2009 10 lecture notes macro

8/8/2019 2009 10 Lecture Notes Macro

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1Macroeconomics

It studies not only a single good, a single price, or a

s ng e mar e , u e economy as a w o e:

for instance, the Italian economy;

or the Euro ean econom

or the American economy;

or the world economy;

more in general, any economy; and so on.

There are, in fact, important questionsthat occur at aggregate

level, that is, relate to theperformance(the success, the health,the difficulties) of the economy as a whole. Such questions are

treated by Economics with specific methods and models

prec se y ose per a n ng o acroeconom cs .

Macroeconomics Definitions and statistical regularities


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2 The most im ortant uestions1. Economic Growth: there is a general tendency of the

of growth is not uniform over time, and is not equal among

different economies.

2. Economic Fluctuations: in the short run, the dynamics of

the econom shows an irre ular alternation of hases of

accelerated growth (booms) and phases of slowdown, orphases of contraction (recessions).

3. Unemployment: the economic system is unable to create

jobs for all who wish to work (also the unemployment ratefluctuates significantly).

4. Inflation: on average, the prices of goods and services tend

to increase (deflation is a far more rare phenomenon).Macroeconomics Definitions and statistical regularities


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3The Domestic ProductThe level of economic activityof a country is measured by the

GDP.

Definition: it is the value of goods and services produced

within a country in a given year, net of goods and servicesconsumed to produce them.

The er ca itaGDP GDP divided b the overall o ulation is

an indicator of the wealth(welfare) of a country.

In the lon run the GDP tends to increase see FIGURES 2-3 .

This phenomenon is the basis of economic development.

The GDP rowth is not re ular. In the short run it showsups and downs, according to the features of economic

fluctuations. Such fluctuations are also called business cycles

(seeFIGURE 4

).Macroeconomics Definitions and statistical regularities


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4Unem lo ment

y : are a persons w o wan o wor

and do notwork.

Labor Forces (NF ): are all Employed (N):

persons who wantto work. are all persons who work.

U=NF NUnemployed:



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5The unem lo ment rate u

Is the share (percentage)u

U

NF No e unemp oye o e

total labor forces:F

1

N

NF

N 1 u

ln NNF

ln1 u

formula, making use oflogarithms

lnN lnNF ln1 u u

Fu n nSetting lnNF = nF

= ,



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6The numbers of unem lo ment

The behavior of the unemployment rate in Italy is

It is much changedover the years (forty years ago it was

us ra e n - :

much lower);

It displays large fluctuationsup and down (it has been

-

2007; but in 2008-2009 it increased by two points);

It chan es slowl ersistence .

A comparison between the dynamics of the unemployment rate in

, . ., , .

There are similarities and differences.



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7Statistical re ularities 1

1. The dynamics of unemployment in Italy and Europe are

very similar(though, on average, the Italian

unemployment rate is slightly higher).2. Europe and the U.S. display, instead, very different

dynamics: in particular, the U.S. fluctuationsare more

.

3. Another difference between Europe and the U.S.

concerns the lon run: until the 1980s unem lo ment in

Europe is lower; later, the opposite occurs.

4. a an has a different histor : unem lo ment is muchlower, but there has been a sharp deterioration in

recent years.



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8Inflation

Definition: It is a situation characterized by a continuous , ,

decrease in the purchasing power of money.

computes itspercentage variation.

considered:n

pit

t

i1

ipi

0

i

therefore, one hasigi = 1.B we indicate the values of rices at a conventional initial0

date (called the index base year). Thus one has ).0 100Macroeconomics Definitions and statistical regularities


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9Level and variationsGeneral price level (P). The value of the index depends onthe prices considered in the computations, that is, on the vector

Pt

, and on their weights, that is, on the vector

. An ideal index should consider allthe prices ofg

g1,

,gn

p p1,,pn

goo s an serv ces, an e we g s a ac e o e goo s

quantities actuallypurchased.This ideal index is called eneral rice leve.

In practice, one computes the weights using a bundle of goods,which is representative of the expenditures of a household type

Rate of inflation ( ). It is the percentage variation of :P Pt PtPt1

(or in un another way that we will see later).

t Pt1

Taking logs and setting , one can easily obtain:lnPt pt

t

pt

pt

1

p tMacroeconomics Definitions and statistical regularities


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10Statistical re ularities 2

FIGURE 12 displays the inflation dynamics in Europe, Italy, and

. .

1. The general price level always (almost always, see FIGURES- , ,

positive; currently it is close to zero, but in the past has been

much hi her in other eriods and or in other countries hu e .

2. The three dynamics are quite similar, though not identical;this suggests that there are common causesfor inflation, but

also specific causes.

3.There is a clear ranking: on average, inflation in Italy washigher than inflation in Europe, which in turn was higher than

inflation in the U.S.; this suggests that common causes

.



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11The Philli s curve

If one displays in a scatter plot graph the numbers for theunemp oymen ra e an e n a on ra e , one o a ns a

clear inverse correlation: the higher the inflation rate, the lower

the unem lo ment rate.

FIGURE 19 illustrates the case of Italy. But one can find a similar

re at on a so or ot er countr es.

u withWe thus have u

This inverse correlation is called:

Phillips Curve



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12A little of caution

We must a attentionto statistical re ularities.

e re a ons p e ween n a on an

unemployment may prove to be more

com licatedthan that su ested

by the Phillips curve.

In FIGURE 20we plot the data of a larger period;

and the inverse relationship becomes confused.

s ac sugges s a e ssue s more

complex.



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13ComovementsThe correlation between inflation and unemployment is not the

onl t e of correlation between a re ate variables.

In FIGURE 7we plot the variations in GDP and

unem lo ment in the U.S. econom .

They are clearly mirrorcurves.

The unemployment dynamics is negatively correlated with

.

,

unemployment decreases; if it grows a little (or decreases)

unemployment increases.

This stylized factis called:

un aw



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14The Okun LawThe Okun Law for the U.S. economy is presented within a

unemployment) in FIGURE 8.

The interce twith the vertical axis indicates the GDP rowth

It emerges a clear inverse correlation.

above which unemployment decreases (about 3.6%).

unemployment associated, on average, to a one-point increase

in GDP (about 0.6%).This is an elasticity:


n n


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15Out ut and unem lo ment in Ital

FIGURE 9 shows that for Italy the relationshipbetween changes

n ou pu an n unemp oymen s remar a y wee

(almost not existent).

This is due to an institutional difference(in Italy it is much

more difficult to lay off/in people because of the presence of

r ng costs .

There is still a relation between output and labor employed; but

it applies in an alternative way:

The relation is between GDP fluctuations and hours worked.

See the scatter plot in FIGURE 10, commented in the next slide.



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16GDP Fluctuations and hours worked

In Italy we have a sui generisOkuns law,

w c , prec se y, oes no concern

employment, but hours worked.

Hours worked increase

(with an elasticity of about 0.5,

as s own n e s ope o e s ra g ne

when the GDP growsby more than 1%

as shown in the interce t on the vertical axis .

CONCLUSION:

The short-runrelationship

between outputand labor-utilization dynamics

o s a so n a y o s n a coun r es .



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17Shocks and ro a ation

The fluctuationsconcern the main macroeconomic variables:, ,

inflation (see FIGURES 12 and 13). But they concern also other

variables, like exchange rates (see FIGURE 17) andstoc mar et n exes see FIGURE .

The origin of fluctuations are generally related to shocks,

that hit the economy, hence altering the equilibrium.But fluctuations also de end on the wa

in which economies respondto shocks, that is, onthe so-calledpropagation mechanisms.

The propagation mechanisms, the laws underlying thebehavior of the economy, are different across countries, but

ave some mportant common eatures.



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18 The oil riceIts dynamics (FIGURE 16) does provide several examplesof shocks:

- .

The second(1978-79) is an example ofpersistentshock.

There are also tem orar shocks for instance in 1991 .

(it is known as counter-shock).

In recent years there is a rising tendency.

ompare t ese s oc s to , unemp oyment

(FIGURE 6) and inflation (FIGURE 12) dynamics.

FIGURE 16plots the different dynamics for the oil price in dollars,

in euros (lire), and in real terms. The real oil price measures

the quantity of goods (GDP) that one needs to purchase it.Macroeconomics Definitions and statistical regularities


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19Wh macroeconomics?

