Income and ExpenditureChapter 11

SECOND CANADIAN EDITION

MACROECONOMICSPaul Krugman | Robin Wells

Iris Au | Jack Parkinson

© 2014 Worth Publishers

• The “multiplier”, which shows how initial changes in spending lead to further changes.

• The meaning of the aggregate consumption function, which shows how current disposable income affects consumer spending

• How expected future income and aggregate wealth affect consumer spending

• The determinants of investment spending, and the distinction between planned investment spending and unplanned inventory investment

• How the inventory adjustment process moves the economy to a new equilibrium after a change in demand

• Why investment spending is considered a leading indicator of the future state of the economy

WHAT YOUWILL LEARN

IN THIS CHAPTER

The Multiplier: A First Look

(D - denotes change)• The marginal propensity to consume, or MPC, is the

increase in consumer spending when disposable income rises by $1.e.g. MPC=0.6 then $0.60 of each extra $1 of income is spent on

consumer goods.

(disposable income? Income plus transfers minus taxes)

The Multiplier: a first look• Autonomous spending: spending on goods and services that does not

depend on income. • The multiplier is concerned with how much output and income

ultimately rise due to an increase in autonomous spending.

• The ultimate rise is likely larger than the autonomous spending increase that set it off. Why?

The extra autonomous spending becomes someone’s income. The increase in autonomous spending causes businesses to produce more, hire

more workers, make more profits etc. So income increases.

• This Extra income leads to additional increases in spending and income. - Businesses produce still more, incomes rise further, more spending etc.

This is the multiplier process. Process builds on the relationship between output, income and spending (Ch.7)

The Multiplier Effect: an example

Say autonomous investment spending increases by $10 billionFirst-round spending and incomes rise by $10 billion

+ Second-round increase in consumer spending = MPC × $10 billion (income rose $10b in first round, MPC is share spent)

+ Third-round increase in consumer spending = MPC2 × $10 billion (income rose by MPCx$10b in 2nd round so multiply by MPC)

+ Fourth-round increase in consumer spending = MPC3 × $10 billion (income rose by MPC2x$10b in 3rd round so multiply by MPC)

etc. (process continues) Total increase in real GDP = (1 + MPC + MPC2 + MPC3 + . . .)× $10 billion

i.e. sum of the rise in spending at each round.

The Multiplier: An example

• So the $10 billion increase in investment spending sets off a chain reaction in the economy. The net result of this chain reaction is that a $10 billion increase in investment spending leads to a change in real GDP that is a multiple of the size of that initial change in spending.

• How large is this multiple? Use result for a geometric series: (1 + MPC + MPC2 + MPC3 + . . .) = 1/(1-MPC) (if 0<MPC<1)

• So: the Total Increase in real GDP from a $10 billion rise in investment:

$10 billion x

Geometric Series (for those who want to know!)Sum of a to exponent i: Sai = 1 + a +a2 + a3 + …+ aN

Multiply by ‘a’ to get: aSai = a +a2 + a3 + …+ aN+1

Subtract the second expression from the first to get:(1-a)Sai = 1 - aN+1

Divide by (1-a): Sai = (1 - aN+1)/(1-a)

If 0<a<1 (like our MPC) and N goes to infinity then aN+1→0

Then: Sai = 1 /(1-a) (this is the result we used with a=MPC)

The Multiplier: Numerical Example

Rounds of Increases of Real GDP when MPC = 0.6Multiplier = 1/(1-MPC) = 1/(1-.6) = 2.5

The Multiplier: Numerical Example

• In the end, real GDP rises by $25 billion as a consequence of the initial $10 billion rise in investment spending:

1/(1 − 0.6) × $10 billion = 2.5 × $110 billion = $25 billion

Multiplier = = = 2.5

The Multiplier

• DAE0 is an autonomous change in aggregate spending. i.e. an initial change in the desired level of spending by firms, households, or government at a given level of real GDP.

DY = x DAE0

• The multiplier is the ratio of the total change in real GDP caused by an autonomous change in aggregate spending (DY) to the size of that autonomous change (DAE0).

Multiplier = =

The Simple Multiplier: Underlying Assumptions• Assumptions underlying the version of the process above:

Producers are willing to supply extra output at a fixed price should demand increase.

Interest rate is assumed constant (unaffected by the change in income and output that is part of the process)

No government: no taxes, transfers or spending. No imports or exports.

• More complicated multiplier processes relax these assumptions but still build on the interdependence between spending, output and income.

(relaxing these assumptions will decrease the multiplier)

ECONOMICS IN ACTION

The Multiplier and the Great Depression

• The concept of the multiplier was originally devised by economists trying to understand the Great Depression.

• Most economists believe that the slump from 1929 to 1933 was driven by a collapse in investment spending.

i.e. fall in investment spending was the autonomous spending change (about -$3.7 billion 1929-33).

