Download Chapter 9: Introduction to Business Cycles

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Chapter 9: Introduction to Business Cycles:
Consumption and the Multiplier
J. Bradford DeLong
--Draft 1.0-1999-03-04: 6,906 words
Real GDP in the American economy grows at an average rate of some 2.5 percent
per year. The unemployment rate in the American economy fluctuates around an
average level of about 5.5 percent. In recent years the inflation rate in the U.S.
economy has averaged about 2 percent per year.
If chapters 4, 5, and 6 gave a complete picture of how the macroeconomy
behaved, economic growth would be smooth. Real GDP would grow by 2.5
percent per year--the rate of growth of potential GDP--year after year, not just on
average. The unemployment rate would remain steady at its natural rate of 5.5
percent. Inflation would be steady as well.
And this page would be the last page of this textbook.
But chapters 4, 5, and 6 do not give a complete picture. For growth is not at all
smooth. In 1982 real GDP was not 2.5 percent more but 2.1 percent less than in
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1981. The unemployment rate rose by 4.1 percentage points between 1979 and
1982--and again by 2.2 percentage points between 1989 and 1992. Inflation
reached its post-World War II era high in 1981, when the GDP deflator grew by
9.4%--and inflation has fallen since, so that in 1999 the GDP deflator grew by
only 2.2%.
The U.S. economy undergoes relatively large year-by-year fluctuations--in
unemployment, in production, and in prices--about its long run growth trend.
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For more than one hundred years economists have called these fluctuations
business cycles.
Economists divide business cycles into two parts. Economic expansions are the
times when output and employment are rising (and the unemployment rate is
usually falling). Recessions are the times when production and employment are
falling--and the unemployment rate is rising. An especially steep recession is
called a "depression." Politicians in office don't want to speak the word
"recession"--so they often speak in euphemisms: periods of "adjustment," "slow
growth," and so on. An expansion and the subsequent recession make up a
complete business cycle.
Sticky short-run prices
Models in which prices are "sticky".
Two key differences.
There are two key differences between the analysis of chapter 6--in which GDP
was always equal to potential output, and in which there were no business cycle
fluctuations--and the analysis of the rest of the book. First, in chapter six prices
were flexible. Any changes in supply and demand conditions produced shifts in
prices that restored the balance of supply and demand. That was what allowed
us to start our analyses by noting that actual GDP was and would remain equal
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to the economy's potential output.
The rest of this textbook is a sticky-price textbook.
From this point in the textbook on, prices are "sticky": they don't move freely and
instantaneously in response to changes in demand and supply. Instead,
businesses first expand or contract production in response to changes in demand
and cost, while prices remain fixed at predetermined levels.
Such "sticky prices" make a big difference.
What happens when prices are sticky?
For a preview of this difference, consider a situation like that at the very end of
chapter 6, in which a liquidity squeeze induced by central bank monetary policy
leads to a significant decline in the economy's money stock--in the amount of
wealth held in the form of readily-spendable purchasing power.
In the full-employment model.
In the full-employment model of chapter 6, such a liquidity squeeze has no impact
on the level of real GDP: prices will shift to keep demand for the factors of
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production equal to their supplies, and so real GDP will remain equal to
potential output:
Y  0
What impact will such a fall in the economy's money stock have on prices?
According to chapter 6, the quantity equation:
P
MV
Y
will continue to hold, so:
P 
V 
M
Y 
We can describe in words the process by which such a change in monetary
conditions--a reduction in the economy's nominal money supply, its nominal
stock of assets that can be easily used to purchase commodities--leads to no
change in the level of production but to a decline in the price level. As the
nominal supply of money falls, consumers and investors find themselves illiquid,
short of cash. They cut back on their spending as they try to devote a share of
their incomes to building-up their liquid cash reserves.
As firms see spending on their products fall, they cut their nominal prices--and
they cut the nominal wages that they can afford to pay workers. The workers
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don't care because they realize that the decline in nominal wages is not a decline
in real wages--that falling prices mean that their lower (nominal) wages buy the
same commodities as before. The business managers don't care because they
realize that the decline in nominal prices for their products is matched by an
equal decline in the wages and other costs they must pay.
Price
Level
When prices are flexible, a fall
in total nominal spending...
...induces an
equivalent fall
in prices...
If total nominal spending is constant,
the lower the price level, the higher is
total real spending...
...so that total real
spending remains
constant.
Real GDP
This process continues until the total nominal flow of spending is once again
proportioned to the economy's supply of liquid assets, with the price level lower
but with the level of real GDP unchanged, equal to potential output.
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In the sticky-price model.
But things are very different if prices are "sticky." As the nominal supply of
money falls, consumers and investors find themselves illiquid, short of cash.
They cut back on their spending as they try to devote a share of their incomes to
building-up their liquid cash reserves. They try to borrow from banks to build up
their stocks of liquid assets. Their borrowing increases demand for loanable
funds, and pushes real interest rates up. So not only does consumption fall, but
investment falls as well.
Graphic: Sticky Prices Mean That Shifts in Nominal Demand Do Shift Real GDP
Price
Level
When prices are fixed, a fall
in total nominal spending...
..has no effect
on prices...
If total nominal spending is constant,
the lower the price level, the higher is
total real spending...
...so that total real
spending falls.
