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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
8. The Essence of the General Theory: Relaxing the Classical Tradition
John Maynard Keynes birthed macroeconomics as a distinct field of study with his
1936 book, The General Theory of Employment, Interest, and Money, or just The General
Theory for short. In The General Theory, Keynes claimed that the widely accepted
“Classical” theory was a special case of his more general theory. Since then, most
macroeconomic research has stemmed from either the Classical tradition or the
Keynesian tradition. Using the theory developed in chapters 4 and 5, this chapter
explores the Keynesian and Classical traditions. In doing so, we examine a variety of
theoretical and policy issues.
The General
Theory
8.1 The Essence of the General Theory
In Chapter 3 of The General Theory, Keynes presented his theory using a simple
macroeconomic model. Using the original notation, the model Keynes presented is
(8.1)
D1  D2  D
(8.2)
D1   ( N ) ,
 ' 0
(8.3)
D   (N ) ,
 ' 0
Endogenous (3): D1, D, N
Exogenous (1): D2
D is what Keynes called effective demand. It is composed of consumption demand
D1 and investment demand D2. Consumption demand depends upon the level of
employment according to the “propensity to consume” function  because the
employment level determines the income level that, in turn, determines the level of
consumption expenditure. Investment demand is exogenous. The supply of output
depends upon the employment level according to the “aggregate supply function” .
Finally condition (8.3) is an equilibrium condition which indicates that Keynes was
considering an economy where the effective demand for output is equal to the aggregate
supply of output.
Substituting (8.1) and (8.2) into (8.3), we obtain
(8.4)
 ( N )   ( N )  D2 .
The only endogenous variable in (8.4) is N. Thus, equation (8.4) implicitly determines
the equilibrium level of employment. A particular “Keynesian” adjustment process in the
event of disequilibrium is also implied: If the effective demand for output is not equal to
the aggregate supply of output, then the employment level will adjust until equation (8.4)
holds. For example, if aggregate supply exceeds the effective demand so that a surplus of
output exists, producers would lay off workers until the surplus is eliminated.
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Effective
Demand
Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
Keynes said that the “essence of the general theory of employment” is that the volume
of employment in equilibrium depends upon the aggregate supply function , the
propensity to consume function , and the volume of investment demand D2. By
differentiating (8.4), we can see what Keynes meant:
(8.5)
 ' dN   ' dN  dD2
The derivative  ' gives the change in output when employment increases by one unit,
while  ' gives the change in consumption when employment increases by one unit. The
left side of (8.5) gives the change in income generated by the increase in employment.
The right side of (8.5) gives the total change in effective demand. Keynes assumed
 '   ' . With  '   ' , an increase in employment generates an excess supply of output--i.e., the left side of (8.5) increases faster than the right side---unless investment increases
to fill the gap. Or, put differently, with  ' and  ' fixed, the only way the equilibrium
level of employment can increase is for the level of investment to increase, which can be
seen by solving (8.5) for dN:
(8.6)
dN 
1
dD2 .
 '  '
To understand this result more fully, it is useful to reproduce Keynes’ model using the
notation we presented in chapters 4 and 5. What Keynes called effective demand is
equivalent to what we called aggregate demand; i.e., D  AD . Consumption and
investment in our model are equivalent to Keynes’ notions of consumption and
investment; i.e., D1  AD and D2  I . In our model, we have a production function,
where output depends upon labor and capital. Keynes’ aggregate supply function  ( N )
can be thought of as a production function which only recognizes labor as being variable.
If we assume capital stock is fixed and subsume it into our production function, then our
production function reduces to Y ( N )   ( N ) . Keynes model does not include a foreign
sector nor a government sector. By eliminating government purchases and net taxes from
our model, our consumption function reduces to C(Y ) and the definition of aggregate
demand reduces to AD  C  I .
Consumption in Keynes’ model depends upon
employment rather than income. By substituting our production function into our
consumption function, we can replicate Keynes’ consumption relationship; i.e.,
 ( N )  C(Y ( N )) . Finally, we can add the equation Y=C+S to show how income is
allocated. Using these relationships, we can present Keynes’ model in our notation as
(8.7)
AD  C  I
(8.8)
C  C(Y ) ,
0  C'  1
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
(8.9)
Y CS
(8.10) Y  AD
(8.11)
Y  Y(N )
Y' 0
Endogenous (5): AD,C, S, Y, N
Exogenous (1): I
Equations (8.7)-(8.10) represent a capital market model, while equation (8.11) is a
production function. Thus, we see that the “essence of the general theory of
employment” consists of a capital market and a production function---no money market
or labor market. Substituting equations (8.7), (8.8), and (8.11) into equation (8.10), we
obtain
(8.12)
Y ( N )  C(Y ( N ))  I .
Because Y ( N )   ( N ) ,  ( N )  C(Y ( N )) , and D2  I , equation (8.12) is equivalent to
equation (8.4). Differentiating (8.12) and solving for dN, we obtain
(8.13) dN 
1
dI .
Y '[1  C ']
Because  '   '( N )  Y '( N )  Y ' ----i.e.,  ' is the marginal product of labor---and
 '   ( N )  C' Y ' ---i.e.,  ' is the additional consumption generated by an additional unit
of labor, condition (8.13) is equivalent to (8.6).
Dividing (8.6) and (8.13) by dI  dD2 , we obtain the employment multiplier for
investment:
(8.14)
dN
1
1