But as the economy shrank, consumer spending also fell

sharply, multiplying the effect on real GDP. - Real GDP fell by -$5.1 billion 1929-33 suggesting a multiplier of

about 1.4 ($5.1 billion/$3.7 billion = DY/DAE0 )

Consumer Spending

The individual consumption function is an equation showing how an individual household’s consumer spending (c) varies with the household’s current disposable income (yd).

c= ac + MPC yd∙

Where: ac=autonomous consumption spending. MPC = marginal propensity to consume (as before)

The Consumption Function

The Consumption Function

• Deriving the slope of the consumption function

Disposable Income and Consumer Spending in 2010

A Consumption Function fitted to the data

Aggregate Consumption Function

• The aggregate consumption function is the relationship for the economy as a whole between aggregate current disposable income and aggregate consumer spending.

• Aggregate: sums over individuals.

• Text assumes it is linear (doesn’t have to be):C = ac + MPC yd∙

C = total or aggregate consumer spending ac = autonomous consumer spending (aggregate)yd = total disposable income (across all individuals)MPC = marginal propensity to consume (between 0 and 1)

Shifts in the Aggregate Consumption Function• The aggregate consumption function shifts up or down as autonomous

consumption spending changes.

• What might cause autonomous C to change? Changes in expected future disposable income

- say it rises: might save less now or borrow against extra future income -- so current C rises!

- say it falls: might save more now (or borrow less) in order to have more funds in the future – so current C falls!

Changes in aggregate wealth- Value of assets (houses, financial assets). More wealth, more

financial resources to fund C.

Changes in interest rates: affects incentive to save rather than consume. e.g. higher interest rate, save more, consume less.

Consumption Function Shift e.g due to a rise in wealth, a fall in interest rates, or a rise in expected future income

Aggregate Consumption Function

Aggregate Consumption Function

Investment Spending (I)

• Planned investment spending is the investment spending that businesses plan to undertake during a given period.

• What determines I? interest rates: negative effect on Investment spending

Cost of borrowing to finance investment spending;Opportunity cost of a business using its own profits for investment

spending. expected future real GDP: positive effect on I.

Higher future GDP means more demand for goods and services, businesses expand to meet this demand. (this and perceived future business opportunities in Ch. 10)

current production capacity: negative effect on I. If lots of extra capacity to produce output, less likely to need to expand

to meet future demand. demand for Loanable funds (Ch. 10) suggested government policy

tax incentives aimed at investment.

Investment Spending

• According to the accelerator principle, a higher rate of growth in real GDP leads to higher planned investment spending to meet the extra demand for goods.

• According to the accelerator principle, a lower growth rate of real GDP leads to lower planned investment spending (less capacity is needed)

• Investment spending is more volatile than consumption spending. Plays an important role in recessions, recoveries and booms. Is it volatile because it depends on expectations?

• Investment spending is autonomous in this model (doesn’t depend on current GDP).

Investment Spending in recessions

Inventories and Unplanned Investment Spending

• Inventories are stocks of goods held to satisfy future sales.

• Inventory investment is the value of the change in total inventories held in the economy during a given period.

• Unplanned inventory investment occurs when actual sales are more or less than businesses expected, leading to unplanned changes in inventories.

Inventories and Unplanned Investment Spending

• Actual investment spending is the sum of planned investment spending and unplanned inventory investment.

ECONOMICS IN ACTION

Interest Rates and the Canadian Housing Market

• In the early 2000s, the Bank of Canada reduced interest rates to deal with various causes of economic uncertainty in the marketplace, such as the events of 9/11 and an information technology stock price bubble.

• The low interest rates led to a large increase in residential investment spending, reflected in a surge of housing starts. Unfortunately, the housing boom eventually turned into too

much of a good thing.

ECONOMICS IN ACTION

Interest Rates and the Canadian Housing Market

• Between late 2008 and early 2009, interest rates fell and housing starts also fell. Why? Interest rates aren’t the only variable determining investment!

These were the years of the Great Recession, when many had lost their jobs. The Bank of Canada deliberately kept interest rates low to stimulate the sluggish economy, but people were still hesitant to buy homes.

ECONOMICS IN ACTION

Interest Rates and the Canadian Housing Market

Income-Expenditure Model

• Assumptions underlying the multiplier process: Changes in overall spending lead to changes in aggregate

output. The aggregate price level is fixed. The interest rate is fixed. Taxes, transfers, and government purchases are all zero. Exports and imports are both zero. There is no foreign

trade.

Planned Aggregate Spending and GDP

Planned aggregate spending is the total amount of planned spending in the economy.

AEPlanned = C + Iplanned

So: AEplanned= AC + MPC ∙ YD + Iplanned

Example: C= 300 +.6 YD , Iplanned=500

so: AEplanned= 800 + .6 ∙ YD = 800+.6 GDP∙

GDP = C + I (G=X=IM=0)YD = GDP (no taxes or transfer)

C = AC + MPC ∙ YD (consumption)

Planned Aggregate Spending and GDP

Income–Expenditure Equilibrium

• The economy is in income–expenditure equilibrium when aggregate output, measured by real GDP, is equal to planned aggregate spending.

