Download Chapter 12: Aggregate Expenditure and Output in the Short Run

Chapter 12: Aggregate Expenditure and Output
in the Short Run
Yulei Luo
SEF of HKU
February 28, 2016
Learning Objectives
1. Understand how macroeconomic equilibrium is determined in
the aggregate expenditure model.
2. Discuss the determinants of the four components of aggregate
expenditure and de…ne the marginal propensity to consume
and the marginal propensity to save.
3. Use a 45 line diagram to illustrate macroeconomic
equilibrium.
4. De…ne the multiplier e¤ect and use it to calculate changes in
equilibrium GDP.
5. Understand the relationship between the aggregate demand
curve and aggregate expenditure.
Output and Expenditure in the Short Run
I
In this chapter, we explore the causes of the business cycle by
examining the e¤ect of ‡uctuations in total spending (i.e.,
aggregate expenditure) on real GDP (total production).
I
Aggregate expenditure (AE) The total amount of spending in
the economy: the sum of consumption, planned investment,
government purchases, and net exports.
I
(Conti.) During some years, AE increases about as much as
does the production of goods and services:
I
I
During other years, AE increases more than the production:
I
I
Most …rms sell about what they expected to sell and they will
remain production and employment unchanged.
Firms will increase production and hire more workers.
However, during some year, AE didn’t increase as much as
total production:
I
Firms cut back on production and laid o¤ workers.
The Aggregate Expenditure Model
I
Aggregate expenditure model A macroeconomic model that
focuses on the relationship between total spending and real
GDP, assuming the price level is constant.
I
It is used to study the business cycle involving the interaction
of many economic variables.
I
The key idea of AE model: In any particular year, the level of
GDP is determined mainly by the level of AE that have several
components.
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Economists began to study the relationship bw ‡uctuations in
AE and ‡uctuations in GDP during the Great depression of
the 1930s:
I
In 1936, John M. Keynes systematically analyzed this
relationship in his famous book (“The general theory of
Employment, Interest, and Money”) and identi…ed four
categories of AE that together equal to GDP (these are the
same four categories).
Aggregate Expenditure
I
AE = C + I + G + NX
(1)
1. Consumption (C ): Spending by HHs on G&S such as
furniture, food, etc.
2. Planned Investment (I ): Planned spending by …rms on capital
goods, such as machinery, buildings, etc. or by HHs on new
houses.
3. Government Purchases (G ): Spending by local, state, and
federal governments on G&S, such as building airport,
highway, and salaries of gov. employees.
4. Net Exports (NX ): Spending by foreign …rms and hhs on
G&S produced in the US minus spending by US …rms and
HHs on G&S produced in other countries.
The Di¤erence between Planned Investment and Actual
Investment
I
Notice that planned investment spending, rather than actual
investment spending, is a component of aggregate
expenditure.
I
The amount of that …rms plan to spend on investment can be
di¤erent from the amount they actually spend.
I
The reason is that we need to consider inventories:
I
I
Inventories: Goods that have been produced, but not yet sold.
Changes in inventories are included as part of investment
spending:
I
Assume that the amount businesses plan to spend on
inventories may be di¤erent from the amount they actually
spend.
I
(Conti.) Changes in inventories depend on sales of goods,
which …rms cannot always forecast with perfect accuracy.
I
E.g., an auto company may produce 15, 000 cars and expect to
sell them all. If it does sell all 15, 000, its inventories will be
unchanged, but if it sells only 10, 000 it will have an unplanned
increase in inventories.
I
Hence, for the economy as a whole, we can say that actual
investment spending (IS) will be greater (less) than planned IS
when there is an unplanned increase (decrease) in inventories.
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Actual investment will equal planned investment only when
there is no unplanned change in inventories.
Macroeconomic Equilibrium
I
Macroeconomic equilibrium is similar to microeconomic
equilibrium (demand=supply of a product), in which the
quantity of apples produced and sold will not change unless
the demand or supply of this good changes.
I
For the economy as a whole, macro equilibrium occurs where
total spending equals to total production, that is,
Aggregate Expenditure = GDP
Adjustments to Macro Equilibrium
I
Increases and decreases in AE cause the year-to-year
‡uctuations in GDP.