Real GDP
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As firms see spending on their products fall, they do not cut their nominal prices-remember, prices are sticky. Instead, they respond to falls in demand by
reducing their production in order to avoid uncontrollable rises in unsold
inventory. Thus in the short run, to a first approximation, as long as the velocity
of money reamins constant (which it may well not be), the effect of a change in
monetary policy that reduces the money supply will be no change in the "sticky"
level of prices:
P  0
But a significant fall in real GDP:
Y 
V 
M
P 
We will develop the argument of the paragraphs above--in words, diagrams, and
algebra--at extended length over the next several chapters.
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Understanding the difference between full-employment and sticky-price models.
Price stickiness causes problems only if inflation expectations are not accurate.
Note that stickiness of prices not a serious problem if expectations of the change
of prices--expectations of inflation--turn out to be equal to actual inflation. If
people accurately foresee changes in the overall level of prices, then even "sticky"
prices will not keep the market system from producing a level of real GDP equal
to potential output. Prices and wages are sticky, but not that sticky. With
sufficient advance notice unions and businesses can strike wage bargains, and
businesses can adjust their selling prices, so that they can match their productive
capacity to demand and will not have to cut back on production and fire workers
in order to keep unsold inventory from exploding.
Both stickiness of prices in the short run and a failure to accurately foresee future
changes in the overall price level are needed to create the short-term year-byyear fluctuations in production and unemployment we call "business cycles."
[Box: Examples] An unanticipated change in government purchases
The text example above showed how a liquidity squeeze--a fall in the
economy's stock of liquid assets and a rise in real interest rates--leads
to a recession fall in production and rise in unemployment even
though such a liquidity squeeze would generate only a change in the
price level in the full-employment model of chapter 6. But why do
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other kinds of shocks--an unanticipated decline in government
purchases, say--generate a fall in production and a rise in
unemployment?
Follow the chain of cause and effect. A fall in government purchases
reduces total sales. With production remaining at its previous pace,
inventories build up. Firms react to rising inventories by cutting back
production, and firing workers.
In the full-employment model of chapter 6, a fall in government
purchases generates an increase in public saving, and so an expansion
in savings supply in the market for loanable funds. The interest rate
falls, and so investment (and net exports) expand. In equilibrium real
GDP remains equal to potential output.
Why doesn't this same full-employment chain of logic work when
prices are sticky, and firms react to shocks by cutting spending rather
than prices? Because as firms cut production and fire workers they cut
back on the incomes that they pay. And the fall in total incomes paid
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reduces the supply of loanable funds--so there is no fall in interest
rates to trigger higher investment (and a depreciated exchange rate,
and expanded net exports), and so there is nothing to offset the
reduction in government purchases and keep actual GDP from falling
beneath potential output.
What stops this sticky-price unemployment-generating logic from
working when prices are flexible? Suppose firms see that as a result of
the fall in government purchases demand is greater than supply, then
they respond by cutting their prices (and the wages they pay). But the
real, inflation-adjusted incomes received by households do not fall.
There is no reduction in the (real, inflation-adjusted) private supply of
loanable funds to offset the rise in public saving--and so there is a fall
in interest rates to trigger higher investment (and a depreciated
exchange rate, and expanded net exports) to keep real GDP from
falling below potential output.
[Box: Examples] An anticipated change in government purchases
Suppose that government purchases increases--as in the box above-but this time the increase is foreseen far enough in advance for wages
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and prices in the economy to adjust. Then the shift in government
spending will have the same impact as it had in chapter 6--an increase
in G, a rise in interest rates, a reduction in investment spending and
net exports.
Why? Because businesses will have foreseen the decline in government
purchases, and planned in advance to cut the prices they charge (and
the wages they pay) when government purchases fall. Since they cut
prices and not production, there are no fired workers and no declines
in (real, inflation-adjusted) incomes. Thus there is no reducation in the
(real, inflation-adjusted) private supply of loanable funds to offset the
rise in public saving--and so there is a fall in interest rates to trigger
higher investment (and a depreciated exchange rate, and expanded net
exports) to keep real GDP equal to potential output.
Sources of price stickiness.
Note that prices could be "sticky" for any of a number of reasons. Why don't
prices adjust quickly and smoothly to maintain production at full employment?
Why do businesses respond to fluctuations in demand first by hiring (or firing)
workers and accelerating (or shutting down) production lines? Why don't they
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response first by raising or lowering prices.
There are a number of possible reasons that have been sketched out by
economists. But there is great uncertainty about which reasons are truly
important. First, businesses and workers can find that changing prices or wages
is costly, hence prefer to keep prices and wages fixed as long as shocks are not
too large. Second, businesses and workers can lack information and so confuse
changes in total economy-wide spending with changes in demand for their
products. Third, the level of wages and prices may be a sociological as well as an
economic variable--determined as much by what values people think as "fair" as
by what values balance supply and demand. Fourth, workers and managers can
suffer from simple "money illusion" and neglect to take account of price-level
changes when assessing the impact of changes in wages or the flow of nominal
spending.
All these are potential powerful sources of price stickiness. Your course lecturer-and your section leader--may have strong views as to which of these is most
likely to be correct. I do not. I think that our knowledge is more limited--I at least
am not sure that the evidence is strong enough to provide clear and convincing
support for the position that any particular one of these sources of price and
wage stickiness is the most important.