Theproblemsillustrated in the preceding slides

unemp oymen , n a on, uc ua ons o s ow

evident links(Phillips curve, Okuns law).

Therefore, these problems should not be studied

in isolation but taking into account these links.

Macroeconomicsinvestigates this.

t stu es t e e av or o an econom c system as a w o e,

highlighting the linksbetween different economic phenomena.

o ac eve s as , ras ca y re uces e num ero

agents and goods (and hence also of prices and markets).

Macroeconomics A simplified model

oes s y aggrega ng.


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20A ver sim lified modelThe simplest macroeconomic model considers

an econom with onl two markets:

Thegoods(Y) market, whose price isP;

The labor(N) market, whose price is W;There are only two aggregate agents:

Firms: they produce the good with the technology Y=F(N),

buy labor (d

), sell the good (Ys

), and distribute profits () tohouseholds;

ouse o s: uy t e goo , se a or to rms , an

obtain profits ().

Two budget constraints:

PYd= WNs + (households)

= rms



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21The link between the two marketsAdding both sides of the two constraints, simplifying and

This identityis called

s + s =

a ras aw

expressions within the bracket) is equal to zero; if in the goodsmarket supply Ys exceeds demand Yd(negativeexcess demand),in the labor market the opposite occurs (and viceversa); if in the

market there is equilibrium(demand equals supply), there must

e equ r um a so n t e ot er mar et.

So one can concentrate on what happens in one of the two

markets (the other will adjust accordingly).Macroeconomics A simplified model


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The oods market 22

Assumption: in the labor market, the wage does not reactto

,

assumption in the short run). We shall thus write

and concentrate on the goods market.

,

1. Description of buyers behavior (demand curve):Yd D P D 0with

2. Description of sellers behavior (supply curve):

Ys S P S

0with3. Compatibility between the two behaviors (equilibrium

condition): Yd=Ys;

4. Description of what happens off the equilibrium (reactions).



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23The law of demand and su lEquilibrium: ifP=PL, the quantity demanded is equal to the

uantit su lied Yd= YS= Y and the market is in e uilibrium.

Off the equilibrium: ifPPL, for instanceP=PH, the quantity

demanded is lessthan that supplied (Yd< YS), and in the marketa competition between sellersstarts,

causing the price to lower.

SS

P


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24The labor market

According to the Walras Law, what occurs in the goods markets

,

the second is in equilibrium; if in the first there is an excess

demand then in the second there is an excess su l .

The law of demand and supply, which is operative in the goods

market leads to e uilibriumalso the labormarket even if the

wage is rigid( ) since is fixed in contracts.W W 1Labor demand and su l de end on the real wa e W .

In the presence of excess demand in the goods market, changes

in brin about o osite-si n chan es in the real wa e whichreduce excess supply in the labor market.

At the end the two markets simultanousl arrive at e uilibrium.



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25 The effective demand rinci le

Empirical observation: even prices of goods react a little (and

.

What happens to the goods market ifpricesare rigid( )?P

Firms react in a different way to excess demand:

they rise production (Y> 0) when Yd> Ys;

they reduce production ( < ) in the opposite case ( < s).

LetE= Yd be the quantity demanded at a given price .P

The firms behavior is described by the following equation:

dYdt Y

con Y

In macroeconomics, this equation is called the

effective demand principle



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26Macroeconomic e uilibrium

Assume that in the goods marketpricesare rigid( ), andP

.When the system arrives at Y=E, the market is in equilibrium

(the formula says that output does not change). But this is adifferentequilibrium with respect to the equilibrium that results

when the law of demand and supply is operative.

S

e n cate t y M . t s t emacroeconomicequilibrium.

L

happens in the market when we

have Y YM (that is, when the

D

market is not in equilibrium).

Indeed, firms reactby changing

0 YLYM Ythe output produced.



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27A re ate variables

Let construct a richer model. Instead of two goods (output

and labor), we shall consider four:

1. Out ut Y which re resents all oods and servicesproduced (it corresponds to the GDP). It can be consumed

(C), or used as a mean of production (I). The means of

production accumulated in the past are capital goods ( ).2. Labor(N), which is another means of production (withK).

. , .

4. A fixed-income Bond(B ), purchased by those who save.

This if we abstract from foreign trade (closed economy). To model open

economies one needs to add at least forei n out ut Y forei n mone or

currency ($), and foreign bonds (BF

).

Macroeconomics Aggregation and Walars Law


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28A re ate a entsAlso the number of agentsis augmented by one:

1. HOUSEHOLDS. The a re ate all consumers of

microeconomics. They own firms (obtaining profits) and

supply labor. They spend their (capital and labor) incomes,buying pieces of Y for consumption( ), or bonds for

saving(S).. . , ,

households (C), to the firms themselves investments(I) or to the State (G ); to finance their activities, they can issue

bonds.3. The STATE. It purchases goods and services public

expen ure an ma es rans ers o ouse o s r .finances itself by taxes (T), or issuing money and bonds.

. ,

BANKS and the CENTRAL BANK).Macroeconomics Aggregation and Walars Law


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29Prices and marketsWe have four goods, so also four pricesand four markets: the

, , , .

1. The price of outputis thegeneral price levelP.2. The price of laboris the nominal wageW.

3. The rice of thebond ; we will see that it is an inversePb

relation of the interest rater: with .b

r 0Pb br4. The price of moneyis 1 (money is the numeraire).

The relative pricesare obtained dividing prices byP: we thus

The distinction between nominal variables, i.e. expressed in euros, and real

variables i.e. ex ressed in units of out ut is ver im ortant. The real variables

.

are obtained dividing the corresponding nominal variables byP.



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30Domestic roduct and domestic incomeFIRMSproduce goods Q , sell them at priceP, and obtain profits

that distribute to HOUSEHOLDS .

Rt Ct

The domestic product Yis the value of goods and services produced,

net of goods and services consumed to produce them. That is:Y PQ Mr K

That is, domestic product equals the sum of all incomes.

Let us set = 1 (for simplicity). It follows: Y WN rK

represen s o omes cpro uc an omes c ncome.

Households domesticincome (Y) and disposableincome (Yd):

Yd= Y SF

T+ Tr (retained profits, taxes, transfers)



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31Bud et constraintsA simplified world: FIRMS and HOUSEHOLDS (without the STATE)

FTherefore: Yd= Y

rms u ge cons ra n : ss: = , b =

REVENUES: Q + BS PAYMENTS: Mr+ WN+ rK+ K+ +I

Q + S

= Mr+ WN+ rK+ +I+ BS= I

Households budget constraint:

REVENUES: Yd=Y PAYMENTS: C+ S=C + d

Y= C+ S



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32The Walras lawAdding both sides of the two budget constraints yields:

S= D

Let us bring all terms to the left-hand-side and rearrange:

C+I Y + D S = 0First bracket: excess demandin thegoodsmarket;

Second bracket: excess demandin the bondsmarket.

Walras law: the sum(of values) of the two excess demand is zero; If in one market there is equilibrium, there mustbe

equilibrium also in the other one;

It highlights the linkbetween the two markets.

.

Question. Why in the Walras law the labor market does notappear?



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33Fixed rices?In the formula of Walras law, prices do not appear

we im osed for sim licit = 1 = 1

Is it justified to neglect prices? Yes and No.

,

the goods market (fixed-pricehypothesis).

, .

In several goods markets this hypothesis is justified.

ssum ng xe pr ces, t e a ras aw ena es us to concentrate

only on thegoods market(overlooking the bonds market).

Also in the labor marketthis hypothesis is justified.

This means indeed that if there is a negative excess demand in the labor

market unem lo ment the wa e does not var ri id-wa eh othesis .

Macroeconomics Aggregate expenditure

Wages vary only in the longrun.


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34A re ate ex enditure and effective demandIn thegoods marketthere is equilibriumwhen output is sufficient

to meet all households and firms re uests:

Y = C+I

- -

C+I = E

When there is no equilibrium ( ), prices o notvary (by ass.).

Quantities produceddo vary, instead: if output exceeds aggregate

expenditure (Y>E), firms produce less (Y< 0); if output is lower

than requests (Y 0). Production

.dYdt

E Y That is, the differential equation with > 0 holds.

This equation describes the effective demand principle.Macroeconomics Aggregate expenditure


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35The model h othesesLet us recall again the model hypotheses:

1. Fixed rices

2. Output adjusts to demand.

For 2 to hold, we need a third hypothesis:3. Availability of spare production capacity.

