%,
then gx = 0.05. The product of
two decimals is small enough
to be ignored: for example,
0.05 × 0.04 = 0.0020.
If Z = X ÷ Y then gz = gx – g y
x
z
y
z y  x
gz  g y  gx
gz  gx  g y
If Z =
a
X
then gz = a × gx
zx 
x 
x 
x

a
a times
gz  gx  gx  gx  a  gx

a times
The economy in the long run:
production and the division of
income
Macroeconomics
26 September 2019
The Long Run
‖This great increase of the quantity of work
which, in consequence of the division of
labour, the same number of people are
capable of performing, is owing to three
different circumstances; first to the increase
of dexterity in every particular workman;
secondly, to the saving of the time which is
commonly lost in passing from one species
of work to another; and lastly, to the
invention of a great number of machines
which facilitate and abridge labour, and
enable one man to do the work of many.‖
(Adam Smith: An Inquiry into the Nature and
Causes of the Wealth pf Nations, Book I,
Chapter I)
Introduction
• In the last lecture we defined and measured some
key macroeconomic variables.
• Now we start building theories about what
determines these key variables.
• In the next couple lectures we will build up
theories that we think hold in the long run, when
prices are flexible and markets clear.
• Called Classical theory or Neoclassical.
The Neoclassical model
Is a general equilibrium model:
• involves multiple markets;
• each with own supply and demand;
• price in each market adjusts to make quantity
demanded equal quantity supplied.
Neoclassical model
The macroeconomy involves three types of markets:
1. Goods (and services) Market
2. Factors Market or Labor market , needed to
produce goods and services
3. Financial market (the market for loanable funds)
Three types of agents in an economy:
1. Households
2. Firms
3. Government
The circular flow -- extended
Neoclassical model
Agents interact in markets, where they may be
demander in one market and supplier in another
1) Goods market:
Supply: firms produce the goods
Demand: by households for consumption,
government spending, and other firms demand
them for investment
Neoclassical model
2) Labor and capital market (factors of production)
Supply: Households sell their labor services.
Demand: Firms need to hire labor and capital to
produce the goods.
3) Financial market
Supply: households supply private savings: income
less consumption
Demand: firms borrow funds for investment;
government borrows funds to finance expenditures.
Neoclassical model
• We will develop a set of equations to
characterize supply and demand in these markets
• Then use algebra to solve these equations
together, and see how they interact to establish a
general equilibrium.
• Start with production…
Supply in goods market: Production
Supply in the goods market depends on a
production function:
denoted Y = F (K, L)
Where
K = capital (tools, machines, and structures used
in production)
L =
labor (the physical and mental efforts of
workers)
The production function
• shows how much output (Y ) the economy
can produce from
K units of capital and L units of labor.
• reflects the economy‘s level of technology.
• Generally, we will assume it exhibits
constant returns to scale.
Returns to scale
Initially Y1 = F (K1 , L1 )
Scale all inputs by the same factor z:
K2 = zK1 and L2 = zL1
for z>1
(If z = 1.25, then all inputs increase by 25%)
What happens to output, Y2 = F (K2 , L2 ) ?
• If constant returns to scale, Y2 = zY1
• If increasing returns to scale, Y2 > zY1
• If decreasing returns to scale, Y2 < zY1
Exercise: determine returns to
scale
Determine whether each of the following
production functions has constant, increasing,
or decreasing returns to scale:
a) F (K , L )  2K  15L
b) F (K , L )  2 K  15 L
Exercise: determine returns to scale
Does F (zK , zL )  zF (K , L )?
a) Suppose F (K , L )  2K  15L
F (zK , zL )  2  zK   15  zL 
 z (2K  15L )
 zF (K , L )
Yes, constant returns to scale
slide 120
Exercise: determine returns to scale
b) Suppose F (K , L )  2 K  15 L
F (zK , zL )  2 zK  15 zL
 2 z K  15 z L

 z 2 K  15 L

 z F (K , L )
 zF (K , L )
No, decreasing returns to scale
slide 121
Assumptions of the model
1. Technology is fixed.
2. The economy‘s supplies of capital and
labor are fixed at
K K
and
L L
Determining GDP
Output is determined by the fixed factor
supplies and the fixed state
of technology:
So we have a simple initial theory of
supply in the goods market:
Y  F (K , L )
Equilibrium in the factors market
• Equilibrium is where factor supply
equals factor demand.
• Recall: Supply of factors is fixed.
• Demand for factors comes from
firms.
Demand in factors market
Analyze the decision of a typical firm.
• It buys labor in the labor market, where
price is wage, W.
• It rents capital in the factors market, at
rate R.
• It uses labor and capital to produce the
good, which it sells in the goods market,
at price P.
Demand in factors market
Assume the market is competitive:
Each firm is small relative to the market, so its
actions do not affect the market prices.
It takes prices in markets as given - W,R, P.
Demand in factors market
It then chooses the optimal quantity of Labor and
capital to maximize its profit.
Profit
= revenue -labor costs -capital costs
= PY
- WL
- RK
= P F(K,L) - WL
- RK
Demand in the factors market
• Increasing hiring of L will have two
effects:
1) Benefit: raise output by some amount
2) Cost: raise labor costs at rate W
• To see how much output rises, we need
the marginal product of labor (MPL)
Marginal product of labor (MPL)
An approximate definition (used in text)
:
The extra output the firm can produce
using one additional labor (holding
other inputs fixed):
MPL = F (K, L +1) – F (K, L)
Exercise: compute & graph
MPL
a. Determine MPL at each
value of L
b. Graph the production
function
c. Graph the MPL curve with
MPL on the vertical axis and
L on the horizontal axis
L
L
0
1
2
3
?4
5
6
7
8
9
10
Y MP
0
10
19
27
34
40
45
49
52
54
55
?
?
8
?
?
?
?
?
?
?
The MPL and the production function
Y
outp
ut
F (K , L )
MP
1 L
1
MP
L
1
slide 131
As more labor
is added, MPL

MP
L
Slope of the
production function
equals MPL: rise over
run
lab
or
L
Diminishing marginal returns
• As a factor input is increased, its marginal
product falls (other things equal).
• Intuition:
L while holding K fixed
 fewer machines per worker
 lower productivity
MPL as a derivative
As we take the limit for small change in L:
F (K , L  L )  F (K , L )
MPL  lim
L 0
L
 FL (K , L )
Which is the definition of the (partial)
derivative of the production function with
respect to L, treating K as a constant.
This shows the slope of the production
function at any particular point, which is what
we want.
slide 133
The MPL and the production function
Y
outp
ut
MPL is slope of the
production
function (rise over
run)
F (K , L )
F (K, L +L) – F (K, L))
L
L
lab
or
A brief calculus review: Derivatives
1) Y  F (L )  2L  3
Y
 FL  2
L
Y
3
Slope =
2
Intercept at 3
L
Firm problem: hiring L
Firm chooses L to maximize its profit.
How will increasing L change profit?
Δ profit = Δ revenue - Δ cost
= P * MPL - W
If this is:
> 0 should hire more
< 0 should hire less
= 0 hiring right amount
Firm problem continued
So the firm‘s demand for labor is determined by the condition:
P ×MPL = W
Hires more and more L, until MPL falls enough to satisfy
the condition.
Also may be written:
MPL = W/P, where W/P is the ‗real wage‘
Real wage
Think about units:
• W = $/hour
• P = $/good
• W/P = ($/hour) / ($/good) = goods/hour
The amount of purchasing power, measured in
units of goods, that firms pay per unit of work
Example: deriving labor demand
• Suppose a production function for all firms in
the economy:
Y  K 0.5L0.5
MPL  0.5K 0.5L0.5
Labor demand is where this equals real wage:
0.5 0.5 W
0.5K L 
P
Labor demand
or rewrite with L as a function of real wage
W
0.5K L 
P
2
2
W 
0.5 0.5
0.5K L    P 
2
1 1  P 
K L  
0.25
W  2
P 
demand
L
 0.25K  
W 
So a rise in wage  want to hire less labor;
rise in capital stock  want to hire more labor
0.5 0.5
Labor market equilibrium
Take this firm as representative, and sum
over all firms to derive aggregate labor demand.
Combine with labor supply to find equilibrium wage:
demand: 0.5K
0.5
L

demand 0.5
W

P
supply: Lsupply  L
0.5
W
0.5
equilibrium:  0.5K L
P
So rise in labor supply  fall in equlibrium
real wage
MPL and the demand for labor
Units of
output
labor supply

