MBA Lectures 6 - 7

8/6/2019 MBA Lectures 6 - 7

1/67

Intermediate

Macroeconomics

QUB, Autumn05

Lectures 5 - 6

Lutfun N. Khan Osmani

Chapter 3

Spending, Income and theInterest Rate


2/67

3-2

Contents

Theory of income determination

Economy in and out of equilibrium

Determining equilibrium real GDP

The multiplier effect

Multiplier at work: fiscal policy

Balanced budget multiplier Relation of autonomous spending to interest rate

The IS curve:

Relation of the IS curve to the demand for autonomous

spending

Shift in the IS curve

What rotates the IS curve?


3/67

3-3

Concepts

It is assumed that you know these concepts clearly:

Exogenous

Endogenous

Autonomous Consumption

Induced consumption

Induced savings

Marginal propensity to consume


4/67

3-4

Business Cycle and the Theory of Income Determination

We know the goals of fiscal and monetary policy is to dampenthe business cycle so that real GDP grows steadily from oneyear to the next.

The real world is much different from that ideal world.

What could be reason for this volatility?


5/67

3-5

Figure 3-1 Real GDP Growthin the United States, 19502004


6/67

3-6


We know (and will also see later in the lecture) that unstable upsand downs of real GDP can be caused by changes in consumerconfidence, business optimism, government spending andforeign events that influence export and import (remember the

Keynesian Cross diagram).

These shocks to aggregate demand (called demand shock) arethe basic source of business cycle and economic volatility.


7/67

3-7


Shocks to aggregate demand can change either real GDP, the

price level (GDP deflator), or both.

Changes in aggregate supply depends on costs of productionfor business firms including the wages and prices of rawmaterials such as oil. We shall learn about it in chapter7 & 8.


8/67

3-8


In order to focus on changes in aggregate demand we assumeprice level to be fixed in the short-run

Therefore, changes in AD Changes in real GDP = --------------------------

Fixed price level

So, any change in AD automatically cause changein real GDP.


9/67

3-9

Concepts

Endogenous variables: those explained by an economic theory,e.g., Q = f(P). Q is endogenous P is exogenous.

Exogenous variables: relevant for the model but their behaviournot explained by economic theory, e,g., money supply, level of

government expenditures, tax rates.


10/67

3-10

Concepts

The consumption function:

Numerical Example:

C = 500 + 0.75(Y T)


C = Ca + c(Y T)

Ca p autonomous consumption

c(Y T) p induced consumption

c p marginal propensity to consume ( Y T) p disposable income


11/67

3-11

Planned Expenditure

Planned expenditure:E| C + I + G + NX


C = Ca + c(Y T)

Induced saving and marginal propensity to save:

Savings = personal disposable income minus consumption

S = Y T C p savings function

S = Y T- Ca - c(Y T)

= (1 c)(Y T) Ca


12/67

3-12

The savings function

Numerical example:

S = Y T C

S = Y T- 500 0.75(Y T)

= (1 c)(Y T) Ca

= (1 0.75)(Y T) 500

= 0.25(Y T) 500

= - 500 + 0.25(Y T)


13/67

3-13

Figure 3-2 A Simple Hypothesis Regarding Consumption Behavior


14/67

3-14

Economy in and out of Equilibrium

In chapter2 we learnt that actual expenditure (E) and totalincome (Y) are always equal by definition.

But there is no reason why planned expenditure (Ep) andincome should be the same. Only when the economy is inequilibrium then income is equal to planned expenditure.


15/67

3-15


In equilibrium, households, firms, government and the foreignsector want to spend exactly the amount of income that is beinggenerated by the current level of production (remember the KC

diagram).


16/67

3-16


When the economy is out of equilibrium, production and incomeis out of line with planned expenditure, and business firms willbe forced to raise or lower production (before or above thecrossing of the planned aggregate expenditure line with the 450

line) .


17/67

3-17


We know consumption depends on income, but we dont knowwhat the level of income is going to be.

To construct the theory of income determination we introduceextra element unplanned expenditure.

