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macroeconomicsfifth edition
N. Gregory Mankiw
PowerPointSlides
by Ron Cronovich
macro
2002 Worth Publishers, all rights reserved
Topic 7:
Money and Inflation(chapter 4)
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m
C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 2
In thi% chapter yo& will learnIn thi% chapter yo& will learn
The classical theory of ination causes
eects
social costs
Classical -- assumes prices are
exible & markets clear.
Applies to the lon run.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3
'.. inflation it% trend*'.. inflation it% trend* +,-/0++,-/0+
0
2
4
6
!0
!2
!4
!6
!"60 !"6# !"$0 !"$# !"0 !"# !""0 !""# 2000
1
pery
ear
inflation rate
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4
'.. inflation it% trend*'.. inflation it% trend* +,-/0++,-/0+
0
2
4
6
!0
!2
!4
!6
!"60 !"6# !"$0 !"$# !"0 !"# !""0 !""# 2000
1peryear
inflation rate inflation rate trend
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #
The connection 2etweenThe connection 2etween
money and price%money and price%
!nation rate " the percentae increasein the a#erae le#el of prices.
price " amount of money re$uire% tobuy a oo%.
ecause prices are %e'ne% in terms ofmoney( )e nee% to consi%er the natureof money(
the supply of money( an% ho) it iscontrolle%.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 6
Money: definitionMoney: definition
MoneyMoneyis the stockis the stock
of assets that canof assets that can
be rea%ily use% tobe rea%ily use% tomake transactions.make transactions.
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Money: f&nction%Money: f&nction%
1. medium of exchangewe use it to buy stuf
2. store of value
transers purchasing power romthe present to the uture
3. unit of accountthe common unit by whicheveryone measures prices andvalues
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Money: type%Money: type%
1. at money* has no intrinsic value
* example: the paper currency we
use
2. commodity money* has intrinsic value
* examples: gold coins,
cigarettes in P.O.W. camps
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Discussion QuestionDiscussion Question
+hich of these are money,a. Currency
b. Checks
c. eposits in checkin accountscalle% %eman% %eposits/
d. Cre%it car%s
e. Certi'cates of %epositcalle% time %eposits/
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !0
The money %&pply monetary policyThe money %&pply monetary policy
The money supplyis the $uantityof money a#ailable in the economy.
Monetary policyis the control
o#er the money supply.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !!
The central 2ankThe central 2ank
0onetary policy is con%ucte% by acountry1s central bank.
!n the 2.3.(
the centralbank is
calle% the
Federal
Reservethe
Fed/. The Federal Reserve BuildingWashington, DC
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !2
Money %&pply mea%&re%*Money %&pply mea%&re%* !pril 00!pril 00
43ymbol Assets inclu%e% Amount billions/4
C Currency 5678.9
0: C ; %eman% %eposits( ::9 0: ; small time %eposits( 6 ; lare time %eposits( 8=6
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !3
The 3&antity Theory of MoneyThe 3&antity Theory of Money
A simple theory linkin theination rate to the ro)thrate of the money supply.
eins )ith a concept calle%velocity@
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !4
elocityelocity
basic concept: the rate at )hich moneycirculates
denition: the number of times thea#erae %ollar bill chanes han%s in a
i#en time perio% example !n >==:(
* 56== billion in transactions*
money supply " 5:== billion*The a#erae %ollar is use% in '#etransactions in >==:
* 3o( #elocity " 6
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !#
elocity*elocity* cont.cont.
This suests the follo)in %e'nition
=T
VM
)hereV" #elocity
T" #alue of all transactions
M" money supply
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !6
elocity*elocity* cont.cont.
2se nominal B as a proxy for totaltransactions.
Then( P YV
M
=
)here
P " price of output B
%eator/
Y " $uantity of output real B/
P Y " #alue of output nominal
B/
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !$
The 5&antity e5&ationThe 5&antity e5&ation
The uantity euationM V" P Y
follo)s from the prece%in %e'nition
of #elocity.
!t is an identity:
it hol%s by %e'nition of the #ariables.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !
Money demand and the 5&antity e5&ationMoney demand and the 5&antity e5&ation
MP" real money balances( thepurchasin po)er of the money supply.