0
dI Y '[1  C']  '  '
This multiplier is positive because Y '[1 C']   '  ' is positive. Our notation gives us a
nice interpretation of Keynes’ quantity  '  ' . For employment to increase by one unit,
output and hence income must increase by Y’. The increase in saving due to a one unit
increase in income is given by the marginal propensity to save of 1-C’. Thus, one
interpretation of  '  '  Y '[1  C'] is that it is the increase in saving which occurs due to
a one unit increase in employment. An increase in employment of dN units will increase
saving by Y '[1 C']dN . This increase in employment can be supported only if the
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Propensity to
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
additional
saving generated can find its way
Y '[1 C']dN  dI must hold as in (8.13) and (8.14).
into
investment.
Thus,
An alternative interpretation is obtained by recognizing that a one unit increase in
employment increases production capacity by Y’. When the output is sold, income also
increases by Y’. This leads to an increase in consumption (and consequently an increase
in aggregate demand) of C’Y’. Because C’<1, the increase in production capacity is
greater than the increase in aggregate demand. Keynes described this situation by saying,
“When our income increases our consumption increases also, but not by so much. The
key to our practical problem is to be found in this psychological law:” That is, Keynes
recognized  '  '  Y '[1  C'] as the extent to which aggregate demand is deficient when
it comes to supporting one additional unit of employment. If dN additional units of
employment are desired, then aggregate demand is deficient by Y '[1 C']dN . An
increase in employment equal to dN can be supported only if this deficient demand is
offset by an increase in investment. Thus, Y '[1 C']dN  dI must hold as in (8.13) and
(8.14).
Differentiating the production function Y=Y(N), we obtain dY=Y’dN . This implies
(8.15)
Autonomous
Spending
Multiplier
dY
dN
Y'
1
 Y'