• Income–expenditure equilibrium GDP is the level of real GDP at which real GDP equals planned aggregate spending.

Income–Expenditure Equilibrium• Call Y* the equilibrium level of real GDP (where AEplanned=Y)

Diagram: occurs where AE intersects the 45-degree line. Planned spending equals output, no unplanned changes in

inventory, production stays at its current level.

• When planned aggregate spending is larger than Y*, unplanned inventory investment is negative; there is an unanticipated reduction in inventories and firms increase production to rebuild inventories.

So when: AEplanned>Y then Iunplanned<0

• When planned aggregate spending is less than Y*, unplanned inventory investment is positive; there is an unanticipated increase in inventories and firms reduce production to limit inventory build-up.

So when: AEplanned<Y then Iunplanned>0

Income–Expenditure Equilibrium

Algebra behind the previous diagramAEplanned= A + MPC YD ∙ (A = autonomous C and I)

= 800 + .6 GDP ∙ (with no taxes or transfers YD=GDP)

Equilibrium: AEplanned= GDP

800 + .6 GDP = GDP∙solve for GDP:

GDP = 800/(1-.6) =2000 (=Y* in diagram)

Notice:equilibrium GDP = autonomous spending x multiplier

Multiplier = 1/(1-MPC) =1/(1-.6) =2.5

Effect of a Change in Autonomous spending• Say autonomous C rises or planned I rises by DA.

• Now: AEplanned = A + MPC GDP +∙ DA

Diagram? AE shifts up by DA (DA =400 in diagram) AEplanned >Y* (old equilibrium GDP)

inventories fall below planned levels, firms produce more, GDP is rising, incomes are higher, multiplier process underway!

Effect of a change in autonomous spending• Finding new equilibrium after rise in A? • Set AEplanned = GDP then solve for GDP:

A + MPC GDP +∙ DA = GDP

solving: GDP =(A+ DA) /(1-MPC) = (A+ DA) x Multiplier

Effect? GDP is higher by: DA x Multiplier

• Example: DA =400 and multiplier=2.5 so GDP is higher by 1000 (see diagram below: Y* rises by 1000)

The Multiplier

The Multiplier Process and Inventory Adjustment

The Paradox of Thrift

• In the paradox of thrift, households and producers cut their spending in anticipation of future tough economic times. Like a fall in autonomous spending. GDP falls immediately and still more via the multiplier

effect.

• These actions depress the economy, leaving households and producers worse off than if they hadn’t acted virtuously to prepare for tough times.

• It is called a paradox because what’s usually “good” (saving to provide for your family in hard times) is “bad” (because it can make everyone worse off).

ECONOMICS IN ACTION

Inventories and the End of a Recession

Summary

1. An autonomous change in aggregate spending leads to a chain reaction in which the total change in real GDP is equal to the multiplier times the initial change in aggregate spending.

The size of the multiplier, 1/(1 − MPC), depends on the marginal propensity to consume, MPC, the fraction of an additional dollar of disposable income spent on consumption.

2. The individual consumption function shows how an individual household’s consumer spending is determined by its current disposable income. The aggregate consumption function shows the relationship for the entire economy.

Summary

3. Planned investment spending depends negatively on the interest rate and on existing production capacity; it depends positively on expected future real GDP.

The accelerator principle says that investment spending is greatly influenced by the expected growth rate of real GDP.

Summary

4. Firms hold inventories of goods so that they can satisfy consumer demand quickly. Inventory investment is positive when firms add to their inventories, negative when they reduce them. Often, however, changes in inventories are not a deliberate decision but the result of mistakes in forecasts about sales. The result is unplanned inventory investment, which can be either positive or negative.

Actual investment spending is the sum of planned investment spending and unplanned inventory investment.

Summary

5. In income–expenditure equilibrium, planned aggregate spending, which in a simplified model with no government and no trade is the sum of consumer spending and planned investment spending, is equal to real GDP.

At the income–expenditure equilibrium GDP, or Y*, unplanned inventory investment is zero.

The Keynesian cross shows how the economy self-adjusts to income–expenditure equilibrium through inventory adjustments.

Summary

6. After an autonomous change in planned aggregate spending, the inventory adjustment process moves the economy to a new income–expenditure equilibrium.

The change in income–expenditure equilibrium GDP arising from an autonomous change in spending is equal to [1/(1 − MPC)] ×∆AE0.

• Marginal propensity to consume (MPC)

• Marginal propensity to save (MPS)

• Autonomous change in aggregate spending

• Multiplier• Individual consumption

function• Aggregate consumption

function• Planned investment

spending

• Accelerator principle• Inventory investment• Unplanned inventory

investment• Actual investment spending• Planned aggregate

expenditure• Income–expenditure

equilibrium• Income–expenditure

equilibrium GDP• Keynesian cross

Key Terms