Aggregate Expenditure and Equilibrium Output. The Core of Macroeconomic Theory.

Aggregate Expenditureand Equilibrium Output

The Core of Macroeconomic Theory

Aggregate Output andAggregate Income (Y)

• Aggregate output is the total quantity of goods and services produced (or supplied) in an economy in a given period.

• Aggregate income is the total income received by all factors of production in a given period.

Aggregate Output andAggregate Income (Y)

• Aggregate output (income) (Y) is a combined term used to remind you of the exact equality between aggregate output and aggregate income.

• When we talk about output (Y), we mean real output, or the quantities of goods and services produced, not the dollars in circulation.

Explaining Spending Behavior

• All income is either spent on consumption or saved in an economy in which there are no taxes.

Saving Aggregate Income Consumption

Household Consumption and Saving

• Some determinants of aggregate consumption include:1. Household income2. Household wealth3. Interest rates4. Households’ expectations about the future

• In The General Theory, Keynes argued that household consumption is directly related to its income.


• The slope of the consumption function (b) is called the marginal propensity to consume (MPC), or the fraction of a change in income that is consumed, or spent.

C a bY=

0 1 b<


• The fraction of a change in income that is saved is called the marginal propensity to save (MPS).

1MPC + MPS

• Once we know how much consumption will result from a given level of income, we know how much saving there will be. Therefore,

S Y C

An Aggregate Consumption FunctionDerived from the Equation C = 100 + .75Y

• At a national income of zero, consumption is $100 billion (a).

• For every $100 billion increase in income (Y), consumption rises by $75 billion (C).

C Y 1 0 0 7 5.

Consumption Function (alternative formulation)

)( TYccC c -Autonomous consumption

c -Marginal Propensity to Consume (MPC)

)( TY -Disposable Income (DI) (Income - Net Taxes)

The Determinants of Consumption

• Wealth– Affects consumption

expenditures• The price level

– Affects real purchasing power of financial assets

• The interest rate– Causes consumers to

postpone consumption• Expectations (of income or

prices)– A more optimistic outlook on

the economy will raise consumers’ expenditures

Y

$CC’

C’’

Deriving a Saving Functionfrom a Consumption Function

S Y C Y - C = S

AGGREGATEINCOME

(Billions of Dollars)

AGGREGATE CONSUMPTION


AGGREGATE SAVING


0 100 -100

80 160 -80

100 175 -75

200 250 -50

400 400 0

600 550 50

800 700 100

1,000 850 150

C Y 1 0 0 7 5.

Planned Investment (I)

• Investment refers to purchases by firms of new buildings and equipment and additions to inventories, all of which add to firms’ capital stock.

• One component of investment—inventory change—is partly determined by how much households decide to buy, which is not under the complete control of firms.

change in inventory = production – sales

Actual versus Planned Investment

• Desired or planned investment refers to the additions to capital stock and inventory that are planned by firms.

• Actual investment is the actual amount of investment that takes place; it includes items such as unplanned changes in inventories.

The Planned Investment Function

• For now, we will assume that planned investment is fixed. It does not change when income changes.

• When a variable, such as planned investment, is assumed not to depend on the state of the economy, it is said to be an autonomous variable.

Investment Function

II Investment is autonomous (independent of income)

Present ValueInternal Rate of Return

nn

iiiPV

1

$...

1

$

1

$2

21

1

The Present Value of a stream of payments

Where I can be interpreted as the internal rate of return

Present ValueInternal Rate of Return

191 1

5...

1

55

i

mil

i

milmilPV

The Present Value of a 100 million Lotto pay off

Interest Rate Present Value6.0% ($60,790,582.46)7.0% ($56,677,976.21)8.0% ($53,017,996.00)9.0% ($49,750,573.90)10.0% ($46,824,600.46)15.0% ($35,991,155.97)20.0% ($29,217,478.40)

Investment and the Investment Function

• At this point investment is planned investment expenditures (I)

• Investment is closely linked to the interest rate, since interest represents the opportunity cost of investing in capital

• The investment function will shift with changes in expectations for business profits

Investment spending (I)

Nominalinterest rate

D

D’

Autonomous Investment• Although investment is related

to the interest rate and business expectations, investment does not depend in any significant way on disposable income– As such, investment is

“autonomous”• However, changes in the

interest rate or expectations for profits will still shift autonomous investment

Real disposable income

$

I

I”

I’

Determinants of Investment

• Below are all the things that can cause a shift in the investment function

– The interest rate– Expectations of future profits – Technology

Planned Aggregate Expenditure (AE)

• Planned aggregate expenditure is the total amount the economy plans to spend in a given period. It is equal to consumption plus planned investment.