Real
wag
e
Each firm hires
labor
up to the point
where MPL =
W/P

MPL,
Labor
demand
L
Units of
labor, L
Determining the rental rate
We have just seen that MPL = W/P
The same logic shows that MPK = R/P :
• diminishing returns to capital: MPK 
as K 
• The MPK curve is the firm‘s demand
curve
for renting capital.
• Firms maximize profits by choosing K
such that MPK = R/P .
How income is distributed
We found that if markets are competitive, then
factors of production will be paid their marginal
contribution to the production process.
W
total labor income =
L  MPL  L
P
total capital income R
K  MPK  K
=
P
Euler’s theorem:
Under our assumptions (constant returns to scale,
profit maximization, and competitive markets)…
total output is divided between the payments to
capital and labor, depending on their marginal
products, with no extra profit left over.
Y  MPL  L  MPK  K
nation
al
incom
e
labor
incom
e
capital
incom
e
slide 145
Mathematical example
Consider a production function with Cobb-Douglas
form:
Y = AKL1-
where A is a constant, representing technology
Show this has constant returns to scale:
multiply factors by Z:
F(ZK,ZY) = A (ZK) (ZL)1-
= A Z K Z1- L1-
= A Z Z1- K L1-
= Z x A K L1-
= Z x F(K,L)
slide 146
Mathematical example
• Compute marginal products:
MPL = (1-) A K L-
MPK =  A K-1L1-
• Compute total factor payments:
MPL x L + MPK x K
= (1-) A K L- x L +  A K-1L1- x K
= (1-) A K L1- +  A K L1-
= A K L1- =Y
So total factor payments equals total production.
End-of-chapter problems
Use the neoclassical theory of distribution to predict the impact
on the real wage and the real rental price of capital of each of
the following events:
a) A wave of immigration increases the labor force.
b) An earthquake destroys some of the capital stock.
c) A technological advance improves the production function.
d) High inflation doubles the prices of all factors and outputs
in the economy.
End-of-chapter problems
Suppose the production function in medieval Europe is Y=K 0.5L0.5,
where K is the amount of land and L is the amount of labor. The
economy begins with 100 units of land and 100 units of labor. Use a
calculator and equations in the chapter to find a numerical answer to
each of the following questions.
a) How much output does the economy produce?
b) What are the wage and the rental price of land?
c) What share of output does labor receive?
d) If a plague kills half the population, what is the new level of
output?
e) What is the new wage and rental price of land?
f) What share of output does labor receive now?
End-of-chapter problems
According to the neoclassical theory of distribution, a worker‘s
real wage reflects her productivity. Let‘s use this insight to
examine the incomes of two groups of workers: farmers and
barbers. Let Wf and Wb be the nominal wages of farmers and
barbers, Pf and Pb be the prices of food and haircuts, and Af and
Ab be the marginal productivity of farmers and barbers.
a) For each of the six variables defined above, state as precisely
as you can the units in which they are measured. (Hint: Each
answer takes the form ―X per unit of Y.‖)
b) Over the past century, the productivity of farmers Af has
risen substantially because of technological progress.
According to the neoclassical theory, what should have
happened to farmers‘ real wage, Wf/Pf ? In what units is this
End-of-chapter problems
c) Over the same period, the productivity of barbers Ab has
remained constant. What should have happened to barbers‘
real wage, Wb/Pb? In what units is this real wage measured?
d) Suppose that, in the long run, workers can move freely
between being farmers and being barbers. What does this
mobility imply for the nominal wages of farmers and
barbers, Wf and Wb?
e) What do your previous answers imply for the price of
haircuts relative to the price of food, Pb/Pf ?
f) Suppose that barbers and farmers consume the same basket
of goods and services. Who benefits more from
technological progress in farming—farmers or barbers?
Explain how your answer is consistent with the results on
End-of-chapter problems
(This problem requires the use of calculus.) Consider a Cobb–
Douglas production function with three inputs. K is capital (the
number of machines), L is labor (the number of workers), and H
is human capital (the number of college degrees among the
workers). The production function is
Y =K1/3L1/3H1/3.
a) Derive an expression for the marginal product of labor. How
does an increase in the amount of human capital affect the
marginal product of labor?
b) Derive an expression for the marginal product of human
capital. How does an increase in the amount of human
capital affect the marginal product of human capital?
End-of-chapter problems
c) What is the income share paid to labor? What is the income
share paid to human capital? In the national income accounts
of this economy, what share of total income do you think
workers would appear to receive? (Hint: Consider where the
return to human capital shows up.)
d) An unskilled worker earns the marginal product of labor,
whereas a skilled worker earns the marginal product of labor
plus the marginal product of human capital. Using your
answers to parts (a) and (b), find the ratio of the skilled wage
to the unskilled wage. How does an increase in the amount
of human capital affect this ratio? Explain.
e) Some people advocate government funding of college
scholarships as a way of creating. a more egalitarian society.
Others argue that scholarships help only those who are able
to go to college. Do your answers to the preceding questions
shed light on this debate?
The economy in the long run: demand
and equilibrium on market for goods
and services
Macroeconomics
3 October 2018
Questions for this lecture
• What determines the demand for goods and services?
• How is equilibrium in the goods market achieved?
• What determines the real interest rate?
Two productive resources and one produced
good
• There are two productive resources:
• Capital, K
• Labor, L
• These two productive resources are used to produce one
• final good, Y (GDP)
Consumption Expenditure
• Now that we know what determines total output (Y), the next
question is:
• What happens to that output?
• In particular, what determines how much of that output is
consumed?
• What determines C?
Consumption, C
• Net Taxes = Tax Revenue – Transfer Payments
• Denoted T and always assumed exogenous
• Disposable income (or, after-tax income) is total
income minus net taxes: Y – T.
• Assumption: Consumption expenditure is directly
related to disposable income
Predictions
Y
C
Capital,
K
+
+
Labor, L
+
+
Technolo
gy
+
+
The Consumption Function
C
C (Y –
T)
1
MP
C
The slope of the
consumption
function is the
MPC.
Marginal propensity to consume
(MPC) is the increase in
consumption (C) when disposable
income (Y – T) increases by one
Y–
T
The MPC is usually a
positive fraction: 0 <
MPC < 1.
Consumption, C
• Assumption: Consumption expenditure
is directly related to disposable income
• Consumption function: C = C (Y – T )
• Specifically, C = Co + Cy × (Y – T)
• Co represents all other exogenous
variables that affect consumption, such
as asset prices, consumer optimism, etc.
• Cy is the marginal propensity to
consume (MPC), the fraction of every
additional dollar of income that is
consumed
Predictions
Y
C
Capital,
K
+
+
Labor, L
+
+
Technolo
gy
+
+
Taxes, T
−
Co
+
The Consumption Function
C = Co2 + Cy∙(Y
– T)
C
C = Co1 + Cy∙(Y
– T)
Predictions Grid
𝐾 , 𝐿,
Technology
F(K, L)
– T1
T1 >
T2
F(K, L)
– T2
Consumption shift factor: greater
consumer optimism, higher asset prices
Y
C
+
+
Taxes, T
−
Co
+
Y–
T
Consumption: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10. Then Y =
30.85.
• Suppose T = 0.85. Therefore, disposable income is Y – T =
30.
• Now, suppose C = 2 + 0.8×(Y – T).
Private Saving is defined as
• Then, C = 2 + 0.8 ×30 = 26
disposable income minus
consumption, which is Y
– T – C = 30 – 26 = 4.
K, L, F(K,
L)
Y
C
C(Y – T),
T
Marginal Propensity to Consume
• The marginal propensity to consume is a positive fraction (1 >
MPC > 0)
• That is, when income (Y) increases, consumption (C) also
increases, but by only a fraction of the increase in income.
• Therefore, Y↑⇒ C↑ and Y – C↑
• Similarly, Y↓⇒ C↓ and Y – C↓
Predictions
Y C Y–
C
K, L,
Technology
Taxes, T
+ +
+
−
+
Government Spending
• Assumption: government spending (G) is exogenous
• Public Saving is defined as the net tax revenue of the
government minus government spending, which is T – G
National Saving and Investment
•
•
•
•
•
•
In chapter 2, we saw that Y = C + I + G + NX
In this chapter, we study a closed economy: NX = 0
Therefore, Y = C + I + G
Y−C−G=I
Y − C − G is defined as national saving (S)
Therefore, S = I
K, L, F(K,
L)
Y
G
C
C(Y – T),
S=I=Y–
C–G
Investment: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10. Then Y =
30.85.
• Suppose T = 0.85. Therefore, disposable income is Y – T =
30.
• Now, suppose C = 2 + 0.8×(Y – T).
Public Saving = T –
• Then, C = 2 + 0.8 ×30 = 26
G = 0.85 – 3 = –
2.15
• Suppose G = 3
• Then, I = S = Y – C – G = 30.85 – 26 – 3 = 1.85
The Real Interest Rate
• Imagine that lending and borrowing take place in the
economy, but in commodities, not cash
• That is, you may borrow some amount of the final good,
as long as you pay back the quantity you borrowed plus a
little bit extra as interest
• The real interest rate (r) is the fraction of every unit of the
final good borrowed that the borrower will have to pay to the
lender as interest
The nominal interest rate
• The interest rate that a bank charges you for a cash loan is
called the nominal interest rate (i)
• It is the fraction of every dollar borrowed that the lender
must pay in interest
• The nominal interest rate is not adjusted for inflation
Investment and the real interest rate
• Assumption: investment spending is inversely related to the real
interest rate
• I = I(r), such that r↑⇒ I↓
r
I
(r
)I
Investment and the real interest rate
• Specifically, I = Io − Irr
• Here Ir is the effect of r on I
and
• Io represents all other factors
that also affect business
investment spending
• such as business
optimism, technological
progress, etc.
r
Io2 −
I rr
Io1 −
I rr
I
The Real Interest Rate: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10.
Then Y = 30.85. Suppose T = 0.85. Therefore,
disposable income is Y – T = 30.
• Now, suppose C = 2 + 0.8✕(Y – T). Then, C = 2 +
0.8 ×30 = 26
• Suppose G = 3. Then, I = S = Y – C – G = 30.85 –
26 – 3 = 1.85
• Suppose I = 11.85 – 2r is the investment function
• Then, 11.85 – 2r = 1.85. Therefore, r = 5 percent
Whole chapter in one slide!
• 𝑌 = 𝐴 ∙ 𝐾 0.3 𝐿0.7
• 𝐶 = 𝐶0 + 𝐶𝑦 ∙ (𝑌 − 𝑇)
• 𝐼 =𝑆 =𝑌−𝐶−𝐺
• 𝐼 = 𝐼0 − 𝐼𝑟 ∙ 𝑟 which gives 𝑟 =
Predictions
Y C
S, I
r
K, L, A
(Technology)
+ +
+
−
Net Taxes, T
−
+
−
Co
+
−
+
−
+
Govt
Spending, G
𝐼0 −𝐼
𝐼𝑟
The Real Interest Rate
• Recall that the amount of investment has already been
determined
• The investment function can therefore be used to determine
the real interest rate
K, L, F(K,
L)
Y
G
C
C(Y – T),
I(r
)
S=I=Y–
C–G
r
The Real Interest Rate
r
I = Y – C(Y-T) – G
Predictions
I = F(K, L) – C(F(K, L)
– T) – G
Y C S, I
r
+ +
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L,
Technology
I(r) = Io −
I rr
Govt, G
Io
I
K, L, F(K,
L)
Y
G
C
C(Y – T),
+
I(r
)
S=I=Y–
C–G
r
The Real Interest Rate: predictions
As investment and the real
interest rate are inversely related,
any exogenous variable that
affects investment one way will
affect the real interest rate the
other way.
Predictions Grid
Y C S, I
r
+ +
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L,
Technology
Govt, G
Io
+
Q: Why is it that business
optimism or technological
progress shifts the
investment curve upwards,
but does not affect the
amount of investment in
the long run?
The Real Interest Rate: predictions
Predictions Grid
• The amount of business
investment has already been
determined
• So, any increase in business
optimism must be cancelled
out by an increase in the real
interest rate
• The result that an increase
in businesses‘ desire to
invest may not lead to more
investment shows the
benefit of the
macroeconomic approach
Y C S, I
r
+ +
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L,
Technology
Govt, G
Io r
+
I = F(K, L) – C(F(K, L)
– T) – G
Io2 −
I rr
Io1 −
I rr
I
Budget surpluses and deficits
• If T > G, budget surplus
= (T – G )
= public
saving.
• If T < G, budget deficit
and public saving is negative.
= (G – T )
• If T = G , ―balanced budget,‖ public saving
= 0.
• The U.S. government finances its deficit by
issuing Treasury bonds – i.e., borrowing.
CASE STUDY:
The Reagan deficits
• Reagan policies during early 1980s:
• increases in defense spending: G > 0
• big tax cuts: T < 0
• Both policies reduce national saving:
S Y  C (Y T )  G
G   S
T   C   S
CASE STUDY:
The Reagan deficits
1. The increase
in the deficit
reduces
saving…
2. …which
causes the real
interest rate to
rise…
3. …which
reduces the
level of
investment.
r
S2
S1
r
2
r
1
I
I
2
1
I
(r )
S,
I
Are the data consistent with these results?
3.9
.4
3
.4
variable
1980s
T–G
1970s
–2.2
–
S
19.6
17
r
1.1
6.
I
19.9
19
T–G, S, and I are expressed as a percent
of GDP
All figures are averages over the decade
shown.
NOW YOU TRY:
The effects of saving
incentives
• Draw the diagram for the loanable funds model.
• Suppose the tax laws are altered to provide more
incentives for private saving.
(Assume that total tax revenue T does not
change)
• What happens to the interest rate and
investment?
End-of-chapter problems
The government raises taxes by $100 billion. If the marginal
propensity to consume is 0.6, what happens to the following? Do
they rise or fall? By what amounts?
a) Public saving
b) Private saving
c) National saving
d) Investment
End-of-chapter problems
Suppose that an increase in consumer confidence raises
consumers‘ expectations about their future income and thus
increases the amount they want to consume today. This might be
interpreted as an upward shift in the consumption function. How
does this shift affect investment and the interest rate?
End-of-chapter problems
Consider an economy described as follows:
Y = C+ I + G.
Y = 8,000.
G = 2,500.
T =2,000.
C =1000+(2/3)(Y-T ).
I =1,200 -100r.
a) In this economy, compute private saving, public saving, and national
saving.
b) Find the equilibrium interest rate.
c) Now suppose that G is reduced by 500. Compute private saving,
public saving, and national saving.
d) Find the new equilibrium interest rate.
End-of-chapter problems
Suppose that the government increases taxes and
government purchases by equal amounts. What
happens to the interest rate and investment in
response to this balanced-budget change?
Explain how your answer depends on the marginal
propensity to consume.
Money supply
Macroeconomics
10 October 2019
Three Main Questions
1) What is money?
2) What is the role of a nation‘s banking system in determining
the quantity of money in the economy?
3) How does a nation‘s central bank influence the banking
system and the quantity of money?
What is money?
Money is the stock of assets that can be readily used to make
transactions.
• Functions of money
– Medium of exchange: we use it to buy stuff
– Store of value: transfers purchasing power from the
present to the future
– Unit of account: the common unit by which everyone
measures prices and values
Two Types of Money
• Fiat money
People accept fiat money either because a government decree
(or, fiat) requires them to do so or simply because others
would also accept it as payment
• Commodity money
This money is valuable in itself (e.g., gold coins) or can by
law be converted into something valuable (as in a gold standard
system)
The Quantity of Money
The quantity of money, amount of money, and supply of money
all refer to the same thing:
• The total value of all assets in the economy that can be
used as money
• It is denoted M
The Quantity of Money
There are several prominent measures of the quantity of money
(M)
What counts as money?
• The dollar value of the currency we carry, C, should clearly be