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[Box: Details] Menu costs.
What are "menu costs"? Businesses and workers can find that changing
their prices or the wages they demand is costly. Hence they will prefer
to keep their prices and wages unchanged as long as the shocks
affecting the economy are relatively small, or rather as long as the
change that they would wish to make in their prices and wages (if it
was costelss to change them) is small. Such "menu costs" can
themselves arise for a large number of reasons: perhaps people wish to
stabilize commercial relationships by signing long-term contracts,
perhaps it is expensive to reprint a catalog, perhaps your customers
find frequent price changes annoying, perhaps other firms are not
changing their prices and what matters most to your firm is your price
relative to the price of your competitors.
[Box: Details] Price misperceptions.
Businesses and workers can lack complete information about the state
of the economy. They can be unsure whether a change in the flow of
spending on their products reflects a change in overall aggregate
demand, or a change in demand for their particular product which
they should respond to by changing how much they produce.
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[To be written]
[Box: Details] Fairness.
Consider yet another reason for prices and wages to be sticky. Are
workers really the flinty-eyed rational economic maximizers of our
theories? First, work effort and work intensity depends on whether
employees believe that they are being treated fairly. And for your boss
to cut your nominal wages is almost universally perceived as "unfair."
Wages depend on social norms that usually evolve slowly. Thus wages
are sticky by nature. And if wages are sticky, firms will find that it is
best for them to respond to shifts in demand by hiring and firing
workers rather than by changing prices and trying to pass those
changes in prices through to what they pay workers.
[To be written]
[Box: Details] Money illusion.
For yet another reason--and this is another theory in which workers
are not the flinty-eyed rational economic maximizers of economists'
theories--a significant body of evidence suggests that workers,
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consumers, and managers can confuse changes in nominal prices with
changes in real (that is, inflation-adjusted) prices. Firms may react to
higher (nominal) prices by thinking (falsely) that it is more profitable
to produce more, even though it isn't because their costs have risen in
proportion. Workers may react to higher (nominal) wages by searching
more intensively for jobs and working more overtime hours, even
though rises in prices have erased any increase in the real purchasing
power of the wage paid for an hour's work.
[To be written]
How to reconcile chapters 7 and 8 with the rest of the book.
How are we to reconcile the analyses of the rest of the book--in which changes in
government policy and the economic environment have effects not only on the
composition but the level of real GDP--with the analysis of chapter 6, in which
changes in government policy and in the economic environment affect the
composition but not the level of real GDP?
The conventional way is to say that the analyses of chapter 7 forward are "short
run" analyses and that the analysis of chapter 6 (and 5, and 4) are "long run"
analyses. In the short run prices are sticky, and so shifts in policy or the
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environment that affect the total flow of nominal spending affect the level of
output (but not the level of prices)--in the short run. In the long run prices are
flexible, and so shifts in policy or the environment that affect the total flow of
nominal spending affect the level of prices (but not the level of production)--in
the long run.
But when does the "long run" arrive? Do we change from living in the short run
of chapters 7 forward to the long run of chapter 6 on June 19, 2005? Clearly not.
The long run is an analytical construct. A change is "long run" if people see it
coming far enough in advance, or have had long enough to adjust to it to
renegotiate all their contracts and change their standard operating procedures.
And if those changes in contracts and standard operating procedures are also
foreseen that those affected by them have had time to adapt and adjust as well.
If expectations of inflation rates and the economic environment are accurate, then
even in the month-by-month or quarter-by-quarter context the world works as if
we were in the full-employment model of chapter 6. The long run is now. And if
expectations of inflation and of the economic environment are not accurate, then
the world may not work as if we were in the full-employment model of chapter 6
even if the shock or change to the economy took place five or ten years ago.
How fast it takes the long-run to arrive thus depends on how expectations of
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inflation and other variables in the economy are formed. Economists consider
three benchmark types of processes for forming expectations that fall along a
spectrum. Expectations can be static, expectations can be adaptive, or expectations
can be rational. The closer the processes for forming expectations are to the front
end of the spectrum, the less relevant is the full-employment model of chapter 6
to understanding the economy. The closer the processes for forming expectations
are to the back end of the spectrum, the more relevant is the full-employment
model of chapter 6.
[Box: Details] Static expectations
[To be written]
[Box: Details] Adaptive expectations
[To be written]
[Box: Details] Rational expectations
[To be written]
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The income-expenditure diagram
Higher aggregate demand boosts national product, which boosts employment
and incomes. Higher incomes give a further boost to consumption, which in turn
boosts aggregate demand. A shift in aggregate demand leads to an amplified
shift in national product because of the induced shift in consumption.
John Maynard Keynes was one of the first to stress the importance of this
multiplier process. In booms it induces an upward spiral in production (although
also an acceleration of inflation). In bad times it is a source of misery: a
downward shock is amplified as those thrown out of work cut back on their
consumption spending. The multiplier is quantitatively important because--as
we saw above--consumption spending is more than two-thirds of aggregate
demand. Hence any positive-feedback process by which higher spending leads
to higher production which leads to higher incomes which leads to higher
consumption spending has the potential to be quantitatively important.
The rest of this chapter sets out how the level of aggregate demand is determined
in the sticky-price context. The approach is a bottom-up approach: build up
planned expenditure on domestic products E out of the determinants of each of
its components, consumption spending C, investment spending I, government
purchases G, and net exports NX:
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E  C  I  G  NX
Building up planned expenditure.
