MBA Lectures 6 - 8

8/6/2019 MBA Lectures 6 - 8

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ECO 502

BRAC University,Spring, 2006Lectures 6 ± 8

Lutfun N. Khan Osmani

Chapter 3

Spending, Income and theInterest Rate

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 interestrate

� The IS curve:

� Relation of the IS curve to the demand for autonomous spending

� Shift in the IS curve

� What rotates the IS curve?

Concepts

It is assumed that you know theseconcepts clearly:

� Exogenous

� Endogenous

� Autonomous Consumption

� Induced consumption

� Induced savings

� Marginal propensity to consume

Business Cycle and the Theory of Income Determination

� We know the goals of fiscal and monetarypolicy is to dampen the business cycle so that

real GDP grows steadily from one year to thenext.

� The real world is much different from that

ideal world.

� What could be reason for this volatility?

Figure 3-1 Real GDP Growthin the United States, 1950±2004

� We know (and will also see later in thelecture) that unstable ups and downs of realGDP can be caused by changes in consumer

confidence, business optimism, governmentspending and foreign events that influenceexport and import (remember the KeynesianCross diagram).

� These shocks to aggregate demand (calleddemand shock) are the basic source of business cycle and economic volatility.

� Shocks to aggregate demand can changeeither real GDP or the price level (GDPdeflator), or both.

� Changes in aggregate supply depends oncosts of production for business firms

including the wages and prices of rawmaterials such as oil. We shall learn about itin chapter 7 & 8.

� In order to focus on changes in aggregatedemand we assume price 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 change in real GDP.

Concepts

� Endogenous variables: those explained by aneconomic theory, e.g., Q = f(P). Q is

endogenous P is exogenous.

� Exogenous variables: relevant for the modelbut their behaviour not explained by themodel, e,g., price level (P).

Concepts

� The consumption function:

� 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

Concepts

� The consumption function:

� Numerical Example:

� C = 500 + 0.75(Y ± T)

Planned Expenditure

� Planned expenditure:

E | C + I + G + NX

The consumption function:

C = Ca + c(Y ± T)

Planned Expenditure

� Induced saving and marginal propensity tosave:

� Savings = personal disposable income minusconsumption

S = Y ± T ± C p savings function

S = Y ± T - Ca - c(Y ± T)

= (1 ± c)(Y ± T) ± Ca

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)

Figure 3-2 A Simple Hypothesis RegardingConsumption Behavior

Economy in and out of Equilibrium

� In chapter 2 we learnt that actual expenditure(E) and total income (Y) are always equal by

definition.� But there is no reason why planned

expenditure (Ep) and income should be thesame. Only when the economy is in

equilibrium then income is equal to plannedexpenditure.

� In equilibrium, households, firms, government

and the foreign sector want to spend exactlythe amount of income that is being generatedby the current level of production (remember the KC diagram).

� When the economy is out of equilibrium,

production and income is out of line withplanned expenditure, and business firms willbe forced to raise or lower production (beforeor above the crossing of the planned

aggregate expenditure line with the450

line) .

� We know consumption depends on income,but we don¶t know what the level of income isgoing to be.

� To construct the theory of incomedetermination we introduce extra element ±

unplanned expenditure.

� Total expenditure that people want to make isthe planned expenditure (Ep). The rest of the

expenditure (E - Ep) is the unplanned andundesired.

� To simplify, we assume that only investment

expenditure contains unplanned component,consumption (C), government expenditure(G), and net export (NX) are always equal tothe planned amount. So,

� Planned expenditure (or planned aggregateexpenditure or PAE)

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 equationthat do not depend on total income (Y), wecan call them autonomous plannedexpenditure (Ap)

� T usually has two parts: Ta and tY� Where Ta is autonomous tax (does not

depend on income, e.g. council tax, poll tax,etc.) and t is the rate of tax. tY rises as Y

rises.

� Autonomous planned expenditure:

Ap = Ca ± cTa + Ip + G + NX

� Therefore,

Ep = Ap + cY

� Numerical example:

� Autonomous planned expenditure:

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

� Therefore, Ap = 500 ± 0.75(Ta) + 1200 + 0 ± 200 = 1,500

� So, total planned expenditure (Ep) has two

parts; autonomous spending (Ap) andinduced consumption cY.