counted as money
• Moreover, when we do our shopping, we use checks and debit
cards exactly the way we use currency. Therefore, the dollars
that we can spend this way should also be counted as money.
The Measures of Money
Simplified version: Money Supply (M) = Currency (C) +
Demand Deposits (D)
C, M1, M2 in the United States
Banks’ role in the monetary system
• The money supply equals currency plus demand (checking
account) deposits:
M=C+D
• Since the money supply includes demand deposits, the
banking system plays an important role.
A few preliminaries
• Reserves (R): the portion of deposits that banks have not lent.
• A bank‘s liabilities include deposits; assets include reserves and
outstanding loans.
• 100-percent-reserve banking: a system in which banks hold all
deposits as reserves.
• Fractional-reserve banking: a system in which banks hold a
fraction of their deposits as reserves.
Banks’ role in the monetary system
To understand the role of banks, we will consider three
scenarios:
1) No banks
2) 100-percent-reserve banking (banks hold all deposits as
reserves)
3) Fractional-reserve banking (banks hold a fraction of deposits
as reserves, use the rest to make loans)
In each scenario, we assume C = $1,000.
SCENARIO 1:
No banks
With no banks,
D = 0 and M = C = $1,000.
SCENARIO 2:
100-percent-reserve banking
• Initially C = $1000, D = $0, M =
$1,000.
• Now suppose households deposit
the $1,000 at ―Firstbank.‖
• After the deposit:
C = $0,
D = $1,000,
M = $1,000
LESSON: 100%-reserve banking has
no impact on size of money supply.
SCENARIO 3:
Fractional-reserve banking
• Suppose banks hold 20% of
deposits in reserve, making loans
with the rest.
• Firstbank will make $800 in loans.
• The money supply now equals
$1,800:
– Depositor has $1,000 in demand
deposits.
– Borrower holds $800 in currency.
SCENARIO 3:
Fractional-reserve banking
• Suppose the borrower deposits the
$800 in Secondbank.
• Initially, Secondbank‘s balance
sheet is:
• Secondbank will loan 80% of this
deposit.
SCENARIO 3:
Fractional-reserve banking
• If this $640 is eventually deposited in Thirdbank,
• Then Thirdbank will keep 20% of it in reserve and loan the
rest out:
Finding the total amount of money:
Original deposit = $1000
+ Firstbank lending = $ 800
+ Secondbank lending = $ 640
+ Thirdbank lending = $ 512
+ other lending…
• Total money supply = (1/rr ) × $1,000 where rr
= ratio of reserves to deposits
• In our example, rr = 0.2, so M = $5,000
The Role of banks in the Monetary
System
Banks’ Liabilities: how do banks get
money?
Banks take deposits (D) from depositors
•
• Banks also borrow money (by selling bonds). This is called
their debt
• The owners of a bank must also invest their own money in
their bank. This is called the bank‘s capital (or, equity)
• Total bank liabilities = deposits + debt
• Total bank funds = liabilities + capital
Banks’ Assets: what do banks do with their
money?
• Some of the banks‘ funds are kept in the banks‘ vaults as
reserves (R)
• Banks‘ funds are also used to make loans
• The interest charged is a source of income
• … and also to make securities purchases
• This too is a source of income
• Total bank assets = reserves + loans + securities purchases
The Role of Banks in the Monetary
System:
Bank’s Balance Sheet
• The bank‘s funds – its liabilities plus capital – are used to buy
assets
• Assets = liabilities + capital
Liabilities and
Owners’ Equity
Assets
Reserves
Loans
Securities
$200
Deposits
500
Debt
300
Capital
(owners’
equity)
$750
200
50
The Role of Banks in the Monetary System:
Leverage
• Leverage is the use of borrowed money (deposits
+ debt) to supplement owners‘ funds for
purposes of investment
• Leverage ratio
= assets/capital
= $(200 + 500 + 300)/$50
= 20
Liabilities and
Assets
Owners’ Equity
Reserves
Loans
Securities
$200
Deposits
500
Debt
300
Capital
(owners’
equity)
$750
200
50
The Role of Banks in the Monetary System:
Leverage
• Being highly leveraged makes banks
vulnerable.
• Example: Suppose the value of our bank‘s
assets falls by 5%, to $950.
• Then, capital = assets – liabilities = 950 – 950
=0
Liabilities and
Owners’ Equity
Assets
Reserves
Loans
Securities
$200
Deposits
500
Debt
300
Capital
(owners’
$750
200
50
The Central Bank’s Influence
• We will now build an algebraic model of the central bank‘s
influence on the monetary system of a country.
• Our first equation is one we have seen already: M = C + D
• All three variables—money supply, currency held by the
public, and demand deposits—will be considered endogenous
Monetary Base
• The monetary base (B) is the total number of dollars held
• by the public as currency (C) or
• by banks as reserves (R)
• So, our second equation is B = C + R
• A country‘s monetary base is directly determined by its central
bank
• B is exogenous; C and R are endogenous
The Money Multiplier
• cd = C/D is the currency-deposit ratio, and
• rd = R/D is the reserve-deposit ratio
Note that 0 < rd < 1
• Although C and R are endogenous, cd and rd will
be considered exogenous
• This is a huge simplification of reality
Demand Deposits
• B = C + R = cd ∙ D + rd ∙ D = (cd + rd) ∙ D
• Therefore, D =
1
∙
cd+rd
B
• We have expressed an endogenous variable, D, entirely in
terms of our exogenous variables (cd, rd, and B)
Currency held by the public
• 𝐶 = 𝑐𝑑 × 𝐷 =
𝑐𝑑
𝑐𝑑+𝑟𝑑
∙𝐵
• Again, we have expressed an endogenous variable, C, entirely
in terms of our exogenous variables (cd, rd, and B)
Reserves held by banks
• 𝑅 = 𝑟𝑑 × 𝐷 =
𝑟𝑑
𝑐𝑑+𝑟𝑑
∙𝐵
• Again, we have expressed an endogenous
variable, R, entirely in terms of our exogenous
variables (cd, rd, and B)
Money Supply
• We know that M = C + D. Therefore,
• 𝑀=
𝑐𝑑
𝑐𝑑+𝑟𝑑
∙𝐵+
1
𝑐𝑑+𝑟𝑑
∙𝐵 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙𝐵
• Again, we have expressed an endogenous variable, M, entirely
in terms of our exogenous variables (cd, rd, and B)
The Money Multiplier
• 𝑀=
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙𝐵
• The factor of proportionality is called the money multiplier:
• 𝑚=
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
• Therefore, 𝑀 = 𝑚 × 𝐵
• Note that, as 0 < rd < 1, it must be that m > 1
• That is, for every dollar of monetary base created by the
central bank, the money supply increases by more than a
dollar
Numerical Example
• Q: Suppose the monetary base is B = $800 billion, the reservedeposit ratio is rd = 0.1, and the currency-deposit ratio is cd =
0.8. Calculate C, R, M, D, and m.
• A: R = $88.89 billion; C = $711.11 billion; D = $888.89
billion; M = $1,600 billion, and m = 2.
The Central Bank
𝑐𝑑 + 1
𝑀=
∙𝐵
𝑐𝑑 + 𝑟𝑑
• When the central bank increases the monetary base, the money
supply increases
• When the reserve-deposit ratio decreases, the money supply
increases
• When the currency-deposit ratio decreases, the money supply
increases (Why?)
The Central Bank
• 𝑀=
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙𝐵
• A country‘s central bank
• directly controls the monetary base, B, and
• indirectly controls the reserve-deposit ratio, rd.
• Therefore, the central bank can change a country‘s monetary
supply
How does the Fed change the monetary base?
• Open-market operations:
• The Fed could print dollars and use them to buy securities
(usually short-term Treasury bonds) from banks or from
the public.
• This reduces ―securities‖ and increases ―reserves‖ (R↑) in
the assets column of the banks‘ balance sheets, and
• Increases cash held by the public (C↑)
• Therefore, the monetary base increases (B = C + R↑)
How does the Fed change the monetary
base?
• Making loans to banks and thereby increasing banks‘ reserves
(R↑)
• This typically happens when banks have lost the trust of
private lenders and are unable to borrow from them.
• The Fed is the ―lender of last resort‖
• The Fed‘s lending can take two forms:
• Discount Window
• Term Auction Facility
How does the Fed change the monetary
base?
Discount Window
• The Fed lends to banks directly and charges them an interest
rate called the discount rate
• When the Fed reduces the discount rate, banks borrow more,
their reserves rise by a bigger amount, and so the monetary
base rises by a bigger amount
How does the Fed change the monetary
base?
Term Auction Facility
• The TAF was a response to the financial crisis of 2008-9
• The Fed decides how much it wants to lend to banks. Eligible
banks then bid to borrow those funds, with the loans going to
the banks that offer to pay the highest interest
• In this way, both banks‘ reserves and the monetary base
increase.
How does the Fed indirectly control the
reserve-deposit ratio?
• We have seen that a decrease in the reserve-deposit ratio (rd↓)
causes the money multiplier and the money supply to increase
• The Fed drives the rd in two ways:
• reserve requirements for banks, and
• interest on banks‘ reserves
How does the Fed indirectly control rd?
Reserve Requirements
• Reserve requirements are Fed regulations that impose a
minimum reserve-deposit ratio on banks
This is to ensure that there will always be enough money in
banks for depositors who may need to withdraw cash
• The required minimum rd is only a minimum
• Still, when reserve requirements decrease, rd tends to fall.
• This causes m, M and B to increase
How does the Fed indirectly control rd?
Interest on Reserves
• This was a response to the financial crisis of 2008-9
• US banks keep their reserves with the Fed
• The Fed now pays banks interest on the reserves they keep at
the Fed
• A reduction in this interest, induces banks to keep fewer
reserves
• This reduces rd, and increases m, M, and B
Case Study: Quantitative Easing
• Prior to the financial crisis of 2008, the US monetary base
rose gradually
• Between 2007 and 2011, it tripled, mainly through openmarket operations
• The Fed printed money and used it to buy riskier securities
than the Treasury bonds it buys during normal times
Case Study: Quantitative Easing
• Although the monetary base tripled during 2007-11, the
money supply rose a lot less: M1 increased 40% and M2
increased 25%
• Why?
• Recall that 𝑀 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙ 𝐵 and 𝑚 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
• Banks had suffered huge losses on their loans. As a result, they
stopped lending.
• The reserve-deposit ratio rose, thereby reducing m
• This is why M did not rise as fast as B
Case Study: Quantitative Easing
• But what if the rd returns to the pre-crisis level?
• Then the huge increase in B would translate into an equally
huge increase in M
• This, as we shall see in Chapter 5, could cause massive
inflation
• Should we be worried?
Case Study: Quantitative Easing
• No, there‘s nothing to worry, says the Fed
• They could simply sell the securities that they had earlier bought,
thereby reducing the monetary base to pre-crisis levels
• Moreover, if there are signs that banks are beginning to lend
the reserves they have accumulated, the Fed could raise the
interest it pays on reserves, thereby reversing any decline in rd
Monetary base in the US
Total reserves in the US
Money multiplier in the US
The Fed’s Monetary Control is Imperfect
• Recall that 𝑀 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙ 𝐵 and 𝑚 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
• The Fed can control the required minimum rd but not the
actual rd. Banks may decide to keep reserves in excess of what
is required.
• The currency-deposit ratio is not under the Fed‘s control. For
example, when people are scared of keeping money in banks,
cd increases.
Case Study: The 1930s
• During the Great Depression of the 1930s, the monetary base
increased but the money supply didn‘t
• Why?
• Recall that 𝑀 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
∙ 𝐵 and 𝑚 =
𝑐𝑑+1
𝑐𝑑+𝑟𝑑
• Both cd and rd increased, which reduced m, making M grow
slower than B
Case Study: The 1930s
• Businesses were losing money and defaulting on their loans
• This caused lots of bank failures
• Ordinary depositors lost faith in banks and chose to keep their
savings in cash
• As a result, the cash-deposit ratio increased
• This reduced the money multiplier
• So, M rose slower than B
The Money Supply and Its Determinants:
1929 and 1933
End-of-chapter problems
End-of-chapter problems
End-of-chapter problems
End-of-chapter problems
End-of-chapter problems
Money and inflation
The quantity theory of money, and the Fisher
effect
The demand for money, the costs of inflation
Macroeconomics
17, 24 October 2019
Topics
• The classical theory of inflation
– causes
– effects
– social costs
• ―Classical‖: assumes prices are flexible &
markets clear and applies to the long run
US inflation
-1
01/01/1999
01/06/1999
01/11/1999
01/04/2000
01/09/2000
01/02/2001
01/07/2001
01/12/2001
01/05/2002
01/10/2002
01/03/2003
01/08/2003
01/01/2004
01/06/2004
01/11/2004
01/04/2005
01/09/2005
01/02/2006
01/07/2006
01/12/2006
01/05/2007
01/10/2007
01/03/2008
01/08/2008
01/01/2009
01/06/2009
01/11/2009
01/04/2010
01/09/2010
01/02/2011
01/07/2011
01/12/2011
01/05/2012
01/10/2012
01/03/2013
01/08/2013
01/01/2014
01/06/2014
01/11/2014
01/04/2015
01/09/2015
01/02/2016
01/07/2016
01/12/2016
01/05/2017
01/10/2017
01/03/2018
01/08/2018
01/01/2019
01/06/2019
Eurozone inflation
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
-0,5
Source: Eurostat
0
-5
1993/ Jan/
1993/ Aug/
1994/ Mar/
1994/ Oct/
1995/ May/
1995/ Dec/
1996/ Jul/
1997/ Feb/
1997/ Sep/
1998/ Apr/
1998/ Nov/
1999/ Jun/
2000/ Jan/
2000/ Aug/
2001/ Mar/
2001/ Oct/
2002/ May/
2002/ Dec/
2003/ Jul/
2004/ Feb/
2004/ Sep/
2005/ Apr/
2005/ Nov/
2006/ Jun/
2007/ Jan/
2007/ Aug/
2008/ Mar/
2008/ Oct/
2009/ May/
2009/ Dec/
2010/ Jul/
2011/ Feb/
2011/ Sep/
2012/ Apr/
2012/ Nov/
2013/ Jun/
2014/ Jan/
2014/ Aug/
2015/ Mar/
2015/ Oct/
2016/ May/
2016/ Dec/
2017/ Jul/
2018/ Feb/
2018/ Sep/
2019/ Apr/
Hungarian inflation
35
30
25
20
15
10
5
Forrás: MNB
The quantity theory of money
• A simple theory linking the inflation rate to the growth rate of
the money supply.
• Begins with the concept of velocity…
Velocity:
• Basic concept: the rate at which money circulates
• Definition: the number of times the average dollar bill
changes hands in a given time period
Velocity
Example: In 2015, $500 billion in transactions
money supply = $100 billion
The average dollar is used in five transactions in 2015
So, velocity = 5
Velocity
This suggests the following definition:
M×V=P×T
or
V=P×T/M
where
V: transactions velocity of money
T : number of transactions
M: money supply
P: value of one typical transaction
The quantity theory of money
Money×Velocity=Price×Output
M×V=P×Y
M: quantity of money
V: income velocity of money (the number of times a dollar bill
enters someone‘s income in a given period of time)
P: price level
Y: income (real GDP)
Money demand and the quantity equation
M/P: real money balances, the purchasing power of the money
supply.
A simple money demand function:
(M/P)d = kY
where
k: how much money people wish to hold for each dollar of
income (k is exogenous)
Money demand and the quantity equation
Money demand: (M/P)d = kY
Quantity equation: M × V = P × Y
The connection between them: k = 1/V
When people hold lots of money relative to their incomes (k is
large), money changes hands infrequently (V is small).
The quantity theory of money with constant
velocity
• Start with quantity equation
• Assumes V is constant and𝐕exogenous:
=𝐕
• Then, quantity equation becomes:
𝐌×𝐕=𝐏×𝐘
The quantity theory of money with constant
velocity
𝐌×𝐕=𝐏×𝐘
• With V constant, the money supply
determines nominal GDP (P × Y ).
• Real GDP is determined by the economy‘s
supplies of K and L and the production
function.
• The price level is
P = (nominal GDP)/(real GDP).
The quantity theory of money with constant
velocity
• The growth rate of a product equals the sum of the growth
rates.
• The quantity equation in growth rates:
𝚫𝐌 𝚫𝐕 𝚫𝐏 𝚫𝐘
+
=
+
𝐌
𝐕
𝐏
𝐘
• The quantity theory of money assumes
• V is constant, so ΔV = 0.
The quantity theory of money
π (Greek letter pi) denotes the inflation rate:
ΔP
π
P
and ΔM ΔP ΔY
 