I
When AE is greater than GDP, inventories will decline, and
GDP and total employment will increase.
I
When AE is less than GDP, inventories will increase, and GDP
and total employment will decrease.
I
Only when AE equals GDP will the economy be in
macroeconomic equilibrium.
Adjustments to Macroeconomic Equilibrium
Just like markets for a particular product may not be in equilibrium
(quantity supplied may not equal quantity demanded at the current
price), the economy may not be in equilibrium.
If . . .
aggregate expenditure is
equal to GDP
aggregate expenditure is
less than GDP
aggregate expenditure is
greater than GDP
then . . .
and . . .
inventories are unchanged
the economy is in
macroeconomic equilibrium.
inventories rise
GDP and employment
decrease.
inventories fall
GDP and employment
increase.
Table 12.1
© Pearson Education Limited 2015
The relationship
between aggregate
expenditure and GDP
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Making The Effect of Unplanned Changes in Inventories
the
Connection
Firms like Apple don’t want to keep
too much inventory on hand. Not
only is it expensive, but technology
quickly becomes outdated.
Apple forecasts its sales each
month, and plans to have adequate
inventory to cover sales. If sales are
stronger than expected, it initially
covers the extra sales through falling
inventories.
• The falling inventories signal to
Apple that it should hire more
workers in order to increase
production.
© Pearson Education Limited 2015
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I
Economists forecast what will happen to each component of
AE. If they forecast that AE will decline in the future, that is
equivalent to forecasting that GDP will decline and that the
economy will enter a recession.
I
Individuals and …rms closely watch these forecasts because
‡uctuations in GDP can have dramatic e¤ects on wages,
pro…ts, and employment.
I
When economists forecast that AE is likely to decline and the
economy is headed for a recession, the gov. may implement
macro policies to head o¤ the decline in AE and avoid the
recession.
Components of Real Aggregate Expenditure
The table below shows the values of the components of expenditure
in 2012, with prices in 2009 dollars.
Expenditure Category
Real Expenditure
(billions of 2009 dollars)
Consumption
$10,518
Planned investment
2,436
Government purchases
2,963
Net exports
−431
Table 12.2
Components of real
aggregate expenditure, 2012
Clearly consumption is the largest portion, with investment and
government expenditures being roughly similarly sized.
Net exports were negative in 2012: the value of U.S. imports was
greater than the value of U.S. exports.
For the next several slides, we will examine each component in more
detail.
© Pearson Education Limited 2015
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Consumption
Consumption tends to follow
a relatively smooth, upward
trend; its growth declines
during periods of recession.
What affects the level
of consumption?
• Current disposable income
• Household wealth
• Expected future income
• The price level
• The interest rate
We will proceed by examining
how each of these affects the
level of consumption.
© Pearson Education Limited 2015
Figure 12.1
Real consumption
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Consumption
The …ve most important variables that determine the level of
consumption:
I
Current disposable income is the most important determinant
of consumption.
I
I
I
Disposable income (DI) is the income remaining to HHs after
paying the personal income tax and receiving gov. transfer
payments.
For most HHs, the higher (lower) their DI, the more (the less)
they spend.
Aggregate (macro) consumption is the total of the
consumption of US HHs. The main reason for the general
upward trend in consumption is that DI has followed a similar
upward trend.
I
(Conti.) Household wealth is the value of its assets minus the
value of its liabilities.
I
I
I
I
I
Assets include home, stock and bond holdings, and bank
accounts.
Liabilities include any loans that it owes.
When the wealth of HHs increases (decreases), consumption
increases (decreases).
Since shares of stock are an important component of HHs’
wealth, consumption should increase with stock prices.
A recent estimate of the e¤ects of changes in wealth on
consumption indicates a permanent one-dollar increase in
wealth induces 4 5 cents increase in consumption.
I
(Conti.) Expected future income: Most people prefer to keep
their consumption fairly stable and smooth over time, even if
their income ‡uctuates signi…cantly. Both current income and
expected future income need to be considered to determine
current consumption.
I
The price level: Changes in the price level a¤ect consumption
mainly through their e¤ect on HHs’wealth. As the price level
rises, the real value of HHs wealth declines and so will HHs
consumption.