A simple money %eman% function
MP/%" kY)here
k" ho) much money people )ish to
hol% for each %ollar of income.kis exoenous/
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide !"
Money demand and the 5&antity e5&ationMoney demand and the 5&antity e5&ation
money %eman% MP/%" kY
$uantity e$uation M V" P Y
The connection bet)een them k"
:DV
+hen people hol% lots of money
relati#e to their incomes kis hih/(
money chanes han%s infre$uently V
is lo)/.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 20
back to the Quantity Theory of Moneyback to the Quantity Theory of Money
starts )ith $uantity e$uation
assumes V is constant & exoenous
=V V
+ith this assumption( the $uantitye$uation can be )ritten as
= M V P Y
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 2!
The 3&antity Theory of MoneyThe 3&antity Theory of Money, cont., cont.
Eo) the price le#el is %etermine%
+ith V constant( the money supply
%etermines nominal B P Y / Feal B is %etermine% by the
economy1s supplies of K an% L an% the
pro%uction function chap ?/
The price le#el is
P" nominal B/Dreal B/
= M V P Y
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 22
The 3&antity Theory of MoneyThe 3&antity Theory of Money, cont., cont.
The $uantity e$uation in ro)th
rates
M V P Y
M V P Y + = +
The $uantity theory of money assumes
is constant( so " =.V
VV
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 23
The 3&antity Theory of MoneyThe 3&antity Theory of Money, cont., cont.
Get Breek letter pi/%enote the ination rate
M P Y
M P Y
= +
PP
=
The result from the
prece%in sli%e
)as3ol#e this
resultfor to et
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 24
The 3&antity Theory of MoneyThe 3&antity Theory of Money, cont., cont.
Hormal economic ro)th re$uires a
certain amount of money supply ro)th
to facilitate the ro)th in transactions.
0oney ro)th in excess of this amount
lea%s to ination.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 2#
The 3&antity Theory of MoneyThe 3&antity Theory of Money, cont., cont.
YY %epen%s on ro)th in the factors of
pro%uction an% on technoloical proressall of )hich )e take as i#en( for no)/.
!ence, the "uantity #heory o $oney predicts
a one%or%one relationbetween changes in the
money growth rate and changes in the
in&ation rate.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 26
International data onInternational data on
inflation and money growthinflation and money growth
!nfation ratepercent(loarithmicscale/
:(===
:=(===
:==
:=
:
=.:
0oney supply ro)th percent( loarith
=.: : := :== :(=== :=(===
'icaragua
(ngola
)ra*il
)ulgaria
+eorgia
,uwait
-.(
/apan0anada
+ermany
Oman
1emocratic 2eof 0ongo
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 2$
'.. data on'.. data on
inflation and money growthinflation and money growth
= > < I
Bro)th in money supply p
8 := :
8
I
=
- >
- >'%your%ige?
The in!ation tax
rintin money to raise re#enue causesination. !nation is like a tax on people
)ho hol% money.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 2"
Inflation and intere%t rate%Inflation and intere%t rate%
Hominal interest rate( inot a%Juste% for ination
Feal interest rate( r
a%Juste% for inationr " i
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 30
The 6i%her #ffectThe 6i%her #ffect
The Kisher e$uation i " r ; Chap ? S " I %etermines r.
Eence( an increase in
causes an e$ual increase in i.
This one-for-one relationship
is calle% the Fisher e"ect.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3!
'.. inflation and nominal intere%t rate%*'.. inflation and nominal intere%t rate%*+,0/+,,8+,0/+,,8
ercent
:I
:
:=
8
I
=
->
'ominalinterest rate
@n&ation
rate
:76= :766 :7I= :7I6 :79=
Lear
:796 :78= :786 :77= >===:776
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 32
Inflation and nominal intere%t rate%Inflation and nominal intere%t rate%acro%% co&ntrie%acro%% co&ntrie%
!nfation rate .percent( loarith
Hominalinterest rate.percent(loarithmicscale/
:==
:=
:: := :== :==
,enya
,a*aAhsta
(rme
'igeria
-ruguay
-nited ,ingdom
-nited .tates
.ingapore
+ermany/apan
Brance
@taly
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 33
Exercise:Exercise:
3uppose V is constant( M is ro)in 6M per
year( Y is ro)in >M per year( an% r " percentae points per year( 'n% i.
c. 3uppose the ro)th rate of Y falls to :M per
year. +hat )ill happen to , +hat must the Ke% %o if it )ishes to
keep constant,
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 34
Answers:Answers:
a. Kirst( 'n% " 6 > " ?.