Therefore, it is a short-runmodel.

We have an equilibrium condition (Y = E) and an equationdescribing the behavior of Youtside the equilibrium, that is the

effective demand principle, Y= (E Y).

To determine the equilibrium value of Y, and study theconvergence to equilibrium, we have to establish what

determines aggregate expenditureE, that is, what determines its

components, consumpt on an nvestment .

Macroeconomics Aggregate expenditure


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36What do CandIde end on?

Some stylized facts about CandIare illustrated in FIGURES 18-

. o a e n o accoun em, assume, or now, w a o ows:

About consumption:C= C(Yd) 0 < C < 1

Consum tion is an increasin functionof dis osable income

(with a derivative lower than one).

I

About investment:

Investment is autonomous(and, for now, exogenous).

The term autonomous means that it does notdepend on Y.

Macroeconomics The consumption function


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37The consum tion functionLet us assume a linearspecification of the relationship between

consum tionand dis osable income:

C> 0 is autonomous consumption.

_ C= C+ cYd_

0 < c < 1 is the marginal propensity to consume.There is no the State, so

C= C+ cY_.

C= C+ cY

_

_e grap o e

consumption functionis

resented in the fi ure. It is C can increasing straight line

with positive intercept and

Yslope lower than 45.Macroeconomics The consumption function

38


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38MicrofoundationQUESTION: is it justified the linearspecification in the relationshipbetween consumptionand disposable incomeshown in slide37?

ANSWER: we will see that, at least, it is consistentwith the(microeconomic) theory of consumers rational choice.

The procedure according to which the choice of the

macroeconomic agent is derived aggregating the rational

Let us assume identical consumers (representative-consumer

c o ce o e n v ua agen s ca e m cro oun a on.

ypo es s , an mo e e c o ce e ween consump on ansaving for the single consumer. Once aggregated, it describes the

choice of all consumers, that is of the a ent HOUSEHOLDS.Microeconomics tells us that the single consumer maximizes herutility functiongiven her budget constraint.

We adapt this to the choice between consumption and saving.


39


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39The intertem oral bud et constraint(Simplifying) HYPOTHESIS: the consumer lives for two periods.

Bud et constraint for the first eriod:

Y= C+ S

Bud et constraint for the second and last eriod:

(1)

S(1 + r) + YF = CF(2)

Let us get S from (2), substitute into (1), and rearrange.We obtainthe intertemporal budget constraint:

C 11r

CF Y1

1rYF(3)

- - F discount factor 1/(1+r) can be interpreted as the price of futureconsum tion ; in the ri ht-hand-side there are the availableresources.


40


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40The ra h of the bud et constraintThe graph of the budget constraint (3) is a decreasing straight line.

The ex licit form of the e uation obtained solvin for C is

CF Y1 r YF 1 rC

The line always passes through point E, with coordinates (Y, YF);it is the point of initial endowments.

CF If the chosen point is S, we haveC< Y, and the consumer savesthe

Y

quant ty = n t e seconperiod she will consume CF > YF).

S

E

(1+ r)

possibility (getting into debt) ofchoosing also a point of the line

D

CY(like D) in which C> Y.Macroeconomics The consumption function

41


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41Consumers referencesThe consumer chooses the preferred combination of currentconsumption (C) and future consumption (CF) among all thoserespecting her intertemporal budget constraint.

Preferencesare described by a utility function. For instance:

> 0 is the sub ective discount ratefor future utilit it is also

UC, CF lnC1

1lnCF

called time preference).This function has positive marginal utilities:

Its mar inal rate of substitutionis decreasin :

U

C

1C

0 UCF

1

1CF 0

MRS U/C

U/CF 1

CFC

dMRSdC

0

ence ts n erence curvesare convex.


42


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42Consumers choice

The chosen combination of Cand CF is graphically identified by,

between the budget line and the indifference curve.

coordinates .C,CF

Given her references, theC

Fconsumer has chosen to save inthe current period the quantity

Y

A

E

CF= .

This choice enables her to

consume in the following

period the quantity

CYC*F F .


43


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43Com utin the choiceThe chosen combination can be computed by twoC,CF

rocedures:(1) Solving the system composed of the budged constraint and

the optimality condition MRS= 1 + rwhich imposes that the slope of the indifference curve is equal to

the slope of the budget line (tangency condition).

omput ng t e constra ne max mum o t e ut ty unct on

using the Lagrangian method.

C 1

2

YF1r

1

2 C c

where we set1

2

YF1r

C and 12

cThe microfoundation confirms the functional form of

.

consumption adopted in the income-expenditure model.Macroeconomics The consumption function

44


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44The income-ex enditure modelStaticversion:

E CI

Definition of aggregate expenditure

c

I

onsumpt on unct on

Investment(autonomous)

The model solution: Y 11c

C

Let us set:

1

Y m

u p er

Autonomous expenditure C

1c

Macroeconomics Income-expenditure model

45


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The model ra h 45

We now construct a graph with domestic product (Y) on thehorizontal axis and a re ate ex enditure E on the vertical axis.

The equilibrium is on the 45 line (exactly where Y=E).

Aggregate expenditureis represented by the line .

cY

E Y=E

e equ r um s ent e y t e ntersect on

point between the two lines.*o e r g o one as ;

so one has Y< 0.*

o e e o one as ;

so one has Y> 0.

45Y>EY


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The d namic version 46

It is used to describe what occurs to the model outsidethee uilibrium. It is based on the effective demand rinci le.

dY

E Y

It is obtained replacing the equilibrium condition Y=Ewith the

differential equation with> 0.This equation describes the behavior of Yover time starting by an

initial value . In particular, it tells us if convergesorY0 Y0 Yt

It is a first-order (linear and with constant coefficients)differential e uation that can be written in the form

no owar e equ r um va ue .

Y 1 cY

w ere we se . eso u ono e equa on s: dt

Yt Y Y0 Ye1ct

And it effectively shows that output convergesto equilibrium.Macroeconomics Income-expenditure model

Th l i li 47


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The multi lier 47

If convergence is guaranteed, one can perform comparative statics,that studies how e uilibrium chan es when an exo enous variable

changes. EXAMPLE: change in autonomous expenditure

dY m Y m

QUESTION: since output responds to aggregate expenditure (Y=Since m > 1, it follows that Y> A.

E), when does expenditure in excess to

Acome from?ANSWER: the variation in autonomous expenditure sets out a

process w c causes consump on o ncrease.

GENERAL IDEA: each time that firms increase output (Y> 0),

,partially spent (C> 0), hence stimulating aggregate expenditureand so once againoutput. A positive-feedbackmechanism starts.


E di h d i 48


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Ex enditure ush and ro a ation 48

Let us investigate step by step the expenditure multiplicationbrou ht about b an autonomous variation > 0:

A E Y C

c

+ cI + cI c2I

c < 1

c+ c + c

+ c3I +

1

+ +

c

Y 1 c c2 cn

ci lim 1cn1

i0c


P d i l 49


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Production la 49

HYPOTHESIS: production requires time: it is equal to demand ofthe revious eriod:

Yt Et1

Y cY Y cY t t t

Ct C cYt Finite-difference (first-order, linear)

t ,

from the model, of Yover (discrete) time.

: w en one as . o owst t1 1c

DYNAMICS: it is described by the general solutionof the finite-

erence equa on, g ven yYt Y Y0 Yct

nce , e secon erm en s o ere s convergence .


S i S 50


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Savin S 50

DEFINITION: in general, S= Yd C . In thismodelwithout the State we have Yd= Y. It thus follows S= Y C.

SAVING FUNCTION. It is derived from the consumption function:

S= YdC= Yd C cYd= C+ 1 c Yd = C+sYd

_ _ _s = 1 c is the marginal propensity to save (0


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Savin and investment 51

In equilibrium: Y= C+I

=

Y C=I S=I

Recall that S= BD and that I= BS.

= D = S

Consistently with the Walras law, the goods market leads to

.

To the right of Y* one has S>I, so D > S and so Y> . It then

follows Y< 0, and so BD < 0.