M P Y
Solve this result for π: ΔM ΔY
π
M

Y
The quantity theory of money
• Normal economic growth requires a certain amount of
money supply growth to facilitate the growth in transactions.
• Money growth in excess of this amount leads to inflation.
• ΔY/Y depends on growth in the factors of production and on
technological progress (all of which we take as given, for
now).
• Hence, the quantity theory predicts a one-for-one relation
between changes in the money growth rate and changes in the
inflation rate.
The origins of the Quantity Theory of Money
goes back to old times
‖Money is not, properly speaking, one of the subjects
of commerce; but only the instrument which men have
agreed upon to facilitate the exchange of one
commodity for another. It is none of the wheels of
trade: It is the oil which renders the motion of the
wheels more smooth and easy. If we consider any one
kingdom by itself, it is evident, that the greater or less
plenty of money is of no consequence; since the prices
of commodities are always proportioned to the plenty
of money….
It is only the public which draws any advantage from
the greater plenty of money; and that only in its wars
and negociations with foreign states.‖
(David Hume (1752): Of Money)
Confronting the quantity theory with
data
The quantity theory of money implies:
1. Countries with higher money growth rates
should have higher inflation rates.
2. The long-run trend in a country‘s inflation rate
should be similar to the long-run trend in the
country‘s money growth rate.
Are the data consistent with these implications?
The quantity theory of money
(103 countries)
GDPD growth rate=-0.055+0,97×(M3 growth)
Source: WDI
The quantity theory of money
(98 countries)
GDPD growth=-0.042+0,88×(M3 growth)
Source: WDI
Source: WDI
United States
Hungary
Argentina
Japan
2018
2016
2014
2012
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
V=PY/M3
10
9
8
7
6
5
4
3
2
1
0
Inflation and interest rate
• Nominal interest rate, i not adjusted for inflation
• Real interest rate, r adjusted for inflation:
r=i−π
The Fisher effect
•
•
•
•
The Fisher equation: i = r + π
S = I determines r.
Hence, an increase in π causes an equal increase in i.
This one-for-one relationship is called the Fisher effect.
Interest rate vs inflation rate
Two real interest rate
Notation: π: actual inflation rate (not known until after
it has occurred)
Eπ: expected inflation rate
Two real interest rates:
i – Eπ ex ante real interest rate: the real interest rate
people expect at the time they buy a bond or take out
a loan
i – π: ex post real interest rate: the real interest rate
actually realized
Money demand and the nominal interest
• In the quantity theory of money, the demand for real money
balances depends only on real income Y.
• Another determinant of money demand: the nominal interest
rate, i, the opportunity cost of holding money (instead of
bonds or other interest-earning assets).
• So, money demand depends negatively on i.
The money demand function
𝐌
𝐏
𝐝
= 𝐋 𝐢, 𝐘
(M/P)d = real money demand, depends
• negatively on i
• i is the opportunity cost of holding money
• positively on Y
• higher Y increases spending on goods and services, so increases need
for money
• (―L‖ is used for the money demand function because money is the
most liquid asset.)
The money demand function
𝐌
𝐏
𝐝
= 𝐋 𝐢, 𝐘 = 𝐋 𝐫 + 𝐄𝛑, 𝐘
• When people are deciding whether to hold
money or bonds, they don‘t know what
inflation will turn out to be.
• Hence, the nominal interest rate relevant for
money demand is r + Eπ.
Equilibrium
𝐌
= 𝐋 𝐫 + 𝐄𝛑, 𝐘
𝐏
The supply of real money balances =real
money demand
What determines what?
Variabl How is it determined in the long run?
e
M
exogenous (central bank)
r
adjusts to ensure S = I
Y
Y =F (K ,L)
P
Adjusts to ensure
𝐌
𝐏
= 𝐋 𝐢, 𝐘
How P responds to ΔM?
𝐌
= 𝐋 𝐫 + 𝐄𝛑, 𝐘
𝐏
For given values of r, Y, and Eπ, a change in M
causes P to change by the same percentage—just
like in the quantity theory of money.
The role of expectations
• Over the long run, people don‘t consistently
over- or under-forecast inflation, so Eπ = π on
average.
• In the short run, Eπ may change when people
get new information.
• E.g.: The Fed announces it will increase M next
year. People will expect next year‘s P to be
higher, so Eπ rises.
• This affects P now, even though M hasn‘t
changed yet...
The role of expectations
𝐌
= 𝐋 𝐫 + 𝐄𝛑, 𝐘
𝐏
For given values of r, Y, and M
E increases  i increases (Fisher effect) (M/P)d
decreases  M/P decreases by an increase in P.
Why is inflation bad?
• Common misperception: inflation reduces real wages
• This is true only in the short run, when nominal
wages are fixed by contracts.
• In the long run, the real wage is determined by
labour supply and the marginal product of
labour, not the price level or inflation rate.
• Consider the data . . .
The social costs of inflation
The classical view: A change in the price level is merely a change in
the units of measurement.
The social costs of inflation fall into two categories:
1. costs when inflation is expected
2. costs when inflation is different than people had expected
The costs of expected inflation
1. Shoeleather cost
Definition: the costs and inconveniences of reducing
money balances to avoid the inflation tax.
• If π increases, i increases (why?), so people reduce
their real money balances.
• Remember: In long run, inflation does not affect
real income or real spending.
• So, same monthly spending but lower average
money holdings means more frequent trips to the
bank to withdraw smaller amounts of cash.
The costs of expected inflation
2. Menu Costs
Definition: The costs of changing prices.
Examples:
• cost of printing new menus
• cost of printing & mailing new catalogues
The higher is inflation, the more frequently firms
must change their prices and incur these costs.
The costs of expected inflation
3. Relative Price Distortions
Firms facing menu costs change prices infrequently.
Example:
• A firm issues new catalogue each January.
• As the general price level rises throughout the year,
the firm‘s relative price will fall.
Different firms change their prices at different times,
leading to relative price distortions causing
microeconomic inefficiencies in the allocation of
resources.
The costs of expected inflation
4. General Inconvenience
• Inflation makes it harder to compare nominal
values from different time periods.
• This complicates long-range financial planning.
Additional cost of unexpected inflation:
Arbitrary redistribution of purchasing power
• Many long-term contracts not indexed, but based
on Eπ.
• If π turns out different from Eπ, then some gain at
others‘ expense.
Example: borrowers & lenders
• If π > Eπ, then (i − π) < (i − Eπ) and purchasing
power is transferred from lenders to borrowers.
• If π < Eπ, then purchasing power is transferred
from borrowers to lenders.
Additional cost of unexpected inflation
• When inflation is high, it‘s more variable and
unpredictable: π turns out different from Eπ
more often, and the differences tend to be
larger, though not systematically positive or
negative.
• So, arbitrary redistributions of wealth more
likely.
• This increases uncertainty, making risk-averse
people worse off.
Seigniorage
• To spend more without raising taxes or selling
bonds, the government can print money.
• The ―revenue‖ raised from printing money is
called seigniorage.
• The inflation tax:
• Printing money to raise revenue causes inflation.
• Inflation is like a tax on people who hold money.
Hyperinflation
• Common definition: π ≥ 50% per month
• All the costs of moderate inflation described
above become huge under hyperinflation.
• Money ceases to function as a store of value,
and may not serve its other functions (unit of
account, medium of exchange).
• People may conduct transactions with barter or
a stable foreign currency.
What causes hyperinflation?
• Hyperinflation is caused by excessive money supply growth.
• When the central bank prints money, the price level rises.
• If it prints money rapidly enough, the result is hyperinflation.
• When a government cannot raise taxes or sell bonds, it must
finance spending increases by printing money.
• In theory, the solution to hyperinflation is simple: stop
printing money.
• In the real world, this requires drastic and painful fiscal
restraint.
Hungarian hyperinflation, 1921-25
2 500 000
5 000 000
4 500 000
2 000 000
4 000 000
3 500 000
1 500 000
3 000 000
2 500 000
1 000 000
2 000 000
1 500 000
500 000
1 000 000
500 000
CPI (1914=100) (left-hand scale)
Source: Sargent (2005:7585)
money supply (million crown) (right-hand scale)
30 April 1925
31 January 1925
31 October 1924
31 July 1924
30 April 1924
31 January 1924
31 October 1923
31 July 1923
30 April 1923
31 January 1923
31 October 1922
31 July 1922
30 April 1922
31 January 1922
31 October 1921
31 July 1921
30 April 1921
0
31 January 1921
0
Hungarian hyperinflation, 1945-46
CPI on 31 July 1946 =399 623×1024 (26 aug. 1939=100) (Siklos 1989:141)
The classical dichotomy
• Recall: Real variables were explained in Chapter 3, nominal
ones in Chapter 5.
• Classical dichotomy: the theoretical separation of real and
nominal variables in the classical model, which implies
nominal variables do not affect real variables.
• Neutrality of money: Changes in the money supply do not
affect real variables.
• In the real world, money is approximately neutral in the long
run.
End-of-chapter problems
In the country of Wiknam, the velocity of money
is constant. Real GDP grows by 3 percent per
year, the money stock grows by 8 percent per
year, and the nominal interest rate is 9 percent.
What is
a) the growth rate of nominal GDP?
b) the inflation rate?
c) the real interest rate?
End-of-chapter problems
Suppose a country has a money demand function (M/P )d = kY,
where k is a constant parameter. The money supply grows by 12
percent per year, and real income grows by 4 percent per year.
a) What is the average inflation rate?
b) How would inflation be different if real income growth were
higher? Explain.
c) How do you interpret the parameter k? What is its
relationship to the velocity of money?
d) Suppose, instead of a constant money demand function, the
velocity of money in this economy was growing steadily
because of financial innovation. How would that affect the
inflation rate? Explain.
End-of-chapter problems
An economy has the following money demand function: (M/P )d=0.2Y/i
1/2.
a) Derive an expression for the velocity of money. What does
velocity depend on? Explain why this dependency may occur.
b) Calculate velocity if the nominal interest rate i is 4 percent.
c) If output Y is 1,000 units and the money supply M is $1,200, what
is the price level P ?
d) Suppose the announcement of a new head of the central bank,
with a reputation of being soft on inflation, increases expected
inflation by 5 percentage points. According to the Fisher effect,
what is the new nominal interest rate?
End-of-chapter problems
e) Calculate the new velocity of money.
f) If, in the aftermath of the announcement,
both the economy’s output and the current
money supply are unchanged, what happens
to the price level? Explain why this occurs.
g) If the new central banker wants to keep the
price level the same after the
announcement, at what level should she set
the money supply?
End-of-chapter problems
Suppose that the money demand function takes the form
(M/P )d =L (i, Y ) =Y/(5i )
a) If output grows at rate g and the nominal interest rate is constant,
at what rate will the demand for real balances grow?
b) What is the velocity of money in this economy?
c) If inflation and nominal interest rates are constant, at what rate, if
any, will velocity grow?
d) How will a permanent (once-and-for-all) increase in the level of
interest rates affect the level of velocity? How will it affect the
subsequent growth rate of velocity?
e) If the central bank wants to achieve a long run target inflation rate
of p, at what rate should the money supply grow?
End-of-chapter problems
In each of the following scenarios, explain and categorize the
cost of inflation.
a) Because inflation has risen, the J. Crew clothing company
decides to issue a new catalog monthly rather than
quarterly.
b) Grandpa buys an annuity for $100,000 from an insurance
company, which promises to pay him $10,000 a year for
the rest of his life. After buying it, he is surprised that high
inflation triples the price level over the next few years.
c) Maria lives in an economy with hyperinflation. Each day
after being paid, she runs to the store as quickly as
possible so she can spend her money before it loses value.
End-of-chapter problems
d) Gita lives in an economy with an inflation rate of
10 percent. Over the past year, she earned a
return of $50,000 on her million-dollar portfolio
of stocks and bonds. Because her tax rate is 20
percent, she paid $10,000 to the government.
e) Your father tells you that when he was your age,
he worked for only $4 an hour. He suggests that
you are lucky to have a job that pays $9 an hour.
The natural rate of unemployment:
job search and real-wage rigidity
Macroeconomics
24 October, 7 November 2019
Chapter objectives
The natural rate of unemployment:
• what it means
• what causes it
• understanding its behavior in the real
world
Labor Force Statistics
• We can devide the population into 3 groups:
• Employed: paid employees, self-employed, and unpaid
workers in a family business
• Unemployed: people not working who have looked for work
during previous 4 weeks
• Not in the labor force: everyone else
• The labor force is the total # of workers, including the
employed and unemployed.
Labor Force Statistics
Unemployment rate (―u-rate‖):
% of the labor force that is unemployed
u-rate
# of
= 100
unemployed
x
labor force
Labor force participation rate:
% of the adult population that is in the labor
force
labor force
= 100 labor force
participation
x
adult
rate
population
Example
Compute the labor force, u-rate, adult
population, and labor force participation rate
using this data:
Adult population of the U.S.
by group, June 2008
# of employed
145.9 million
# of unemployed
8.5 million
not in labor force
79.2 million
Example
Labor force
= employed + unemployed
= 145.9 + 8.5
= 154.4 million
U-rate
= 100 x (unemployed)/(labor
force)
= 100 x 8.5/154.4
= 5.5%
Example
Population
= labor force + not in labor
force
= 154.4 + 79.2
= 233.6
LF partic. rate = 100 x (labor
force)/(population)
= 100 x 154.4/233.6
= 66.1%
Natural Rate of Unemployment
• Natural rate of unemployment:
the average rate of unemployment around
which the economy fluctuates.
• In a recession, the actual unemployment rate
rises above the natural rate.
• In a boom, the actual unemployment rate falls
below the natural rate.
U.S. Unemployment, 1958-2019
A first model of the natural rate
Notation:
L = # of workers in labor force
E = # of employed workers
U = # of unemployed
U/L = unemployment rate
Assumptions
1) L is exogenously fixed.
2) During any given month,
s = fraction of employed workers
that become separated from their jobs,
f = fraction of unemployed workers
that find jobs.
s = rate of job separations
f = rate of job finding
(both exogenous)
The transitions between
employment and unemployment
s
E
Employe
d
Unemploy
ed
f
U
The steady state condition
• Definition: the labor market is in
steady state, or long-run equilibrium,
if the unemployment rate is constant.
• The steady-state condition is:
# of
employed
people
who lose
or leave
their jobs
s E = f
U
# of
unemployed
people who
find jobs
Solving for the “equilibrium” U rate
f U
= s E
= s (L –U )
= s L – s U
Solve for U/L:
(f + s)U = s L
so,
U
s

L s f
Example
• Each month, 1% of employed workers
lose their jobs (s = 0.01)
• Each month, 19% of unemployed workers
find jobs (f = 0.19)
• Find the natural rate of unemployment:
U
s
0.01


