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MACROECONOMICS MACROECONOMICS

Topic 8

Aggregate Demand I:

Building the IS-LM Model

(Chapter 10)

Instructor: Tuan Khai Vu

ICU, Winter Term 2011

Principles of Macroeconomics

Learning objectives

Learning objectives

In this chapter, we will learn :

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the IS curve, and its relation to:

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the Keynesian cross

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the loanable funds model

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the LM curve, and its relation to:

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the theory of liquidity preference

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how the IS-LM model determines income and the interest rate in the short run when P is fixed

Context

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Chapter 9 introduced the model of aggregate demand and aggregate supply.

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^{Long run}

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prices flexible

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output determined by factors of production & technology

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unemployment equals its natural rate

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^{Short run}

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prices fixed

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output determined by aggregate demand

Context

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This chapter develops the IS-LM model, the basis of the aggregate demand curve.

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We focus on the short run and assume the price level is fixed (so, SRAS curve is horizontal).

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This chapter (and chapter 11) focus on the closed-economy case.

I nvestment - A quick review

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^Includes:

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Business fixed investment

Spending on plant and equipment

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Residential fixed investment

Spending by consumers and landlords on housing units

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Inventory investment

The change in the value of all firms’ inventories

The Keynesian Cross

ƒ

A simple closed economy model in which income is determined by expenditure ^(or

aggregate demand) (due to J.M. Keynes) .

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Behavior of firms in this model:

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cannot change prices so must

forecast demand to determine supply.

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if demand forecasted ^≠ actual demand Î ^unplanned inventories occur

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firms adjust their production based on changes in unplanned inventories:

unplanned inventories _Î production

This is the underlying adjustment mechanism that Keynes thought captures reality.

The Keynesian Cross

ƒ

Notation:

I = planned investment

PE = C + I + G = planned expenditure Y = real GDP = actual expenditure

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The relationship btw actual & planned investment

The amount that firms would like to invest

actual investment

planned investment

unplanned inventory investment

= +

The Keynesian Cross

ƒ

^Î The relationship btw actual & planned expenditure

actual expenditure

planned expenditure

unplanned inventory investment

= +

Elements of the Keynesian Cross

consumption function: govt policy variables:

for now, assume planned investment is exogenous: planned expenditure:

equilibrium condition:

actual expenditure = planned expenditure

If Y ^≠ PE _Æ unplanned inventories ^≠ 0 _Æ firms change production _Æ not equilibrium.

G ra p h in g p la n n e d e x p e n d it u re

income, output,Y

PE planned expenditure PE=C+I+G MPC 1 10

Graphing the equilibrium condition

income, output, Y PE

planned expenditure

PE = Y

45º

The equilibrium value of income

income, output, Y PE

planned expenditure

PE = Y

PE = C + I + G

Equilibrium

The goods market is in equilibrium at this point

Y⁰

Adjustment tow ards equilibrium

income, output, Y PE

planned expenditure

PE = Y

PE = C + I + G

Y¹

unplanned inventories < 0 (_Å PE > actual exp. Y) Îfirms increase output

ÎY moves tw Y⁰

unplanned inventories > 0 (_Å PE < actual exp. Y) Îfirms reduce output

Î Y moves tw Y⁰

Y⁰ Y²

An increase in government purchases

^{( G1}_Æ^G2)

Y PE

P^E

=^Y

PE = C + I + G₁

PE₁ = Y₁

PE = C + I + G₂

PE₂ = Y₂ Δ_Y

At Y₁,

there is now an unplanned drop in inventory…

…so firms

increase output, and income rises toward a new

equilibrium.

Δ_G

The government purchases multiplier - -

Solving for ^Δ Y

equilibrium condition in changes

because I exogenous

∆_I=0

because ^ΔC = MPC •^∆Y

Collect terms with ^ΔY on the left side of the equals sign:

Solve for ^ΔY :

The government purchases multiplier

Definition: the increase in income resulting from a

$1 increase in G.

In this model, the govt

purchases multiplier equals

Example: If MPC = 0.8, then

An increase in G causes income to

increase 5 times as much!

Why the multiplier is greater than 1

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Initially, the increase in G causes an equal increase in Y: ^ΔY = ^ΔG.

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^{But ↑Y ⇒ ↑C}

⇒ _further ↑_Y

⇒ _further ↑_C

⇒ _further ↑_Y

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So the final impact on income is much bigger than the initial ^ΔG.