I
(Conti.) The interest rate: When the interest rate (IR) is
high, the reward to saving is increased and HHs are likely to
save more and spend less.
I
I
Note that consumption depends on the real IR that corrects
the nominal IR for the impact of in‡ation.
Spending on durable goods (such as autos, one category of
consumption) is most likely to be a¤ected by the interest rate
because a high real IR increases the cost of spending …nanced
by borrowing.
The Consumption Function
I
Consumption function The relationship between consumption
spending and disposable income.
I
Marginal propensity to consume (MPC): The slope of the
consumption function: the amount by which consumption
spending increases when disposable income increases:
MPC =
I
change in consumption
∆C
=
.
change in disposable income
∆YD
We can also use the MPC to determine how much
consumption will change as income changes:
∆C = MPC
∆YD.
(2)
The Relationship between Consumption and National
Income
I
Shift to discuss the relationship between aggregate
consumption spending and GDP, rather than disposable
income because we are interested in using the AE model to
explain ‡uctuations in real GDP.
I
Note that GDP and national income are almost the same.
I
Note that
Disposable income = National income
Net taxes
(3)
where Net taxes=taxes minus gov transfer payments. Or,
rearranging the equation:
National income = GDP = Disposable income + Net taxes.
(4)
The Consumption Function
How strong is the relationship between
income and consumption?
Figure 12.2
The relationship
between consumption
and income: 1960-2012
As the graphs demonstrate, the answer is “very strong”. A straight
line (called the consumption function) describes this relationship
very well, suggesting that households spend a consistent fraction of
each extra dollar of real disposable income on consumption.
© Pearson Education Limited 2015
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Marginal Propensity to Consume
The graphs showed that consumers seem to have a relatively
constant marginal propensity to consume: the amount by which
consumption spending changes when disposable income changes.
This marginal propensity to consume (MPC) is the slope of the
consumption function, the relationship between consumption
spending and disposable income.
We can therefore estimate the MPC by estimating the slope of the
production function:
𝑀𝑀𝑀𝑀𝑀𝑀 =
For 2002-2003, we find:
Change in consumption
∆𝐶𝐶
=
Change in disposable income ∆𝑌𝑌𝑌𝑌
∆𝐶𝐶
$259 billion
=
= 0.97
∆𝑌𝑌𝑌𝑌 $266 billion
So if incomes rose $10 billion, we estimate consumption would rise
by $10 billion x 0.97 = $9.7 billion.
© Pearson Education Limited 2015
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The Relationship between Consumption and National Income
The table shows the relationship
between consumption and
national income for an imaginary
economy, keeping net taxes
constant.
As national income rises by
$2,000 billion…
… consumption rises by $1,500
billion.
So the marginal propensity to
consume for this economy is:
𝑀𝑀𝑀𝑀𝑀𝑀 =
∆𝐶𝐶 $1,500 billion
=
= 0.75
∆𝑌𝑌 $2,000 billion
Figure 12.3
© Pearson Education Limited 2015
The relationship
between consumption
and national income
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Income, Consumption, and Saving
By definition, disposable income not spent is saved. Therefore we
can write:
National income = Consumption + Saving + Taxes
Y=C+S+T
Any change in national income can be decomposed into changes in
the items on the right hand side:
∆Y = ∆C + ∆S + ∆T
We assume net taxes do not change, so ∆T = 0; then:
∆Y = ∆C + ∆S
Now divide through by ∆Y:
∆Y ∆C ∆S
=
+
∆Y ∆Y ∆Y
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Income, Consumption, and Saving
I
HHs either (1) spend their income, (2) save it, or (3) use it to
pay taxes. For the economy as a whole,
National income = Consumption + Saving + Taxes,
(5)
which means that
Change in national income = Change in consumption
(
+Change in saving + Change in tax
I
Using symbols, where Y represents national income (and
GDP), C represents consumption, S represents saving, and T
represents taxes,
Y = C + S + T and ∆Y = ∆C + ∆S + ∆T .
(7)
I
(Conti.) To simplify, we can assume that taxes are always a
constant amount, in which case ∆T = 0, so that:
∆Y = ∆C + ∆S.