S

Viceversa occurs to the left ofY*

.Y>EY


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The savin aradox 52

Note that S>Iand that SE and thus Y< 0);S< 0because Y 0 .S> 0

It is saving that adjusts to investment, because it is output that

adjusts to aggregate expenditure.For the same reason, in this model, it is bonds demand that

adjusts to bonds supply. _CONSEQUENCE. ouse o s want to save t at s < an or

s > 0), they will notsucceed as long as investment does not=_

The only resultof the higher parsimony is a reductionin Y,

because the autonomous expenditure decreases (when C

< 0)

.

_and/or the multiplier decreases (when s > 0).

EXERCISE. Try to illustrate this saving paradox performing comparative

statics starting from the graph in the previous slide.


53How the bud et constraints chan e


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53How the bud et constraints chan eLet us introduce the State(together with Householdsand Firms).

We abstract tem oraril from the ossibilit to create mone .

The State budget constraint:

S

REVENUES: taxes (T) and issuance of bonds ( );BGS

Households budget constraint:

r

REVENUES: disposable income (Yd= Y T+ Tr);

: consump on an sav ng = .

The Firms budget constraint does not change:

Macroeconomics Income-expenditure with the State

F

54How the Walras law chan es


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54How the Walras law chan esTo derive it, aggregate the threebudget constraints and lead allterms to the left-hand-side. Rearran in we obtain:

CI G Y BD BS 0

that is again the Walras law.

Notice that in the aggregation process, Tand Trcancel out

.

DIFFERENCES WITH RESPECT TO THE FOREGOING VERSION:

. en t ere s t e tate, aggregate eman s not onger

C+I but becomesE= C+I+ G;

. ,issued by firms and the State ( ).B S BF

S B G

S

u e n e ween e wo mar e s rema ns e same as e ore.


55The consum tion function


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55The consum tion function

Consumptionand disposable incomeC C cYd

r

T T tY

Definition of disposable income

Taxfunction

Tr Tr Exogenous transfers

Taxes are artiallSubstitutin ields the function C(Y):

autonomous ( ) andpartially depend on Y

C C cT cTr c1 t

accor ng to t e

marginal ratet. where is the marginal propensity

to consume out of domesticproduct.c1 t

The functional form is similar to that of the model without the

State, but autonomous consumption and the marginal propensityto consume now epen on t e u getary var a es , an .r


56The model


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The model

Let us limit our analysis to the staticversion:

ConsumptionfunctionC C cT cTr c1 tY

u onomous nves men

(Autonomous) public spending

G G

The model solution:

Y mY 1 C cT cTr G

where now we set:

Multiplierm 1c1t

m S/YT/Y


57Bud etar olicies


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Bud etar olicies

When there is the State, the equilibriumvalue Y* dependsuponthe values of the bud etar variables : G Tr and t.T

Y

G m 0

Y

One easily obtains: TrY

T cm 0

G has an expansionaryeffect on Y(measured by the multiplier m);

Y

t

cm2 cmY 0

Trand have an oppositeeffect (but of equal size);T

In general, the increase in the expenditurecomponents of the

governmen u ge s expans onary, w e e ncrease n erevenuecomponents is contractionary.

The State is enabled to use the budget to influencethe level of Yin the desired direction (example of economic policy).


58Two uses of macroeconomic models


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Two uses of macroeconomic models

A macroeconomic model can be read in two ways:

.

of what happens:

.

decidewhat to do:

Given the effective values of

exogenous variables, what

Given the desiredvalues of

endogenous variables, what are

are the results obtained for

the endogenous variables?

the values that the exogenous

policy-controlled variables must

EXAMPLE 1: given G, and EXAMPLE 2: given the desiredlevel

thusA, the model tells us

what is the equilibrium*

YT, what mustbe the level ofA,

and thus of G, which allows to*eve o : t at s = m . o ta n t = T m.


59Deficit


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Deficit

In the model withoutthe State, the equilibrium condition mightbe written in twoequivalent ways: Y=Eand S=I (see slide51).

When there is the State, Y= does always hold (it is obvious) but

S=Idoes not.

= =

In equilibrium: S= (C+I+ G) T+ Tr C=I+ (G T+ Tr).

. .

Therefore, in equilibrium we have: S=I+D . , .

The State finances the deficit by issuing bonds:D = .BGS

ouse o s save an , o ng so, en resources ofirms ( ) and to the State ( ).

BIS

BGS

Y= = + D


B BF B G

60Effects of bud etar olicies


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Effects of bud etar olicies

On Y: we have already studied them(see slide57). Summing up:

than Tr> 0, which has the same effect of (reduction in

autonomous taxes). Whyis public spending more expansionary?

T 0

ANSWER: the variation in public spending

translates allin new demand (G = A ); variations in transfers

an taxes on y part a y r= = c , an so on. .

OnD : the expansionary policies increase thepartof taxes

But, overall, they make the deficit worsen : D > 0.epen ng on : see s e .

dY

dD

dY

1c1t

0

dD

1dG dG 1c1t The balance worsens because of the increase in spending (G >

0), but catches partially up because of the increase in the tax base

(G > T> 0).Macroeconomics Income-expenditure with the State

61The balanced bud et theorem


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The balanced bud et theorem

What is the effect on Y of a simultaneous increase in publics endin and taxes which leaves the bud et balance unchan ed?

SIMPLIFIED EXAMPLE . Assume t= 0, so that .T T

Com ute the effect ofG = T> 0 which im lies D = 0 on Y:The two separate effects are YG = mG and YT= cmT;

Adding both terms we have Y = m(1 c)G = G > 0; recall that,

GENERAL CASE . Hypothesis: (i) G > 0; (ii) D = 0 (and (iii) I = 0).

in our case, we have G = T and (since t= 0).m 1

1c

From S=I+Dwe get S= I+ D = 0; and also Yd = S/s = 0.

Then we have Y = C+ I+ G= G (since C = cYd = 0).

CONCLUSION . An expansionarypublic spending management

financed to prevent effects on the budget balance causes output

to increase by Y = G (the multiplier is 1).


62Deficit and the business c cle


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e c d e bus ess c c e

Beyond the effects of fiscal variables (G, Tr, and t), the levelof deficit de ends alsoon the e uilibrium value ofY*.

T

Taxes depend on the level of income: T= T(Y)with T > 0 .

When domestic product varies for reasons that are independent

of economic policy (for instance because of ), taxes vary andhencealso the deficit.

.

If there isD > 0 because of a recession, one speaks about

Cyclical deficit

If there isD > 0 under full-em lo ment conditions(when output is at itspotential level), one speaks about

Structural deficit


63Public debt


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It is the value of all bonds issued in the past by the State, held byseveral a ents in our sim lified world b households .

We will indicate the level of public debt byB.

What is the link between the deficitand the ublic debt?SIMPLIFYING HYPOTESIS: transfersare composed only of

=

Dt= GtTt+ rBt1

If there isD > 0, the State finances itself by issuing new bonds:

Dt> 0 Bt=BtBt1 =Dt

Thus one has: Dt= GtTt+ rBt1 = t t1 and, solving for t,

Bt= (GtTt) + (1 +r)Bt1

Macroeconomics Public debt

This equation describes thepublic debt dynamics.

64Public debt d namics


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PRIMARY BALANCE (F): it is the difference between publics endin net of interestsand tax revenues. In our case we have

F= G T

We can have a rimar deficit > 0 a rimar sur lus < 0or a primary balance equal to zero(F= 0).

Using the definition of primary balance, the equation describing

= + r B

the dynamics of public debt becomes

This equation shows that public debt tends to explode even when

the rimar balance is e ual to zero = 0 .To prevent an increase in public debt, there must be a primary

surplus:Ft= r Bt1.

Therefore, implementing a counter-cyclical deficit is risky.Macroeconomics Public debt

65Investment choice


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Let us relax the hypothesis of exogenous investment ( ).What does investment de end on?

Rationale at microeconomic level: the decision to buy additional

means of roduction b the sin le firmis motivated b the rofitobjective.

Let be the cost of a iven investment. The firm com ares it

with the expected present discounted flow of future net revenuesthat it plans to obtain (with the present value of the project PV0).

K0 PV0That project will be undertaken (by spendingK0) if

ris the interest ratepv0 1r 1r2 . . . 1rT

Macroeconomics Investment

i = , , , are e expec e u ure ne revenues

66 The net resent value criterion


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Net present value(NPV): it is the difference PV0 K0.Settin = one has

npv

TR i

i

0i0

Notice that

0., that , and that .