This is called the multiplier process.

An increase in taxes

Y PE

P^E

=^Y

PE = C₂ + I + G

PE₂ = Y₂

PE = C₁ + I + G

PE₁ = Y₁ Δ_Y

At Y₁, there is now an unplanned

inventory buildup…

…so firms

reduce output, and income falls toward a new equilibrium

Δ_{C =} −_MPC Δ_T

Initially, the tax increase reduces consumption, and therefore PE:

The tax multiplier - - Solving for ^∆ Y

eq’m condition in changes

I and G exogenous

Solving for ^ΔY :

Final result:

The tax multiplier

definition: the change in income resulting from a $1 increase in T :

If MPC = 0.8, then the tax multiplier equals

The tax multiplier

…is negative:

A tax increase reduces C, which reduces income.

…is greater than one

(in absolute value) suppose MPC>.5_:

A change in taxes has a multiplier effect on income.

…is smaller than the govt spending multiplier:

Consumers save the fraction (1 – MPC) of a tax cut, so the initial boost in spending from a tax cut is

NOW YOU TRY:

Practice w ith the Keynesian Cross

ƒ

Use a graph of the Keynesian cross

to show the effects of an increase in planned investment on the equilibrium level of

income/output.

The I S curve

definition: a graph of all combinations of r and Y that result in goods market equilibrium

i.e. actual expenditure (output)

= planned expenditure The equation for the IS curve is:

Deriving the I S curve

Y₂ Y₁

Y₂

Y₁ ^Y

PE

r

Y

PE = C + I (r₁ )+ G PE = C + I (r₂ )+ G

r₁ r₂

PE = Y

I S Δ_I

↓_r ⇒ ↑_I

⇒ ↑_PE

⇒ ↑_Y

Why the I S curve is negatively sloped

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A fall in the interest rate motivates firms to

increase investment spending, which drives up total planned spending (PE ).

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To restore equilibrium in the goods market, output (or actual expenditure, Y )

must increase.

The I S curve and the loanable funds model

(a) The L.F. model (b) The IS curve

S, I r

I (r ) r₁

r₂

r

Y₁ Y r₁

r₂

Y₂ S₁

S₂

I S

Fiscal Policy and the I S curve

ƒ

We can use the IS-LM model to see how fiscal policy (G and T ) affects aggregate demand and output.

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Let’s start by using the Keynesian cross

to see how fiscal policy shifts the IS curve…

Shifting the I S curve: ^ΔG

Y₂ Y₁

Y₂ Y₁

At any value of r,

↑_G ⇒ ↑_PE ⇒

↑_Y

Y PE

r

Y

PE = C + I (r₁ )+ G₁ PE = C + I (r₁ )+ G₂

r₁

PE = Y

I S₁ The horizontal

distance of the IS shift equals

I S₂

…so the IS curve shifts to the right.

Δ_Y

NOW YOU TRY:

Shifting the I S curve: ^Δ T

ƒ Use the diagram of the Keynesian cross or

loanable funds model to show how an

increase in taxes shifts the IS curve.

The Theory of Liquidity Preference

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Due to John Maynard Keynes.

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A simple theory in which the interest rate is determined by money supply and

money demand.

Money supply

The supply of real money balances is fixed:

M/ P

real money

r

interest rate

Money demand

Demand for real money balances:

M/ P

real money balances

r

interest rate

L(r )

decreasing in r (see topic 3)

Equilibrium

The interest rate adjusts to equate the supply and demand for money:

M/ P

real money

r

interest rate

L(r ) r₁

The money market is in equilibrium at this point.

How the Fed raises the interest rate

M/ P

real money balances

r

interest rate

L(r ) r₁

r₂ To increase r,

Fed reduces M

CASE STUDY:

Monetary Tightening & I nterest Rates

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Late 1970s:

^π

> 10%

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Oct 1979: Fed Chairman Paul Volcker announces that monetary policy

would aim to reduce inflation

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Aug 1979-April 1980: Fed reduces M/P 8.0%

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^{Jan 1983:}

^π

^{= 3.7%}

How do you think this policy change

Monetary Tightening & I nterest Rates, cont.