Total expenditure that people want to make is the plannedexpenditure (Ep). The rest of the expenditure (E- Ep) is theunplanned and undesired.


18/67

3-18


To simplify, we assume that only investment expenditurecontains unplanned component, consumption (C), governmentexpenditure (G), and net export (NX) are always equal to theplanned amount. So,


19/67

3-19


Planned expenditure

Ep = C + Ip + G + NX, or

Ep = Ca + c(Y T) + Ip + G + NX

Ep = Ca + cY cT + Ip + G + NX

Take all the elements of the above equation that do not dependon total income (Y), we can call them autonomous plannedexpenditure (Ap)


20/67

3-20


Autonomous planned expenditure:

Ap = Ca cT + Ip + G + NX

Therefore,Ep = Ap + cY


21/67

3-21


Numerical example:

Autonomous planned expenditure:

Ap = Ca cT + Ip + G + NX

Assume: Autonomous consumption is 500, as before; MPC =0.75; Ip = 1,200; NX = -200; govt. spending and autonomous tax= 0.

Therefore,Ap = 500 0.75(T) + 1200 + 0 200 = 1,500


22/67

3-22


So, total planned expenditure (Ep) has two parts; autonomousspending (Ap) and induced consumption cY.

Ep = Ap + cY or

Ep = 1,500 + 0.75Y


23/67

3-23

Figure 3-4: How Equilibrium Income Is Determined

Equilibriumoccurs at B.

At any otherpoint

economy isout ofequilibriumcausingpressure onbusiness firmsto increase orreduceproductionand income.


24/67

3-24


Equilibrium is a situation in which there is no pressure for change

In the figure equilibrium occurs at B where planned expenditure(Ep) is equal to real income (Y)

At any other point the economy is out of equilibrium

Firms will have to either reduce or expand production


25/67

3-25

Determining Equilibrium Real GDP

At equilibrium, Y = Ep

Subtract cY from both sides

Y cY = Ep cY but

Ep = Ap + cY

Ep cY = Ap

Therefore,

Y cY = Ap, or (1 c)Y = Ap


26/67

3-26

Determining Equilibrium Real GDP

(1 c)Y = Ap

MPSY = Ap; or sY = Ap or

Y = Ap/s

Numerically,

sY = Ap or

0.25Y = 1,500 (since MPC = 0.75)

Y = Ap/s, or Y = 1,500/0.25 = 6,000p Eqm. income (Y)


27/67

3-27


T

he multiplier is the ratio of the change in output ((

Y) to thechange in autonomous planned spending that causes it.

It is 1.0 divided by (1 MPC)

It is also 1.0 divided by the marginal propensity to save (s)

( Y 1

Multiplier (k) = -------- = ------

(Ap s


28/67

3-28


1 1 Multiplier (k) = ----------- = -----

1 - MPC s

( Y 1

Multiplier (k) = ------ = ----- or(Ys = (Ap

(Ap s

(Ap

(Y = --------------

s


29/67

3-29

The Multiplier Effect

Numerically,

( Y 1

Multiplier (k) = ------ = -------- = 4.0

(

Ap0

.25

Increase in autonomous planned spending (Ap) by 500 billionraises income by $2000 (500 4) billion because of multipliereffect.


30/67

3-30

Figure 3-5 The Change in EquilibriumIncome Caused by a $500 Billion Increase in Autonomous Planned Spending


31/67

3-31

The Multiplier Effect

An increase in autonomous planned spending (Ap) by $500billion ($1500- $2000) has moved the Ap line up

The new equilibrium is at J with income (Y) equal to $8,

000.

The multiplier effect has increased income from $1500 billion to$2,000 billion


32/67

3-32

Multiplier at Work: Fiscal Policy

Any change in govt. expenditure or tax revenue hasconsequences for govt. budget.

We know from magic equation (S + T| I + G + NX) that taxrevenue minus govt. expenditure (T G) equals investment plus

net exports minus private saving

T G = I + NX S

So, change in the left-hand side must be balanced by change inright hand side.