NPV0

r 0

NPV0

0 1 0

NPV0

i 0

The NPVis a decreasing function of the interest rate rand of the

project costK0 = R0, while is an increasing function of the

expecte uture net revenues.Thus, when rincreases, a project previously convenient can

.


67The internal rate of return


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Internal rate of return(IRR): it is the discount rate which equalizesthe flow of ex ected future net revenues to the cost of the ro ect.

Let us indicate it by: it is the solution of the equation:

T0

i1

i

1i

e IRR s a genera zat on o t e concept o pro t rate. ett ng

= 1we soon obtain, in fact,

1

0K0

represents the return of one euro investedin theproject.

cr er on: e pro ec w e un er a en r.rrepresents the return of one euro employedin the market.


68From the micro level to the macro level


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Assume that there areNprojects available for the aggregateoperator firms . n , , , n .

We can rank theKnprojects in a decreasing order with respect to

the rofitabilit measured b its own is the most rofitableit followsK2, and so on.)

K1 K2 Ks KN

1 2

s

N

if r>1, then no project is convenient; if rN, all projects willbe undertaken; if r

s

, the firstsprojects will be undertaken,and the aggregate level of investment will be

s

n1


69The investment function


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If rrises, the summation looses terms, andIdecreases ifrfalls the summation ains terms and increases.

n1s Kn

We thus have:

I=I(r)

with I < 0.Assume a linear specification:

rI(r)

br

The arameter re resents the

state of expectations.

The expectations explain the

One could obtain the same result using the NPVcriterion instead

Iobserved fluctuations ofI.

of the IRRcriterion.


70The IS schedule


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In the income-expenditure model, we hadI= . Let us replace itwith the function = r . We obtain the solution

Y 11c1t

C cT cTr Ir G

a s:Y m br

w ere we use e near spec ca on ,r r

and now represents the exogenous component(independentof r of the autonomous ex enditure:

C cT cTr G

The multiplier m, instead, did notchange.

We no longer have a single equilibrium Y*. We have a locus of

equilibrium points, one for each level of r.

This locus of equilibrium points is called IS schedule.

Macroeconomics The IS schedule

71The characteristics of the IS schedule


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The IS identifies all the combinations of Yand rsuch that Y=Esuch that there is e uilibrium in the oods market .

The IS is a decreasing curve (straight line): dYdr

bm 0

Economic reason: the increase in rdecreasesI(since ),dI band the fall in decreases Yby an amount measured by m.

rThe intercept on the Yaxis is

.

So A > 0 moves the IS to the right;the shift is measured b the

multiplier (why?);

b > 0 makes it rotate downwards

(what is the economic reason?);m > 0 makes it rotate upwards

Ym.


72Outside the IS schedule


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The points on the IS identify equilibriumcombinations (of Yand r in the oods market. On the IS we have Y= .

What happens outside the IS? Obviously there is noequilibrium.

To the rightof the IS we have Y>E..Y m br In fact, we have

According to the effective demand principle,

If the system is to the right of the IS,

Y Y Y

>

To the leftof the IS we have Y


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To obtain the IS, we have assumed that the consumption andinvestment functions were linear.

Its main properties hold also withgenericfunctions.

Assume C= C(Y) with 0 < C < 1, and I=I(r) with I < 0.The IS equation then will be Y = C(Y) +I(r) + G ,

and thus also, taking variations, dY = dC+dI+ dG .

To find dY, compute the total differential:

dY CdYIdr dG

ett ng = , one eas y o ta ns t e s opeo t e :dYdr

I

1C 0(1)

Setting dr= 0, one easily obtains the effect of dG:dYdG

1

1C 1(2)

Note the correspondence of (1) and (2) with the results in slide71.


74The bonds rice and the interest rate


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What is the relationship betweenPb and r?EXAMPLE 1 zero-cou on bond : the bond ives the ri ht to a

certain paymentRb after one year; how much is one willing to payit today? Not more nor less than itspresent value:

b b

1r

IfPb >PV, nobody wants to buy the bond and everybodywants to sell it hence S> D and because of the law ofdemand and supply, it follows Pb < 0 (up to thatPb = VA).

The opposite occurs whenPb < VA.

In this example, there is an inverse relationshipbetween the bondprice and the interest rate: dPb

Rb

0

Macroeconomics The bonds price and the interest rate

r 1r

75The inverse relation betweenP and r


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This holds also for bonds other than zero-couponbonds.EXAMPLE 2 level-cou on bond : the bond ives the ri ht to a

constant couponc over Tyears. Because of the arbitrage

mechanism, conditionPb

= VA always holds, that is

b c

1r

c

1r2

cRb

1rT

, , b .

EXAMPLE 3 (perpetuity bond): it gives the right to a constantcou on c forever and it will neverbe re aid. The arbitra e

principle leads to the result:

c

c

where the inverse relationbetween the bond price and the interest

t11rt r

rate emerges in a particularly simple and transparent way.

Macroeconomics The bonds price and the interest rate

76The Sa law


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Let us assume a perpetuity bond with a coupon equal to unity.Therefore 1

In the bonds market, the law of demand and supply holds.

r

en, e a ras aw mus e rewr en as o ows:

E Y PbBD BS 0

Let us assumeE< Y. We then will have D > S; according to

the law of demand and supply, it will followPb > 0; so r< 0; so; so ; an so on, up o e equ r um, w ou any

need about a reduction in Y. The behavior of the bonds market

which is faster than the ad ustment of the oods market caused

The mechanism in which the bonds marketprevailsover the

the effective demand principle to vanish.

Macroeconomics The Say law

goods market, and leads to equilibrium, is called Says law.

77The neoclassical model


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The Say law leads to the goods market equilibriumfor an iven level of Y.

In fact, it is the demandEthat adjusts to the supplyY.The traditional formulation of the Say law is exactly:

upp y creates ts own eman .

But what does determine the level of Y?

In this model, called neoclassical model (in contrast with theKeynesian approach of the income-expenditure model), the

labor marketdetermines it:

Since their production surely finds an outlet, firms have an

ncent ve to emp oy a t e ava a e a or.The neoclassical model displays full employment, unless this

.


78The ra h of the neoclassical model


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FIRST GRAPH: supply of goods; determined at full employment level by theproduction function Y(N) and by the (exogenous) labor supplyNS= .

Y

EYS

YN

SECOND GRAPH: demand of goods,

. m br ErTHIRD GRAPH: bonds market.

0

Y FOURTH GRAPH: inverse

relation betweenPb and r.

Initiall one hasE < andYrN

b

r (in the bonds market)

.B 0D B 0S

b

,

The interest rate falls,

The aggregate expenditure rises,

BDBSbr

b0

until one obtains,simultaneously,

e uilibrium

rB r0rB0S

B0D in both markets.


79The neoclassical and Keynesian approaches


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The behavior of the macroeconomic system in the neoclassicalmodel is symmetricwith respect to that of the Keynesian model:

KEYNESIAN MECHANISMS:1. Output Yadjusts to

NEOCLASSICAL MECHANISMS:1. Aggregate expenditureE

aggregate expenditure .

2. Saving Sadjusts to

adjusts to output Y.

2. InvestmentIadjusts to

3. The goods market prevailsover the bonds market.

3. The bonds market prevailsover the oods market.

Shortcomingsof this neoclassical model.The representation of

the bonds market is too sim le:i there are also old bonds

(not only the new issuances); (ii) there are not only the

saverswho demand bonds (also the speculators); (iii)

it is not considered the role of money(as an alternative to bonds).Macroeconomics The Say law

80Mone


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DEFINITION. In macroeconomics the word money identifies theset of means of paymentscommonly accepted.

Notes and coins are obviously part of money. Theyconstitute the means of payments

The majority of payments does not involve the hand-exchange of

that mustbe accepted (legal money).

ega money. re t car s, c ec s, an trans ers, an so on, are

commonly accepted to make payments. These payments involvethe transfer of bank de osits.

Also the bankde osits, therefore, are mone(bank money).

An means of a ment that became commonl acce ted tickets? would

Macroeconomics - Money

automatically be part of money.

Functions of mone 81


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Three are the main functions:1. The first is that of mean of a ment. Mone solves the

double coincidence of needs problem, which rendersbarterextremely cumbersome.

2. The second is that of unit of account. Its importanceemerges when one has to make payments denominated interms o anot er ore gn currency, or w en t e money

itself is changed (the transition from the lira to the euro).