Δ_{i < 0} Δ_{i > 0}

8/1979: i = 10.4% 8/1979: i = 10.4%

flexible sticky

Quantity theory, Fisher effect

(Classical)

Liquidity preference

(Keynesian)

prediction actual

The effects of a monetary tightening on nominal interest rates

prices model

long run short run

The LM curve

Now let’s put Y back into the money demand function:

The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances.

The equation for the LM curve is:

D e ri v in g t h e L M c u rv e

M/P

r L(r,Y 1)

r 1

r 2

r Y Y 1

r 1L(r,Y 2)

r 2 Y 2

LM

(a)The market for real money balances(b)The LMcurve 38

Why the LM curve is upw ard sloping

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An increase in income raises money demand.

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Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate.

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The interest rate must rise to restore equilibrium in the money market.

H o w Δ M s h if ts t h e L M c u rv e

M/P r L(r,Y 1)r 1

r 2

r Y Y 1

r 1

r 2

LM 1

(a)The market for real money balances(b)The LMcurve LM 2 40

NOW YOU TRY:

Shifting the LM curve

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Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions.

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Use the liquidity preference model to show how these events shift the LM curve.

The short- run equilibrium

The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets:

Y r

I S LM

Equilibrium interest

rate

Equilibrium level of

income

The macro- economy is in equilibrium at this point.

The Big Picture

Keynesian Cross

Theory of Liquidity Preference

IS curve

LM curve

IS-LM model

Agg. demand

curve Agg. supply

Model of Agg. Demand and Agg.

Supply

Explanation of short-run fluctuations

The trip we have been taken so far, and will continue next week

Preview of Chapter 11

In Chapter 11, we will

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use the IS-LM model to analyze the impact of policies and shocks.

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learn how the aggregate demand curve comes from IS-LM.

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use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks.

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use our models to learn about the Great Depression.

Chapter Summary

Chapter Summary

1. Keynesian cross

ƒ basic model of income determination

ƒ takes fiscal policy & investment as exogenous

ƒ fiscal policy has a multiplier effect on income 2. IS curve

ƒ comes from Keynesian cross when planned investment depends negatively on interest rate

ƒ shows all combinations of r and Y

that equate planned expenditure with actual expenditure on goods & services

Chapter Summary

Chapter Summary

3. Theory of Liquidity Preference

ƒ basic model of interest rate determination

ƒ takes money supply & price level as exogenous

ƒ an increase in the money supply lowers the interest rate

4. LM curve

ƒ comes from liquidity preference theory when money demand depends positively on income

ƒ shows all combinations of r and Y that equate demand for real money balances with supply

Chapter Summary

Chapter Summary

5. IS-LM model

ƒ Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.

Practicing:

Solving end- of- the- chapter problems

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Let’s solve problem 2

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Recall the equations describing the model

Elements of the Keynesian Cross

slide #9 reshown

consumption function: govt policy variables:

for now, assume planned investment is exogenous: planned expenditure:

equilibrium condition:

actual expenditure = planned expenditure

2. a&b. PE line & equilibrium

consumption function:

for now, assume planned investment is exogenous: planned expenditure:

equilibrium condition: govt policy variables:

C=200+0.75(Y-T) =200+0.75(Y-100)

=0.75Y +200-75 = 0.75Y +125 T =G=100

I =100

PE = C+I+G = (0.75Y+125)+100 +100 PE = 0.75Y+325

Y = PE _Î Y = 0.75Y+325 _Î 0.25Y = 325 Î Y = 325/0.25 or Y=1300

substitute values assigned

This indicates that the graph of PE is a

straight line with the slope = 0.75 and intercept = 325.

2. c. G = 100 _Æ 125

consumption function:

for now, assume planned investment is exogenous: planned expenditure:

equilibrium condition: govt policy variables:

C=200+0.75(Y-T) =200+0.75(Y-100)

=0.75Y +200-75 = 0.75Y +125 T =100, G=125

I =100

PE = C+I+G = (0.75Y+125)+100 +125 PE = 0.75Y+350

Y = PE _Î Y = 0.75Y+350 _Î 0.25Y = 350 Î Y = 350/0.25 or Y=1400

2. d. G = ? if Y= 1600

planned expenditure: equilibrium condition:

PE = C+I+G = (0.75Y+125)+100 +G PE = 0.75Y+225+G

Y = PE _Î Y = 0.75Y+225+G

Î G = 0.25Y - 225 = 0.25*1600 – 225 = 400 - 225 Î ^{G =175}