� Ep = Ap + cY or

p = 1,500

Figure 3-4How Equilibrium Income Is Determined

Equilibriumoccurs at B. Atany other point

economy is outof equilibriumcausingpressure onbusiness firms

to increase or reduceproduction andincome.

� Equilibrium is a situation in which there is nopressure for change

� In the figure equilibrium occurs at B where

planned expenditure (Ep) is equal to realincome (Y)

� At any other point the economy is out of

equilibrium

� Firms will have to either reduce or expandproduction

Determining Equilibrium Real GDP

� At equilibrium, Y = Ep (PAE)

� Subtract cY from both sides

±cY =

±cY but

� Ep = Ap + cY

� Ep ± cY = Ap

� Therefore,� Y ± cY = Ap, or

� (1 ± c)Y = Ap

Determining Equilibrium Real GDP

� (1 ± c)Y = Ap

� MPS×Y = 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 = 6,000 p Eqm. income (Y)

The multiplier effect

� The multiplier is the ratio of the change inoutput ((Y) to the change in autonomousplanned spending that causes it.

�It is 1.

0divided by (1

±MPC)

� It is also 1.0 divided by the marginalpropensity to save (s)

� ( Y 1 1� Multiplier (k) = -------- = ----------- = ------

� ( Ap 1 - MPC s

The multiplier effect

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

� 1 - MPC s

� ( Y 1

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

� ( Ap s

� ( Ap

� (Y = --------------

The Multiplier Effect

Numerically,

� ( Y 1

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

� ( Ap 0.25

� Increase in autonomous planned spending(Ap) by £500 billion raises income by $2,000 (500 × 4) billion because of multiplier effect.

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

The Multiplier Effect

� An increase in autonomous planned spending(Ap) by $500 billion ($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 incomefrom $6,000 billion to $8,000 billion

Multiplier at Work: Fiscal Policy

� Any change in govt. expenditure or taxrevenue has consequences for govt. budget.

� It follows from magic equation (S + T | I + G +NX) that

� T ± G = I + NX ± S

� So, change in the left-hand side must bebalanced by change in right hand side.

� (T ± (G = ( I + ( NX ± (S

� When govt. boosts its spending by $500 billion as in the earlier diagram, it wasassumed that autonomous consumption,

investment and net export are fixed. ((

I = ( NX = 0) and tax revenue remainsconstant, i.e., (T = 0.

� The only element that changes is G ± creating

a budget deficit of $500 billion

� When G changes pY changes p C changes

� Therefore, S changes

� (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 disposableincome,

� (S = s((Y ± (T)

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

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

� So the value of (S

� (S = s((Y ± (T)

= 0.25( 2,000 ± 0)

� The $2,000 billion increase in output induces$500 billion of extra saving. Each extra dollar

of saving is available for households to buybonds that govt. must sell to finance its $500 billion budget deficit.

� An alternative could be to reduce autonomous taxesby $667 billion.

Use a tax cut to eliminate the gap

Change in spending (500) = tax cut x MPC (0.75)

Tax cut = change in spending / MPC = 500/0.75 =$667

A tax cut of $667 will raise PAE by 500; (500 x0.75) = $667

� It will have exactly same effect on Y

� We know, change in income ((Y) is equal to

change in autonomous planned spending(( Ap) times the multiplier [k = 1/(1 ± MPC) =1/MPS = 1/s].

� We already know,

� And from the above equation only

autonomous tax (cTa) part is changing. So, wecan write:

� (Ap - c(Ta

� (( Y) = ------ = -----------� s s

� Numerically,

� (Ap - c(Ta

� (( Y) = ------ = -----------

� s s

� -(

)(-667

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

� 0.25 0.25

� What would happen if the govt. increasedtaxes instead of reducing it?

� The multiplier for an increase in taxes is the

income change in the earlier equation dividedby (Ta:

� (Y ( Ap - c(Ta - c

� ------=

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

----------=

------

� (Ta s (Ta s (Ta s

� Numerically,

� (Y -0.75

� ------=

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

� (Ta 0.25

� This implies, for every unit increase in tax the

output will fall by a multiple of 3 (667 x 3 =2,000)

� Balanced budget multiplier:

Govt., thus could boost income by $2,000 billion either by raising spending by $500 or

by cutting taxes by $667 billion.

� Either method, however, could create largegovt. deficit which is undesirable.

� However, govt. can still boost the economyeven if it has to maintain a balanced budget.