 1.
dI
dI Y '[1  C'] 1  C'
This is the autonomous spending multiplier presented in many introductory economic
textbooks. The multiplier dY/dI gives the change in output (or income) which results
from a one unit increase in investment spending. When investment increases by one unit,
aggregate demand increases by one unit. Because investment is an exogenous variable,
this initial one unit change in aggregate demand is not due any cause and effect
relationship in the model. Rather, this change in aggregate demand is “autonomous” or
“independent” or “unexplained.” This initial one unit increase in spending generates a
total increase in spending equal to 1/[1-C’]>1.
Why does an autonomous one unit increase in spending generate a total increase in
spending of more than one unit? Think of spending as occurring in successive “rounds.”
In round 1, the one unit autonomous increase in spending occurs. When producers act
fulfill this increase in demand, one additional unit of output is produced which generates
one additional unit of income. (Notice that the additional spending becomes additional
income.) This one unit of additional income increases consumption spending in round 2
by C’. The increase in spending in round 2 again increases income, this time by C’. In
round 3, the round 2 increase in income of C’ generates a further increase in spending and
income equal to [C’][C’]=[C’] 2. These rounds continue indefinitely. It follows that the
total increase in spending in all rounds is given by the infinite series
(8.16) Z  1  C'[ C']2  [ C']3 ...
.
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
Multiplying both sides of (8.16) by C’ yields
(8.17) C' Z  C'[ C']2  [ C']3  [ C']4 ... .
Subtracting (8.17) from (8.16) yields
(8.18) Z  C' Z  1.
Solving (8.18) for Z, yields
(8.19) Z 
1
1  C'
This shows that autonomous spending multiplier given in (8.15) is equal to the sum of all
the rounds of spending generated by the initial one dollar autonomous increase is
spending. The reason the multiplier is greater than one is that any additional spending
becomes additional income, which then tends to promote further consumption spending
and further increases in income.
Notice that the autonomous spending multiplier is larger when the marginal
propensity to consume C’ is larger. This indicates that the employment, output, and
consumption levels in economies where people exhibit a higher propensity to consume
are potentially more volatile. To be more precise, we can say that a higher marginal
propensity to consume makes employment, output, and consumption more sensitive to
autonomous changes is spending.
To conclude this section, let us review this model, which Keynes presented as a simple
characterization of his general theory of employment. As mentioned, it includes a capital
market and a production function. As a result of this construction, the employment level
is derived from the economy’s effective demand (or aggregate demand) for output.
Keynes noted that Say, Ricardo, and Mill each taught what is now commonly referred to
as Says Law: Supply creates its own demand. What we see here is that Keynes turns
Say’s Law on its head. In Keynes’ model, it is the demand for output that brings forth the
employment necessary to supply the output demanded.
The model presented here does not include interest rates, prices, wages, capital stock,
taxes, government purchases, the money supply, or a foreign sector. Any such variables
that are left out of a model are implicitly either being set equal to zero or are being held
fixed. Keynes would probably not apologize for leaving the government and foreign
sectors out of this employment model for he argued that fluctuations in investment to be
“most often at the bottom of the phenomenon of fluctuations in unemployment.” Keynes
recognized that his assumption of fixed nominal wages was only consistent with a labor
surplus. However, he also argued that “a provisional assumption of a rigidity of money-
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Marginal
Propensity to
Consume
Say’s Law
Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
wages... would bring our theory nearest to the facts. Moreover, he argued that “a theory
cannot claim to be a general theory unless it is applicable to the case where ... money
wages are fixed.” In the next section, we add a labor market and explicitly assume a
fixed nominal wage level. We introduce government by adding exogenous variables for
government purchases, net taxes, and the nominal money supply. By adding a money
market, we add the interest rate as an endogenous variable. Finally, by adding the
assumption that the employment level be at a level consistent with producer profit
maximization, we are able to introduce the price level as an endogenous variable. The
result is a model with Keynesian flavor that can explain more that just changes in
employment and output.
8.2 Broadening the Scope of the General Theory
To broaden the scope of Keynes general theory beyond merely explaining variations in
employment, suppose the economy is described by equations (8.20)-(8.28), where the
endogenous variables are as presented below. The significant features of this model are:

The level of investment is endogenously determined by interest rate level r
and the expectations state . The inclusion of the expectations state variable
allows for the unexplained “animal spirit” type of changes in investment due
to changes in expectations. This investment function captures the essential
features of Keynes’ investment theory.

Real money demand depends upon the interest rate according to the money
demand function L(r). As noted by Hicks, Keynes (The General Theory, p.
168) does not include output (or income) Y as a variable which affects money
demand. This implies the LM curve is horizontal or, equivalently, that the
economy is in a liquidity trap.

Producers employ an optimal quantity of labor. This assumption is captured
by equation (8.27). Equation (8.27) indicates that the wage paid to labor is
equal to the value of the marginal product of labor. Or, equivalently, equation
(8.27) indicates that the employment level is associated with a point on the
labor demand curve. (See The General Theory p. 295 for an indication that
Keynes felt this condition determined the economy’s price level.)
Capital Market
(8.20) AD  C  I  G
(8.21) C  C(Y  T ) ,
0  C'  1
(8.22) I  I (r , ) ,
Ir  0 , I  0
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
(8.23) AE  Y
(8.24) AE  AD
Money Market
(8.25) PL(r )  M
L' 0
Production Function
(8.26) Y  Y ( N , K)
YN  0 , YNN  0 , YK  0 , YKK  0
Labor Market
(8.27) W  PYN ( N , K)
Endogenous (8): AD,C, I, AE, Y, N, r, P
Exogenous (6): , K, M, G, T, W
Using substitution, the variables AD, C, I, and AE can be eliminated, reducing the is
system of eight equations to the following system of four equations. Equation (8.28) is
an IS equation representing capital market equilibrium. Equations (8.29) is an LM
equation representing money market equilibrium. Equation (8.30) is a production
function which shows the relationship between the productive inputs and the output level.
Equation (8.31) is a necessary condition for profit maximization with respect to the
employment of labor.
(8.28) Y  C(Y  T )  I ( r , )  G ,
(8.29) PL(r )  M
(8.30) Y  Y ( N , K)
0  C'  1 , Ir  0 , I  0
L' 0
YN  0 , YNN  0 , YK  0 , YKK  0 , YNK  0
(8.31) W  PYN ( N , K)
Endogenous (4): Y, N, r, P
Exogenous (6): , K, M, G, T, W
The model’s endogenous variables are Y, N, r, and P. These four variables are
significant variables in that many people would be interested in understanding what it is
that determines the level of output, the level of employment, the interest rate level, and
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
the price level. This model is nice in that it provides a particular theory as to how these
determined. Endogenous variables are determined by exogenous variables. Thus, this
model tells us that our four variables of interest are determined by the state of expectation
with regard to the profitability of investment, the capital stock level, the money supply
level, the level of net taxes, the level of government purchases, and the nominal wage
level.
By calculating the model’s multipliers, we can obtain more specific information about
how the exogenous variables affect the endogenous variables. To obtain the multipliers,
one could differentiate the four equations and then use Cramer’s rule to solve for the four
endogenous differentials. However, working with four by four determinants is
cumbersome. (If you are a masochist you might try it.) An easier approach in this case
is to further reduce the number of equations in the model by eliminating more
endogenous variables. (If it were not possible to further reduce the number of equations,
one would have to work with four equations and four unknowns.) One can eliminate P
from the system by solving (8.29) for P and substituting the result into (8.31). One can
eliminate Y from the system by using (8.30) to eliminate Y from (8.28). Then, we have
the following two equation system:
(8.32) Y ( N , K )  C(Y ( N , K )  T )  I ( r , )  G ,
0  C'  1 , Ir  0 , I  0 , YN  0 ,
YNN  0 , YK  0 , YKK  0 , YNK  0
(8.33) WL( r )  MYN ( N , K ) ,
L' 0
Endogenous (4): N, r
Exogenous (6): , K, M, G, T, W
To use Cramer’s rule, the next step is to totally differentiate (8.32) and (8.33) and
arrange the resulting linear system in matrix form. Doing so, one obtains
YN [1  C']  I r  dN  [1  C']YK dK  C' dT  I d  dG