 0.05, or 5%
L s  f 0.01  0.19
Policy implication
A policy that aims to reduce the natural
rate of unemployment will succeed only
if it lowers s or increases f.
Why is there unemployment?
• If job finding were instantaneous (f = 1),
then all spells of unemployment would be brief,
and the natural rate would be near zero.
• There are two reasons why f < 1:
– job search
– wage rigidity
Job Search & Frictional
Unemployment
• Frictional unemployment: caused by the time
it takes workers to search for a job
• It occurs even when wages are flexible and
there are enough jobs to go around
• It occurs because
–
–
–
–
workers have different abilities, preferences
jobs have different skill requirements
geographic mobility of workers not instantaneous
flow of information about vacancies and job
candidates is imperfect
Sectoral shifts
• Changes in the composition of demand among
industries or regions
• example: Technological change increases demand
for computer repair persons, decreases demand for
typewriter repair persons
• example: A new international trade agreement
causes greater demand for workers in the export
sectors and less demand for workers in importcompeting sectors.
• It takes time for workers to change sectors, so
sectoral shifts cause frictional unemployment.
Sectoral shifts abound
• Examples:
– Late 1800s: decline of agriculture, increase in
manufacturing
– Late 1900s: relative decline of manufacturing,
increase in service sector
– 1970s energy crisis caused a shift in demand
away from huge gas guzzlers toward smaller
cars.
• In our dynamic economy, smaller (though still
significant) sectoral shifts occur frequently,
contributing to frictional unemployment.
Public Policy and Job Search
Goverment programs affecting unemployment
– Goverment employment agencies:
disseminate info about job openings to better match
workers & jobs
– Public job training programs:
help workers displaced from declining industries get
skills needed for jobs in growing industries
Unemployment insurance (UI)
• UI pays part of a worker‘s former wages for a
limited time after losing his/her job.
• UI increases search unemployment, because it:
– reduces the opportunity cost of being
unemployed
– reduces the urgency of finding work
– hence, reduces f
• Studies: The longer a worker is eligible for UI, the
longer the duration of the average spell of
unemployment.
Benefits of UI
By allowing workers more time to
search,
UI may lead to better matches between
jobs and workers,
which would lead to greater
productivity and higher incomes.
Unemployment from real wage rigidity
If the real wage is
stuck above the
equilibrium level,
then there aren‘t
enough jobs to go
around.
Then, firms must ration
the scarce jobs among
workers.
Structural unemployment: the
unemployment resulting from
real wage rigidity and job
rationing.
Real
wag
e
Rigi
d
real
wa
ge
Supp
ly
Unemploy
ment
Deman
d
Amount
of
labor
hired
Labo
r
Amount of
labor willing
to work
Reasons for wage rigidity
• Minimum wage laws
• Labor unions
• Efficiency wages (employers offer high wage
as incentive for worker productivity and loyalty)
The minimum wage
• The minimum wage is well below the
equilibrium wage for most workers, so it cannot
explain the majority of natural rate
unemployment.
• However, the minimum wage may exceed the
equilibrium wage of unskilled workers, especially
teenagers.
• If so, then we would expect that increases in the
minimum wage would increase unemployment
among these groups.
Source: Eurostat
Slovenia
Luxembourg
Lithuania
Bulgaria
Poland
Portugal
Romania
Ireland
Malta
Hungary
United Kingdom
Serbia
Latvia
Croatia
Germany
Estonia
Spain
Slovakia
Czech Republic
Monthly minimum wage as a proportion of the
mean value of average monthly earnings
60
50
40
30
20
10
0
Labor unions
• Unions exercise monopoly power to secure higher wages for their
members.
• When the union wage exceeds the equilibrium wage,
unemployment results.
• Employed union workers are insiders whose interest is to keep
wages high.
• Unemployed non-union workers are outsiders and would prefer
wages to be lower (so that labor demand would be high enough
for them to get jobs).
Efficiency Wage Theory
• Theories in which high wages increase worker
productivity:
– attract higher quality job applicants
– increase worker effort and reduce ―shirking‖
– reduce turnover, which is costly
– improve health of workers
(in developing countries)
• The increased productivity justifies the cost of
paying above-equilibrium wages.
• The result: unemployment
The duration of unemployment
• The data:
• More spells of unemployment are short-term than
medium-term or long-term.
• Yet, most of the total time spent unemployed is attributable
to the long-term unemployed.
• This long-term unemployment is probably structural
and/or due to sectoral shifts among vastly different
industries.
• Knowing this is important because it can help us craft
policies that are more likely to succeed.
5
Czechia
Japan
Iceland
Germany
Hungary
Malta
Netherlands
Poland
Norway
US
UK
Romania
Austria
Denmark
Slovenia
Bulgaria
Estonia
Luxembourg
Ireland
Belgium
Lithuania
Sweden
Slovakia
Portugal
Latvia
Finland
Croatia
Cyprus
France
Italy
Turkey
Spain
Greece
Unemployment rates in Europe,
2018
25
20
19,3
15
15,3
2,2
2,7
2,4
3,7
3,4
3,7
11,0
10,6
10
3,8
3,9
3,9
4,0
3,9
4,9
5,1
5,4
5,1
Forrás:
EUROSTAT
5,2
5,8
5,5
6,2
8,4 8,4
6,0
9,1
6,3 6,5
7,0
7,4 7,4
4,2
0
European unemployment rates in the long run
14
12
10
8
6
4
2
0
19681970197219741976197819801982198419861988199019921994199619982000200220042006200820102012201420162018
UK
France
Germany
Source: OECD Annual Labor Force Statistics
European unemployment rates in the long run
14
12
10
8
6
4
US
Italy
Sweden
Source: OECD Annual Labor Force Statistics
2018
2016
2014
2012
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
1968
2
The rise in European Unemployment
Two explanations:
1) Most countries in Europe have generous social
insurance programs.
2) Shift in demand from unskilled to skilled
workers, due to technological change.
This demand shift occurred in the U.S., too. But wage
rigidity is less of a problem there, so the shift caused
an increase in the skilled-to-unskilled wage gap instead
of an increase in unemployment.
Chapter summary
1) The natural rate of unemployment
– the long-run average or ―steady state‖ rate of
unemployment
– depends on the rates of job separation and job
finding
2) Frictional unemployment
– due to the time it takes to match workers with
jobs
– may be increased by unemployment insurance
Chapter summary
3) Structural unemployment
– results from wage rigidity - the real wage
remains above the equilibrium level
– causes: minimum wage, unions, efficiency
wages
4) Duration of unemployment
– most spells are short term
– but most weeks of unemployment are
attributable to a small number of long-term
unemployed persons
5) European unemployment
– has risen sharply since 1980
End-of-chapter problems
The residents of a certain dormitory have collected the following
data: people who live in the dorm can be classified as either
involved in a relationship or uninvolved. Among involved people,
10 percent experience a breakup of their relationship every
month. Among uninvolved people, 5 percent enter into a
relationship every month. What is the steady-state fraction of
residents who are uninvolved?
End-of-chapter problems
In this chapter we saw that the steady-state rate of
unemployment is
U/L = s/(s+f ).
Suppose that the unemployment rate does not begin at this level.
Show that unemployment will evolve over time and reach this
steady state. (Hint: Express the change in the number of
unemployed as a function of s, f, and U. Then show that if
unemployment is above the natural rate, unemployment falls, and
if unemployment is below the natural rate, unemployment rises.)
End-of-chapter problems
Consider an economy with the following Cobb–Douglas
production function:
Y=K 1/3L 2/3.
a) Derive the equation describing labor demand in this
economy as a function of the real wage and the capital
stock. (Hint: Review Chapter 3.)
b) The economy has 27,000 units of capital and a labor force
of 1,000 workers. Assuming that factor prices adjust to
equilibrate supply and demand, calculate the real wage,
total output, and the total amount earned by workers.
c) Now suppose that Congress, concerned about the welfare
of the working class, passes a law setting a minimum wage
that is 10 percent above the equilibrium wage you derived
End-of-chapter problems
d) Does Congress succeed in its goal of helping the working
class? Explain.
e) Do you think that this analysis provides a good way of
thinking about a minimum wage law? Why or why not?
Aggregate demand: the Keynesian
Cross and the IS-LM model
Macroeconomics
14, 21 November 2019
Facts about the business
cycle
• GDP growth averages 3–3.5 percent per year over
the long run with large fluctuations in the short run.
• Consumption and investment fluctuate with GDP,
but consumption tends to be less volatile and
investment more volatile than GDP.
• Unemployment rises during recessions and falls
during expansions.
• Okun‘s Law: the negative relationship between GDP
and unemployment.
The US real GDP
(percent change from quarter one year ago)
US real consumption
US real investment
Unemployment in the US
Okun’s law (Hungary)
RGDP growth =1.80-1.85×(change of
u-rate)
Source: KSH,
ILO
Short-Run Theory of Output: it’s all about
demand
• The short-run theory of total real GDP is also called
– Keynesian theory, after the economist John Maynard
Keynes, or
– Aggregate Demand Theory
• This theory assumes that, in the short run, output is
determined by aggregate demand: the economy will
produce as much output as there is demand for
• Keynesian cross: The simplest theory of short-run
equilibrium in the goods market.
Planned Expenditure
• Assumption: The economy is a closed economy
• Planned Expenditure (E) is the total desired
expenditure of the three sectors of the
economy:
– Households (C)
– Businesses (I) and
– Government (G)
E=C+I+G
Consumption, C
• Net Taxes = Tax Revenue – Transfer Payments
Denoted T and always assumed exogenous: 𝑇 = 𝑇
• Recall that GDP is defined as the market value of
all final goods and services produced in an economy
during a given period of time
• But this is also actual total expenditure, which is also
actual total income. Therefore, Y also represents
actual total income.
• Disposable income (or, after-tax income) is total
income minus total net taxes: Y – T.
• Assumption: planned consumption expenditure (C) is
Consumption, C
• Assumption: Planned expenditure by
households is directly related to
disposable income
• Consumption function: C = C (Y – T )
Consumption Function: algebra
• Consumption function: C = C (Y – T )
• Specifically, C = Co + MPC✕(Y – T)
• Co represents all other exogenous variables
that affect consumption, such as asset prices,
consumer optimism, etc.
• MPC is the marginal propensity to consume,
the fraction of every additional dollar of
income that is consumed
Consumption Function: graph
C
C (Y –T) = Co + MPC✕(Y
– T)
1
MP
C
The slope of the
consumption
function is the
MPC.
CoMPC×T
Marginal propensity to consume (MPC) is the
increase in consumption (C) when disposable
income (Y – T) increases by one dollar.
Y
Consumption Function: shifts
C
C = Co2 + MPC✕(Y
– T)
C = Co1 + MPC✕(Y
– T)
Consumption shift factor:
higher consumer optimism,
higher asset prices (Co↑).
Y
Consumption Function: shifts
C
C = Co +
MPC✕(Y – T2)
C = Co + MPC✕(Y
– T 1)
The same shift can also be
caused by lower taxes. (T2 <
T1)
Y
Income and Private Saving
• The marginal propensity to consume is a
positive fraction (0 < MPC < 1)
• That is, when income (Y) increases,
consumption (C) also increases, but by only a
fraction of the increase in income.
• Therefore, Y↑⇒ C↑ and Y – C↑ and Y – T – C↑
• Similarly, Y↓⇒ C↓ and Y – C↓ and Y – T – C↓
Planned Investment
E=C+I+G
• Assumption: Planned investment spending by businesses (I) is
exogenous
• This assumption is a big simplification.
• (Recall that business investment was assumed to be inversely
related to the real interest rate.)
Government Spending
E=C+I+G
• Assumption: government spending (G) is
exogenous
• Public Saving is defined as the net tax revenue
of the government minus government spending,
which is T – G
– This is also called the budget surplus
Planned Expenditure
E=C+I+G
• Therefore, E = C(Y – T) + I + G
• Or, more specifically, E = Co + MPC✕(Y – T) +
I+G
Equilibrium
Assumption: The goods market will be in equilibrium. That is,
actual expenditure will be equal to planned expenditure.
Actual and planned expenditure
• Actual and planned expenditure do not have to
be equal in all circumstances
• Actual expenditure = planned expenditure +
unplanned increase in inventory
– When unplanned increase in inventory > 0, more is
bought than was intended.
– When unplanned increase in inventory < 0, less is
bought than was intended.
Equilibrium
• When unplanned increase in inventory > 0, more is bought
than was intended.
• So, actual expenditure > planned expenditure
• In this case, output will shrink
• In other words, the current output level cannot represent
equilibrium
Equilibrium
• When unplanned increase in inventory < 0, less is bought than
was intended.
• So, actual expenditure < planned expenditure
• In this case, output will increase
• In other words, the current output level cannot represent
equilibrium
Equilibrium
• For an economy to be in equilibrium, unplanned increase in
inventory must be zero
• Therefore, actual expenditure = planned expenditure +
unplanned increase in inventory = planned expenditure
• But recall that actual expenditure is actual GDP or Y, and
planned expenditure is C + I + G
• Therefore, in equilibrium, Y = C + I + G
Graphing planned expenditure
E
planned
expenditure
E =C +I
+G
MP
1 C
income,
output, Y
Graphing the equilibrium condition
E
E
=Y
planned
expendit
ure
45
º
income,
output, Y
The equilibrium value of income
E
planned
expendit
ure
E =Y
E =C +I +G
Output
gap
Y
Equilibri
um
income
𝒀, natural
rate of
output
An increase in government purchases
E
At Y1,
there is
now an
unplanned
drop in

inventory
G
…so firms
…
increase
output, and
income
E1 =
rises toward
Y1
a new
equilibrium.
E =C +I
+G 2
E =C +I
+G 1
Y

Y
E2 =
Y2
Solving for Y
Y C  I G
Y  C  I  G
 C  G
 MPC  Y  G
Collect terms with
Y on the left side
of the equals sign:
(1  MPC)Y  G
equilibrium
condition
in changes
because I
exogenous
because C =
MPC Y
Solve for Y :
 1 
Y  
  G
 1  MPC 
The government purchases multiplier
Definition: the increase in income
resulting from a $1 increase in G.
In this model, the govt
Y
1
purchases multiplier equals 
G
1  MPC
Example: If MPC = 0.8, then
An increase in G
Y
1
causes income to

 5
G
1  0.8
increase 5 times
as much!
Why the multiplier is greater
than 1
• Initially, the increase in G causes an equal increase in Y:
Y = G.
• But Y  C
 further Y
 further C
 further Y
• So the final impact on income is much bigger than the
initial G.
An increase in taxes
E
Initially, the tax
increase reduces
consumption,
and therefore
PE:
E =C1 +I
+G
E =C2 +I
+G
At Y1, there is
now an unplanned
inventory
buildup…
C = MPC
T
…so firms
reduce output,
and income
falls toward a
new
equilibrium
Y
E2 =
Y2

Y
E1 =
Y1
Solving for Y
Y  C  I  G
 C
 MPC   Y  T 
Solving for
Y :
Final
result:
equilibrium
condition in
changes
I and G
exogenous
(1  MPC)Y   MPC  T
  MPC 
Y  
  T
 1  MPC 
The tax multiplier
def: the change in income resulting from
a $1 increase in T :
Y
 MPC

T
1  MPC
If MPC = 0.8, then the tax multiplier
equals
Y
 0.8
 0.8


 4
T
1  0.8
0.2
The tax multiplier
…is negative:
A tax increase reduces
C,
which reduces income.
…is smaller than the
spending multiplier:
Consumers save the
fraction (1 – MPC) of
a tax cut,
so the initial boost in
spending from a tax
cut is
smaller than from an
equal increase in G (or
Tax Cuts: JFK
• Kennedy cut personal and corporate income taxes in 1964
• An economic boom followed.
– GDP grew 5.3% in 1964 and 6.0 in 1965.
– Unemployment fell from 5.7% in 1963 to 5.2% in 1964 to
4.5% in 1965.
• However, it is not easy to prove that the tax cuts caused the
boom
• Even when they agree that the tax cuts caused the boom,
economists can‘t agree on the reason
Tax Cuts: JFK
• Keynesians argued that the tax cuts boosted demand, which
led to higher production and falling unemployment
• Supply-siders argued that demand had nothing to do with it.
The tax cuts gave people the incentive to work harder. So, L
increased. Therefore, Y = F(K, L) also increased.
Tax Cuts: GWB
• Bush cut taxes in 2001 and 2003
• After the second tax cut, a weak recovery
from the 2001 recession turned into a strong
recovery
– GDP grew 4.4% in 2004
– Unemployment fell from its peak of 6.3% in June
2003 to 5.4% in December 2004
• In justifying his tax cut, Bush used the
Keynesian explanation:
– ―When people have more money, they can spend it
on goods and services. … when they demand an
additional good or service, somebody will produce
the good or service.‖
Spending Stimulus: Barack Obama
• When President Obama took office in
January 2009, the economy had suffered the
worst collapse since the Great Depression
• Obama helped enact an $800 billion (5% of
annual GDP) stimulus to be spent over a
two-year period
• About 40% was tax cuts, and 60% was
additional government spending
– White House economists had estimated the
spending multiplier to be 1.57 and the tax-cut
multiplier to be 0.99
Spending Stimulus: Barack Obama
• Much of the new spending was on infrastructure projects
• These projects were fine for the long run, but took a long time
to be implemented, and were therefore not ideal as a short-run
boost
• Obama publicly justified his stimulus bill using Keynesian
demand-side reasoning
End-of-chapter problem
In the Keynesian cross model, assume that the consumption
function is given by
C =120+0.8(Y-T ).
Planned investment is 200; government purchases and taxes are
both 400.
Graph planned expenditure as a function of income.
a) What is the equilibrium level of income?
b) If government purchases increase to 420, what is the new
equilibrium income? What is the multiplier for government
purchases?
c) What level of government purchases is needed to achieve an
income of 2,400? (Taxes remain at 400.)
End-of-chapter problem
Consider the impact of an increase in thriftiness in the
Keynesian cross model. Suppose the consumption function is
C=C0 +MPC(Y-T ),
where C0 is a parameter called autonomous consumption that
represents exogenous influences on consumption and MPC is
the marginal propensity to consume.
a) What happens to equilibrium income when the society
becomes more thrifty, as represented by a decline in C0?
b) What happens to equilibrium saving?
c) Why do you suppose this result is called the paradox of thrift?
d) Does this paradox arise in the classical model of Chapter 3?
Why or why not?
The IS Curve
• The Keynesian Cross model assumed that planned
expenditure by businesses (I) is exogenous
• Recall that, in chapter 3, we had assumed that investment
spending is inversely related to the real interest rate
• The IS Curve theory of the goods market brings back the
investment function I = I(r)
The Real Interest Rate
• Recall that, the real interest rate is the inflation-adjusted
interest rate
• To adjust the nominal interest rate for inflation, you simply
subtract the inflation rate from the nominal interest rate
– If the bank charges you 5% interest rate on a cash loan, that‘s the
nominal interest rate (i = 0.05).
– If the inflation rate turns out to be 3% during the loan period (π = 0.03),
then you paid the real interest rate of just 2% (r = i − π = 0.02)
The Real Interest Rate
• The problem is that when you are taking out a loan you don‘t
quite know what the inflation rate will be over the loan period
• So, economists distinguish between
– the ex post real interest rate: r = i − π
– and the ex ante real interest rate: r = i − Eπ, where Eπ is
the expected inflation rate over the loan period
– We will use the ex ante interpretation of the real interest
rate
Investment and the real interest rate
• Assumption: investment spending is inversely related to the real
interest rate
I = I(r), such that r↑⇒ I↓
r
I
(r
)I
The IS Curve
• Recall that the goods market is in equilibrium when Y = C + I
+G
• The IS curve is a graph that shows all combinations of r and
Y for which the goods market is in equilibrium
• Therefore, the basic equation underlying the IS curve is Y =
C(Y – T) + I(r) + G
Deriving the IS curve: graphs
E =Y
E
r
I
E
Y




E = C + I ( r2
)+G
E = C + I ( r1
)+G
I
r
Any change in the real r
interest rate will cause 1
an opposite change in
r
real total GDP by a
2
multiple determined by
the size of the interest
rate effect.
Y
Y
1
2
Y
I
Y S
1
2
Y
Y
Why the IS curve is negatively sloped
• A fall in the interest rate motivates firms to increase
investment spending, which drives up total planned spending
(E ).
• To restore equilibrium in the goods market, output (a.k.a.
actual expenditure, Y )
must increase.
The IS curve and the loanable funds
model
(a) The L.F.
r
(b) The IS
model
S
S
2
1
r
r
r
2
2
r
r
1
I (r )
S,
I
curve
1
Y
I
SY
Y
2
1
Fiscal Policy and the IS curve
• We can use the IS-LM model to see how fiscal policy (G and
T ) affects aggregate demand and output.
• Let‘s start by using the Keynesian cross to see how fiscal
policy shifts the IS curve…
Shifting the IS curve: G
At any value of
r,  G   E