The consumption function.
Consumption: spending by households on services such as haircuts, nondurable
goods such as food, and durable goods such as washing machines. As incomes
rise, consumption spending rises--thus increasing demand, and setting the
multiplier process in motion. But as we saw in chapter 6 consumption rises less
than dollar-for-dollar with total incomes.
The share of an extra dollar of income that is added to consumption spending is
the marginal propensity to consume, or MPC, denoted in equations by the letter
lower-case c. Note that the MPC depends on the kinds of changes that happen to
people's incomes. If changes in incomes are thought likely to be permanent, then
the marginal propensity to consume will be high: a $1 increase in incomes will
lead to an increase in consumption of about 80 cents. But if changes in income are
thought likely to be temporary, then the marginal propensity to consume will be
low: a $1 increase in incomes will lead to an increase in consumption of only 30
cents or so.
Transitory increases in income have only small effects on consumption because
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people seek to "smooth out" their consumption spending--most people feel it's
better to spend gradually over a year or a decade than to spend nearly all of their
resources at the beginning, and then nearly starve for the rest of the period. But
things are complicated because what looks like consumption smoothing from a
consumer's perspective can look like a great lumping-together of expenditures
from an economist's perspective. For example, consider a consumer who buys a
car to last for 10 years when her income goes up. Her marginal propensity to
consume may be more than 100 percent in the short run, yet from her perspective
she is smoothing her consumption because she will be "consuming" the car for a
long time to come. Even an expensive vacation taken now can be thought of as a
way of smoothing out consumption: the memories--and the pleasure they give-last for a long time.
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T he Ma r gi na l Pr ope ns i t y t o Cons um e
Consumpt i on Spendi ng
$8, 000
$6, 000
$4, 000
Slope = Marginal
Propensity to Consume
$2, 000
$0
$0
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
Nat i onal I ncome
For reasonably long-lasting shifts in the level of income, the MPC it is roughly
about 0.6. That is, 60 cents of every extra income dollar shows up as higher
consumption.
The consumption function is the mathematical relationship that describes the
dependence of consumption spending on economy-wide after-tax incomes, equal
to one minus the tax rate times the level of real GDP, (1-t) x Y:
C  C((1  t)Y)  c0  c(1  t)Y
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Consumption Function Machine
Autonomous
Consumption
MPC
Income
Consumption
Consumption C has two parts: a baseline level of autonomous consumption (c0)
which is independent of the current level of national income; and additional
consumption that does depend on the level of national income and is equal to the
product of after-tax incomes ((1-t) x Y) and the marginal propensity to consume
(c).
[Figure: Consumption as a Function of After-Tax Income]
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Gross
Domes tic
Produc t (GDP)
($7,254 billion)
Deprec iation
($826
billion)
Net Personal
Tax es ($456
billion)
Gross
National
Produc t (GNP)
($7,247 billion)
Personal
Inc ome
($5,777 billion)
Net
National
Produc t (NNP)
($6,421 billion)
Disposable
Inc ome
($5,321 billion)
Net Inc ome
Paid to Foreigners
for U.S. Operations
($7 billion)
Indirect Bus ines s
Tax es, and Earnings
Retained by Corporations
($644 billion)
Private
Saving
($396
billion)
Consumption
Spending
($4.925 billion)
Other components of planned expenditure.
The determinants of the other components of planned expenditure on domestic
products are familiar from chapter six.
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Com pone nt s of A ggr e ga t e De m a nd i n
1 9 9 5 ( bi l l i ons of 1 9 9 2 dol l a r s )
$6, 740
$7, 000
$6, 000
$5, 000
$4, 578
$4, 000
$3, 000
$2, 000
$1, 260
$1, 010
$1, 000
$0
Consumption
Government
- $108
Purchases Net Exports
- $1, 000
Investment
Gross
Domestic
Product
The amount of investment spending that firms, home builders, and others plan
on undertaking is I (and is itself a function of the interest rate, although that is a
subject for the next chapter):
I  I(r)  I0  r
[Figure: Investment as a Subject of the Interest Rate]
The amount of government purchases is set by the Congress and the President:
GG
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The I ncom e- Ex pendi t ur e Di agr am : Gov er nm ent P ur chases
Planned Expenditure
(alternatively,
Aggregate Demand)
$8, 000
Aggr egat e Demand
(or Planned Ex penditure)
$6, 000
G+ I
$4, 000
G+ I + NX
$2, 000
Gov er nment Pur chases
$$-
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively, National Product or GDP)
G: Government purchases
I: Investment spending
NX: Net ex ports
C: Consumption spending
Aggregate Demand = C + I + G +NX
Net exports are a function of the real exchange rate , and the levels of real GDP
or national income, both domestic Y and foreign Yf.
NX  X( ,Y f )  IM(Y)  X 0  xY f    Y
[Three panel figure: Net exports as functions of the exchange rate, foreign
GDP, and domestic GDP]
And we can substitute out the exchange rate by using the interest-rate equation
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for the determination of the exchange rate as a function of the gap between the
home real interest rate r and the foreign real interest rate rf:
   0  (r  r f )
Into the equation determining the level of net exports:
NX  X( 0 ,(r  r f ),Y f )  IM(Y )  X0  xY f   ( 0   (r  r f )) Y
[Two panel figure: Exchange rate as a function of the interest rate differential;
and net exports as a function of the exchange rate.
