edit 12ce ch21

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Copyright © 2008 Pearson Education Canada

Chapter 21

The Simplest Short-Run Macro

Model

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In this chapter you will learn

1. the difference between desired expenditure and actual expenditure.

4. how a change in desired expenditure affects equilibrium income, and how this change is reflected by the multiplier.

3. how to define equilibrium national income.

2. the determinants of desired consumption and desired investment expenditures.

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The national accounts divide actual GDP into its components: - Ca, Ia , Ga, and NXa.

Total desired expenditure is divided into the same categories:

• desired consumption, C

• desired investment, I

• desired government purchases, G

• desired net exports, NX

21.1 DESIRED AGGREGATE EXPENDITURE

Where are the ‘a’ subscripts?

MFC2007MFC2007MFC2007MFC2007MFC2007MFC2007

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Two types of expenditures:

- autonomous expenditures do not depend on the level of national income

- induced expenditures do depend on the level of national income

The sum is called desired aggregate expenditure:

AE = C + I + G + NXWhere are the ‘a’

subscripts?


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What Does “Desired” Really Mean?

“Desired” expenditure is not just a list of what consumers and firms would buy if they had no constraints on their spending — it is much more realistic than that.

Desired expenditure is what consumers and firms would like to purchase, given their real-world constraints of income and market prices.

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Two possible uses of disposable income:

- consumption (C) or saving (S)

Desired Consumption Expenditure

In the simplest theory, consumption is determined primarily by current disposable income (YD).

In more advanced theories, individuals are forward looking, and so consumption depends more on “lifetime” income.

Recall: disposable income (YD) is national income (Y) less taxes (T).

What about taxes and imports?


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An Important Tool: the 45º line - our reference line

45º line

YD

100

C

Properties of the 45º line

- bisects the quadrant - intercept of zero - slope of 1

100

200

200MFC2007MFC2007MFC2007MFC2007MFC2007MFC2007

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C = a + bYD

The simple consumption function is written as:

45º line

YD

a slope (b)

C

Note: the slope of this simple consumption function (b) is less than one.

C = a +bYD

where a represents autonomous consumption expenditure and bYD represents induced consumption expenditure.

intercept (a)


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A numerical example:

Consider C = a + bYd where a = 4000 and b =0.5

Yd = a + bYd = C

$ 0 $4000 $ 0 $ 4000

$ 5000 $4000 $ 2500 $ 6500

$ 8000 $4000 $ 4000 $ 8000

$10000 $4000 $ 5000 $ 9000

$15000 $4000 $ 7500 $11500

$20000 $4000 $10000 $14000


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Picture of the Consumption Function

C

Yd

C= a + bYd

$4000

$0 $5000

$6000

$8000

$8000

$20000

$14000

Intercept

Break even


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Exercise: repeat the previous calculations and draw the graph using the following parameter values

a b you should find

1) $5000 0.5 intercept shifts up

2) $3000 0.5 intercept shifts down

3) $4000 0.7 slope rotates upwards

4) $4000 0.3 slope rotates downwards


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C = a + bYD versus

C = a + b’YD where b’ > b

Changes in the slope of the consumption function

YD

a

C

C = a + bYD

C = a + b’YD

A change in slope causes a rotation of the line


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C = a + bYD versus

C = a’ + bYD where a’ > a

Changes in the intercept of the consumption function

YD

a

C

C = a + bYD

C = a’ + bYD

A change in the intercept causes a shift in the line

a’


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Shifts in the Consumption Function

What might cause a shift in the consumption function (the amount of consumption desired by all households at all levels of income)?

- change in wealth- change in interest rates - change in expectations

- change in population size or age distribution- change in taste- ?


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What about savings?If C = a + bYd and Yd = C + S then S= -a +(1-b)Yd

Yd C Savings = Yd - C

$ 0 $ 4000 -$4000$ 5000 $ 6500 -$1500$ 8000 $ 8000 $ 0$10000 $ 9000 $1000$15000 $11500 $3500$20000 $14000 $6000

Calculate APS = S/YD MPS = S/YD


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The marginal propensity to consume (MPC) relates the change in desired consumption to the change in disposable income that brings it about.