3. The third is that of reserve of value. Money shares withbonds the property of being a financial asset(that is, it

bond: it is a fruitful financial asset (it yields an interest).Advantage of money: it is liquid(it enables one to makepayments w t out costs or ags .


The mone market 82


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The expression money market appears strange: one does notbuy or sell money, and its price is 1 (we have seen that money isunit of account, that is the numeraire).

Recall that, in macroeconomics, a market (model) is defined byour e ements:(i) a description of demand;ii a descri tion ofsu l

(iii) a condition of equilibrium;

(iv) a description of what happens outsidethe equilibrium.

Regarding money, it is possible to define all these four elements:one can speak about money demand(L), money supply(M),

= ,there is no equilibrium.Thus, one can speak about the money market. It should be addedto the goods and bonds (and labor) markets.


Demandin mone 83


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DEFINITION. Money demand (L) is the quantity of money

excluded).

1. The transactionsmotive. One holds money (cash and

which one receives incomes and the dates at which incomesare spent are not synchronized.

. eprecaut onarymot ve. ne o s money ecause t eremight be situations in which one wants or needs to make

a ments.

3. The speculativemotive. One holds money as a financial asset,in alternative to bonds (if one wants to speculate on the

erence e ween e curren an expec e on s pr ce .


84Mone su l


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Money supply. It is the quantity of means of payments (notes,.

sum of currency(Cu) and banks deposits(De):

= Cu +De

Monetary base. It is also called high-powered money. It cane regar e as a synonym o ega money ater on, we w g ve

a more precise definition). Let us indicate it byH. It consists ofcurrenc lus banks reserves e :

H= Cu +Re

Two questions:1. What is the link between monetary base and money supply?

Macroeconomics Money supply

.

85Monetar base and mone su l


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Let us indicate by the currency-deposit ratio:Cu

Let us indicate by the reserve-deposit ratio:

De

We thus have:

eDe

And also:

Cu Re De De De

DerivingDe fromHand substituting into M, one obtains:

M 1

H

e ave > . ence s a mu t p eo .


86The de osit multi lier1


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The coefficient is calleddeposit multiplier.

howa variation Hgenerates a multiple variation M.Suppose that private agents come into possession of a given

amount o cas . ey w str ute t etween currency andeposits according to the parameter: H =De + De = ( +1 De. We thus have a first creation of banks de osits e ual toDe 1

1

. Banks will create a reserve

and lend to the rest of private agents, who in turn, as before, willRi

1

o a s are n erms o currency, epos ng e rema n ngamount. It can easily be shown that the deposit propagation

process is described by the geometric series

De H1

j0

11

j

H

Adding Ci =De , one exactly obtains = .


87Creation of monetar base

?


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How can the monetary base enter the economic circuit?There are three creation(or destruction) channelsofH.

1. TREASURY. When the Central Bank makes a loan to theTreasury (buying bonds issued by it), it pays by H> 0. Whenthe Treasury repays the loan, the monetary base is destroyed(H< 0).

2. FOREIGN SECTOR. When the Central Bank buys foreigncurrencypaying by euros, it introduces monetary base into thec rcu . en, ns ea , se s currency n exc ange oeuros, it takes monetary base away from the circuit (H< 0).

3. CREDIT COMPANIES. When the Central Bank makes a loan tobanks, it creates monetary base (H> 0). When these repay it,

.


88Control of mone su l

I h i f h h h l d ib d i h f i


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In the operation of the three channels described in the foregoingslide, the role of the central bank ispassive. The decisions on Hare taken, in practice, by the Treasury, which buys foreigncurrencies in exchange of euros, and the banks.

But the central bank is also able to control mone su lusing the following instruments:1. Becoming emancipated from the Treasury seignorage. Thisoccurs e cen ra an s no o ge o uy s on s, u can

decide how much and whether purchasing them.2. Managing the coefficient , that incorporates reserverequirements: for a given , one has .

0

3. Managing the official discount rate, that measures the cost of

.by banks, and therefore causes H< 0.4. Buying and selling bonds in the secondary market: the purchaseof bonds creates monetary base ( > 0), the sale destroys it.


89Bud et constraints and mone

L id i lifi d i h b k d i h h


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Let us consider a simplified case, without banks and without thecentral bank. In this case we haveDe = 0 andRe = 0, so thatmoney supply coincides with the monetary base: = .In the budget constraints, moneydoes appear. It is one of the

one of the uses of the private sector (households plus firms),which demands it (L).

The Statebudget constraint:

T S G T

Householdsbudget constraint:

D

Firmsbudget constraint:

S

Macroeconomics The Walras law and money

90The Walras law and mone

A l i th l d f ti f th b d t


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Applying the usual procedure of aggregation of the budgetconstraints one obtains:

(E Y) + (BD BS) + (L M) = 0

To write the formula for the Walras law, we have set:

, .

E CI G

BS BGS

BFS

L LH LF

The presence of money calls into crisis the neoclassical model ofthe Say law. In fact, the potential equilibrium in the bonds market

.


91Stocks and flows

Th W l l b itt i li htl diff t


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The Walras law can be written in a slightly different way:S S

Assume that in theprevious periodthere was equilibrium, i.e. that; it follows that

t1D B t1

S B t1

, t t1 t t1

Using a similar procedure (assuming that also in the money

BD BS BD BS

market there was equilibrium at t1), we can write

L M L

Because of these changes, the Walras law becomes

E Y BD BS L M 0

In the bonds and money markets, one is considering stocks

instead of flows. This enables one to highlight the importance of

old bonds(they are equivalent to new bonds).


92Mone demand for transactions

At the beginning of the month a representative household holds for


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At the beginning of the month a representative household holds formonthl ex enditures the li uid amountL which it s ends re ul-

arly each day (according to a linear pathL(t)). Its money demand

for transactions (quantity of money held on average) will beL0/2.

he time path for liquid stocks of a representative firm increaseswith the sales and decreases with the payments (here, also,

L0 L(t)

.

At aggregate level, money demandfor rivate a ents transactions is

L02

an increasing function of Y(whichis an indicator of the level of

transactions).

T kWe will write:

Macroeconomics Money demand

t1 with k> 0.

93Precautionar mone demand

For its definition see slide 83 It can be identified in a graph with


93/199

For its definition see slide83. It can be identified, in a graph withthe time in the horizontal axis and li uid funds in the vertical

axis, as the minimum level touched by such funds, i.e. by the

functionL(t), during the month (the averageof funds that exceed

the minimum is money demand for transactions purposes).In the graph, the liquid funds decrease

L0L(t)

behavior identifies, beyond the demandfor transactionsL , a recautionar

demandLP.The determinants of this demand are

Yand r. We shall write:T

LP P LPY, r

t1 with and

.

P

Y 0 P

r 0


94Mone as an alternative to bonds

One has a speculative demand when private agents hold money


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One has a speculativedemand when private agents hold money, ,

the average stock).

the interest rate. It represents the price for the liquidity

preference (Keynes), or also, symmetrically, the premium for

not holding liquidity.

At micro level, a single agent (a speculator) exchanges bonds

in her portfolio with money when she foresees that their price

will fall; viceversa when she foresees thatPbwill rise.

The speculator compares the market price bwith what she believ-esis the normal levelPN : if she observesPb >PN , then she sells the

on s v ceversa, s e uys t e on s s e o serves b N .


95The s eculative mone demand

At macro level if Pb is high for the majority of speculators there


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At macrolevel, ifPb is high, for the majorityof speculators therewill be > . Thus, the a ents s eculative mone demand willbe high. If insteadPb is low, for the majority of speculators there

will bePb PNholds: nobodyis

willin to hold bonds and ever bod is willin to hold in theportfolio any quantity of money.


96Mone demand and su l

Aggregating the three components LT + LP + LS one obtains the


96/199

Aggregating the three componentsLT+LP+LS, one obtains the

L =L( Y,r)

Usually, we will assume a linear(but imprecise) specification:

w t Y Y and with r r .

Mone su l will be assumed as an exo enous variable

L( Y,r) = kY hr

M

.In the model, money supply is considered as an

Macroeconomics The LM schedule

econom c po cy mone ary po cy var a e.