We can substitute the determinants of each component of planned expenditure
on domestic products for each component:
E  c0  c(1  t)Y  I  G  X0  xY f   ( 0   (r  r f )) Y
And then regroup in order to classify things that might affect planned
expenditure on domestic products into six: (i) the level of real GDP or national
income [Y, multiplied by the marginal propensity to spend c*=c-ct+)], (ii) the level
of investment [I], (iii) the level of government purchases [G], (iv) the domestic
real interest rate as it affects the exchange rate and thus net exports [r, multiplied
by  x ], (v) conditions abroad that affect net exports [basic export demand X0,
foreign exchange speculators views , the level of production abroad xYf, or the
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level of foreign interest rates rf], and (vi) consumers' optimism or pessimism
about the future [c0]:
E  c(1  t)  Y  I  G  r  X 0   0  xY f  r f  c0 
[Figure: Chain of Causation: Determinants of Planned Expenditure]
Planned expenditure and national income.
The income-expenditure diagram.
The most straightforward way to draw out the implications of this bottom-up
approach to understanding planned expenditure on domestic products is to
draw a diagram, the income-expenditure diagram, sometimes called the
Keynesian cross. On the vertical axis we plot the value of planned expenditure. On
the horizontal axis we plot the value of national income (or real GDP: at this level
of aggregation we neglect the NIPA-definitional differences between the two).
[Figure: the income-expenditure diagram]
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T he I nc om e - Ex pe ndi t ur e Di a gr a m ( f or
1 9 9 6 ; i n Bi l l i ons of Dol l a r s )
Planned Expenditure
(alternatively, Aggregate Demand)
$10, 000
$8, 000
Aggr egat e demand
as a f unct i on of
Nat i onal I ncome
Equi l i br i um Poi nt
$6, 000
$4, 000
$2, 000
$2, 000
$4, 000
$6, 000
$8, 000
National Income (alternatively, National Product or GDP)
$10, 000
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Graphic: Cause and Effect in the Multiplier Process
An initial shock to demand
raises total spending...
Higher spending
raises production...
Higher production
raises incomes...
And higher
incomes raise
total spending
still further.
The planned expenditure line.
On this income-expenditure diagram plot planned expenditure on domestic
products as a function of the level of national income. This planned expenditure
line intercepts the y-axis at a positive value that depends on the parameters of
the model, and on the values of other variables--r, G, rf, and so forth--other than
the level of national income, or real GDP. Changes in the values of these other
variables, or in most of the parameters of the model, will shift this planned
expenditure line up or down.
Start at that spot on the horizontal axis corresponding to some possible value of
GDP,or national income. Look upward until you reach the planned expenditure
line. That vertical height is the level of planned expenditure corresponding to
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that level of national income: the level of total spending people in the economy
would plan to undertake if their level of national income were that given by the
value on the x-axis.
[Figure: income-expenditure diagram, the planned expenditure line]
T he I nc om e - Ex pe ndi t ur e Di a gr a m ( f or
1 9 9 6 ; i n Bi l l i ons of Dol l a r s )
Planned Expenditure
(alternatively, Aggregate Demand)
$10, 000
$8, 000
Aggr egat e demand
as a f unct i on of
Nat i onal I ncome
Equi l i br i um Poi nt
$6, 000
$4, 000
$2, 000
$2, 000
$4, 000
$6, 000
$8, 000
National Income (alternatively, National Product or GDP)
The higher national income, the higher aggregate demand.
$10, 000
Chapter 7
32
The marginal propensity to spend
This planned expenditure line has a positive slope, but a slope less than one. In
fact, the slope of the planned expenditure line, the marginal propensity to spend
[MPS] is:
MPS  c*  c(1 t)  
Each one dollar increase in national income Y carries with it an increase in
planned expenditure of c* = c(1-t) - . A one dollar increase in national income or
real GDP carries with it an increase in imports of --which reduces planned
expenditure on domestic products by reducing net exports--but also an increase
in consumption spending: a one-dollar increase in national income increases
after tax incomes by (1-t) dollars, one minus the tax rate, and leads to an increase
in consumption spending by (1-t) x c, by the increase in after-tax incomes times
the marginal propensity to consume.
The larger the marginal propensity to consume, the steeper the slope of this
planned expenditure line. The higher the tax rate, the shallower the slope of this
planned expenditure line. And the higher the marginal propensity to import ,
the shallower the slope of this planned expenditure on domestic products line.
Because the marginal propensity to consume is less than one, the tax rate is zero
or greater, and the marginal propensity to import  is greater than zero, the
Chapter 7
33
marginal propensity to spend c* and thus the slope of the planned expenditure
line will be less than one.