MPC = C/YD denoted b in our expression and diagram

The MPC is the slope of the consumption function.

In the previous diagram, the MPC is the same at every level of income.


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The average propensity to consume (APC) is equal to total consumption divided by total disposable income.

APC = C/YD

EXTENSIONS IN THEORY 21-1

The Theory of the Consumption Function

In the previous diagram, the APC falls as the level of income rises.

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150

150 300

450

300

450

600

600

45º line

C

150 300 450 6000

-150

150

-30

S

YD

YD

•

C

S

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Since all disposable income is either consumed or saved, we have:

• APC + APS = 1

• MPC + MPS = 1

Is our simple theory of the consumption function supported by empirical evidence? For some Canadian data on aggregate consumption and disposable income, look for “The Consumption Function in Canada” in the Additional Topics section of this book’s MyEconLab.

www.myeconlab.com

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150

150 300

450

300

450

600

600

45º lineC0

150300

450 6000

-150

150

-30

S0

YD

YD

•

•

C1

S1

30

If consumption function shifts upward, the saving function must shift downward.

Shifts in the Consumption Function?

What causes a shift? - wealth- interest rate- expectations

C

S

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Investment expenditure is the most volatile component of GDP:

changes in investment expenditure are strongly associated with short-run fluctuations

Desired Investment Expenditure

• the real interest rate

• changes in the level of sales

• business confidence

Three important determinants of aggregate investment expenditure are:

Recall: Investment refers to purchases of - capital stock (plant & equipment) - residential building - business inventories


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The real interest rate is the opportunity cost for:

- investment in new plants and equipment

- investment in inventories

- investment in residential construction

The Real Interest Rate

Thus, all three components of desired investment expenditure are negatively related to the real interest rate, other things being equal.

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The higher the level of production and sales, the larger the desired stock of inventories:

changes in the rate of sales cause temporary bouts of investment in inventories

When business confidence improves, firms want to invest now so as to reap future profits.

Changes in Sales

Business Confidence

Business confidence and consumer confidence may feed off of one another.

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The Investment Function

Desired investment is treated as autonomous

– completely unrelated to the current level of Y

We can write I = I

Were I is determined by - real interest rates - expectations

(confidence) - changes in sales


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Investment Function (the picture)

Desired Investment

I

Actual National Income

Y

I

0

200

150

100

I’

I’’

interest rate fallsexpectations improve

sales increase

interest rate risesexpectations worsen

sales decrease


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Our Story – a simplified version

We will now start to tell our story (build our macroeconomic model).

Our story has one key purpose: to explain what determines the level of aggregate economic activity (the size of the GDP or Y)

– and to understand what might cause Y to increase and what might cause Y to decrease?


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The Aggregate Expenditure Function

Now what if we get rid of the Government and foreign economies?

A Lou Dobbs economy (or perhaps the Fox Network economy).

Desired aggregate expenditure, or more simply Aggregate Expenditure (AE).

AE = C+I+G+(X-IM)

This is termed a closed economy with no government


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Domestic Households

Domestic FirmsFactor income:wages, rents profits

YD = Y

Revenue from sales of final G & S

= C + I

A closed economy with no government

Savings

Investment

ConsumptionFinancial markets


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The aggregate expenditure function relates the level of desired aggregate expenditure to the level of actual national income (through actual national income’s influence on C)

AE = C + I

The Aggregate Expenditure Function becomesIn the absence of government and international trade, desired aggregate expenditure is just equal to C + I.

(Note the distinction between desired aggregate expenditure and actual national income.)


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AE = C + I

But, C= a + bYD (the consumption function)

and YD = Y (no government – no taxes)

Therefore AE = a + bY + I

AE = a + I + bY

The aggregate expenditure function relates the level of desired aggregate expenditure to the level of actual national income.

