The Multiplier and the
Consumption Function
Module 16
Spending
In 2009, the US Congress passed the American
Recovery and Reinvestment Act – a $787 billion
program to spark job growth and combat the
recession.
Why did economists think a stimulus package
would help the economy?
Spending
The Government Spends
Money that ends up in
someone’s pocket
That person spends some
of that money and it ends
up in someone else’s
pocket
And so on…
And so on…
Each $1 spent by the government would
produce some multiple of dollars earned and
spent by consumers
Spending
But spending can also
come from other sources –
including investment…
Figure 10.1 The Circular-Flow Diagram
Ray and Anderson: Krugman’s Macroeconomics for AP, First Edition
Copyright © 2011 by Worth Publishers
Spending
Suppose the housing construction industry spent an
additional $100 billion on new construction of homes:
1) That’s an additional $100 billion to GDP
2) That $100 billion goes to others who will spend some of it
3) Let’s say the people who get the $100 billion save $20 billion
and spend the rest
4) That’s $80 billion in more activity that goes into pockets as
profits or wages
5) Those people in turn save $16 billion and spend $64 billion
6) And so on…
The Multiplier
The initial $100 billion investment is called the
autonomous change in spending.
How much total increase to GDP should result from this
$100 billion autonomous change in spending?
We could add up all the rounds of spending…
Change in GDP = ($100 billion + $80 billion + 64 billion + …)
But this is an infinite series, and who has the time?
The Multiplier
Instead, we can calculate the multiplier (M) – a value by
which we can multiply the autonomous change in
spending to obtain the change in output:
ΔY = M x ΔAAS
Δ = change in
Y = output (GDP)
AAS = autonomous spending
The Multiplier
To determine the value of this multiplier, we need to
know what proportion of the money people receive
they will end up spending
We call this the marginal propensity to consume (MPC)
MPC =
Δ Consumer spending
Δ Disposable income
The Multiplier
Total spending would equal:
AAS + MPC (AAS) + MPC2(AAS) + MPC3(AAS)…
Or
AAS (1 + MPC + MPC2 + MPC3…)
And
(1 + MPC + MPC2 + MPC3…) =
1
=M
(1-MPC)
The Multiplier
In our example, people spent $80 billion of the
$100 billion, so:
MPC = 80/100 = .8
We can then use the formula for the multiplier:
M = 1/(1-MPC)
M = 1/(1-.8) = 1/.2 = 5
Total increase in GDP =
ΔY = M x ΔAAS = 5 x $100 Billion = $500 Billion
Spending and Saving
Notice in our example that whatever money was not
spent, was saved.
We can also calculate a marginal propensity to save (MPS)
MPS = Δ Consumer savings
Δ Disposable income
Spending and Saving
Since these represent the only two options for disposing
of income, we can say that:
MPC + MPS = 1
Which also means:
MPS = 1-MPC
So the multiplier = 1/(1-MPC) OR 1/MPS
Example
1. Data show that when consumers received an
additional $20 million in income, they put $5
million in the bank
a. Calculate the marginal propensity to consume
b. How much would output increase with an
autonomous aggregate spending increase of $30
million
Example
2. Suppose a $1 million business investment
generates a $2.5 million increase in GDP
a. Calculate the marginal propensity to consume
Household Consumption
How does household consumer spending relate
to household income?
There will be some spending, no matter what
income level – we call this autonomous
consumer spending
And then spending of additional income will be
governed by the MPC
Figure 16.1 Current Disposable Income and Consumer Spending for American Households in 2008
Ray and Anderson: Krugman’s Macroeconomics for AP, First Edition
Copyright © 2011 by Worth Publishers
The Consumption Function
An equation showing how an individual
household’s consumer spending varies with the
household’s disposable income
c = a + MPC × yd
Where:
c = consumer spending
a = autonomous consumer spending
yd = disposable income
Figure 16.2 The Consumption Function
Ray and Anderson: Krugman’s Macroeconomics for AP, First Edition
Copyright © 2011 by Worth Publishers
Aggregate Consumption Function
An equation showing how aggregate consumer
spending varies with aggregate disposable
income
C = A + MPC × YD
Where:
C = aggregate consumer spending
A = autonomous aggregate consumer
spending
YD = aggregate disposable income
Income Effect
• If you expect that your income will continue to
rise, you will spend more now than your
current income would otherwise indicate
• Permanent Income Hypothesis
– Milton Friedman
– Consumer spending is more dependent on
expectations of future income than of current
income
Effect of Expected Income
Incomes expected to rise:
Increase in autonomous spending
Incomes expected to fall:
Decrease in autonomous spending
Figure 16.4 Shifts of the Aggregate Consumption Function
Ray and Anderson: Krugman’s Macroeconomics for AP, First Edition
Copyright © 2011 by Worth Publishers
Wealth Effect
• Wealth
– accumulated savings and assets over time
– Affects consumer spending
– Increased aggregate wealth increases aggregate
spending
• Life-Cycle Hypothesis
– People plan their spending across their lifetimes
– Save more earlier, spend out of savings later
Investment Spending
• Investment spending also drives GDP and the
business cycle, though to a lesser extent than
consumer spending
• Recessions often start with declines in
investment spending
– Planned v. actual spending
– What affects investment spending?
Interest Rates
• The cost of borrowing money
• Particularly affects construction industry as
interest rates will be faced by both producers
and consumers
• Inverse relationship – as interest rates rise,
investment spending falls
Expected Growth in GDP
• If businesses expect sales to grow more in the
future, they will increase investment spending
in the present
– New production capacity
• If business expect slow growth, investment
spending declines
– maintain or replace obsolete production capacity
Inventories
• Businesses will often satisfy demand out of
inventories
• Higher than planned inventories can result from
lower than expected sales
– Unplanned inventory investment
– Increasing inventories could mean economy is slowing
Actual Investment Spending=
Planned investment spending + Unplanned inventory investment
Problems
For each event, explain whether the initial effect is a change in
planned investment spending or a change in unplanned
inventory investment, and indicate the direction of the change
1. An unexpected increase in consumer spending
2. A sharp rise in the cost of borrowing
3. A sharp increase in the economy’s growth rate of real GDP
4. An unanticipated fall in sales