IC AE

Equilibrium Aggregate Output (Income)

• Equilibrium occurs when there is no tendency for change. In the macroeconomic goods market, equilibrium occurs when planned aggregate expenditure is equal to aggregate output.

Equilibrium AggregateOutput (Income)

Y > C + Iaggregate output > planned aggregate expenditure

inventory investment is greater than plannedactual investment is greater than planned investment

Disequilibria:

C + I > Yplanned aggregate expenditure > aggregate output

inventory investment is smaller than plannedactual investment is less than planned investment

aggregate output Yplanned aggregate expenditure AE C + I

equilibrium: Y = AE, or Y = C + I


C Y 1 0 0 7 5. I 2 5Deriving the Planned Aggregate Expenditure Schedule and Finding Equilibrium (All Figures in Billions of Dollars) The Figures in Column 2 are Based on the Equation C = 100 + .75Y.

(1) (2) (3) (4) (5) (6)

AGGREGATEOUTPUT

(INCOME) (Y)AGGREGATE

CONSUMPTION (C)PLANNED

INVESTMENT (I)

PLANNEDAGGREGATE

EXPENDITURE (AE)C + I

UNPLANNEDINVENTORY

CHANGEY (C + I)

EQUILIBRIUM?(Y = AE?)

100 175 25 200 100 No

200 250 25 275 75 No

400 400 25 425 25 No

500 475 25 500 0 Yes

600 550 25 575 + 25 No

800 700 25 725 + 75 No

1,000 850 25 875 + 125 No


Y Y 1 0 0 7 5 2 5.

Y C I (1)

C Y 1 0 0 7 5.(2)

I 2 5(3)

By substituting (2) and (3) into (1) we get:

There is only one value of Y for which this statement is true. We can find it by rearranging terms:

Y Y 1 0 0 7 5 2 5.

Y Y .7 5 1 0 0 2 5Y Y .7 5 1 2 5

.2 5 1 2 5Y

Y 1 2 5

2 55 0 0

.

The Saving/InvestmentApproach to Equilibrium

If planned investment is exactly equal to saving, then planned aggregate expenditure is exactly equal to aggregate output, and there is equilibrium.

The S = I Approach to Equilibrium

• Aggregate output will be equal to planned aggregate expenditure only when saving equals planned investment (S = I).

The Multiplier

• The multiplier is the ratio of the change in the equilibrium level of output to a change in some autonomous variable.– An autonomous variable is a variable that is assumed not

to depend on the state of the economy—that is, it does not change when the economy changes.

• In this chapter, for example, we consider planned investment to be autonomous.

The Multiplier

• The multiplier of autonomous investment describes the impact of an initial increase in planned investment on production, income, consumption spending, and equilibrium income.

• The size of the multiplier depends on the slope of the planned aggregate expenditure line.

The Multiplier Equation

• The marginal propensity to save may be expressed as:

M P SS

Y

M P SI

Y

• Because S must be equal to I for equilibrium to be restored, we can substitute I for S and solve:

therefore, Y IM P S

1

m ultip lierM P S

1 , or m ultip lier

M P C

1

1

The Multiplier

• After an increase in planned investment, equilibrium output is four times the amount of the increase in planned investment.

The Size of the Multiplierin the Real World

• The size of the multiplier in the U.S. economy is about 1.4. For example, a sustained increase in autonomous spending of $10 billion into the U.S. economy can be expected to raise real GDP over time by $14 billion.

The Paradox of Thrift

• When households become concerned about the future and decide to save more, the corresponding decrease in consumption leads to a drop in spending and income.

• Households end up consuming less, but they have not saved any more.

Government Expenditures and Autonomous Net Taxes

• We will assume that government expenditures (G) and net taxes (T) are autonomous– This assumption will keep

our models from becoming overly complex

– It will also allow us to easily analyze fiscal policy as both G and T change

• It would be possible to consider taxes that vary with GDP (income taxes)

Real income

$

GT

GG

TT

Autonomous Net Exports (X - M)

• If both exports (X) and imports (M) are autonomous, then net exports are autonomous


$

X-M

X’-M’

X’’-M’’

MXMX

Determinants of X-M

• The following will cause a shift in the net export function. – The Exchange Rate

• If the Dollar appreciates, then exports fall and imports rise, both causing net exports to fall, or shift down.