33/67

3-33


(T (G = ( I + ( NX (S

When govt. boosts its spending by $500 billion as in the earlierdiagram, it was assumed that autonomous consumption,investment and net export are fixed. (( Ca = ( I = ( NX = 0) andtax revenue remains constant, i.e., (T = 0.

The only element that changes is G creating a budget deficit of$500 billion

When G changespY changesp C changes

Therefore, S changes


34/67

3-34


(T (G = ( I + ( NX (S

We saw (G was 500

What is the value of(S?

We know, saving changes by the marginal propensity to save

times the disposable income,

(S = s((Y (T)


35/67

3-35


We know when G changes by (G, Y changes by

(G x multiplier (k) = 500 4 = 2,000

So the value of

(

S

(S = s((Y (T)

= 0.25( 2,000 0)

= 500


36/67

3-36


The $2,000 billion increase in output induces $500 billion of extrasaving. Each extra dollar of saving is available for households tobuy bonds that govt. must sell to finance its $500 billion budgetdeficit.


37/67

3-37


An alternative could be to reduce autonomous taxes by $667billion.

It will have exactly same effect on Y

We know, change in income ((Y) is equal to change inautonomous planned spending ((Ap) times the multiplier [k =1/(1 MPC) = 1/MPS = 1/s].


38/67

3-38


We already know,

Ap = Ca cTa + Ip + G + NX

And from the above equation only autonomous tax (cTa) part ischanging, we can write

(Ap -c(Ta

((Y) = ------ = -----------

s s


39/67

3-39


Numerically,

(Ap -c(Ta

((Y) = ------ = -----------

s s

-(0.75)(-667) 500

((Y) = ------------------ = -------- = 2,000

0.25 0.25


40/67

3-40


What would happen if the govt. increased taxes instead ofreducing it?

The multiplier for an increase in taxes is the income change inthe earlier equation divided by (Ta:

(Y (Ap -c(Ta - c

------ = ----------- = ---------- = ------

(Ta s(Ta s(Ta s


41/67

3-41


Numerically,

(Y -0.75

------ = ----------- = -3.0

(Ta 0.25

This implies, for every unit increase in tax the output will fall by amultiple of3 (667 x 3 = 2,000)


42/67

3-42


Balanced budget multiplier:

Govt., thus could boost income by $2,000 billion either byraising spending by $500 or by cutting taxes by $667 billion.

Either method, however, could create large govt. deficit which isundesirable.

However, govt. can still boost the economy even if it has tomaintain a balanced budget.


43/67

3-43



In order to maintain balanced budget, any additional govt.

expenditure must be balanced by equal amount of additionaltaxes


44/67

3-44



To see this, we can use the multiplier for govt. spending (k =1/s) and for a change in taxes (tax multiplier = - c/s)


45/67

3-45



1 - c 1 - c

------ + ----------- = ---------- = 1.0

s s s

Numerically,

1 - 0.75 1 0.75

------ + ----------- = ---------- = 1.0

0.25 0.25 0.25


46/67

3-46



That is, multiplier for a balanced budget fiscalexpansion is always 1.0.

It happens because

(1) One dollar of govt. spending raises autonomousplanned expenditure by exactly one dollar.

(2) But extra dollar of tax reduces autonomousplanned expenditure by c times one dollar. (Recall c

is less than one).


47/67

3-47


Thus positive effect of $1 of expenditure on Y islarger than the negative effect of $1 tax increase.

Therefore, on balance, there is a positive effect onthe economy.


Thus govt. can achieve desired income and real GDPby sufficiently large increase in govt. spendingaccompanied by exactly same increase in tax rates


48/67

3-48

The Relation of Autonomous planned Spending to the Interest

Rate

Thus far autonomous consumption and planned investment havebeen assumed to be exogenously given.

In fact they depend on interest rate, which in turn depends onmonetary policy.

To understand the effect of monetary policy, we first have tounderstand the relationship between interest rate and plannedaggregate spending.


49/67

3-49


Rate

We start by the question why planned investment depends oninterest rate?

Firms borrow funds to buy investment goods

They can stay in business only if earnings of investment goodsare enough to pay the interest on borrowed funds.


50/67

3-50


Rate

Note: The rate of return on an investment project is its annualearnings divided by its total cost.