We often find it convenient to simplify the expression of the planned expenditure
on domestic products line. The most radical simplification simply sets forth:
E  A c* Y
As the equation for the planned expenditure line. With the marginal propensity
to spend c* equal to:
c*  c(1  t)   
And with the level of autonomous spending A set equal to everything else:
A      r  xY f  r f   c0  I0  G  X 0   0 
Chapter 7
34
Planned Expenditure
(alternatively,
Aggregate Demand)
Autonomous Spending and the
Income-Expenditure Diagra
$8, 000
$6, 000
$4, 000
$2, 000
Aut onomous Spendi ng
$$-
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively , National Produc t or GDP)
This equation is a short version, hiding all the details, of the longer equation for
the determination of planned expenditure above. E--plotted on the y-axis--stands
for planned expenditure. Y is national income; c* is the marginal propensity to
spend. And A stands for autonomous spending: what aggregate demand would
be if national income were to be equal to zero (which it never is).
[Figure: Planned Expenditure Line on Income-Expenditure Diagram]
Chapter 7
35
T he I nc om e - Ex pe ndi t ur e Di a gr a m ( f or
1 9 9 6 ; i n Bi l l i ons of Dol l a r s )
Planned Expenditure
(alternatively, Aggregate Demand)
$10, 000
$8, 000
Aggr egat e demand
as a f unct i on of
Nat i onal I ncome
Equi l i br i um Poi nt
$6, 000
$4, 000
$2, 000
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively, National Product or GDP)
[Box: Examples] Calculating the marginal propensity to spend.
[To be written]
[Box: Examples] Calculating the level of autonomous spending
[To be written]
[Box: Examples] Things that change the marginal propensity to spend.
[To be written]
[Box: Examples] Things that change the level of autonomous spending
Chapter 7
36
[To be written]
Equilibrium
Because the slope of the planned expenditure on domestic products line is less
than one, there will be a level of national income at which the planned
expenditure line crosses a 45 degree diagonal line drawn up and to the right
from the bottom-left origin of the income-expenditure diagram. At this point
planned expenditure is equal to national income and real GDP--and by the
circular flow principal real GDP and national income are equal to actual
expenditure, to total aggregate demand.
When planned expenditure is equal to actual expenditure, is equal to aggregate
demand, then the income-expenditure diagram is in equilibrium: there are no
forces pushing for an immediate expansion or contraction of the level of national
income, real GDP, and aggregate demand.
[Income-expenditure diagram: Equilibrium is where the curves cross]
Chapter 7
37
T he I nc om e - Ex pe ndi t ur e Di a gr a m ( f or
1 9 9 6 ; i n Bi l l i ons of Dol l a r s )
Planned Expenditure
(alternatively, Aggregate Demand)
$10, 000
$8, 000
Aggr egat e demand
as a f unct i on of
Nat i onal I ncome
Equi l i br i um Poi nt
$6, 000
$4, 000
$2, 000
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively, National Product or GDP)
Equilibrium and inventory adjustment.
In equilibrium.
On the income-expenditure diagram the economy is always on the plannedexpenditure line. When the economy is also on the 45-degree line, planned
expenditure is equal to national income or real GDP, and is by the circular flow
principal equal to actual expenditure and aggregate demand.
If the economy is not on the 45-degree line, then planned expenditure is not
Chapter 7
38
equal to actual expenditure. Then there is either excess supply or excess demand
for the goods produced by businesses. Either the flow of production exceeds
aggregate demand, inventories are building up, and firms are about to cut
production and lay off workers; or demand exceeds production, inventories are
falling, and firms are about to expand production and hire.
Inventory Investment in the 1990s
(Billions of Dollars per Year)
$80
$60
Inventory investment
strongly negative: aggregate
demand larger than national
product
$40
$20
Average
$0
Inventory investment
strongly positive: national
product ahead of aggregate
demand
-$20
-$40
199 0
199 1
199 2
199 3
199 4
199 5
199 6
The circular flow principle states that every expenditure is someone's income,
and every piece of income is spent: either spent on consumption, taxed and spent
by the government, or saved, loaned out to an individual or firm and then used
Chapter 7
39
to finance investment spending or net exports. Whenever aggregate demand is
less than national income, some people are planning to save and spend less than
they earn. Some firms are producing more goods than they can sell and are
losing money. Their behavior will have to change before (or after) they go
bankrupt. And when it changes, national income and aggregate demand will
match.
Goods Market Equilibrium and the
Income-Expenditure Diagram
Planned Expenditure
(alternatively,
Aggregate Demand)
Goods market equilibrium
$8, 000
Aggregate Demand
(or Planned Expenditure)
Ri si ng
i nv ent or i es
$6, 000
$4, 000
Fal l i ng
i nv ent or i es
$2, 000
I ncome = Ex pendi t ur e
$$-
$2, 000
$4, 000
$6, 000
$8, 000
National Income (alternatively , National Produc t or GDP)
$10, 000
Chapter 7
40
Inventory adjustment: planned expenditures high.
What happens if the economy is not in goods-market equilibrium?
Suppose planned expenditures add up to more than national income or real
GDP. Then businesses are selling more than they are making. Inventories fall.
Some businesses respond to the fall in inventories by boosting prices, trying to
earn more profit per good sold. But the bulk of businesses respond to the fall in
inventories by expanding production to match demand. They hire more workers.
Production, and real GDP, and national income expand.