97The LM schedule

Let us set M = L, and substitute into the equality between the two


97/199

Let us set M L, and substitute into the equality between the two

This equation is the equilibrium conditionin the money market.

kY h

t ent es a t e com nat onso an rw c ensure suc anequilibrium. It is called the LM schedule.

r

L = M

r

k

h Y

1

hdr

k

dY hThe position of the curve is

controlled by M: for example, M

> 0 moves the curve downwards.The liquidity trap imposes that

r

Yr r.


98A ain on the LM schedule

QUESTION. Why, in the equilibrium between L and M (beyond


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Q . Why, in the equilibrium betweenL and M(beyond,

higher level of the interest rate r?

ANSWER. A hi her level ofYim lies a hi her mone demand

for transactions kY; since money supply is fixed at the level ,the remaining part of money demand (the speculative one

hr) must be lower, and hence rmust be higher.

QUESTION. Why does M> 0 move the LM downwards?

ANSWER. When one has M> 0, it follows that, given Y, at the

old level of rone has >L. To restore equilibrium, it isnecessary a higher level ofL. This requires, given Y, a lower

eve o .


99Outside the LM

The points onthe LM depict equilibriumpositions (combinationsf Y d i h k i hi h h i h L


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The points o the LM depict equ b u positions (combinationsof Yand r in the mone market in which that is one has L = .

In the points underthe LM, for a given Y, ris lower, money

demand is higher (sinceLr< 0) and one thus hasL > M.

Agents try to obtain the missing money by selling bonds.

Therefore it follows Pb < 0 and r> 0.

r

L = ML < M

e oppos te occurs n t e po nts a ove

the LM: the reaction causes r< 0.,

outside the equilibriumarere resented b the arrows.

L > MThe market dynamicsis given

by the differential equation:

Y r rL


100The IS-LM model

The macroeconomic equilibriumis the combination of Yand rhi h i l l ilib i i h d k


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qwhich simultaneousl ensures e uilibrium in the oodsmarket

(E= Y) and in the moneymarket (L = M). When this occurs,equilibrium in the bondsmarket is ensured by the Walras law.

It is identified by the ntersect onpoint between the IS schedule(whereE= Y) and the LM schedule (whereL = M).

r

LM

by solving the following system forthe unknowns Yand r:IS

r* Y m br

kY hr

The first equation is the IS; the

Macroeconomics The IS-LM model

YY second equation is the LM.

101Solution of the IS-LM model

Deriving rfrom the LM, substituting into the IS and solving for Yi ld ft l b th f ll i lt


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g , g gield after some al ebra the followin result:

Y m1 m2

m1

11c1tbk/h

m

m2 m1 h

C cT cTr G

m1 > 0 is the multiplierof (the exogenous component of)

autonomous expenditure, ; it is lower than the multiplier m,due to the presence of the term bk/h > 0 in the denominator.

2 s e mu p er o money supp y.


102The d namic version of the model

Outside the equilibrium, we have the system of differentiale uations:


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q , ye uations: Y

r rL M

(see slide72, and slide99).

The dynamics of the system is

Y 0 r 0 described by thephase diagram

(see the GRAPH):

The trajectory changes direction

ever time that it meets a curve

and it does converge to theequilibrium, where one has

LM IS

Y Y= Y and r= r .


103The effective d namics

In practice, the adjustment in the two markets occurs with verydifferent velocities: in the mone market it is almost instantaneous


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p , j ydifferent velocities: in the mone market it is almost instantaneous

Thus, firstthe system switches to the LM, and thenit runs along while in the goods market it is relatively slow ( ).r Y

t e unt reac ng a so t e equ r um n t e goo s mar et.See the GRAPH:

,

the interest rate falls (r< 0)until arriving to the LM;

IS LM

Y* at this point,

investments grow and, along

with them, aggregateexpenditure grows, until arriving

*

Y.


104Monetar retroaction

In the IS-LM model, a variation in autonomous expenditurefor instance G > 0 affects the e uilibrium out ut Y


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pfor instance G > 0 affects the e uilibrium out ut Y.

but it is lowerthan in the income-expenditure model: m1 < m.

The effect ispositive: Y

G m1 0

G > 0 shifts the IS by an amount equal to mG;thereby lowering the level ofI.

*

but alsothe equilibrium interest rate rises,

= 1 . r

LMISO

N

Monetary retroaction:

Y

0

rO

rN

It de ends on three arameters:

r 0 I 0

mGLY

k Ir

brL

1h

YYO YNthat is .


105The Ke nes effect

In the IS-LM model, the equilibrium output Yis alsoinfluencedb a chan e in mone su l for instance > 0


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b a chan e in mone su l for instance > 0 .

The increase in Mshifts the LM downwards, the interest rate

The effect ispositive: Y

m2 0

decreases, and the equilibrium output increases.The transmission mechanism is:

r LMO

IS LMN r 0 I 0 E 0

0 L b 0

rO

r

.

and onr 1I

b

Its size depends on:

That is, on how much the policymakes rfall and how muchI

YYO YNreacts to the fall in r.Macroeconomics The IS-LM model

106Economic olic

In the IS-LM model, the equilibrium output Yis influenced byeconomic olic


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economic olic .

BUDGETARY POLICY(or fiscal policy): change in G, Tr, and t; it

-

T

.expenditure model, because of the monetary-retroaction effect.MONETARY POLICY: change in M(through the instruments for

controlling money supply); it acts shifting the LM.

In this model, money has real effect(is not neutral).

The effectivenessof the two policies depends on the slopesof the

two curves: I(1) the steeper the IS (the lower ), the less effective

monetary policy; Lr

(2) the steeper the LM (the lower ), the lesseffective fiscal policy; L(3) the flatter the LM (the higher ),the less effective monetary policy and more effective fiscal policy.


107O en economies

So far we have supposed that there were no transactionswith therest of the world. Now we shall relax such a restriction.


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rest of the world . Now we shall relax such a restriction.

RESIDENTS: those who carry out their main economic activity

(consumption, production, labor, and so on) within the country.

REST OF THE WORLD: those who carry out their maineconomic activity abroad.

An economic system is open when its residents make economic

transactions with the rest of the world.

ECONOMIC TRANSACTIONS:

transact ons o goo s an serv ces; transactions of financial assets (bonds);

.

Macroeconomics Open economies

108 The balance of a ments

It records all economic transactionsbetween


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.

Residents revenuesare recorded with the sign plus;paymentsare

.We will indicate byBp the balance of payments.The current accountbalance (Bc) is the difference between

revenues and payments associated to the transactions of goods

and services.e cap a accoun a ance s e erence e ween

revenues and payments associated to the transactions of bonds.The followin identit holds:

Bp = Bc + Bk

For simplicity, we neglect transactions of real capitals and transfers.


109The exchan e rate

FOREIGN CURRENCY: it is the mean of payment used fortransactions between residents and the rest of the world i.e.


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it is the international money). Alternatively, one can assume it

is the money used in the rest of the world. Let indicate it by $.

NOMINAL EXCHANGE RATE (e): it is the number of unities of

domestic money needed to buy one unity of foreign currency;

i.e., it is the pr ce o ore gn currency(for instance, it

measures the number of euros needed to buy one dollar).

REAL EXCHANGE RATE(v): it measures the number of unities

of domestic product needed to buy one unity of foreign

pro uct: v ePF

where F is the price level in the rest of the world.


110Some sim lificationsTo write the agents budget constraints and derive the Walras

law in an open economy, we use the following hypotheses(they


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are not essential, but simplify formulas): Domestic and foreign goods (and bonds)pricesarefixedand

equa o . o ows a e nom na exc ange ra ecoincides with the real exchange rate (v);

There are no banks there is onl the Central Bank . It follows

that one has M=H;

Only households demand money. It follows that one has F = 0 (and F = );

Transactions between residents and the rest of the world

.

absence of capital mobility hypothesis (it will be relaxed); The sizes of the economy are smallwith respect to those of

the rest of the world. This is the small country hypothesis.Macroeconomics Open economies

111The old bud et constraints

Budget constraints for households, firms and the State changever little with res ect to those of slide89:


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HOUSEHOLDS:

D

FIRMS: H

BS STATE:

T BGS G Tr

The State does not issue mone the central bank does it

TWO OBSERVATIONS:

The purchases of goods by agents (C,I, G) can concern bothdomestic products (Y) and foreign products, i.e., imports (Z).


112The new bud et constraints

They are that of the central bank and that of the rest of the world:


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The central bank creates mone to bu bonds and currenc .