Y
…so
the IS curve
shifts to the
right.
The horizontal
r
distance of
r
the
1
IS shift equals
1
Y 
1 MPC
E
E
=Y
Y
Y
1
2

G
Y
IS
Y
Y
Y
1
2
E = C + I ( r1
)+G2
E = C + I ( r1
)+G1
1
IS
2Y
THE MONEY MARKET IN THE
SHORT RUN:
THE LM CURVE
The Theory of Liquidity Preference
(review)
• Liquid assets are assumed to earn no interest
• Illiquid assets are assumed to earn the nominal interest rate i
• Therefore, an increase in i is assumed to reduce the demand for
money
• That is, money demand (Md) is assumed to be inversely related
to the nominal interest rate (i)
(M/P)d=L(i)
Prices are sticky in the short run
• Recall that the long-run analysis assumed that P
is endogenous.
– Recall also that in the long run P changes
proportionately with M.
• The short-run analysis in the IS-LM model
assumes that P is exogenous: it is what it is, it is
historically determined
– That is, the overall price level is ―sticky‖: what it was
last week, it will be this week too
Prices are sticky in the short run
• This sticky-prices assumption is the crucial distinction
between long-run and short-run macroeconomic analysis
• Except this assumption, all assumptions made in short-run
analysis are also assumed in long-run analysis
• So, the differences between long-run and short-run theories
are caused by this sticky-prices assumption
The Theory of Liquidity
Preference
r
interest
rate
M P 
r
s
L (r)
1
M P
M/P
real money
balances
Reduction in the money supply
r
interest
rate
By decreasing
the money
supply the
central bank
increases the
interest rate.
r
2
r
L (r )
1
M2
P
M1
P
M/P
real money
blances
How the Fed raises the interest rate
r
To increase r,
Fed reduces
M
intere
st
rate
r
2
r
1
L (r
M2
P
M1
P
)
M/P
real
money
balance
s
CASE STUDY:
Monetary Tightening & Interest Rates
• Late 1970s:  > 10%
• Oct 1979: Fed Chairman Paul Volcker
announces that monetary policy
would aim to reduce inflation
• Aug 1979-April 1980:
Fed reduces M/P 8.0%
• Jan 1983:  = 3.7%
How do you think this policy change
would affect nominal interest rates?
Monetary Tightening & Interest
Rates, cont.
The effects of a monetary tightening
on nominal interest rates
short run
long run
Liquidity
preference
Quantity theory,
Fisher effect
(Keynesian)
(Classical)
prices
sticky
flexible
prediction
i > 0
i < 0
actual
outcome
8/1979: i = 10.4%
4/1980: i = 15.8%
8/1979: i =
10.4%
1/1983: i = 8.2%
model
End-of-chapter problem
Suppose that the money demand function is
(M/P )d=800-50r,
where r is the interest rate in percent. The money supply M is
2,000 and the price level P is fixed at 5.
a) Graph the supply and demand for real money balances.
b) What is the equilibrium interest rate?
c) What happens to the equilibrium interest rate if the supply
of money is reduced from 2,000 to 1,500?
d) If the central bank wants the interest rate to be 4 percent,
what money supply should it set?
The LM curve
Now let‘s put Y back into the money demand
function:
M P 
d
 L (r ,Y )
The LM curve is a graph of all
combinations of r and Y that equate the
supply and demand for real money balances.
The equation for the LM curve is:
M P  L (r ,Y )
Deriving the LM curve
(a) The market for
real money
r
balances
(b) The LM
r curve
L
M
r
r
2
2
r
1
M1
P
L (r ,
Y2 )
L (r ,
Y1 )
M/
P
r
1
Y
Y
1
2
Y
Why the LM curve is upward sloping
• An increase in income raises money demand.
• Since the supply of real balances is fixed, there is now excess
demand in the money market at the initial interest rate.
• The interest rate must rise to restore equilibrium in the money
market.
How M shifts the LM curve
(a) The market for
real money
r
balances
(b) The LM
r curve
r
r
2
2
r
r
1
M2
P
M1
P
L (r ,
Y1 )
M/
P
L
M
2LM
1
1
Y
1
Y
NOW YOU TRY:
Shifting the LM curve
• Suppose a wave of credit card fraud causes
consumers to use cash more frequently in
transactions.
• Use the liquidity preference model to show how
these events shift the LM curve.
SHORT-RUN EQUILIBRIUM IN
THE IS-LM MODEL
Short-run equilibrium
The short-run equilibrium is
the combination of r and Y
that simultaneously satisfies the
equilibrium conditions in both
the goods and money markets:
Y  C (Y T )  I (r )  G
r
L
M
I
S Y
M P  L (r ,Y )
Equilibriu
m
interest
rate
Equilibriu
m
level of
income
Short-run equilibrium
By insisting that both the r
goods market and the
money market need to be
in equilibrium, we have
managed to find a way to
pinpoint both r and Y
simultaneously!
Y  C (Y T )  I (r )  G
M P  L (r ,Y )
Equilibriu
m
interest
rate
L
M
I
S Y
Equilibriu
m
level of
income
Short-run equilibrium
Note that the short-run
equilibrium GDP does not
have to be equal to the longrun equilibrium GDP (𝑌, also
called potential GDP and
natural GDP)
Thus, like the Keynesian Cross
the IS-LM
model can
But,model,
the Keynesian
Cross
Equilibriu
explain
recessions
and
booms.
model could determine
only equilibrium GDP.
The IS-LM model
determines the
m
interest
rate
r
L
M
𝒀
I
S Y
Equilibriu
m
level of
income
End-of-chapter problem
The following equations describe an economy.
Y=C +I+G
C=50+0.75 (Y-T).
I=150-10 r.
(M/P)d =Y-50r.
G=250.
T =200.
M=3,000.
P =4.
a) Identify each of the variables and briefly explain their meaning.
b) From the above list, use the relevant set of equations to derive the IS
curve. Graph the IS curve on an appropriately labeled graph.
c) From the above list, use the relevant set of equations to derive the LM
curve. Graph the LM curve on the same graph you used in part (b).
d) What are the equilibrium level of income and the equilibrium interest
rate?
Economic policy in the IS-LM
model
Macroeconomics
21, 28 November 2019
Context
We will use the IS-LM model to
– see how policies and shocks affect
income and the interest rate in the
short run when prices are fixed
– derive the aggregate demand curve
– explore various explanations for
the
Great Depression
Equilibrium in the IS-LM Model
The IS curve
represents equilibrium
in the goods market.
r
LM
Y  C (Y T )  I (r )  G
The LM curve
represents money
market equilibrium.
r
1
M P  L (r ,Y )
Y
The intersection determines
1
the unique combination of Y and r
that satisfies equilibrium in both
markets.
IS
Y
Policy analysis with the IS-LM Model
Y  C (Y T )  I (r )  G
r
LM
M P  L (r ,Y )
Policymakers can affect
macroeconomic variables
r
with
1
• fiscal policy: G
and/or T
• monetary policy: M
We can use the IS-LM
model to analyze the
effects of these policies.
IS
Y
1
Y
Fiscal Policy and the IS curve
• We can use the IS-LM model to see how fiscal policy (G and
T ) affects aggregate demand and output.
• Let‘s start by using the Keynesian cross to see how fiscal
policy shifts the IS curve…
Shifting the IS curve: G
At any value of r,
G  E 
Y
…so the IS curve
shifts to the
right.
The horizontal
r
distance of
r
the
1
IS shift equals
1
Y 
1 MPC
E
E
=Y
Y
Y
1
2

G
Y
IS
Y
Y
Y
1
2
E = C + I ( r1
)+G2
E = C + I ( r1
)+G1
1
IS
2Y
An increase in government purchases
1. IS curve shifts right
1
by
G
1  MPC
r
r
causing output
2 2
& income to
. r
rise. raises
1
2. This
money demand,
causing the
interest rate to
3. …which reduces
rise…
investment, so the
1 Y
final
increase
in
is smaller than
G
1  MPC
LM
1
.
Y Y
1
3
.
2
IS2
IS1
Y
A tax cut
Because consumers
save (1MPC) of
the tax cut, the
initial boost in
spending is smaller
for T than for an
equal G…
r
LM
r
2 2
. r
1
1
IS2
. IS
1
MPC
T
and1the IS curve
1  MPC
.
shifts by
2 …so the effects on r
. and Y are smaller for
a T than for an
equal G.
Y Y
1
22
.
Y
How M shifts the LM curve
(a) The market for
real money
r
balances
(b) The LM
r curve
r
r
2
2
r
r
1
M2
P
M1
P
L (r ,
Y1 )
M/
P
L
M
2LM
1
1
Y
1
Y
Monetary Policy: an increase in M
r
1. M > 0 shifts
the LM curve
down
(or to the right)
2. …causing the
interest rate to
fall
3. …which
increases
investment,
causing output
& income to
rise.
LM
1
LM
2
r
1
r
2
IS
Y Y
1
2
Y
Interaction between monetary & fiscal policy
• Model:
monetary & fiscal policy variables
(M, G and T ) are exogenous
• Real world:
Monetary policymakers may adjust M
in response to changes in fiscal policy,
or vice versa.
• Such interaction may alter the impact of the
original policy change.
The Fed‘s response to G > 0
• Suppose the government increases G.
• Possible Fed responses:
1) hold M constant
2) hold r constant
3) hold Y constant
• In each case, the effects of the G
are different:
Response 1: hold M constant
If the government
raises G,
the IS curve shifts
right
If Fed holds M
constant, then LM
curve doesn‘t shift.
r
LM
1
r
r2
1
IS2
IS1
Results:
Y  Y 2  Y1
r  r2  r1
YY
1 2
Y
Response 2: hold r constant
If the government
raises G,
the IS curve shifts
right
To keep r
constant, Fed
increases M to
shift LM curve
Results:
right.
Y  Y 3  Y1
r  0
r
LM
1
LM
2
r
r2
1
IS2
IS1
YYY
1 2 3
Y
Response 3: hold Y constant
If the government
raises G,
the IS curve shifts
right
To keep Y
constant, Fed
reduces M to
shift LM curve
Results:
left.
Y  0
r  r3  r1
r
LM
2 LM
1
r
r3
r2
1
IS2
IS1
YY
1 2
Y
Shocks in the IS-LM Model
IS shocks: exogenous changes in the demand for
goods & services.
Examples:
• stock market boom or crash
 change in households‘ wealth
 C
• change in business or consumer
confidence or expectations
 I and/or C
Shocks in the IS-LM Model
LM shocks: exogenous changes in
the demand for money.
Examples:
• a wave of credit card fraud
increases demand for money.
• more ATMs or the Internet reduce
money demand.
EXERCISE:
Analyze shocks with the IS-LM model
Use the IS-LM model to analyze the effects of
1. A boom in the stock market makes consumers
wealthier.
2. After a wave of credit card fraud, consumers
use cash more frequently in transactions.
For each shock,
a. use the IS-LM diagram to show the effects of
the shock on Y and r .
b. determine what happens to C, I, and the
unemployment rate.
The Great Depression
220
billions of 1958 dollars
30
Unemploy
ment (right
scale)
25
200
20
180
15
160
10
140
120
1929
1931
1933
Real
GNP
(left
scale)
1935
1937
5
0
1939
percent of labor force
240
The Spending Hypothesis:
Shocks to the IS Curve
• asserts that the Depression was largely due to
an exogenous fall in the demand for goods &
services -- a leftward shift of the IS curve
• evidence:
output and interest rates both fell, which is
what a leftward IS shift would cause
The Spending Hypothesis:
Reasons for the IS shift
1. Stock market crash  exogenous C
• Oct-Dec 1929: S&P 500 fell 17%
• Oct 1929-Dec 1933: S&P 500 fell 71%
2. Drop in investment
• ―correction‖ after overbuilding in the 1920s
• widespread bank failures made it harder to obtain
financing for investment
3. Contractionary fiscal policy
• in the face of falling tax revenues and increasing
deficits, politicians raised tax rates and cut
spending
The Money Hypothesis:
A Shock to the LM Curve
• asserts that the Depression was largely due to
huge fall in the money supply
• evidence:
M1 fell 25% during 1929-33.
But, two problems with this hypothesis:
1) P fell even more, so M/P actually rose
slightly during 1929-31.
2) nominal interest rates fell, which is the
opposite of what would result from a
leftward LM shift.
The Money Hypothesis Again:
The Effects of Falling Prices
• asserts that the severity of the Depression was due
to a huge deflation:
• P fell 25% during 1929-33.
• This deflation was probably caused by the fall in
M, so perhaps money played an important role
after all.
• In what ways does a deflation affect the economy?
The Money Hypothesis Again:
The Effects of Falling Prices
The stabilizing effects of deflation:
• P  (M/P )  LM shifts right  Y
• Pigou effect:
P
 (M/P )
 consumers‘ wealth 
 C
 IS shifts right
 Y
The Money Hypothesis Again:
The Effects of Falling Prices
The destabilizing effects of unexpected deflation:
debt-deflation theory
P (if unexpected)
 transfers purchasing power from borrowers to
lenders
 borrowers spend less, lenders spend more
 if borrowers‘ propensity to spend is larger than
lenders, then aggregate spending falls, the IS
curve shifts left, and Y falls
The Money Hypothesis Again:
The Effects of Falling Prices
The destabilizing effects of expected deflation:
e