Then( 'n% i " r; " < ; ? " 9.
b. i " >( same as the increase in themoney ro)th rate.
c. !f the Ke% %oes nothin( " :.
To pre#ent ination from risin( Ke% mustre%uce the money ro)th rate by :
percentae point per year.
3upposeV
is constant(M
is ro)in 6M peryear( Y is ro)in >M per year( an% r "
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3#
Two real intere%t rate%Two real intere%t rate%
" actual ination ratenot kno)n until after it has occurre%/
e" expecte% ination rate
i e " ex antereal interest rate
)hat people expect at the time they buya bon% or take out a loan
i " ex post real interest rate)hat people actually en% up earnin ontheir bon% or payin on their loan
M d d d
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 36
Money demand andMoney demand andthe nominal intere%t ratethe nominal intere%t rate
The Nuantity Theory of 0oney assumesthat the %eman% for real money balances%epen%s only on real income Y.
+e no) consi%er another %eterminant of
money %eman% the nominal interest rate.The nominal interest rate i is the
opportunity cost of hol%in money instea%of bon%s or other interest-earnin assets/.
Eence( i in money %eman%.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3$
The money demand f&nctionThe money demand f&nction
MP /%" real money %eman%( %epen%s
neati#ely on i
i is the opp. cost of hol%in money positi#ely on Y
hiher Y
more spen%in
so( nee% more money
L is use% for the money %eman% functionbecause money is the most li$ui% asset./
( ) ( , )%
M P L i Y =
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3
The money demand f&nctionThe money demand f&nction
+hen people are %eci%in )hether tohol% money or bon%s( they %on1t kno)
)hat ination )ill turn out to be.
Eence( the nominal interest rate
rele#ant for money %eman% is r ; e.
( ) ( , )%
M P L i Y =( , )eL r Y+=
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 3"
#5&ili2ri&m#5&ili2ri&m
( , )eM
L r YP
= +
The supply of
real moneybalances
Feal money%eman%
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 40
What determines whatWhat determines what
#ariable ho) %etermine% =in the long run?
M exoenous the Ke%/
r a%Justs to make S" I
Y
( , )eM
L r YP
= +
. ( /Y F K L=
P a%Justs to
make ( /
ML i Y
P=
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4!
owow PP re%pond% tore%pond% to MM
Kor i#en #alues of r( Y( an% e(
a chane in M causes P to chane
by the same percentae --- Just like
in the Nuantity Theory of 0oney.
( , )eM
L r YP
= +
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 42
What about expected infation!What about expected infation!
O#er the lon run( people %on1t consistently
o#er- or un%er-forecast ination(
so e"on a#erae.
!n the short run( emay chane )hen people
et ne) information. PQ 3uppose Ke% announces it )ill increase
M next year. eople )ill expect next year1s
P to be hiher( so erises.
This )ill aect P no)( e#en thouh M hasn1t
chane% yet.=continuedC?
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 43
owow PP re%pond% tore%pond% to ee
( , )eM
L r YP
= +
the Kisher eect/e
i
( )%
M P
( ) to make fall
to re-establish e$Rm
P M P
Kor i#en #alues of r( Y( an% M(
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 44
Discussion QuestionDiscussion Question
Why is infation bad? +hat costs %oes ination impose on
society, Gist all the ones you can think
of. Kocus on the lon run.
Think like an economist.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4#
! common mi%perception! common mi%perception
Common misperceptionin&ation reduces real wages
This is true only in the short run( )hennominal )aes are 'xe% by contracts.
Chap ?/ !n the lon run(the real )ae is %etermine% by laborsupply an% the marinal pro%uct of labor(not the price level or in&ation rate
. Consi%er the %ata@
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 46
!9erage ho&rly earning% the C"I!9erage ho&rly earning% the C"I
0
2
4
6
!0
!2
!4
!6
!