I
Marginal propensity to save (MPS) The change in saving
divided by the change in income:
1=
∆S
∆C
+
or 1 = MPC + MPS
∆Y
∆Y
Planned Investment
Investment has increased over
time, but unlike consumption, it
has not increased smoothly,
and recessions decrease
investment more.
What affects the level of
investment?
• Expectations of future
profitability
• Interest rate
• Taxes
• Cash flow
We will proceed by examining
how each of these affects the
level of planned investment.
© Pearson Education Limited 2015
Figure 12.4
Real investment
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Planned Investment
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Expectations on future pro…tability
I
I
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Investment goods (equipment, o¢ ce buildings) are long-lived.
A …rm is unlikely to make a new investment unless it is
optimistic that the demand for its product will remain strong
for several years.
The optimism or pessimism of …rms is an important
determinant of investment.
I
(Conti.) The interest rate
I
I
I
I
Borrowing takes the form of issuing corporate bonds or
receiving loans from banks. A signi…cant fraction of
investment is …nanced by borrowing. HHs also borrow to
…nance most of their spending on new houses.
Because households and …rms are interested in the cost of
borrowing after taking into account the e¤ects of in‡ation,
investment spending depends on the real interest rate.
Holding the other factors that a¤ect investment spending
constant, there is an inverse relationship between the real
interest rate and investment spending:
A higher real interest rate results in less investment spending,
and a lower real interest rate results in more investment
spending.
I
(Conti.) Taxes
I
I
I
I
Firms focus on the pro…ts that remain after paying taxes.
A reduction in the corporate income tax on the pro…ts
increases the after-tax pro…tability of investment.
Investment tax incentives (it provides …rms with a tax
reduction when they spend on new investment goods) also
increase investment spending.
Cash ‡ow
I
I
I
The di¤erence between the cash revenues received by the …rm
and the cash spending by the …rm.
Most …rms use their own funds to …nance investment goods
instead of borrowing outside.
The largest contributor to CF is pro…t. The more pro…table a
…rm is, the greater its CF and the greater its ability to …nance
investment.
Government Purchases
Real government purchases
include purchases at all levels
of government: federal, state,
and local.
• This category does not
include transfer payments;
only purchases for which
the government receives
some good or service.
Government purchases have
generally, though not
consistently, increased over
time; exceptions include the
early 1990s (end of cold war)
and due to state and local
cutbacks after 2009.
© Pearson Education Limited 2015
Figure 12.5
Real government
purchases
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Net Exports
I
The price level in US relative to the price levels in other
countries: If prices in US increase more slowly than the prices
of other countries, the demand for US products increases
relative to other countries.
I
The growth rate of GDP in US relative to the growth rates of
other countries: When incomes (GDP) rise faster in US than
in other countries, US consumers’purchases of foreign G&S
will increase faster than foreign consumers’purchases of US
G&S.
I
The exchange rate between the dollar and other currencies:
An increase in the value of the US dollar will reduce exports
and increase imports.
Net Exports
Net exports equals exports
minus imports.
The value of net exports is
affected by:
• Price level in U.S. vs. the
price level in other countries
• U.S. growth rate vs. growth
rate in other countries
• U.S. dollar exchange rate
U.S. net exports have been
negative for the last few
decades. The value typically
becomes higher (less
negative) during a recession,
as spending on imports falls.
© Pearson Education Limited 2015
Figure 12.6
Real net exports
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Determinants of Net Exports
U.S. Net
Exports
will…
…because…
…U.S. price level
rises faster than
foreign price levels…
decrease
U.S. goods become more expensive
relative to foreign goods; so imports
rise and exports fall.
…slower…
increase
The opposite is true.
…U.S. GDP grows
faster than foreign
GDP…
decrease
U.S. demand for imports rises faster
than foreign demand for our exports.
…slower…
increase
The opposite is true.
…$US rises in value
relative to other
currencies…
decrease
Imports are cheaper, and our
exports are more expensive.
So imports rise and exports fall.
…falls…
increase
The opposite is true.
If…
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Making
the
Connection
The iPhone Is Made in China… or Is It?
When an iPhone is shipped from China
to the U.S., GDP statistics register a
$275 import from China to the U.S..
