Chapter 5
The Keynesian System (I)
The supply side dominated the economy in the classical model. The level of out put was
determined there and the demand side of the economy only determined the share of the
output that households, firms and the government received.
In the Keynesian view aggregate supply adjusts to aggregate demand. A prototype
Keynesian model is shown in Figure 5—1. It demonstrates some of the key ideas of
Keynesian thought. The aggregate supply curve, Y s , is flat over a large range and then
turns vertically upward. Here aggregate demand Y d determines the level of output in the
economy anywhere Y d intersects Y s to the left of Y f (which we will call the full
employment level of output). Any point to the left of the full employment level is a level
of output due to some instability (recession, business cycle) in the economy. Point to the
right of the full employment level cannot be reached in the Keynesian view (all resources
in the economy are fully employed and can’t produce any more—an abstraction, but
useful for thinking).
In the Keynesian view aggregate supply follows aggregate demand. Shifts in the
aggregate demand curve determine the level of output in the economy as long as the
aggregate demand curve intersects aggregate supply to the left of the full employment
point. If the economy is at the full employment point and the aggregate demand curve
shifts to the right the only effect is to raise the price level. No further output is generated
because resources are fully employed. Note that there are no price changes to the left of
full employment.
Figure 5—1. A prototype Keynesian model
We will assume that the aggregate supply curve looks like the one shown in Figure 5—1
in this chapter. We will see why the aggregate supply curve might look something like
that in a subsequent chapter. If the aggregate supply curve does look like the one shown
in Figure 5—1, the cause of instability in the economy is clear – the aggregate demand
curve keeps shifting about the full employment level of output. If the aggregate demand
curve moves to the left of the full employment point that is a recession, if it is to the right
of the full employment that is inflation. The Keynesians want to examine what if
anything that might cause these shifts and, if possible, develop government policy
necessary to keep aggregate demand at the full employment point.
A further point you might note is that prices do not change at points to the left of the full
employment point. From a historical point that is a fairly accurate view of those people
we could call early Keynesians. They had experienced a severe depression where the
economy looked as though it we far to the left of the full employment point and that it
intended to stay there. These Keynesians were not particularly worried about inflation
(“Oh it might be possible, but have you ever seen it? Really.”) because they had not
experienced it. They tended to dismiss those who worried about inflation as being overly
concerned with something very unlikely to occur.
I will use the following symbols in this chapter
Y  aggregate supply = output = income
E  aggregate demand = spending on output
C  household consumption
I  investment = firms purchase of output
G  government spending on output
T  taxes
The economy will be at equilibrium if E  Y . If E  Y then more output is being
purchased than is being currently produced. This will show up as a reduction in
inventories held by firms. When firms notice this occurring they will place orders to
replenish the inventories which will cause producers to hire more labor input to produce
the desired level of demand. This will increase household income. So one means of
increasing household income is to increase spending.
If E  Y inventories will start increasing. Inventories are very expensive—funds tied up
in inventory can’t be used elsewhere. Firms don’t want to have excess inventories so
they will reduce new orders until the excess inventories are purchased (Why don’t firms
have sales in the Keynesian model?). Producers will not want to produce as much now
so they reduce labor hire and this reduces household income. So reductions in spending
reduce household income.
We need to model spending in the Keynesian economy. The entities (call them agents)
that spend in the economy are households, firms, and governments.
Keynes assumed that the household consumption decision would be primarily determined
by household income and that increases in household income would cause households to
consume more.
General consumption function
C  C y Y  T   Cr r  CwW 
Keynes view of what is important
C  C0  C y Y  T 
A general consumption function is a list of all things that might affect consumption. In
Keynes view the most important one is disposable income—all the rest are lumped
together in a term we will call C0 as being less important to the model than disposable
income. A graph of the Keynesian consumption function is shown in Figure 5—2. In
this graph the consumption function is written as
C  C0  C y Y  T   C0  C yY  C yT
C   C0  C yT   C yY
Keynes thought that changes in household consumption were primarily caused by
changes in household income. If income increases from Y1 to Y2 then consumption
increases from C1 to C2 as shown in Figure 5—2.
Figure 5—2. The Keynesian consumption function—a change in consumption caused by
a change in income.