r  for each value of i
I  because I = I (r )
planned expenditure & agg. demand 
income & output 
Why another Depression is unlikely
• Policymakers (or their advisors) now know
much more about macroeconomics:
• The Fed knows better than to let M fall
so much, especially during a contraction.
• Fiscal policymakers know better than to raise
taxes or cut spending during a contraction.
• Federal deposit insurance makes widespread bank
failures very unlikely.
• Automatic stabilizers make fiscal policy
expansionary during an economic downturn.
End-of-chapter problem
According to the IS–LM model, what happens in the short
run to the interest rate, income, consumption, and investment
under the following circumstances? Be sure your answer
includes an appropriate graph.
a) The central bank increases the money supply.
b) The government increases government purchases.
c) The government increases taxes.
d) The government increases government purchases and
taxes by equal amounts.
End-of-chapter problem
Use the IS–LM model to predict the short-run effects of each of the
following shocks on income, the interest rate, consumption, and
investment. In each case, explain what the Fed should do to keep
income at its initial level. Be sure to use a graph in each of your answers.
a) After the invention of a new high-speed computer chip, many firms
decide to upgrade their computer systems.
b) A wave of credit card fraud increases the frequency with which
people make transactions in cash.
c) A best-seller titled Retire Rich convinces the public to increase the
percentage of their income devoted to saving.
d) The appointment of a new ―dovish‖ Federal Reserve chair increases
expected inflation.
End-of-chapter problem
An economy is initially described by the following equations:
C =500+0.75(Y-T); I =1,000-50r; M/P =Y-200r;
G=1000; T=1000; M =6,000; P =2.
a) Derive and graph the IS curve and the LM curve. Calculate the equilibrium
interest rate and level of income. Label that point A on your graph.
b) Suppose that a newly elected president cuts taxes by 20 percent. Assuming
the money supply is held constant, what are the new equilibrium interest rate
and level of income? What is the tax multiplier?
c) Now assume that the central bank adjusts the money supply to hold the
interest rate constant. What is the new level of income? What must the new
money supply be? What is the tax multiplier?
d) Now assume that the central bank adjusts the money supply to hold the level
of income constant. What is the new equilibrium interest rate? What must
the money supply be? What is the tax multiplier?
e) Show the equilibria you calculated in parts ( b), (c), and (d) on the graph you
drew in part (a). Label them points B, C, and D.
End-of-chapter problem
The Fed is considering two alternative monetary policies:
• holding the money supply constant and letting the interest
rate adjust, or
• adjusting the money supply to hold the interest rate constant.
In the IS–LM model, which policy will better stabilize output
under the following conditions? Explain your answer.
• All shocks to the economy arise from exogenous changes in
the demand for goods and services.
• All shocks to the economy arise from exogenous changes in
the demand for money
The economic policy message
public authority must be called in
aid to create additional current
incomes through the expenditure
of borrowed or printed money
…
Thus, as the prime mover in the
first stage of the technique of
recovery, I lay overwhelming
emphasis on the increase of
national purchasing power resulting
from governmental expenditure
which is financed by loans and is
not merely a transfer through
taxation, from existing incomes.
Long-run versus short-run equlibrium:
aggregate demand and aggregate
supply
Macroeconomics
28 November 2019
Topics
• how the short run differs from the long run
• an introduction to aggregate demand
• an introduction to aggregate supply in the short run
and long run
• how the model of aggregate demand and aggregate
supply can be used to analyze the short-run and longrun effects of ―shocks.‖
Facts about the business
cycle
• GDP growth averages 3–3.5 percent per year over
the long run with large fluctuations in the short run.
• Consumption and investment fluctuate with GDP,
but consumption tends to be less volatile and
investment more volatile than GDP.
• Unemployment rises during recessions and falls
during expansions.
• Okun‘s Law: the negative relationship between GDP
and unemployment.
Time horizons in macroeconomics
• Long run:
Prices are flexible, respond to changes in supply
or demand.
• Short run:
Many prices are ―sticky‖ at some predetermined
level.
The economy behaves much
differently when prices are sticky.
Short run vs long run
…though the high price of commodities
be a necessary consequence of the
encrease of gold and silver, yet it follows
not immediately upon that encrease; but
some time is required before the money
circulates through the whole state, and
makes its effect be felt on all ranks of
people. At first, no alteration is
perceived; by degrees the price rises, first
of one commodity, then of another; till
the whole at last reaches a just
proportion with the new quantity of
specie which is in the kingdom.
David Hume (1752): Of Money .
Price stickiness
Forrás: Álvarez et al.
(2005:12)
Price stickiness
Forrás: Álvarez et al.
(2005:15)
Recap of classical macro theory
• Output is determined by the supply side:
• supplies of capital, labor
• technology.
• Changes in demand for goods & services (C, I, G ) only affect
prices, not quantities.
• Assumes complete price flexibility.
• Applies to the long run.
When prices are sticky…
…output and employment also depend on demand, which is
affected by
• fiscal policy (G and T )
• monetary policy (M )
• other factors, like exogenous changes in
C or I.
The model of aggregate demand
and supply
• the paradigm most mainstream economists
and policymakers use to think about economic
fluctuations and policies to stabilize the economy
• shows how the price level and aggregate output are
determined
• shows how the economy‘s behavior is different
in the short run and long run
Aggregate demand
• The aggregate demand curve shows the relationship between
the price level and the quantity of output demanded.
• For this chapter‘s intro to the AD/AS model,
we use a simple theory of aggregate demand based on the
quantity theory of money.
• Later we will develop the theory of aggregate demand in more
detail.
The Quantity Equation as Aggregate Demand
Recall the quantity equation
MV = PY
For given values of M and V,
this equation implies an inverse relationship between P and Y :
The downward-sloping AD curve
An increase in
the price level
causes a fall in
real money
balances (M/P ),
causing a
decrease in the
demand for
goods &
services.
P
A
D
Y
Shifting the AD curve
P
An increase in
the money
supply shifts
the AD curve
to the right.
A
A D2
D1
Y
Aggregate supply in the long run
Recall :
In the long run, output is determined
by
factor supplies
Y  F(K ,and
L) technology
Y is the full-employment or natural level of
output, the level of output at which the
economy‘s resources are fully employed.
“Full employment” means that
unemployment equals its natural rate (not zero).
The long-run aggregate supply curve
P
Y does
LRA
S
not depend
on P,
so LRAS is
vertical.
Y
 F (K , L )
Y
Long-run effects of an increase in M
P
P
In the long
2
run, this
P
raises the
1
price
level…
…but leaves
output the
same.
LRA
S
Y
An
increase in
M shifts
AD to the
right.
A
A D2
D1
Y
Aggregate supply in the short run
• Many prices are sticky in the short run.
• For now, we assume
• all prices are stuck at a predetermined level in
the short run.
• firms are willing to sell as much at that price
level as their customers are willing to buy.
• Therefore, the short-run aggregate supply
(SRAS) curve is horizontal:
The short-run aggregate supply
curve
The SRAS
curve is
horizontal:
The price
level is fixed
at a
predetermine
d level, and
firms sell as
much as
buyers
demand.
P
P
SRAS
Y
Short-run effects of an increase in
M
In the short
run when
prices are
sticky,…
P
…an
increase in
aggregate
demand…
P
…causes
output to
rise.
Y
Y
1
2
SRAS
A
A D2
D1
Y
From the short run to the long run
Over time, prices gradually become
―unstuck.‖ When they do, will they rise or
fall?
In the shortthen over
run
time,
equilibrium, if P will…
rise
Y Y
Y Y
Y Y
fall
remain
constant
The adjustment of prices is what moves the
economy to its long-run equilibrium.
The SR & LR effects of M > 0
P
A = initial
equilibrium
B = new
short-run
eq’m after
Fed
increases M
C = longrun
equilibrium
LRA
S
C
P
2
P
B SRAS
A
Y
Y
2
A
A D2
D1
Y
Shocks
• shocks: exogenous changes in agg. supply or
demand
• Shocks temporarily push the economy away from
full employment.
• Example: exogenous decrease in velocity
• If the money supply is held constant, a decrease in
V means people will be using their money in fewer
transactions, causing a decrease in demand for
goods and services.
The effects of a negative demand
shock
AD shifts left,
depressing
output and
employment
in the short
run.
Over time,
prices fall
and the
economy
moves down
its demand
curve toward
full-
P
LRA
S
B
P
P
A
SRAS
C
A
D1
A
D2
2
Y
2
Y
Y
Supply shocks
• A supply shock alters production costs,
affects the prices that firms charge. (also
called price shocks)
• Examples of adverse supply shocks:
• Bad weather reduces crop yields,
pushing up
food prices.
• Workers unionize, negotiate wage
increases.
• New environmental regulations require
firms to reduce emissions. Firms charge
higher prices to help cover the costs of
compliance.
CASE STUDY:
The 1970s oil shocks
• Early 1970s: OPEC coordinates a reduction in
the supply of oil.
• Oil prices rose
11% in 1973
68% in 1974
16% in 1975
• Such sharp oil price increases are supply shocks
because they significantly impact production
costs and prices.
CASE STUDY:
The 1970s oil shocks
The oil price
P
shock shifts
SRAS up,
causing output
and employment
P2
to
fall.
In absence of
further price
shocks, prices
will fall over
time and
economy
moves back
toward full
LRA
S
B
SRAS
2
A
P1
SRAS
A
D
Y
2
Y
1
Y
CASE STUDY:
The 1970s oil shocks
70%
Predicted effects
of the oil shock:
• inflation 
• output 
•
unemploymen
t
…and then a
gradual recovery.
12%
60%
50%
10%
40%
8%
30%
20%
6%
10%
0%
1973
1974
1975
1976
Change in oil prices (left scale)
Inflation rate-CPI (right scale)
Unemployment rate (right scale)
4%
1977
CASE STUDY:
The 1970s oil shocks
60%
Late 1970s:
As economy
was
recovering,
oil prices shot
up again,
causing
another huge
supply shock!!!
14%
50%
12%
40%
10%
30%
8%
20%
6%
10%
0%
1977
4%
1978
1979
1980
Change in oil prices (left scale)
Inflation rate-CPI (right scale)
Unemployment rate (right scale)
1981
CASE STUDY:
The 1980s oil shocks
40%
1980s:
A favorable
supply shocka significant
fall in oil
prices.
As the model
predicts,
inflation and
unemployme
nt fell:
10%
30%
8%
20%
10%
6%
0%
-10%
4%
-20%
-30%
2%
-40%
-50%
1982
0%
1983
1984
1985
1986
Change in oil prices (left scale)
Inflation rate-CPI (right scale)
Unemployment rate (right scale)
1987
Stabilization policy
• def: policy actions aimed at reducing the severity of short-run
economic fluctuations.
• Example: Using monetary policy to combat the effects of
adverse supply shocks:
Stabilizing output with
monetary policy
P
The
adverse
supply
shock
moves the
economy
to
point B.
P2
LRA
S
B
SRAS
2
A
P1
SRAS
1
A
D1
Y
2
Y
Y
Stabilizing output with
monetary policy
But the Fed
accommodat
es the shock
by raising
agg. demand.
results:
P is
permanently
higher, but Y
remains at its
fullemployment
P
P2
LRA
S
B
C
SRAS
2
A
P1
Y
2
Y
A
A D2
D1
Y
Chapter Summary
1) Long run: prices are flexible, output and
employment are always at their natural rates,
and the classical theory applies.
Short run: prices are sticky, shocks can push
output
and employment away from their
natural rates.
2) Aggregate demand and supply:
a framework to analyze economic
fluctuations
Chapter Summary
3) The aggregate demand curve slopes
downward.
4) The long-run aggregate supply curve is
vertical, because output depends on
technology and factor supplies, but not
prices.
5) The short-run aggregate supply curve is
horizontal, because prices are sticky at
predetermined levels.
Chapter Summary
6) Shocks to aggregate demand and supply
cause fluctuations in GDP and employment
in the short run.
7) The Fed can attempt to stabilize the
economy with monetary policy.
End-of-chapter problems
An economy begins in long-run equilibrium, and then a change in
government regulations allows banks to start paying interest on
checking accounts. Recall that the money stock is the sum of currency
and demand deposits, including checking accounts, so this regulatory
change makes holding money more attractive.
a) How does this change affect the demand for money?
b) What happens to the velocity of money? If the Fed keeps the
money supply constant, what will happen to output and prices in
the short run and in the long run?
c) If the goal of the Fed is to stabilize the price level, should the Fed
keep the money supply constant in response to this regulatory
change? If not, what should it do? Why?
d) If the goal of the Fed is to stabilize output, how would your
End-of-chapter problems
Suppose the Fed reduces the money supply by 5 percent. Assume the
velocity of money is constant.
a) What happens to the aggregate demand curve?
b) What happens to the level of output and the price level in the
short run and in the long run? Give a precise numerical answer.
c) In light of your answer to part (b), what happens to
unemployment in the short run and in the long run according to
Okun‘s law? Again, give a precise numerical answer.
d) What happens to the real interest rate in the short run and in the
long run? (Hint: Use the
e) model of the real interest rate in Chapter 3 to see what happens
when output changes.) Here, your answer should just give the
End-of-chapter problems
Let‘s examine how the goals of the Fed influence its response to
shocks. Suppose that in
scenario A the Fed cares only about keeping the price level stable and
in scenario B the Fed cares only about keeping output and
employment at their natural levels. Explain how in each scenario the
Fed would respond to the following.
a) An exogenous decrease in the velocity of money.
b) An exogenous increase in the price of oil.
The theory of Aggregate Supply and
the Short-Run Tradeoff Between
Inflation and Unemployment
Macroeconomics
5 December 2019
Two models of aggregate supply
1) The sticky-wage model
2) The sticky-price model
Both models imply:
Y  Y    P  EP 
agg.
outp
ut
natural
rate of
output
a
positive
parame
ter
the
expected
price level
the
actual
price
level
The sticky-wage model
• Assumes that firms and workers negotiate
contracts and fix the nominal wage before they
know what the price level will turn out to be.
• The nominal wage they set is the product of a
target real wage and the expected price level:
W   EP
W
EP
 
P
P
Target
real
wage
The sticky-wage model
W
EP
 
P
P
If it turns out that
P  EP
P  EP
P  EP
then
unemployment and
output are at their
natural
rates
Real wage
is less than its
target, so firms hire more
workers and output rises
above
its natural
Real wage
exceedsrate
its
target,
so firms hire fewer workers
and output falls below its
natural rate
The sticky-wage model
• Implies that the real wage should be counter-cyclical , it
should move in the opposite direction as output
over the course of business cycles:
– In booms, when P typically rises, the real wage
should fall.
– In recessions, when P typically falls, the real
wage should rise.
• This prediction does not come true in the real
world:
Percentage change
in real wage
The cyclical behavior of the real wage
4
1972
3
1998
2
1960
1997
1999
1
1996
1970
0
2000
1984
1993
1992
1982
1991
-1
1965
1990
-2
1975
-3
1979
1974
-4
-5
1980
-3
-2
-1
0
1
2
3
4
5
6
7
8
Percentage change in real GDP
Wages, employment, and prices during
the Great Depression
Bordo, M. D., Erceg, Ch. J.,
Evans, Ch. L. (2000): Money,
Sticky Wages, and the Great
Depression. American Economic
Review, 90(5), 1447-1463., p. 1448
Problem (not from the book)
In an economy where the conditions of the sticky-wage model
of AS hold, the production function is given by: Y=K0.5N0.5, and
the capital stock is 1600. The target real wage is 2.
a) Calculate the natural rate output.
b) Derive the short-run aggregate supply curve.
The sticky-price model
• Reasons for sticky prices:
– long-term contracts between firms and customers
– menu costs
– firms not wishing to annoy customers with frequent price
changes
• Assumption:
– Firms set their own prices
(e.g., as in monopolistic competition).
The sticky-price model
An individual firm‘s desired price is:
p  P  a(Y  Y )
where a > 0.
Suppose two types of firms:
• firms with flexible prices, set prices as above
• firms with sticky prices, must set their price
before they know how P and Y will turn out:
p  EP  a( EY  EY )
The sticky-price model
p  EP  a( EY  EY )
• Assume sticky price firms expect that output will
equal its natural rate. Then,
p  EP
• To derive the aggregate supply curve,
first find an expression for the overall price level.
• s = fraction of firms with sticky prices.
Then, we can write the overall price level as…
The sticky-price model
P  s[ EP ]  (1  s )[ P  a(Y  Y )]
price set by
price set by
flexible price
sticky price
firms
firms
• Subtract (1s)P from both sides:
sP  s[ EP ]  (1  s )[a(Y  Y )]
• Divide both sides by s :
(1 s )a
P  EP 
(Y  Y )
s
The sticky-price model
(1 s )a
P  EP 
(Y  Y )
s
• High EP High P
If firms expect high prices, then firms that must
set prices in advance will set them high.
Other firms respond by setting high prices.
• High Y  High P
When income is high, the demand for goods is
high. Firms with flexible prices set high prices.
• The greater the fraction of flexible price firms, the
smaller is s and the bigger is the effect of Y on
P.
The sticky-price model
(1 s )a
P  EP 
(Y  Y )
s
Finally, derive AS equation by solving for Y :
Y  Y   (P  EP ),
s
where  
0
(1  s )a
Summary & implications
P
LRA
S
Y  Y   (P  EP)
P  EP
SRA
S
P  EP
P  EP
Y
Y
Both models
of agg.
supply imply
the
relationship
summarized
by the SRAS
curve &
equation.
Summary & implications
SRAS equation:
Y  Y   (P  EP)
Suppose a positive
AD shock moves
SRA
output above its
P
LRA
S2
natural rate and
S
SRA
P above the level
S1
people had
expected.
P3  EP3
P2
Over time, EP rises,
EP2  P1  EP1
SRAS shifts up,
and output returns
to its natural rate.
AD
2
AD
1
Y3  Y1  Y
Y2
Y
Inflation, Unemployment,
and the Phillips Curve
The Phillips curve states that  depends on
– expected inflation, E.
– cyclical unemployment: the deviation of
the actual rate of unemployment from the
natural rate
– supply shocks,  (Greek letter ―nu‖).
  E   (u  u )  
n
where  > 0 is an exogenous
constant.
Deriving the Phillips Curve from SRAS
(1) Y  Y   (P  EP )
(2) P  EP  (1  )(Y  Y )
(3) P  EP  (1  )(Y  Y )  
(4) (P  P1 )  ( EP  P1 )  (1  )(Y Y )  
(5)   E  (1  )(Y  Y )  
(6)
(1  )(Y  Y )    (u  un )
(7)
  E   (u  un )  
Comparing SRAS and the Phillips
Curve
SRAS: Y  Y   (P  EP )
Phillips curve:
  E   (u  un )  
• SRAS curve:
Output is related to
unexpected movements in the price level.
• Phillips curve:
Unemployment is related to
unexpected movements in the inflation
rate.
Adaptive expectations
• Adaptive expectations: an approach that
assumes people form their expectations of
future inflation based on recently observed
inflation.
• A simple version:
Expected inflation = last year‘s actual
inflation
E   1
Then, P.C. becomes
   1   (u  un )  
Inflation inertia
   1   (u  un )  
In this form, the Phillips curve implies that
inflation has inertia:
– In the absence of supply shocks or cyclical
unemployment, inflation will continue
indefinitely at its current rate.
– Past inflation influences expectations of
current inflation, which in turn influences the
wages & prices that people set.
Two causes of rising & falling inflation
   1   (u  un )  
• cost-push inflation:
inflation resulting from supply shocks
Adverse supply shocks typically raise
production costs and induce firms to raise
prices, ―pushing‖ inflation up.
• demand-pull inflation:
inflation resulting from demand shocks
Positive shocks to aggregate demand cause
unemployment to fall below its natural rate,
which ―pulls‖ the inflation rate up.
Graphing the Phillips curve
In the short
run, policymakers
face a tradeoff
between  and u.