But iPhones are only assembled in
China; no Chinese firm makes any of the
iPhone’s components.
• Only 4% of the value of the iPhone
should be attributed to the assembly,
according to one study.
Pascal Lamy of the WTO: “The concept
of country of origin for manufactured
goods has gradually become obsolete.”
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The Important Role of Inventories
I
Whenever aggregate expenditure is less than real GDP, some
…rms will experience an unplanned increase in inventories.
I
If …rms don’t cut back on their production promptly, they will
accumulate excess inventories. As a result, even if spending
quickly returns to its normal levels, …rms will have to sell their
excess inventories before they can return to producing at
normal levels.
I
This possibility can explain why a brief decline in AE can
result in a fairly long recession. Hence, e¢ cient systems of
inventories control help make recessions shorter and less
severe.
The 45°-Line Diagram
Suppose in the whole
economy there is a single
product: Pepsi.
For the economy to be in
equilibrium, the amount of Pepsi
produced must equal the amount
of Pepsi sold.
Then any point on the 45° line
could be an equilibrium—like
points A or B.
At point C, the economy’s
inventories of Pepsi
are being depleted, and
production must rise.
At point D, inventories of Pepsi are
growing, so production must fall.
© Pearson Education Limited 2015
Figure 12.7
An example of a
45°-line diagram
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The 45°-Line Diagram (or Keynesian Cross)
We can apply this model to
a real economy, with real
national income (GDP) on
the x-axis, and real
aggregate expenditure on
the y-axis.
This model is also known
as the Keynesian cross,
because it is based on the
analysis of economist John
Maynard Keynes.
Only points on the 45° line
can be a macroeconomic
equilibrium, with planned
aggregate expenditure
equal to GDP.
© Pearson Education Limited 2015
Figure 12.8
The relationship between
planned aggregate expenditure
and GDP on a 45°-line diagram
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Determining the Macroeconomic Equilibrium
Any point on the 45° line could be an equilibrium; but how do we
know which one will be the equilibrium in a given year?
• To determine this, recall that when they receive additional income,
households consume some of it, and save some of it.
• The resulting consumption function tells us how much consumers
will spend (real expenditure) when they have a particular income
(real GDP).
This will determine Consumption (C) in the equation
Y = C + I + G + NX
Macroeconomic equilibrium simply means the left side (real GDP)
must equal the right side (planned aggregate expenditure).
• The trick is to find the “right” level of C. For that, we use the 45°
line diagram.
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Finding Macroeconomic Equilibrium—part 1
We start by placing
the consumption
function on the
diagram.
If there was no other
expenditure in the
economy, then the
macroeconomic
equilibrium would be
where the
consumption function
crossed the 45° line;
there, income (GDP)
equals expenditure.
Figure 12.9
© Pearson Education Limited 2015
Macroeconomic equilibrium
on the 45°-line diagram
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Finding Macroeconomic Equilibrium—part 2
But there are other
expenditures. We will
assume they are not
affected by income;
that they are predetermined.
Then we add the other
expenditures: planned
investment…
… government purchases…
… and net exports.
These are vertical shifts in
real expenditure, because
their values do not depend
on real GDP.
© Pearson Education Limited 2015
Figure 12.9
Macroeconomic equilibrium
on the 45°-line diagram
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Finding Macroeconomic Equilibrium—part 3
At last, we have
macroeconomic
equilibrium: the point at
which
1. Income equals
expenditure, i.e.
Y = C + I + G + NX
2. The level of
consumption is
consistent with the
level of income,
according to the
consumption function.
We call this top-most line
the aggregate expenditure
function.
© Pearson Education Limited 2015
Figure 12.9
Macroeconomic equilibrium
on the 45°-line diagram
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Adjustment to Macroeconomic Equilibrium
In this economy,
macroeconomic
equilibrium occurs
at $10 trillion.
What if real GDP were
lower, say $8 trillion?
• Aggregate expenditure
would be higher than
GDP, so inventories
would fall.
• This would signal firms
to increase production,
increasing GDP.
The reverse would occur if
real GDP were above $10
trillion.
