SECOND CANADIAN
EDITION
MACROECONOMICS
Paul Krugman | Robin Wells
Iris Au | Jack Parkinson
Chapter 11
Income and Expenditure
© 2014 Worth Publishers
WHAT YOU
WILL LEARN
IN THIS
CHAPTER
• 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
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 billion
First-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:
1
$10 billion x
1−𝑀𝑃𝐶
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 = 0.6
Multiplier = 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 =
1
1−𝑀𝑃𝐶
=
1
1−.6
= 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.
1
DY =
x DAE0
1−𝑀𝑃𝐶
• 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).
DY
Multiplier =
=
DAE0
1
1−𝑀𝑃𝐶
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
GDP = C + I
(G=X=IM=0)
YD = GDP (no taxes or transfer)
C = AC + MPC ∙ YD (consumption)
Planned aggregate spending is the total amount of planned
spending in the economy.
So:
AEPlanned = C + Iplanned
AEplanned= AC + MPC ∙ YD + Iplanned
Example:
so:
C= 300 +.6 YD , Iplanned=500
AEplanned= 800 + .6 ∙ YD = 800+.6 ∙GDP
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 diagram
AEplanned= A + MPC ∙YD
= 800 + .6 ∙GDP
(A = autonomous C and I)
(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.
Key Terms
• 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