[Figure: income-expenditure diagram starting from falling inventories]
Chapter 7
41
I nc om e - Ex pe ndi t ur e Di a gr a m
Planned Expenditure
(alternatively,
Aggregate Demand)
$8, 000
New
Ex pendi t ur e
I ni t i al
Ex pendi t ur e
$6, 000
$4, 000
$2, 000
$$-
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively , National Produc t or GDP)
Suppose that businesses see inventories fall and boost production to equal last
month's planned expenditure. Would such an increase bring the economy back
into goods-market equilibrium, with planned expenditure equal to national
income and GDP? No. To boost production, firms must hire workers. When they
hire workers, they pay more in wages. When they sell more products, they earn
more in profits. Thus households' incomes rise. And when incomes rise, total
expenditure rises as well. The increase in production and income generates a
further expansion in aggregate demand.
Chapter 7
42
After production has increased by the initial gap between aggregate demand and
national income, the economy is not in equilibrium. Inventories will still be
falling. Hiring more workers has increased production, yes. But hiring more
workers has also boosted total incomes, and increase planned expenditure.
Production will have to expand by a multiple of the initial gap in order to
stabilize inventories.
[Figure: income-expenditure diagram: multiplier]
The process comes to an end--the economy finds itself in equilibrium, with
planned expenditure equal to national income and no pressure to expand or
contract employment--only when both have risen to the level at which the
planned expenditure line crosses the 45-degree income-equals-expenditure line.
Inventory adjustment: planned expenditures low.
The same process works in reverse if planned expenditure is below national
income. The circular flow principle tells us that every piece of expenditure
becomes someone's income, and every piece of income will be spent--spent on
consumption, taxed and spent by the government, or saved, that is, loaned out to
an individual or firm and then used to finance investment spending or net
exports.
Chapter 7
43
Production Larger than Sales
Incomes
Production
Consumers,
Investors,
Government
Businesses,
Producers
Unplanned
“investment”
in
Sales of
inventories Goods and
Services
NIPA Expenditures
Whenever planned expenditure is less than national income, some people will be
planning to save and spend less than they earn. And some firms will be
producing more goods than they can sell and will lose money. Their inventories
will rise as unsold goods pile up in stores, factories, and along distribution
channels. These firms' behavior will have to change.
[Figure: income-expenditure diagram starting from rising inventories]
Inventories rise, firms cut production--but the cutback causes demand to fall and
inventories to rise further.
After production has fallen by the initial gap between planned expenditure and
Chapter 7
44
national income, the economy is not in equilibrium. Inventories will still be
rising. Firing more workers has decreased production, yes. But firing workers
has also reduced total incomes, and decreased planned expenditure.
Production will have to fall by a multiple of the initial gap in order to stabilize
inventories.
The process comes to an end--the economy finds itself in equilibrium, with
planned expenditure equal to national income and no pressure to expand or
contract employment--only when both have fallen to the level at which the
planned expenditure line crosses the 45-degree income-equals-expenditure line.
[Box: Details] How fast does the economy move to equilibrium?
Note that there is nothing to force the economy to be in short-run
equilibrium in the goods market. Total expenditure can exceed GDP
and national income, and inventories can fall, for as long as a year.
There are strong forces pushing the economy toward short-run
equilibrium: businesses don't like to lose money by producing things
that they cannot sell or by not having things on hand that they could
sell. But it takes at least months, usually quarters, and possibly even
more time for businesses to expand or cut back production.
[Box: Examples] Inventory investment and planned expenditure in recent business cycles
Chapter 7
45
[To be written]
[Box: Details] A picky point.
The economy can be out of equilibrium, with planned expenditure
either higher or lower than national income and GDP, with inventories
falling or rising. Yet by definition of the circular flow, economy-wide
actual total expenditure--synonymous with aggregate demand--always
equals national income or GDP.
Isn't this a contradiction?
The answer is that statisticians who compile the national income and
product accounts (NIPA) define "actual expenditure" in a peculiar
way.
When production is greater than spending and inventories pile up
unexpectedly, the statisticians say the producing company has made
an "expenditure," has made an investment in increasing its inventory.
Suppose Mammoth Motors produces an extra 100,000 cars, valued at
$15,000 each, which it fails to sell. Mammoth thus has the unpleasant
surprise of seeing its inventory rise by 100,000 cars: an unexpected
inventory increase of $1.5 billion.
Chapter 7
46
For Mammoth this is a disaster--it spent a huge sum making things it
could not sell. But NIPA statisticians record this as an "expenditure" by
Mammoth: an investment in inventories of $1.5 billion.
Never mind that Mammoth certainly did not want to make this
"investment." The NIPA system is set up to call all changes in every
business's inventory an "expenditure" by that business, so that the
circular flow principle holds, and (save for accounting definitions and
the statistical discrepancy) national income and GDP have to be equal
to actual expenditure--planned plus unplanned.
The multiplier.
The magnitude of the multiplier.
Changes in autonomous spending.
Suppose that something happens to change the level of planned expenditure for
each different possible level of national income. Such changes have a large
number of potential causes. Anything that affects the level of A in the simplified
planned-expenditure equation:
E  A c* Y
Chapter 7
47
And A is affected by a lot of things:
A      r  xY f  r f   c0  I0  G  X 0   0 
Anything--that affects the level of autonomous spending A affects the intercept
and position of the planned expenditure line. Maybe government purchases
changed. Maybe foreign interest rates rose.
What would then happen to the equilibrium level of national income and GDP?