© Pearson Education Limited 2015
Figure 12.10 Macroeconomic
equilibrium
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Recession on the 45°-Line Diagram
Macroeconomic equilibrium
can occur anywhere on the
45° line. Ideally, we would like
it to occur at the level of
potential GDP.
If equilibrium occurs at this level,
unemployment will be low—at the
natural rate of unemployment, or
the full employment level.
But for various reasons, this might
not occur. For example, maybe
firms are pessimistic and reduce
investment spending.
• Then the equilibrium will occur
below potential GDP—a
recession.
© Pearson Education Limited 2015
Figure 12.11 Showing a recession
on the 45°-line diagram
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A Numerical Example of Macroeconomic Equilibrium
The table below shows several hypothetical combinations of real
GDP and planned aggregate expenditure.
Real
GDP
(Y)
Consumption
(C)
Planned
Investment
(I)
Government
Purchases
(G)
Net
Exports
(NX)
Planned
Aggregate
Expenditure
(AE)
Unplanned
Change in
Inventories
Real GDP
Will …
$8,000
$6,200
$1,500
$1,500
− $500
$8,700
−$700
increase
9,000
6,850
1,500
1,500
−500
9,350
−350
increase
be in
equilibrium
10,000
7,500
1,500
1,500
−500
10,000
0
11,000
8,150
1,500
1,500
−500
10,650
+350
decrease
12,000
8,800
1,500
1,500
−500
11,300
+700
decrease
Note: The values are in billions of 2009 dollars
Table 12.3
Macroeconomic equilibrium
As real GDP changes, consumption changes but planned
investment, government purchases, and net exports stay constant.
Macroeconomic equilibrium can occur only at $10,000 billion;
otherwise, the unplanned change in inventories will cause firms to
change production and real GDP will change.
© Pearson Education Limited 2015
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The Multiplier E¤ect
I
Autonomous expenditure: Expenditure that does not depend
on the level of GDP.
I
I
Planned investment, gov. spending, and net exports are all
autonomous expenditures.
Note that consumption also includes an autonomous
component. E.g., if HHs decide to spend more of their
incomes and save less at every level of income there will be an
autonomous increase in consumption.
I
Multiplier: The increase in equilibrium real GDP divided by
the increase in autonomous expenditure.
I
Multiplier e¤ect: The process by which an increase in
autonomous expenditure leads to a larger increase in real GDP.
Summarizing the Multiplier E¤ect
I
The multiplier e¤ect occurs both when autonomous
expenditure increases and when it decreases.
I
I
The multiplier e¤ect makes the economy more sensitive to
changes in autonomous expenditure than it would otherwise
be.
I
I
I
For example, with an MPC of 0.75, a decrease in planned
investment of $100 billion will lead to a decrease in equilibrium
income of $400 billion.
Because of the multiplier e¤ect, a decline in spending and
production in one sector of the economy can lead to declines in
spending and production in many other sectors of the economy.
The larger the MPC, the larger the value of the multiplier.
1
The formula for the multiplier, 1 MPC
, is oversimpli…ed
because it ignores some real world complications, such as the
e¤ect that an increasing GDP can have on imports, in‡ation,
and interest rates. These e¤ects combine to cause the simple
formula to overstate the true value of the multiplier.
Autonomous and Induced Expenditures
You may have noticed that
a small change in planned
aggregate expenditure
causes a larger change in
equilibrium real GDP.
In our model, planned investment,
government purchases, and net
exports are autonomous
expenditures: their level does not
depend on the level of GDP.
• But consumption has both an
autonomous and induced
effect. So its level does depend
on the level of GDP, and this
produces the upward-sloping
Figure 12.12
AE line.
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The multiplier effect
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Autonomous and Induced Expenditures—cont.
An increase in an
autonomous expenditure
shifts the aggregate
expenditure line upward.
When this happens, real
GDP increases by more
than the change in
autonomous expenditures;
this is the multiplier effect.
• The value of the
increase in equilibrium
real GDP divided by the
increase in autonomous
expenditures is the
multiplier.