In order to maintain balanced budget, anyadditional govt. expenditure must bebalanced by equal amount of additional taxes

�Balanced budget multiplier:

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

�Balanced budget multiplier:1 - c 1 - c

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

� s s s� Numerically,

- 0.75

1 ± 0

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

� 0.25 0.25 0.25

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

It happens because

(1) One dollar of govt. spending raisesautonomous planned expenditure by exactlyone dollar.

(2) But extra dollar of tax reducesautonomous planned expenditure by c timesone dollar. (Recall c is less than one).

� Thus positive effect of $1 of expenditure on Yis larger than the negative effect of $1 taxincrease.

� Therefore, on balance, there is a positiveeffect on the economy.

Thus govt. can achieve desired income and

real GDP by sufficiently large increase ingovt. spending accompanied by exactly sameincrease in tax rates

The Relation of Autonomous plannedSpending to the Interest Rate

� Thus far autonomous consumption andplanned investment have been assumed to beexogenously given.

� In fact they depend on interest rate, which inturn depends on monetary policy.

� To understand the effect of monetary policy,

we first have to understand the relationshipbetween interest rate and planned aggregatespending.

� We start by the question why plannedinvestment depends on interest rate?

� Firms borrow funds to buy investment goods

� They can stay in business only if earnings of investment goods are enough to pay the

interest on borrowed funds.

� Note: The rate of return on an investmentproject is its annual earnings divided by itstotal cost.

� An increase in planned investment reducesthe rate of return (diminishing marginalproductivity of capital)

� So, interest rate must fall to induce firms toundertake more investment. (See nextdiagram.)

Figure 3-6

An increase in

plannedinvestmentreduces the rateof return.

� Rate of interest influences businessinvestment as well as householdconsumption.

� (Other things remaining the same) Adecrease in the rate of interest increasesautonomous planned spending (Ip + Ca) and

vice versa.

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

�If the level of business and consumer confidence were to increase, the return linewould shift to the right ± at the same interestrate autonomous planned spending would be

higher.

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

The IS Curve

� We now have seen that autonomous plannedspending (Ap) depends on the interest rate

� And real GDP and real income depends onautonomous planned spending

� It follows logically that real GDP and real

income must depend on interest rate

The IS Curve

� We shall derive a graphical schedule thatshows the different possible combinations of interest rate and real income that are

compatible with equilibrium.� That schedule is called the IS curve

� In doing so we assume that business and

consumer confidence, the MPS (s), the levelof govt. spending (G), taxes (T) and netexport (NX) as given.

IS Curve

� The IS curve connects all combinations of {r,Y} for which the goods or product market is in

equilibrium

� The IS curve is based on the idea that asinterest rate falls investment rises and

therefore planned aggregate spending rises,real GDP rises.

Figure 3-9 Relation of the IS Curve to theDemand for Autonomous Spending

The IS Curve

� Ap is the demand schedule in the left frameshowing that demand for autonomousplanned spending depends on interest rate.

� 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 onthe right frame (point C)

� Higher interest p lower Ap p lower incomeand vice versa

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) ± hr Y(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

Effect on the IS Curve of a Rightward Shift inthe Demand for Autonomous Planned Spending

Shift in the IS curve

� Anything that shifts the Ap demand schedulewill shift the IS curve in the same direction.

� The factors that shift the IS curve to the right

include an increase in business confidence or consumer confidence, an increase in govt.expenditure or net exports, and a decrease intaxes.

�Opposite change will shift the IS curve to theleft

� For example, an increase in govt. purchasesraises the planned expenditure.

� For any given interest rate, the upward shift of planned expenditure of �G leads to anincrease in income of �G/(1 ± MPC)

� The IS curve shifts outward.

� A decrease in taxes also expandsexpenditure and income, the IS curve shifts

outward.

� A decrease in govt. expenditure or increasein taxes reduces income and therefore IScurve shifts inward.

� Let Ap is the value of autonomous plannedspending that takes place at zero rate of interest.

In the figure Ap line intersects the horizontalaxis(at zero rate of interest) at $2,500 billion.

� So, Apo = 2, 500.

� The IS curve always lies at a horizontal

distance 4.0 times the Ap line (since multiplier is equal to 4.0).

� So the IS curve crosses the horizontal line atincome 10,000

� With the new demand curve Ap1 = 3, 000 and the corresponding IS curvecrosses the horizontal line at income 12,000

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