But how? Through actual national income’s influence on C

(Note the distinction between desired aggregate expenditure and actual national income.)


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Consider the following example.

The investment function is:

I = 75

The consumption function is:

C = 30 + (0.8)Y

The AE function is then given by:

AE = C + I = 30 + (0.8)Y + 75

==> AE = 105 + (0.8)Y

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Y C I AE 30 54 75 129

120 126 75 201 150 150 75 225 300 270 75 345 450 390 75 465 525 450 75 525 600 510 75 585 900 750 75 825

600

300

105

300 600

900

900

AE =C + I

Actual National IncomeD

esi

red

Ag

gre

ga

te

Exp

en

ditu

re

The slope of the AE function is the marginal propensity to spend. In the simplest model with no taxes and no international trade, this is just the MPC.

7530

C

I


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Exercise

Repeat the above calculations and graphing for the following economies

1) C = 30 + (0.8)Y and I = 125

2) C = 60 + (0.8)Y and I = 75

3) C = 30 + (0.6)Y and I = 75


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The AE function combines the spending plans of households and firms. It shows, for any level of actual national income, the level of desired aggregate spending.

What happens to AE if the consumption function shifts up or down?

What happens to AE if the slope of the consumption function increases or decrease?

What happens to AE if the investment function shifts up or down?

What happens to AE if the slope of the investment function increases or decrease? (We will assume that it is always zero?)

Summary


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21.2 EQUILIBRIUM NATIONAL INCOME

If desired aggregate expenditure exceeds actual output:

- what is happening to inventories?

- there is pressure for output to rise

If desired aggregate expenditure is less than actual output:

- what is happening to inventories?

- there is pressure for output to fallMFC2007MFC2007MFC2007MFC2007MFC2007MFC2007

Recall: desired aggregate expenditure is what buyers want to buy during the period (C+I)

actual output is what firms actually produce during the period (Y)

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Copyright © 2008 Pearson Education CanadaCopyright © 2005 Pearson Education Canada Inc.

Equilibrium occurs where aggregate desired expenditure equals actual national income (output).

National

Income (Y) OUTPUT

Desired Aggregate

Expenditure (AE = C + I)

Effect

30 129 Pressure 120 201 On output 150 225 to rise 300 345 450 465 525 525 Equilibrium income 600 585 900 825 Pressure on output

to fall


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How the Economy Gets to Equilibrium – Inventory Adjustment Mechanism

What happens if output (GDP) is greater than desired AE?

AE < Y

- Firms cannot sell all that they are producing

- Inventories build up (this is unintended I)

- This is the firms’ signal that a decrease in output is necessary

- Firms decrease output until AE=Y


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How the Economy Gets to Equilibrium – Inventory Adjustment Mechanism

What happens if output (GDP) is less than desired AE?

AE > Y

- Firms are selling more than they are producing

- Inventories are being run down (this is unintended I)

- This is the firms’ signal that an increase in output is necessary

- Firms increase output until AE=Y


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Equilibrium Mechanism Illustrated

600

300

105

300 600

900

900

AE

De

sire

d A

gg

reg

ate

E

xpe

ndi

ture

•

45º line

Equilibrium national income is that level of national income at which desired aggregate expenditure equals actual national income.

At an actual national income of 300, AE > Y(How do you know?)

therefore inventories are falling and firms expand output.

Actual National Income

At an actual national income of 900, AE <Y(How do you know?)

therefore inventories are increasing and firms decrease output.


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600

300

105

300 600

900

900

AE

Actual National IncomeD

esi

red

A.E

.

•

45º line

In words: Equilibrium national income is that level of national income where desired aggregate expenditure equals actual national income.

In this model, output is said to be demand determined.

The equilibrium condition is:

Y = AE(Y)

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Remember!

INVENTORIES!

INVENTORIES!

INVENTORIES!