  MY

WL'  dr  
MYNK dK  YN dM  LdW
NN


Letting A denote the matrix on the left side of this equation,
(8.34)
A  YN [1  C']WL' I r MYNN  0
The Cramer’s rule determinants A1 and A2 are
A1  WL' dG  WL' C' dT  I rYN dM  WL' I d  I r LdW   I r MYNK  WL'[1  C']YK dK
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
and
A2  MYNN dG  MYNN C ' dT  [YN ]2 [1  C ' ]dM  MYNN I d  YN [1  C ' ]LdW
Yn [1  C' ] MYNK  MYNN [1  C' ]YK dK .
Using these results, we can solve for the endogenous differentials:
(8.35) dN 

A1
A

WL'
WL' C '
IY
WL' I
IL
dG 
dT  r N dM 
d  r dW
A
A
A
A
A
 I r MYNK  WL'[1  C' ]YK  dK
A
and
A2
MYNN
MYNN C''
[YN ]2 [1  C']
MYNN I
dr


'
dG

dT

dM

d
(8.36)
A
A
A
A
A

Y [1  C ' ]MYNK  MYNN [1  C ' ]YK  dK
YN [1  C ' ]L
dW  n
A
A
We will now use these results to discuss, economic policy and theoretical issues.
8.3 Fiscal Policy in a Keynesian Economy
An increase in government purchases increases both aggregate demand and the budget
deficit. The “dG multipliers” express the economic impact of a one unit increase in
government purchases on the model’s endogenous variables.
Using (8.35), we can
obtain the multiplier dN/dG as
(8.37)
dN
1

 0.
dG Y [1  C ' ]  I r MYNN
N
WL'
Using (8.30), we know that dY / dG  YN [ dN / dG ] . Thus,
(8.38)
dY
1

0
dG [1  C ' ]  I r MYNN
YN WL'
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
Using (8.36), we can obtain the multiplier dr/dG as
MYNN
dr
WL'
(8.39)

 0.
dG Y [1  C ' ]  I r MYNN
N
WL'
Using (8.29), we know that dP / dG  [  PL' /L][dr / dG ] . Thus,
PMYNN
dP
WL
(8.40)

0
dG Y [1  C']  I r MYNN
N
WL'