© Pearson Education Limited 2015
Figure 12.12
The multiplier effect
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The Multiplier Effect in Action
Initially, real GDP
rises by the amount
of the increase in
autonomous
expenditure. This
causes an increase
in real GDP, which
causes an increase
in production, which
causes an increase
in real GDP…
Table 12.4
The multiplier effect in
action
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Round 1
Round 2
Round 3
Round 4
Round 5
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Round
10
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Round
15
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Round
19
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Round n
Additional
Autonomous
Expenditure
(investment)
$100 billion
0
0
0
0
.
.
.
Additional
Induced
Expenditure
(consumption)
$0
75 billion
56 billion
42 billion
32 billion
.
.
.
Total Additional
Expenditure =
Total Additional
GDP
$100 billion
175 billion
231 billion
273 billion
305 billion
.
.
.
0
8 billion
377 billion
.
.
.
.
.
.
.
.
.
0
2 billion
395 billion
.
.
.
.
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0
1 billion
398 billion
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.
0
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0
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.
$400 billion
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Eventual Effect of the Multiplier
We cannot say how long this adjustment to macroeconomic
equilibrium will take—how many “rounds”, back and forth.
But we can calculate the value of the multiplier, as the eventual
change in real GDP divided by the change in autonomous
expenditures (planned investment, in this case):
∆Y
Change in real GDP
$400 billion
=
=
=4
∆I Change in investment spending $100 billion
With a multiplier of 4, each $1 increase in planned investment (or any
other autonomous expenditure) eventually increases equilibrium real
GDP by $4.
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Making The Multiplier in Reverse: the Great Depression
the
Connection
The multiplier can work in reverse
too, like it did during the Great
Depression of the 1930s.
Several events, including the
stock market crash of October
1929, led to reductions in
investments by firms.
Real GDP fell, so consumers cut
back on spending, prompting
firms to reduce production more,
so consumers spent even less…
Year
Consumption
1929
$781 billion
1933
$638 billion
Investment
Exports
Real GDP
Unemployment Rate
$124 billion
$40 billion
$1,056 billion
2.9%
$27 billion
$22 billion
$778 billion
20.9%
Note: The values are in 2009 dollars.
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Making
the
Connection
The Multiplier in Reverse—continued
The 45°-line diagram can
help to illustrate this
process.
• Aggregate expenditures
fell initially, due to the
decrease in investment.
• This prompted a
multiplied effect on
equilibrium real GDP.
Recovery from the Great
Depression took many
years; unemployment
remained above 10% until
the U.S. entered World
War II in 1941.
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The Multiplier and the Marginal Propensity to Consume
How can we know the eventual value of the multiplier?
• In each “round”, the additional income prompts households to
consume some fraction (the marginal propensity to consume).
The total change in equilibrium real GDP equals:
The initial increase in planned investment spending
= $100 billion
Plus the first induced increase in consumption
= MPC × $100 billion
Plus the second induced increase in consumption
= MPC × (MPC × $100 billion)
= MPC2 × $100 billion
Plus the third induced increase in consumption
= MPC × (MPC2 × $100 billion)
= MPC3 × $100 billion
Plus the fourth induced increase in consumption
= MPC × (MPC3 × $100 billion)
= MPC4 × $100 billion
And so on …
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A Formula for the Multiplier
This becomes the infinite sum:
Total change in GDP = $100 billion + MPC × $100 billion + MPC2
× $100 billion + MPC3 × $100 billion + MPC4 × $100 billion + …)
Which we can rewrite as:
Total change in GDP = $100 billion × (1 + MPC + MPC2 + MPC3
+ MPC4 + …)
by factoring out the initial $100 billion increase in investment.
Since MPC is less than 1, the expression in parentheses is:
1
1 − MPC
In our case, MPC = 0.75; so the multiplier is 1/(1-0.75) = 4. A $100
billion increase in investment eventually results in a $400 billion
increase in equilibrium real GDP.
The general formula for the multiplier is:
Multiplier =
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Change in equilibrium real GDP
1
=
Change in autonomous expenditur e 1 − MPC
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The Paradox of Thrift
I
In discussing the AE model, John Maynard Keynes argued
that if many households decide at the same time to increase
their saving and reduce their spending, they may make
themselves worse o¤ by causing aggregate expenditure to fall,
thereby pushing the economy into a recession.