An increase in planned investment reduces the rate of return(diminishing marginal productivity of capital)

So, interest rate must fall to induce firms to undertake moreinvestment. (See next diagram.)


51/67

3-51

Figure 3-6

An increase in

plannedinvestmentreduces therate of return.


52/67

3-52


Rate

Rate of interest influences business investment as well ashousehold consumption.

(Other things remaining the same) A decrease in the rate ofinterest increases autonomous planned spending (Ip + Ca) andvice versa.


53/67

3-53

Figure 3-7 Effect on Autonomous Planned Spending of anIncrease in Business and Consumer Confidence


54/67

3-54


Rate

If the level of business and consumer confidence were toincrease, the return line would shift to the right at the same

interest rate autonomous planned spending would be higher.


55/67

3-55

Figure 3-8 Relation of the Various Components of AutonomousPlanned Spending to the Interest Rate


56/67

3-56

The IS Curve

We now have seen that autonomous planned spending (Ap)depends on the interest rate

And real GDP and real income depends on autonomous

planned spending

It follows logically that real GDP and real income must dependon interest rate


57/67

3-57

The IS Curve

We shall derive a graphical schedule that shows the differentpossible combinations of interest rate and real income that arecompatible with equilibrium.

That schedule is called the IS curve

In doing so we assume that business and consumer confidence,the MPS (s), the level of govt. spending (G), taxes (T) and netexport (NX) as given.


58/67

3-58

IS Curve

The IS curve connects all combinations of {r, Y} for which thegoods or product market is in equilibrium

The IS curve is based on the idea that as interest rate fallsinvestment rises and therefore planned aggregate spendingrises, real GDP rises.


59/67

3-59

Figure 3-9 Relation of the ISCurve to the Demand for Autonomous Spending


60/67

3-60

The IS Curve

Ap is the demand schedule in the left frame showing that

demand for autonomous planned spending depends on interestrate.

For example, at 10% interest rate level of Ap is $1,500 billion(point C).

Taking multiplier to be 4.0, the equilibrium level of income is$6,000 billion and plotted on the right frame (point C)

Higher interest p lower Ap p lower income and vice versa


61/67

3-61

The IS Curve in Equations

Product market equilibrium:

Y = E = C + I + G + NX

Y = Ca + c(Y T) hr + G + NX

Y = Ca + cY cT hr + G + NX

Y - cY = Ca cT hr + G + NX

Y(1

c) = (Ca

cT

+ G +NX

)

hrY(1 c) = Apn hr

hr = Apn - Y(1 c)

r = Apn/h - {(1 c)/h}Y p the IS equation

Intercept = Apn/h > 0

Slope = - (1 c)/h < 0


62/67

3-62

Effect on the ISCurve of a Rightward Shift in the Demand forAutonomous Planned Spending


63/67

3-63


Anything that shifts the Ap demand schedule will shift the IScurve in the same direction.

The factors that shift the IS curve to the right include an increasein business confidence or consumer confidence, an increase in

govt. expenditure or net exports, and a decrease in taxes.

Opposite change will shift the IS curve to the left


64/67

3-64


For example, an increase in govt. purchases raises the plannedexpenditure.

For any given interest rate, the upward shift of plannedexpenditure ofG leads to an increase in income ofG/(1 MPC)

The IS curve shifts outward.


65/67

3-65


A decrease in taxes also expands expenditure and income, theIS curve shifts outward.

A decrease in govt. expenditure or increase in taxes reducesincome and therefore IS curve shifts inward.


66/67

3-66


Let Ap is the value of autonomous planned spending that takesplace at zero rate of interest.

In the figure Ap line intersects the horizontal axis(at zero rate ofinterest) at $2,500 billion.

So, Apo = 2, 500.

The IS curve always lies at a horizontal distance 4.0 times the Apline (since multiplier is equal to 4.0).


67/67


So the IS curve crosses the horizontal line at income 10,000

With the new demand curve

Ap1 = 3, 000 and the corresponding IS curve crosses thehorizontal line at income 12,000

Documents

MBA Lectures 6 - 7