Income changes will affect consumption as we have just seen. However other things can
affect consumption as well. Mathematically  C0  C yT  represents an intercept term. If
one of the non—income spending components in C0 increases that will shift the curve
up (more spending); if the spending component decreases it will shift the curve down.
Suppose that non-income component of consumption C0 has some value, for
convenience we will call this value Ca so that the intercept term is C0  C yT . Suppose
that household wealth increases so households now decide to consume more even though
household income has not changed. Call this new value of non--income determined
consumption Cb where Cb  Ca . This shifts the consumption curve up as shown in
Figure 5—3.
Figure 5—3. The Keynesian consumption function – a change in consumption caused by
a change in autonomous consumption
Households will be affected by tax changes because these change (Y-T). The effects of a
tax increase are shown in Figure 5—3. At tax rate T1 households consume C1 out of
disposable income. If taxes increase to T2 households will reduce consumption to C2 .
Note that income did not change here. It stayed fixed at Y1 but households just get to
keep less of it so they spend less of it. Because income is fixed we must shift the curve to
show how spending changes even though income has not.
Figure 5—4. The effects of an increase in taxes on the Keynesian consumption function
In the Keynesian model consumption will increase as income increases but consumption
does not increase as fast as income does. Keynes assumed that households would
consume some of an extra dollars income but not all of if. Suppose that the household
receives $1.00 extra income but spends ninety cents of it. That represents how much
C will increase for a unit increase in Y . Keynes called this the marginal propensity to
consume (MPC).
MPC 
C
change in consumption

Y $1 change in household income
Let
C1  C0  C y Y1  T0 
C2  C0  C y Y2  T0  , so
C2  C1  C0  C y Y2  T0   C0  C y Y1  T0 
C2  C1  C0  C yY2  C yT0  C0  C yY1  C yT0
C2  C1  C0  C0  C yY2  C yY1  C yT0  C yT0
C2  C1  C yY2  C yY1  C y Y2  Y1 
C  C y Y
C
 MPC
Y
So if MPC=0.9 then households spend 90 cents out of an additional dollar of disposable
income.
Cy 
Determining equilibrium in the Keynesian model – the aggregate
expenditures approach.
Another set of agents that purchase output are firms. We will initially take firms
purchase of output to be exogenously determined. We call this the investment function(
or the business spending function). For now we write it as
I  I 0  Investment or business spending
where the I 0 term indicates that a lot of factors may determine investment but that we
just don’t want to talk about them now.
The third agent that buys output is the government. The government adds to the spending
stream when it purchases output but subtracts from the spending stream when it taxes
households.
G  G0  government spending
T  T0  taxes
A fourth set of agents that purchases U.S. output are foreigners. This represents an
addition to the spending stream. Of course when U.S. agents purchase foreign goods this
is a subtraction from the spending stream. We will postpone discussion of the foreign
sector until much later.
Figure 5—5. Aggregate spending in the Keynesian model.
So aggregate spending in the Keynesian model is
E C  I G
I  I0
G  G0
T  T0
E  C0  C y Y  T0   I 0  G0
A graph of aggregate spending is shown in Figure 5--5. There C1 is the level of
consumption determined by an income level Y1  C  I  G 1 represents aggregate
expenditures at that income level. An increase in I or G shifts the curve up (hold the
independent variable constant). A change in taxes shift the consumption function so it
also shift the curve.
Figure 5—6. A line of points where spending=output=income
Figure 5—6 is a graph of values of E and Y where spending=output=income. Recall that
we assume that all the value of all output sold provides income to agent in the household
sector, so this means output=income. But the economy will be in equilibrium if
spending=output or if E=Y. So this curve locates equilibrium points of the economy. So
the economy will be in equilibrium if E=C+I+G=Y. Note – this does not say that E=Y
always only that the economy is in equilibrium at those points. Points below the curve
are points where E<Y and points above the curve are points where E>Y. Those are
disequilibrium points.
The equilibrium level of output and income in the economy is determined in Figure 5—7.
This is determined where $E=C+I+G=Y$ and this occurs at income level Y1 .