!"64 !"6 !"$2 !"$6 !"0 !"4 !" !""2 !""6 2000
:perho&r
0
2#
#0
$#
!00
!2#
!#0
!$#
200
22#
2#0
C"I%!"
3&!00'
Average
hourly
earnin s
Hourly earnings
in 2001 dollars
Consumer
Price Index
0
2
4
6
!0
!2
!4
!6
!
!"64 !"6 !"$2 !"$6 !"0 !"4 !" !""2 !""6 2000
:perh
o&r
0
2#
#0
$#
!00
!2#
!#0
!$#
200
22#
2#0
C"I%!"3&!00'
Average
hourly
earnin s
Hourly earnings
in 2001 dollars
Consumer
Price Index
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4$
The cla%%ical 9iew of inflationThe cla%%ical 9iew of inflation
#he classical view:A chane in the price le#el is merely achane in the units of measurement.
o why, then, iso why, then, is
in&ation a socialin&ation a social
problemDproblemD
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4
The %ocial co%t% of inflationThe %ocial co%t% of inflation
@fall into t)o cateories:.costs )hen ination is expecte%
>. a%%itional costs )hen ination is
%ierent than people ha%expecte%.
The co%t% of e;pected inflation:The co%t% of e;pected inflation:
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 4"
The co%t% of e;pected inflation:The co%t% of e;pected inflation:11..shoeleather costshoeleather cost
%ef the costs an% incon#eniences of re%ucinmoney balances to a#oi% the ination tax.
i
real money balances
Femember !n lon run( ination %oesn1taect real income or real spen%in.
3o( same monthly spen%in but lo)er
a#erae money hol%ins means morefre$uent trips to the bank to )ith%ra) smalleramounts of cash.
The co%t% of e;pected inflation:The co%t% of e;pected inflation:
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #0
The co%t% of e;pected inflation:The co%t% of e;pected inflation:22..menu costsmenu costs
%ef The costs of chanin prices. Pxamples
print ne) menus
print & mail ne) catalosThe hiher is ination( the more
fre$uently 'rms must chane their
prices an% incur these costs.
The co%t% of e;pected inflation:The co%t% of e;pected inflation:
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The co%t% of e;pected inflation:The co%t% of e;pected inflation:33..relative price distortionsrelative price distortions
Kirms facin menu costs chane pricesinfre$uently.
Pxample3uppose a 'rm issues ne) catalo each
Sanuary. As the eneral price le#el risesthrouhout the year( the 'rm1s relati#e price)ill fall.
ierent 'rms chane their prices at %ierent
times( lea%in to relati#e price %istortions@
@)hich cause microeconomic inecienciesin the allocation of resources.
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The co%t% of e;pected inflation:The co%t% of e;pected inflation:
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #3
The co%t% of e;pected inflation:The co%t% of e;pected inflation:$$..%eneral inconvenience%eneral inconvenience
!nation makes it har%er to comparenominal #alues from %ierent timeperio%s.
This complicates lon-rane 'nancialplannin.
!dditional co%t oft ona co%t o unexpectedunexpecte inflation:n at on:
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #4
ppar2itrary redi%tri2&tion% of p&rcha%ingar2itrary redi%tri2&tion% of p&rcha%ing
powerpower 0any lon-term contracts not in%exe%(
but base% on e.
!f turns out %ierent from e(then some ain at others1 expense.
Pxample borro)ers & len%ers
* !f V e( then i / W i e/an% purchasin po)er is transferre%
from len%ers to borro)ers.* !f W e( then purchasin po)er is
transferre% from borro)ers to len%ers.
!dditional co%t of high inflation:!dditional co%t of high inflation:
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide ##
!dditional co%t of high inflation:!dditional co%t of high inflation:increa%ed &ncertaintyincrea%ed &ncertainty
+hen ination is hih( it1s more#ariable an% unpre%ictable
turns out %ierent from e moreoften( an% the %ierences ten% to be
larer =though not systematicallypositive or negative?
Arbitrary re%istributions of )ealthbecome more likely.