I
The lower incomes in the recession might mean that total
saving does not increase, despite the attempts by many
individuals to increase their own saving.
I
Keynes referred to this outcome as the paradox of thrift
because what appears to be something favorable to the
long-run performance of the economy might be
counterproductive in the short run.
The Aggregate Demand Curve
I
When demand for a product increases, …rms will usually
respond by increasing production, but they are also likely to
increase prices. So far, we have …xed the price level (PL).
I
In fact, as we will see, increases (decreases) in the PL will
cause AE decrease (rise). There are 3 reasons for this inverse
relationship between changes in the PL and changes in AE.
I
1. (Conti.) A rising PL decreases consumption by decreasing the
real value of household wealth.
2. If the PL in US rises relative to the PLs in other countries, US
exports will become relatively more expensive and foreign
imports will become relatively less expensive, causing net
exports to fall.
3. When prices rise, …rms and HHs need more money to …nance
buying and selling. If the central bank doesn’t increase money
supply, the result will increase the IR and then reduce
investment as …rms and HHs borrow less to build new
factories, ect., and new houses, respectively.
I
Aggregate demand curve (AD) A curve showing the
relationship between the price level and the level of planned
aggregate expenditure in the economy, holding constant all
other factors that a¤ect aggregate expenditure.
The Effect of a Change in Price Level on Real GDP
Figure 12.13 The effect of a change in
the price level on real GDP
The diagrams show the effects described on the previous slide:
a. Increases in the price level cause AE and real GDP to fall.
b. Decreases in the price level cause AE and real GDP to rise.
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The Aggregate Demand Curve
Consequently, there is an
inverse relationship between
the price level and real GDP.
This relationship is known as
the aggregate demand
curve.
Aggregate demand (AD)
curve: A curve that shows
the relationship between the
price level and the level of
planned aggregate
expenditure in the economy,
holding constant all other
factors that affect aggregate
expenditure.
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Figure 12.14
The aggregate
demand curve
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Why Build a Numerical Model?
Graphical analysis of macroeconomic equilibrium can tell us the
qualitative changes that take place.
• But an equation-based model can allow us to make quantitative or
numerical estimates of what will occur.
Economists in universities, firms, and the government rely on
econometric models in which they statistically estimate the
relationships between economic variables.
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Aggregate Expenditure Equations
Based on the example in the text, we can generate the following
equations (changing the MPC so as to generate different results):
1. C = 1,000 + 0.65Y
Consumption function
2. I = 1,500
Planned investment function
3. G = 1,500
Government spending function
4. NX = −500
Net export function
5. Y = C + I + G + NX
Equilibrium condition
In using the model, researchers would estimate the parameters
of the model—like the MPC or the values of the autonomous
expenditure components like planned investment—using
statistical methods and years of observations of data.
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Solving the Model
The first four equations can be used to form the aggregate
expenditure function—the right hand side of the fifth equation.
The fifth equation is the essential “equilibrium condition”, representing
the effect of the 45°-line.
Substituting the first four equations into the fifth gives:
Y = 1,000 + 0.65Y + 1,500 + 1,500 − 500
Subtracting 0.65Y from both sides gives:
Y − 0.65Y = 1,000 + 1,500 + 1,500 − 500
Which simplifies to:
0.35Y = 3,500
Y=
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3,500
= 10,000
0.35
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General Aggregate Expenditure Equations
More generally, we could allow the parameters of the model to be
represented by letters.
1. C = C + MPC (Y )
Consumption function
2. I = I
Planned investment function
3. G = G
Government spending function
4. NX = NX
Net export function
5. Y = C + I + G + NX
Equilibrium condition
The letters with bars over them are parameters—fixed
(autonomous) values.
For example, C was 1000 in our example.
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Solving the General Aggregate Expenditure Equations
Solving now for equilibrium, we get
Y = C + MPC (Y ) + I + G + NX
Y − MPC (Y ) = C + I + G + NX
Y (1 − MPC ) = C + I + G + NX
Y=
C + I + G + NX
1
= (C + I + G + NX ) ×
1 − MPC
1 − MPC
The last equation makes clear that:
Equilibrium GDP = Autonomous expenditure × Multiplier
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