Figure 5-7 Equilbrium in the Keynesian model
Suppose that household have a marginal propensity to consume of 0.9 and that firms hire
household to produce $1.00 worth of extra output which generate $1.00 of extra income
for households (household income increases to Y2 from Y1 ). Households will spend 90
cents of this extra dollar of income. So one dollar of extra output is produced buy only
90 cents of the extra output is purchased. Inventories build up, firms reduce output and
hire less labor, and household income drops back to Y1 where spending=output.
Suppose we were at a point to the left of Y1 , say Y3 . In this case more output is being
purchased than is being produced. Inventories become depleted, firm place orders to
replenish them, more labor is hired to produce this additional output and household
income increases.
Determining equilibrium in the Keynesian model—the savings—
injections approach.
Another way of determining equilibrium in the Keynesian model is called the savings—
injections approach. Start with the identities
AE  C  I  G
Y  C  S  T.
In equilibrium Y=AE so another equilibrium must be
C  S T  C  I  G
S T  I  G
where S+T represents something removed from the spending stream and I+G something
returned (injected into) the spending stream.
The second equilibrium condition is easier to use than the aggregate expenditures
approach because it leads to simpler graphs.
The Keynesian savings function is determined from
Y  C  S T
S  Y  T  C  Y  T  C0  C y  Y  T 
S  C0  Y  T   C y Y  T 
S  C0  1  C y  Y  T 
S  C0  1  C y  T  1  C y  Y
Note that 0  C y  1 so 0  (1  C y )  1 as well, so the saving curve slopes upward.
Recall that C y  MPC and is the amount that households consume out of an extra dollars
income. So 1  C y   MPS is how much of that extra dollar that is saved. If MPS were
negative the extra dollar of income would cause them to reduce savings which seems
unlikely. The savings function is shown in Figure 5—8.
Figure 5—8. The Keynesian savings function.
In Figure 5—8 S1 is the level of savings produced by an income level Y1 and S 2 the level
of savings produced by Y2 . The effects of income changes are shown by movements
along the curve. Other changes are shown by shifting the curve. Suppose that all other
spending components are represented by C0  Ca and that there is a increase in interest
rates. In this case households will reduce consumption and save more. So now we have
C0  Cb  Ca . This situation is shown in Figure 5—9. Note that the minus sign before
the C0 causes a decrease in the value of C0 to have a larger value and this shifts the
savings curve up. So savings increases from S1 to S2
Figure 5—9. A decrease in autonomous consumption causes an increase in autonomous
savings.
The effects of an increase in taxes are shown in Figure 5—10. Initially households save
S1 at income level Y1 where taxes are T1 . An increase in taxes shifts the savings curve
down (Households look at a dollar increase in taxes just like a dollar reduction in income.
If the MPC is 0.9 they reduce consumption by 90 cents and savings by 10 cents.
Figure 5—10. The effects of a tax increase on the savings function.
But we must be careful here. The equilibrium condition is S  T  I  G . The
expression we have graphed in Figure 5—10 is S not S+T. To get the equilibrium
condition we must add T to S.
S  T  C0  1  C y  T  1  C y  Y  T
S  T  C0  T  C yT  1  C y  Y  T
S  T  C0  C yT  1  C y  Y
Note that an increase in taxes shifts the savings curve down but shifts the (S+T) curve up
and the equilibrium occurs where S+T=I+G. Suppose taxes increase by $1.00. Then
savings decrease by $0.10. So the total change in S+T is not $1.00 but $0.90. S+T
measures how much spending will be removed from the spending stream by the tax
increase. Spending will be reduced by $0.90 (the MPC).
Figure 5—11. The (S+T) curve
Figure 5—12. Injections into the spending stream.
I+G represents injections (additions) to the spending stream. Equilibrium occurs when
injections equal removals from the spending stream. The injections graph is shown in
Figure 5—12. These lines indicate that neither investment nor government spending
depend on income. Or, what is the same thing, changes in income don’t affect
investment or government spending.
Figure 5—13. Equilibrium using the savings=injections approach.
Table 5—1 shows how inventories and income react to various regions of the graph in
Figure 5—13. At points to the right of Y1 income is greater than expenditures so
inventories should build up causing firms to reduce production and hire less labor.
Household income should fall as a result. Points to the left of Y1 is where expenditures
exceed income leading to inventory depletion causing firms to order more production
leading to increased demand for labor and an increase in household income.