An upward shift in the planned expenditure line would increase equilibrium
national income. A downward shift would decrease the level of national income
at equilibrium where inventories are neither rising nor falling. The first thing to
happen in response to an upward shift in the planned expenditure line would be
that planned expenditure--at the prevailing level of production, national product,
and national income--would be suddenly larger than national product.
Businesses would find themselves selling more than they were making. Their
inventories would fall.
In response, businesses would boost production to try to keep inventories from
being exhausted. Production would expand. How much production would
expand depends on the magnitude of the initial change in autonomous spending,
and the value of the multiplier.
Chapter 7
48
T he Multiplier
Planned Expenditure
(alternatively, Aggregate Demand)
$10, 000
New Equi l i br i um
$8, 000
$6, 000
Change in another
component of demand
$4, 000
Change
Ol d Equi l i br i um in equilibrium
national
income
$2, 000
$$-
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively, National Product or GDP)
The value of the multiplier.
The slope of the planned expenditure line--c*, the MPS, the marginal propensity
to spend--is important because it determines the size of the multiplier: the
steeper the aggregate demand line, the greater the multiplier. And it is the
multiplier that can amplify small shocks to spending patterns into large changes
in total production and incomes.
The income-expenditure is the quickest way to see how small changes in
Chapter 7
49
autonomous spending are amplified by changes in consumption spending into
large shifts in the equilibrium level of national income or GDP.
[Figure: income-expenditure diagram and the multiplier]
T he Mul t i pl i e r
Planned Expenditure
(alternatively,
Aggregate Demand)
New Aggregate Demand
New Equi l i br i um
Old Equilibrium
Old Aggregate Demand
$8, 000
$6, 000
Change in
autonomous
spending A
$4, 000
Change in national
income equals
change in autonomous
spending
A
1- c
$2, 000
$$-
$2, 000
$4, 000
$6, 000
$8, 000
$10, 000
National Income (alternatively, National Product or GDP)
Any shift in the planned expenditure line shifts the level at which national
income and aggregate demand are equal by a multiple of the initial shift in
autonomous spending. Take the shift in autonomous spending A and divide it
by 1-c* (1 minus the marginal propensity to spend). You then have the change in
equilibrium national income:
Chapter 7
50
Y 
A
A

1  c * 1  c  tc  
The factor 1/(1-c*) is the multiplier: it multiplies the upward shift in the planned
expenditure line into a change in the equilibrium level of real GDP, national
income, and aggregate demand.
[Effect on excess demand of a $1 change in national income]
Why 1/(1-c*)? Think of it this way. The marginal propensity to spend--c*--(1-t)c --is the slope of the planned expenditure line. A $1 increase in national income
raises the equilibrium level of planned expenditure by $1, and it raises the level
of planned expenditure by $c. Thus a $1 increase in the level of national income
closes $(1-c) of the gap between planned expenditure and national income. Thus
to close the full initial gap $A between planned expenditure and national
income, the equilibrium level of national income needs to increase by A/(1-c*).
Changing the multiplier.
Fiscal automatic stabilizers.
One factor tending to make the multiplier smaller than it would otherwise be is
the government's fiscal automatic stabilizers. The government doesn't simply levy
lump-sum taxes of a total amount T on the economy. Instead the government
Chapter 7
51
imposes roughly proportional (actually slightly progressive) taxes on the
economy, so that government tax collections are roughly equal to a tax rate t
times the level of GDP Y: the total tax take equals t x Y.
This means that the government collects more in tax revenue when GDP is
relatively high--and this collection of extra revenue dampens swings in after-tax
income and thus reduces consumption. Similarly, the government collects less in
tax revenue when GDP is relatively low--thus after-tax income is higher than
under lump-sum taxes, and the higher after-tax incomes boost consumption.
Because the fall in consumption is smaller, the multiplier is smaller. Disturbances
to spending are not amplified as much as they used to be. And so shocks to the
economy tend to cause smaller business cycles.
The automatic workings of the government's tax system (and, to a lesser extent,
its social welfare spending programs) function as an automatic stabilizer reducing
the magnitude of fluctuations in real GDP and unemployment. The multiplier in
the presence of a proportional tax system is:
Y
1
1


A 1  c * 1  c  tc  
While if the government levied only lump-sum taxes, the value of the multiplier
would be:
Chapter 7
52
Y
1
1


A 1  c * 1  c  
How large are these fiscal automatic stabilizers in the U.S. today:? When national
product and national income drop, income tax and social security tax collections
fall automatically. Thus, the fall in consumers' disposable income is only twothirds as great as the fall in national income and the fall in consumption is only
two-thirds as large as it would be in the absence of automatic stabilizers. In other
words, the MPC in response to a change in national income is smaller than it
used to be because of this cushioning effect of the tax system.
Openness and the multiplier.
A more open economy will also have a smaller multiplier. The more open the
economy, the greater the marginal propensity to spend on imports. The more of
every extra dollar in income that is spent on imports, the less is left to be devoted
to planned expenditure on domestic products--and the smaller is the multiplier.
The potential change in the multiplier from an open economy:
Y
1
1


A 1  c * 1  c  tc  
to a closed economy:
Chapter 7
53
Y
1
1


A 1  c * 1  c  tc
can be considerable if the propensity to import  is large.
Chapter summary
Main points
[To be written]
Analytical exercises
[To be written]
Policy exercises
[To be written, and revised for each year within editions]