– Foreign GDP (Income)• As foreign income rises, they import more goods from around the

world including the US. So our exports will rise as we satisfy their demand for our goods.

Variable Imports

• Imports may very well be related to income

• This makes net exports decrease with income


$

X-M)( TYmmM

Aggregate Expenditure and Income

Planned Expenditures

• What about the behavior (the “plans”) of our economic actors?– Consumption (C) is “planned” on the basis of disposable income– Investment (I) is “planned” based on the interest rate and business

expectations (although it is autonomous with respect to GDP, or income)

– G and (X-M) are simply autonomous

• According to Keynes, aggregate planned expenditures (demand) determine output and income, even in the long run

The Income-Expenditure Model

• A relationship between aggregate income and planned aggregate expenditures that determines, for a given price level, where income (and GDP) equals planned expenditures

• The aggregate expenditure function is a relationship showing the amount of planned spending for each level of income

• Equilibrium occurs in the model where planned aggregate expenditures equal income (GDP)– Unintended changes in inventories play a key role

Planned Aggregate Expenditure (trillions of dollars)

RealGDP

NetTaxes

Dis.Income Cons. Saving

PlannedInv.

Gov'tPurchases

NetExport

PlannedExp.

$6.0 $1.0 $5.0 $4.7 $0.3 $0.6 $1.0 -$0.1 $6.2$6.5 $1.0 $5.5 $5.1 $0.4 $0.6 $1.0 -$0.1 $6.6$7.0 $1.0 $6.0 $5.5 $0.5 $0.6 $1.0 -$0.1 $7.0$7.5 $1.0 $6.5 $5.9 $0.6 $0.6 $1.0 -$0.1 $7.4$8.0 $1.0 $7.0 $6.3 $0.7 $0.6 $1.0 -$0.1 $7.8

Deriving Equilibrium Income and Output

Real GDP

$

C+I+G+(X-M)

45o

Equilibrium Real GDP

The Simple Spending Multipliers

Real GDP

$

C+I+G+(X-M)

45o C+I’+G+(X-M)

GDP

ISimple spending multiplier =

GDP/I = 1/(1-MPC) = 1/MPS

Simple spending multiplier =

GDP/I = 1/(1-MPC) = 1/MPS

The Spending Multiplier and the Circular Flow (MPC = .8)

RoundNew

Spending

CumulativeNew

SpendingNew

Saving

CumulativeNew

Saving1 $100.00 $100.002 $80.00 $180.00 $20.00 $20.003 $64.00 $244.00 $16.00 $16.004 $51.20 $295.20 $12.80 $12.80. . . . .. . . . .. . . . .

$0.00 $500.00 $0.00 $100.00

Keynes and the Great Depression• John Maynard Keynes argued that prices and wages are not sufficiently

flexible to ensure the full employment of resources• Furthermore, Keynes argued that when resources (especially labor) are

not fully employed (due to a lack of private investment expenditures), the government could provide offsetting expenditures as a means of stabilizing the economy

• Thus, Keynesian economics places emphasis on planned expenditures and all its components

Appendix B--The Algebra of the Income and Expenditure Model

{

44444444444 344444444444 21

4444 344444 21

SpendingAutonomous

MultiplierSimple

C

MXGITccc

Y

MXGITcccY

MXGITYcc

MXGICY

)(1

1

)(1

)(

)(

*

Appendix B--Introducing Variable Imports

SpendingAutonomous

MultiplierEconomyOpen

MC

TmmXGITccmc

Y

TmmXGITccmcY

TYmmXGITYcc

MXGICY

)1

1

1

))(((

)(

*

Appendix

• Slides after this point will most likely not be covered in class. However they may contain useful definitions, or further elaborate on important concepts, particularly materials covered in the text book.

• They may contain examples I’ve used in the past, or slides I just don’t want to delete as I may use them in the future.


• The relationship between consumption and income is called the consumption function.

• For an individual household, the consumption function shows the level of consumption at each level of household income.

Income, Consumption,and Saving (Y, C, and S)

• A household can do two, and only two, things with its income: It can buy goods and services—that is, it can consume—or it can save.

• Saving (S) is the part of its income that a household does not consume in a given period. Distinguished from savings, which is the current stock of accumulated saving.