Condition
Inventories Y
C  S  T  C  I  G S  T  I  G S+T=I+G Unchanged Equilibrium
Y  AE
Increase
Falls
C  S T  C  I  G S T  I  G
Y  AE
Fall
Increases
C  S T  C  I  G S T  I  G
Y  AE
Table 5—1 The relationship between income and inventories, AE, S+T and I+G.
Figure 5—14. A reduction in investment spending drives the economy from a full
employment level of output Y f to Y1
Figure 5—14 shows the economy initially at equilibrium at Y f . Suppose that firms, for
some reason (animal spirits) decide to reduce investment spending. Expenditures now
exceed income, firms hire less labor and household income falls. So now the economy is
in a recession. So what might the government do to get the economy out of recession? A
spending decrease created the problem so a spending increase ought to solve it (from the
Keynesian view). The government can increase its’ purchase of output as shown in
Figure 5—15. In that case we move back to the full employment level of income.
Figure 5—15. Offsetting the investment spending decline with a government spending
increase.
Figure 5—16. The government can offset the investment spending decrease with a tax
decrease.
The second way the government can increase spending is to reduce taxes. In that case
households have more to spend (recall MPC) and this will cause income to rise. This is
shown in Figure 5—16.
The algebra of the Keynesian model.
The graphical analysis is useful for showing the general tendency of how things will
occur in the Keynesian model. It does not do such a good job of indicating the magnitude
of the changes. A little algebra in needed for that task.
We will start with a basic Keynesian model in algebraic form and solve for a value of Y
where the economy is in equilibrium.
C  C0  C y Y  T 
I  I0
G  G0
T  T0
Y  C  I G
(the equilibrium condition)
Y  C0  C y Y  T0   I 0  G0
Y  C0  C yY  C yT0  I 0  G0
Y  C yY  C0  C yT0  I 0  G0
1  C  Y  C
y
Y
0
 I 0  G0  C yT0
C0  I 0  G0  C yT0
1  C 
y
I hope you see now why we want to take things a bit slow initially. We can make them
more complicated easily enough. Note that we have not used any numbers yet. Even
without numbers some things should be clear. An increase in any autonomous spending
component should cause an increase in income. An increase in taxes should cause a
decrease in income.
Example 8.1 From Froyen, Problem 8, Chapter 4 (7 ed)
C0  25
C y  0.8
I 0  100
G0  75
T0  100
Y
Y
C0  I 0  G0  C yT0
1  Cy

25  100  75  (0.8)(100)
1  0.8
120
 600
0.2
Suppose government spending increase by 10. What is the new equilibrium level of
income?
C0  25
C y  0.8
I 0  100
G0  85
T0  100
Y
Y
C0  I 0  G0  C yT0
1  Cy

25  100  85  (0.8)(100)
1  0.8
130
 650
0.2
So the increase of 10 in government spending caused a increase of 50 in the equilibrium
level of income. This suggests that government spending increases (decreases) are
multiplied through the economy. Suppose however that the government had decided to
reduce taxes by 10.
C0  25
C y  0.8
I 0  100
G0  75
T0  90
Y
Y
C0  I 0  G0  C yT0
1  Cy

25  100  75  (0.8)(90)
1  0.8
128
 640
0.2
In this case the reduction in taxes of 10 increased income by 40. So there was an
increase, but the increase was not as large.
Multipliers
These are examples of Keynesian multipliers. The suggest that the economy is extremely
sensitive to changes in spending. So if there are changes in C0 , I ,G or T the results will
be magnified through the consumption function to have large effects on the economy. So
the economy would tend to be very unstable in the Keynesian view of the world.
However, spending decreases in one place can be offset by spending increases
somewhere else. In particular the government can increase its spending or can reduce
taxes to give household more disposable income. We can use Keynesian multipliers to
predict the magnitude of these spending changes.
Let
Y1 
Y2 
C0  I 0  G0  C yT0
1  Cy
C0  I 0  G0  C yT0
1  Cy
Y2  Y1 
Y2  Y 
Y 
C0  I 0  G0  C yT0
1  Cy

C0  I 0  G0  C yT0
1  Cy
C0  C0
1  Cy
C0
1  C0
Keynesian autonomous consumption multiplier 
Y
1

C0 1  C0