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A different, but equivalent, way of thinking about the equilibrium level of national income involves comparing desired saving withdesired investment. For more details, look for “Investment, Saving, and Equilibrium GDP” in the Additional Topics section of this book’s MyEconLab.

www.myeconlab.com

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21.3 CHANGES IN EQUILIBRIUM NATIONAL INCOME

‘Movement along’ vs. ‘shifts’ in the AE Function

e1

AE

Y0 Y1

Y

ee0

AE0

Y0 Y1

e´´

AE1

e´

Y Y

AE AE


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e´1

Y0 Y1

e0

AE0

Y0 Y1

AE1

AE0

AE1

e1

•

•

••

AE =Y

E1

E0

E1

E0e0

e2

AE =Y

Two types of ‘shifts’ can occur with the AE function:

1. The AE function can shift parallel to itself

2. The slope of the AE function can change (should not really be called a ‘shift’)

Y Y

AEAE


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The MultiplierThe multiplier is a measure of the size of the change in equilibrium Y that results from a change in autonomous expenditure.

In our simplest of macro models, the multiplier exceeds one.

APPLYING ECONOMIC CONCEPTS 21-1

The Multiplier: A Numerical Example

For example, a $1 billion increase in desired investment expenditure will increase the equilibrium level of national income by more than $1 billion.


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e´1

Y0 Y1

e0

AE0

AE1

e1 •

•

AE =Y

E1

E0

•

A

Y

Simple multiplier =

Y

A=

1

1-z

Where z is the marginal propensity to spend out of national income and A is the change in autonomous expenditure.

Y

AE

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Y0 Y1

AE0

AE1

•

AE =Y

E1

E0

A

Y

Y0 Y1

AE0

AE1•

•

AE =Y

E1

E0

A

Y

The larger is z, the steeper is the AE curve and the larger is the simple multiplier.

•

AE AE

Y Y

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Example of the multiplier and its use

e´1

Y0 Y1

e0

AE0

AE1

e1 •

•

AE =Y

E1

E0

•

A

Y

Y A= multiplier x

If we know that the multiplier

is 4 and we know that the

A is $500 million, then we

can calculate that the Y

is going to be $2,000 million

Y

AE

What is the value of the multiplier in the real world? Canada = 1.20 or so Windsor = ? Maybe 1.06


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Another example of the multiplier and its use

e´1

Y0 Y1

e0

AE0

AE1

e1 •

•

AE =Y

E1

E0

•

A

Y

What if the marginal propensity to spend (z) is 0.75 and GM decides to build a new auto plant for $500 million, what would the change in equilibrium Y be?

Simple multiplier =

Y

A=

1

1-zSo the multiplier is 1 / (1-0.75) = 1 / 0.25 = 4

The change in equilibrium Y will be 4 x $500 million = $2,000 million ($2 billion). A = $500 million and Y=$2,000 million

Y

AE


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EXTENSIONS IN THEORY 21-2

The Algebra of the Simple Multiplier

Politicians in Canada and elsewhere are often heard “talking up” their economies. This can be understood by examining the role that expectations play in booms and recessions. Formore on this topic, look for “Recessions and Booms as Self-Fulfilling Prophecies” in the Additional Topics section of this book’s MyEconLab.

www.myeconlab.com

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Economic Fluctuations as Self-Fulfilling Prophecies

Households and firms base their desired investment and consumption partly on their expectations of the future:

changes in expectations can lead to real changes in the current state of the economy

Example:

- imagine that firms feel optimistic about the future

- this increases their desired investment, shifting up the AE curve

- this increases Y, justifying the initial optimism

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Now imagine the opposite scenario. It should be clear that if firms and households are pessimistic about the future in large numbers, the ensuing change in their behaviour will lead to a self-fulfilling prophecy of reduced national income.

Could the Prime Minister (or the Governor of the Bank of Canada) ever announce to the country

that they might have made a ‘big’ mistake?

For example: suppose that government analysts report to the Prime Minister that having signed the Kyoto Accord might result in a recession.


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edit 12ce ch21

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