S Y C

An Aggregate Consumption FunctionDerived from the Equation C = 100 + .75Y

AGGREGATEINCOME, Y

(BILLIONS OF DOLLARS)

AGGREGATE CONSUMPTION, C

(BILLIONS OF DOLLARS)

0 100

80 160

100 175

200 250

400 400

400 550

800 700

1,000 850

C Y 1 0 0 7 5.

Aggregate Demand and Changes in the Price Level

• An increase in the price level has a negative impact on real GDP for three reasons– As the price level increases the real value of fixed financial assets is

diminished. This reduces consumption demand and GDP.– An increase in the price level puts upward pressure on interest

rates and downward pressure on investment– As the price level increases, foreign goods become more attractive

• Of course all of these effects are reversed for a decrease in the price level

The Aggregate Demand Curve

Y

PAE (P)

Y

P

45o AE’’ (P’’)

AE’ (P’)

PP’

P’’

AD

Shifts in the Aggregate Demand Curve

Y

PC+I+G+(X-M)

Y

P

45o

AD

C+I’+G+(X-M)

AD’

Appendix A--Variable Net Exports

Real GDP

P X-M

P

Real GDP

C+I+G

C+I+G+(X-M)

The Circular Flow of Income and Expenditure

aggregate income = GDP

aggregate income = GDP

transfer paymentstransfer payments

taxestaxesDisposable incomeDisposable income

Financialmarkets

consumption (C)consumption (C)

SS

Investment (I)Investment (I)

Gov’t (G)Gov’t (G)

X-MX-M

C+I+G+X-M

Review Terms and Concepts

actual investmentactual investment

aggregate incomeaggregate income

aggregate outputaggregate output

aggregate output (income) (aggregate output (income) (YY))

autonomous variableautonomous variable

change in inventorychange in inventory

consumption functionconsumption function

desired, or planned, investment (desired, or planned, investment (II))

equilibriumequilibrium

identityidentity

investmentinvestment

marginal propensity to consume (marginal propensity to consume (MPCMPC))

marginal propensity to save (marginal propensity to save (MPSMPS))

multipliermultiplier

paradox of thriftparadox of thrift

planned aggregate expenditure (planned aggregate expenditure (AEAE))

saving (saving (SS))

Consumption and Aggregate Expenditure

Classical Economists

• A group of 18th- and 19th-century economists who believed that recessions and depressions were short-run phenomena that corrected themselves through natural market forces; thus the economy was self-adjusting

Consumption

• Consumption is the portion of disposable income that is spent and not saved

• Consumption spending bears a close relationship to disposable income

• Consumption makes up the largest share of aggregate planned expenditures

• Approximately 2/3 of GDP

The Consumption and Savings Functions

real disposable income

$ C

$

C

DI MPC = C/DIMPC = C/DI

real disposable income

SMPS = S/DIMPS = S/DI

The Marginal Propensity to Consume and Save

• The marginal propensity to consume (MPC) is the fraction of a change in income that is spent on added consumption

• The marginal propensity to save (MPS) is the fraction of a change in income that is devoted to added savings

• 0 < MPC < 1• MPS = 1 - MPC

Planned Versus Actual Investment

• Planned investment is the amount of investment firms plan to undertake during a year

• Actual investment is the amount of investment actually undertaken during a year

• Actual investment equals planned investment plus unplanned changes in inventories

The Income Half of the Circular Flow

• Since profits (the difference between expenditures on output and production-related costs) are paid to firms’ owners, GDP equals income:

GDP = Aggregate Income• Since disposable income is aggregate income minus taxes

(less transfer payments), GDP must equal disposable income (DI) plus net taxes (T):

GDP = Aggregate income = DI + T

The Expenditure Half of the Circular Flow

• Disposable income is either spent on consumption (C) or put into savings (S): DI = C + S

• From an earlier chapter, aggregate expenditure has four components– Consumption (C), Investment (I), Government

Purchases (G) , Net Exports (X - M)• As a result,

C + I + G + ( X - M ) = GDP

Leakages Equal Injections• The two equalities for GDP written together give,

GDP = Y=DI + T = C + I + G + ( X - M )

• Since S = DI - C

S + T + M = I + G + X(leakages = injections)

Leakages and Injections

• A leakage is any diversion of income from the domestic spending stream

• An injection is any payment of income other than by firms, or any spending other than by domestic households

Aggregate Expenditure and Equilibrium Output. The Core of Macroeconomic Theory.

Documents

Transcript of Aggregate Expenditure and Equilibrium Output. The Core of Macroeconomic Theory.