  E   (u  un )  

1
The shortrun
Phillips
curve
E  
u
n
u
Shifting the Phillips curve
People

adjust their
expectations
over time,
E 2  
so the
tradeoff
E1  
only holds
in the short
run. E.g., an
increase
in E shifts
the short-run
P.C. upward.
  E   (u  un )  
u
n
u
The sacrifice ratio
• To reduce inflation, policymakers can contract agg.
demand, causing unemployment to rise above the natural
rate.
• The sacrifice ratio measures the percentage of a year‘s real
GDP that must be foregone to reduce inflation by 1
percentage point.
• A typical estimate of the ratio is 5.
The sacrifice ratio
• Example: To reduce inflation from 6 to 2 percent,
must sacrifice 20 percent of one year‘s GDP:
GDP loss = (inflation reduction) × (sacrifice ratio)
= 4 ×5
• This loss could be incurred in one year or spread
over several, e.g., 5% loss for each of four years.
• The cost of disinflation is lost GDP.
One could use Okun‘s law to translate this cost into
unemployment.
Use the Phillips curve to explain
what Milton Friedman is saying
‖Only surprises matter. If everyone
anticipated that prices would rise at, say,
20 percent a year, then this anticipation
would be embodied in future wage (and
other) contracts, real wages would then
behave precisely as they would if
everyone anticipated no price rise, and
there would be no reason for the 20
percent rate of inflation to be associated
with a different level of unemployment
than a zero rate‖.
(Friedman, M. (1976), Inflation and
Unemployment, Nobel Memorial
Use the Phillips curve to explain
what Milton Friedman is saying
‖what matters is not inflation per se,
but unanticipated inflation; there is
no stable trade-off between inflation
and unemployment; there is a
―natural rate of unemployment‖…,
which is consistent with the real
forces and with accurate perceptions;
unemployment can be kept below
that level only by an accelerating
inflation; or above it, only by
accelerating deflation‖.
(Friedman, M. (1976), Inflation and
Unemployment, Nobel Memorial
Problem 2 (Mankiw, p. 432)
Suppose that an economy has the Phillips curve =-1 -0.5(u-5)
What is the natural rate of unemployment?
a) Graph the short-run and long-run relationships between
inflation and unemployment.
b) How much cyclical unemployment is necessary to reduce
inflation by 4 percentage points?
c) Inflation is running at 6 percent. The central bank wants to
reduce it to 2 percent. Give two scenarios that will achieve
that goal.
Rational expectations
Ways of modeling the formation of expectations:
– adaptive expectations:
People base their expectations of future inflation
on recently observed inflation.
– rational expectations:
People base their expectations on all available
information, including information about current
and prospective future policies.
Painless disinflation?
Proponents of rational expectations believe that the
sacrifice ratio may be very small:
• Suppose u = un and  = E = 6%, and suppose the
Fed announces that it will do whatever is necessary to
reduce inflation from 6 to 2 percent as soon as
possible.
• If the announcement is credible, then E will fall,
perhaps by the full 4 points.
• Then,  can fall without an increase in u.
Painless disinflation?
An alternative "rational expectations" view
denies that there is any inherent momentum in
the present process of inflation…An
implication of this view is that inflation can
be stopped much more quickly than advocates
of the "momentum" view have
indicated…This is not to say that it would be
easy to eradicate inflation. On the contrary, it
would require far more than a few temporary
restrictive fiscal and monetary actions. It
would require a change in the policy regime.
Sargent, Th. (1982): The Ends of Four
Big Inflations, p. 42)
Thomas Sargent
Calculating the sacrifice ratio for the
Volcker disinflation
1981:  = 9.7%
1985:  = 3.0%
Total disinflation =
6.7%
year
u
un
uu n
1982
9.5%
6.0%
3.5%
1983
9.5
6.0
3.5
1984
7.4
6.0
1.4
1985
7.1
6.0
1.1
Total
9.5%
Calculating the sacrifice ratio for the
Volcker disinflation
• From previous slide: Inflation fell by 6.7%, total
cyclical unemployment was 9.5%.
• Okun‘s law:
1% of unemployment = 2% of lost output.
• So, 9.5% cyclical unemployment
= 19.0% of a year‘s real GDP.
• Sacrifice ratio = (lost GDP)/(total disinflation)=
19/6.7 = 2.8 percentage points of GDP were lost
for each 1 percentage point reduction in inflation.
The natural rate hypothesis
Our analysis of the costs of disinflation,
and of economic fluctuations in the
preceding chapters, is based on the natural
rate hypothesis:
Changes in aggregate demand affect output
and employment only in the short run.
In the long run, the economy returns to the
levels of output, employment, and
unemployment described by the ‖classical
model‖.
Problem 5 (Mankiw 2015, p. 433 )
Suppose that the economy is initially at a long-run equilibrium. Then the Fed
increases the money supply.
a) Assuming any resulting inflation to be unexpected, describe any changes in
GDP, unemployment, and inflation that are caused by the monetary
expansion. Explain your conclusions using three diagrams: one for the IS–
LM model, one for the AD–AS model, and one for the Phillips curve.
b) Assuming instead that any resulting inflation is expected, describe any
changes in GDP, unemployment, and inflation that are caused by the
monetary expansion. Once again, explain your conclusions using three
diagrams: one for the IS–LM model, one for the AD–AS model, and one
for the Phillips curve.
Problem 6 (Mankiw 2015, p. 433 )
Assume that people have rational expectations and that the economy is described
by the sticky price model. Explain why each of the following propositions is true.
a) Only unanticipated changes in the money supply affect real GDP. Changes
in the money supply that were anticipated when prices were set do not have
any real effects.
b) If the Fed sets the money supply at the same time as people are setting
prices, so that everyone has the same information about the state of the
economy, then monetary policy cannot be used systematically to stabilize
output. Hence, a policy of keeping the money supply constant will have the
same real effects as a policy of adjusting the money supply in response to
the state of the economy. (This is called the policy irrelevance proposition.)
c) If the Fed sets the money supply well after people have set prices, so that
the Fed has collected more information about the state of the economy,
then monetary policy can be used systematically to stabilize output.
The imperfect-information model:
a problem (not from the book)
Suppose that in an economy in which the imperfect-information
model holds, the supply curve of a milk producer can be described by
the equation:
Q=a×Pmilk/EP,
where Q is the quantity produced, a>0 is a constant, Pmilk is the price
of milk and EP is the expected price level. Suppose that both the price
level and the price of milk increase by 10 percent.
a) Since in this economy the aggregate demand fluctuates very
frequently, the producer will think that the probability that the
increase of the price of milk is caused by an increase in the price
level is 80 percent, and the probability of an increase in relative
demand is only 20 percent. With what percentage will the
producer increase production as a reaction to this 10 percent
increase in the price level?
b) Suppose, instead, that aggregate demand shocks are not that
frequent, and the producer will, therefore, think that there is only a
40 percent probability that an increase in the price level is
A review of the course
Macroeconomics
12 December 2019
Measuring
GDP
• Three approaches to GDP: expenditure, income, value added
• Real and nominal GDP
Inflation
• GDP deflator inflation
• Consumer Price Index  inflation
Unemployment
• Employed, Unemployed, not in the labour force
• Unemployment rate
Simple labour market statistics
Compute the labor force, u-rate, adult
population, and labor force participation rate
using this data:
Adult population of the U.S.
by group, June 2008
# of employed
145.9 million
# of unemployed
8.5 million
not in labor force
79.2 million
Long-run issues
Production and the division of income (the classical
model)
• Model of the market for loanable funds  real interest rate
• Euler theorem (neoclassical theory of income distribution)
Money and inflation
•
•
•
•
The money supply (money multiplier)
Demand for money, the Fisher equation
The quantity theory of money
Costs of inflation
Unemployment (theories of the natural rate of
unemployment)
• Frictions from job search
• Real wage rigidity (stickiness)
Euler’s theorem:
Under our assumptions (constant returns to scale,
profit maximization, and competitive markets)…
total output is divided between the payments to
capital and labor, depending on their marginal
products, with no extra profit left over.
Y  MPL  L  MPK  K
nation
al
incom
e
labor
incom
e
capital
incom
e
slide 527
Euler’s theorem:
Suppose the production function in Europe is Y=K 1/3L2/3,
where K is the amount of capital and L is the amount of labor.
The economy begins with 100 units of land and 100 units of
labor. Use a calculator and equations in the chapter to find a
numerical answer to each of the following questions.
a) How much output does the economy produce?
b) What are the wage and the rental price of capital?
c) What share of output does labor receive?
Market for loanable funds
Consider an economy described as follows:
Y = C+ I + G.
Y = 1,200.
G = 150.
T =100.
C =125+0.75(Y-T ).
I =200 -10r.
a) In this economy, compute private saving, public saving, and national saving.
b) Find the equilibrium interest rate.
Money supply
End-of-chapter problems
An economy has the following money demand function: (M/P )d=0.2Y/i
1/2.
a) Derive an expression for the velocity of money. What does
velocity depend on? Explain why this dependency may occur.
b) Calculate velocity if the nominal interest rate i is 4 percent.
c) If output Y is 1,000 units and the money supply M is $1,200, what
is the price level P ?
d) Suppose the announcement of a new head of the central bank,
with a reputation of being soft on inflation, increases expected
inflation by 5 percentage points. According to the Fisher effect,
what is the new nominal interest rate?
End-of-chapter problems
e) Calculate the new velocity of money.
f) If, in the aftermath of the announcement,
both the economy’s output and the current
money supply are unchanged, what happens
to the price level? Explain why this occurs.
g) If the new central banker wants to keep the
price level the same after the
announcement, at what level should she set
the money supply?
Natural rate of unemployment
In this chapter we saw that the steady-state rate of
unemployment is
U/L = s/(s+f ).
Suppose that the unemployment rate does not begin at this level.
Show that unemployment will evolve over time and reach this
steady state. (Hint: Express the change in the number of
unemployed as a function of s, f, and U. Then show that if
unemployment is above the natural rate, unemployment falls, and
if unemployment is below the natural rate, unemployment rises.)
Natural rate of unemployment
On a labour market the demand curve can be described as
LD(w/p)=32000/(w/p)2, where w/p denotes the real wage. The
labour supply is 8000 and independent of the real wage.
a) Calculate the equilibrium (market clearing) real wage. Calculate
the unemployment rate.
b) Suppose that a minimum wage of 2.1 is introduced by the
government. Calculate employment and the unemployment
rate after the minimum wage is introduced.
Short-run issues
Keynesian cross: the short-run model of the market for
goods and services
IS-LM model
• Deriving the IS curve form the Keynesian cross, and the LM curve from
the money market equilibrium
• IS-LM equilibrium: the effect of policy actions and shocks on real GDP
and real interest rate
Aggregate demand and aggregate supply
•
•
•
•
AD as derived form the QTM
LRAS-SRAS-AD model
Positively sloped AS as derived form the sticky wage/sticky price model
Phillips curve
Keynesian cross
C(Y-T)=125+0.75(Y-T)
I=100
G=150
T=100
Equilibrium income
The effect of a fiscal policy change or of some other shock.
IS-LM model
SRAS-LRAS-AD
Let‘s examine how the goals of the Fed influence its response to
shocks. Suppose that in
scenario A the Fed cares only about keeping the price level stable and
in scenario B the Fed cares only about keeping output and
employment at their natural levels. Explain how in each scenario the
Fed would respond to the following.
a) An exogenous decrease in the velocity of money.
b) An exogenous increase in the price of oil.
Sticky wage model -- problem (not from the
book)
In an economy where the conditions of the sticky-wage model
of AS hold, the production function is given by: Y=K0.5N0.5, and
the capital stock is 1600. The target real wage is 2.
a) Calculate the natural rate output.
b) Derive the short-run aggregate supply curve.
Phillips curve
Suppose that an economy has the Phillips curve π= π-1-0.5(u-5)
a) What is the natural rate of unemployment?
b) Graph the short-run and long-run relationships between
inflation and unemployment.
c) How much cyclical unemployment is necessary to reduce
inflation by 4 percentage points?
d) Inflation is running at 6 percent. The central bank wants to
reduce it to 2 percent. Give two scenarios that will achieve
that goal.
A complex problem for the short-run model
Suppose that the economy is initially at a long-run equilibrium. Then the Fed
increases the money supply.
a) Assuming any resulting inflation to be unexpected, describe any changes in
GDP, unemployment, and inflation that are caused by the monetary
expansion. Explain your conclusions using three diagrams: one for the IS–
LM model, one for the AD–AS model, and one for the Phillips curve.
b) Assuming instead that any resulting inflation is expected, describe any
changes in GDP, unemployment, and inflation that are caused by the
monetary expansion. Once again, explain your conclusions using three
diagrams: one for the IS–LM model, one for the AD–AS model, and one
for the Phillips curve.