This creates hiher uncertainty( )hichmakes risk a#erse people )orse o.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #6
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #$
yperinflationyperinflation
%ef
6=M per month
All the costs of mo%erate ination %escribe%
abo#e become HUGEun%er hyperination.
0oney ceases to function as a store of #alue(an% may not ser#e its other functions unit ofaccount( me%ium of exchane/.
eople may con%uct transactions )ith barter or
a stable forein currency.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide #
=hat ca&%e% hyperinflation>=hat ca&%e% hyperinflation>
Eyperination is cause% by excessi#emoney supply ro)th
+hen the central bank prints money(the price le#el rises.
!f it prints money rapi%ly enouh( theresult is hyperination.
$ecent epi%ode% of hyperinflation$ecent epi%ode% of hyperinflation
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$ecent epi%ode% of hyperinflation$ecent epi%ode% of hyperinflation
slide #"
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 60
=hy go9ernment% create hyperinflation=hy go9ernment% create hyperinflation
+hen a o#ernment cannot raisetaxes or sell bon%s(
it must 'nance spen%in increases byprintin money.
!n theory( the solution tohyperination is simple stop printinmoney.
!n the real )orl%( this re$uires %rastican% painful 'scal restraint.
Th Cl i l ?i h tTh Cl i l ?i h t
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The Cla%%ical ?ichotomyThe Cla%%ical ?ichotomy
Real ariablesare measure% in physical units
$uantities an% relati#e prices( e.. $uantity of output pro%uce%
real )ae output earne% per hour of )ork
real interest rate output earne% in the future
by len%in one unit of output to%ay!o"inal ariables: measure% in money units(e..
nominal )ae %ollars per hour of )ork
nominal interest rate %ollars earne% in futureby len%in one %ollar to%ay
the price le#el the amount of %ollars nee%e%to buy a representati#e basket of oo%s
slide 6!
Th Cl i l ?i h tTh Cl i l ?i h t
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 62
The Cla%%ical ?ichotomyThe Cla%%ical ?ichotomy
Hote Feal #ariables )ere explaine% in Chap?(nominal ones in Chap
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 63
6riendly 5&i@ AB6riendly 5&i@ AB(rite answers to the followin) 44*+estions on a*+estions on a
sheet of ,a,er to hand in %each worth ! ,oint'-sheet of ,a,er to hand in %each worth ! ,oint'-:/Lour name an% section %ayDtime
3uppose V is constant( M is ro)in M per year( an% r "?.
>/ 3ol#e for the ination rate.
?/ 3ol#e for i the nominal interest rate/.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 64
Answers:Answers:
>/ " M " >M.
?/ i " r; " ?M ; >M " 6M =.=6/.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 6#
Chapter %&mmaryChapter %&mmary
:. Nuantity theory of money assumption #elocity is stable conclusion the money ro)th
rate %etermines the ination
rate.
>. 0oney %eman% %epen%s on income in the
Nuantity Theory more enerally( it also %epen%s
on the nominal interest rateX
Ch tCh t
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 66
Chapter %&mmaryChapter %&mmary
?. Hominal interest rate e$uals real interest rate ; ination. Kisher eect it mo#es one-for-one
)ith expecte% ination.
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C!"T#$ 4C!"T#$ 4 Money and Inflation Money and Inflation slide 6$
Chapter %&mmaryChapter %&mmary
9. Classical %ichotomy
!n classical theory( money is neutral--
%oes not aect real #ariables.
3o( )e can stu%y ho) real #ariables are
%etermine% )Do reference to nominalones.
Then( e$1m in money market %etermines
price le#el an% all nominal #ariables.
0ost economists belie#e the economy)orks this )ay in the lon run.
$egrade policy$e
grade policy: If yo& wo&ld like yo&r te%t regraded*: If yo& wo&ld like yo&r te%t regraded*%&2mit a written %tatement e;plaining why o&r entire%&2mit a written %tatement e;plaining why o&r entire
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%&2mit a written %tatement e;plaining why. o&r entire%&2mit a written %tatement e;plaining why. o&r entire
te%t will 2e regraded* %o point% might 2e lo%t on net.te%t will 2e regraded* %o point% might 2e lo%t on net.
0e%ian M/
0ean ?7.< 9=M/
Eih 6I
Out of 6I