M BCBD

e$CB

The opposite holds, too: by selling bonds ( ) or

currency ( ), the central bank destroys money.$CB 0BCB

D 0

REST OF THE WORLD:eZ e$S X e$D

The rest of the world buys pieces of of the country domestic

product (exports X), paying by supplying currency (e$S),

an se s to ouse o s, rms, an t e tate p eces oforeign product (imports Z), getting currency (e$D). It soon

e = p = e


113Walras law and o en markets

Add the five agents budget constraints; aggregate according tothe relative market as usual translate the anal sis from flows to


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stocks; we obtain a new version of the Walras law, this time also

involving the currency market:

E Y BD BS L M e$D $S $CB 0

n t e rst rac et we set:

E= C+I+ G + (X eZ)

That is, the demand of domestic products (E) equals the demand

of roducts comin from domestic o erators C+I+ G to

which we must subtractthe part of the demand for foreignproducts (importsZ), but we must addthe demand of domestic

products coming from the rest of the world (exports ).Macroeconomics Open economies

114Currenc reserves

The forth element of the Walras law is the currency market(orexchan e market :


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The last term $ ertains to the central bank interventions

e[($D $S) + $CB]

that is, to its netpurchases of currency.

The central bank ensures the daily operation of the currency

market, selling currency to operators when it is demanded, and

buying currency from operators when it is supplied.e mar e s n equ r um, a s, = , e cen ra

banks purchases and sales balance each other, and so $BC = 0.

operators requests) to do an interventionin the market: deciding

$CB > 0, it accumulates currency in its own currency reserves;

deciding instead $CB < 0, it draw currency out of reserves.Macroeconomics Open economies

115Exchan e rate re imesIn the exchange market, in the absence of interventions by the

central bank, the law of demand and supply holds:


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dedt

e$D $S $CB

.direct function of its excess demand. Nevertheless, the central

bank, intervening in the market, is able to control its variation

e

and, in the limit case, completely eliminate it.

If the central bank never intervenes ($CB = 0), we have amar et- ase exc ange rate reg me or oat ng exc ange rates .

If the central bank systematically intervenes to compensate the= D S

exchange rateregime. If the central bank will intervene whenever it believes thatdoing so is appropriate, we have a managed floatingregime.


116Floatin exchan e ratesIt is the exchange rate regime that one has when the central bank

never makes interventions($CB = 0) and lets market forcesd i h h Th i h


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determine the exchange rate. That is, we have:

with e 0de D S

In the very short run(the market day), the currency demandis a

decreasin function of the exchan e rate while the currenc

t

supplyis an increasingfunction of the exchange rate:

D e with $

D 0

e

$S Se with $S

e 0

The reason is similar to that of the speculative money demand:for given needs of currency, one anticipates the purchase when

the price is low and delays it when the price is high.Macroeconomics Open economies

117E uilibrium in the exchan e marketIn the very short run, there is equilibriumwhen one has:

e = e


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This equation determines the equilibrium exchange ratee*.

e e

Graphically, it is identified by the intersection point between thedemand curve and the supply curve.

e

$S$D

If the exchange rate is higher

that the equilibrium one (e > e*),

e*

than the supply ($D < $S), so thatthe exchan e rate tends to fall

( ). The opposite occurswhen e < e* .

dedt 0

$$*hus, this equ r umis sta e.


118Fixed exchan e ratesWe have a fixed exchange rate when the central bank intervenes

in the currency market with the rule $BC= $S $D (see slide115).


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Three main cases:

EXCHANGE RATE AGREEMENT. The central bank of a country

draws up a treaty with the central banks of other countries inwhich it commits itself to keep the exchange rates fixed;

UNILATERAL PEGGING. he central bank of a country

commits explicitly itself to keep its own exchange rate linked to

EXCHANGE RATE MANAGEMENT. The central bank of acountr s stematicall intervenes to kee stable the exchan e

rate also in the absence of an explicit commitment.Fixed exchange rates require availability of currency reservesto

finance interventions implying currency sales.Macroeconomics Open economies


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120The three fundamental e uationsThere are several versions of the Mundell-Fleming model. We will

see four. In all these versions, we will work under the assumption

of small country (see slide 110) So what happens within our


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of small country (see slide110). So what happens within our

economy does not affectthe economy in the rest of the world.

E= Y equilibrium in the goods market (the IS);

Allversions are based on three equations:

L = M equilibrium in the money market (the LM);

Bp = 0 balance of payment equal to zero (the BB).

The distinctions between the four versions relate to two elements:

Fixed or floatin exchan e rates;

the type of transactions with the rest of the world: Only goods and services ( absence of capital mobility);

Also bonds (capital mobility).

Macroeconomics Open economy and macroeconomic equilibrium

121Im orts and ex ortsIn an open market, the definition ofE(see slide113) is as follows:

E= C+I+ G + X vZ = C+I+ G + c


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where, to value imports, we used the realexchange rate v.

.

X=X(v,YF), withX

v 0 and

X

YF 0

. .,

both the real exchange rateand the world demand);

Z=Z v,Y, with and 0 Z 1Z 0

(i.e., imported quantities are a decreasingfunction of the real

exchange rateand an increasingfunction of domestic product);

v

Therefore, the current account balanceBc depends (positively) onYF and (negatively) on Y. It also depends on the real exchange

rate. How? Positively or negatively?Macroeconomics Open economy and macroeconomic equilibrium

122Current account and exchan e rateAn increase in the exchange rate has two effectsof opposite sign

on the current account balanceBc:

It increases exports and decreases imports; and this improves


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It increases exports and decreases imports; and this improves

the current account (quantity effect);

It makes imports more expensive; and this worsens the currentaccount (price effect);

o see w a o e wo e ec s preva s, e us compu e e

derivative of the current account with respect to the exchange

rate: dBc dX dZ

One can show, after some algebra, that this derivative ispositive

dv dv dv

.e., e ncrease n e exc ange ra e mproves e curren

account) ifthe Marshall-Lerner condition holds, that is, if:

Macroeconomics Open economy and macroeconomic equilibrium

123The Marshall-Lerner condition

We have just seen that its formula isX + Z > 1


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where Xand Zare, respectively, the elasticitiesof exports and

X Z

imports with respect to the (real) exchange rate:

dX / dv dX v dZ v

The condition states that an increase in the (real) exchange rate

v v

mproves e curren accoun a ance e sum o e

elasticitiesof exports and imports isgreater than one, that is, the

respect to changes in the exchange rate in order to offset thehigher cost of imports brought about by the increase in the

exchange rate.Macroeconomics Open economy and macroeconomic equilibrium

124Fixed exchan e rates: the IS scheduleWe assume a small country and fixed exchange rates. Exports

become exogenous: we set

We also assume a linear relationship between imports and


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p p

domestic income: we setZ Z zY

From condition Y= , definition = +I+ + c, and, we derive the usual IS formula:c X vZ zY

where now we have (one can easily show it):

m r

(open-market multiplier)m 1c1tvz

(autonomous expenditure) C cT cTr G X v

Note that the multiplieris smaller than that in the closed market.Note also that now in the autonomous expenditurethere are

Macroeconomics IS-LM and fixed exchange rates

exports and (with the sign minus) imports.

125The current account and the level ofYWhat is the effect of an increase in Yon the current account?At first sight, the answer is: the increase in Yrises imports (Z=

zY) and so worsensBc. But the answer is only partial.


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) y p

One must take into account what has generated the increasein Y.

o o t s, et use t e ta ng constant, or s mp c ty, r .Consider the effect of an exogenous variation X> 0:

n output: we ave = m > ;

On the current account: we haveBc = (1 mz)X

; makingm

,

which is a positive number (even if it is less than one). Therefore,

1 zm 1c1t

1c1t

Instead,Bcworsens when the increase in output is triggered by athe increase in output caused by X> 0 improvesBc.

change in the domesticautonomous expenditure (e.g. G > 0).Macroeconomics IS-LM and fixed exchange rates

126Fixed exch. rates: the LM scheduleRegarding money demand, nothing changes: we have (as in the

closed economy)

L = kY hr


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k h

Regarding money supply, things change.

From the central banks budget constraint (cfr. s e122), settingBBC= 0 (for the sake of simplicity and/or realism), it follows

D

= CB(where we set e = 1). That is, money supply does not vary

2009 10 lecture notes macro

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