Crowding Out
A Keynesian story explaining these results can be told as follows. The one unit
increase in government purchases represents an autonomous one unit increase in
aggregate demand. Given the additional demand, producers are willing to produce
additional output. However, with a fixed capital stock, employing more labor to produce
additional output will decrease labor productivity; i.e., labor is subject to diminishing
returns. Thus, firms will not willingly hire additional labor unless the real wage
decreases. Because the nominal wage is assumed to be exogenously fixed, the price level
P must increase in order for the real wage decrease to occur. Firms are able to obtain a
higher price for output due to the excess demand. As the price level increases, firms hire
more labor and output increases. The increase in output induces an increase in
consumption demand, which induces further increases in the output level and price level.
Because the increase in government purchases is an autonomous change, the output
multiplier (8.38) for government purchases---dY/dG---is an autonomous spending
multiplier. Notice that this autonomous spending multiplier, obtained for this more
complete model, would be equal to the autonomous spending multiplier (8.15), obtained
I r MYNN / YN WL' were equal to zero.
for the simpler model, if
Because
 I r MYNN / YN WL'  0 , the multiplier (8.38) is smaller than the multiplier (8.15). That is,
an autonomous increase in spending has a greater impact on output in the simple model
than in this more complete model. The reason for the decrease in the autonomous
spending multiplier is that, while prices were implicitly assumed to be fixed in the simple
model, the increase in prices “crowds out” some spending in the more complete model.
What is crowding out and why does it occur? As noted, an increase in the price level
is necessary if producers are to hire the additional labor necessary to produce the output
so as to satisfy the autonomous increase in aggregate demand. Examining equation
(8.29), note that the increase in prices increases nominal money demand or, equivalently,
decreases the real money supply. Thus, the increase in the price level creates an excess
demand for money. Keynes stressed that the interest rate is “the reward for not hoarding”
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
money as opposed to “a reward for not spending,” which Keynes argued was the Classical
view. Using Keynes’ terminology, an excess demand for money represents an excessive
desire to hoard. In such a situation, those who wanted to hold money would sell assets to
obtain money. This would decrease asset prices and increase the interest rate level. The
higher interest rate would represent a greater reward for not hoarding money. This would
discourage some from holding money, thereby eliminating the excess demand for money.
However, the increase in the interest rate decreases investment demand, as is indicated by
equation (8.22). Thus, the autonomous increase in government purchases crowds out
some investment spending because of the increase in interest rates caused by the increase
in the price level.
Examining the multiplier (8.38), note that the extent of the crowding depends upon Ir .
There is no crowing out if investment is totally insensitive to a change in the interest rate
(Ir=0) for then an increase in the interest rate does not affect spending. It depends upon
YNN . There is no crowding out if there are no diminishing return (YNN=0) for then the
price level would not have to increase to accommodate additional employment. Finally,
it depends upon L’. There is no crowing out if money demand is extremely sensitive to a
change in the interest rate (L’=+) for then an infinitesimally small increase in the
interest rate could eliminate any excess demand for money, leaving investment spending
unaffected.
An increase in net taxes decreases both aggregate demand and the budget deficit. The
“dT multipliers” express the economic impact of a one unit increase in government
purchases on the model’s endogenous variables. It is left as an exercise for the reader to
find and interpret these multipliers. However, because the affect of an increase in net
taxes on aggregate demand is exactly the opposite as an increase in government
purchases, it is apparent that the sign for each dT multiplier should be the opposite of that
obtained for the comparable dG multiplier. In particular, higher net taxes lead to a
decrease in the price level, the interest rate level, the output level, and the employment
level.
In summary, these results lead us to the following “Keynesian” conclusions:

Expansionary fiscal policy---i.e., increasing the budget deficit---can be used to lift an
economy out of a recession. It increases employment, reduces unemployment,
increases output, and increases incomes.

Contractionary fiscal policy---i.e., reducing the budget deficit---can cause a recession.
It decreases employment, increases unemployment, decreases output, and decreases
incomes.

Expansionary fiscal policy will tend to generate inflation and increase the real interest
rate level
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition

Contractionary fiscal policy will tend to be deflationary and reduce the real interest
rate level.
8.4 Monetary Policy in a Keynesian Economy
An increase in the money supply M creates an excess supply of money. The “dM
multipliers” economic impact of a one unit increase in the money supply on the model’s
endogenous variables. Using (8.35), we can obtain the multiplier dN/dM as
I rYN
dN
WL'
(8.37)

 0.
dM Y [1  C' ]  I r MYNN
N
WL'
Using (8.30), we know that dY / dM  YN [ dN / dM ] . Thus,
I r YN
dY
WL'
(8.38)

0
dM [1  C' ]  I r MYNN
YN WL'
Using (8.36), we can obtain the multiplier dr/dM as
[YN ]2 [1  C' ]
dr
WL'
(8.39)

 0.
dM Y [1  C' ]  I r MYNN
N
WL'
Using (8.31), we know that dP / dM  [ PYNN / YN ][ dN / dM ] . Thus,
PY I
 NN r
dP
WL'
(8.40)

0
dM Y [1  C ' ]  I r MYNN
N
WL'
A Keynesian story explaining these results can be told as follows. The one unit
increase in the money supply creates an excess supply of money. As people spend move
the excess money into assets, asset prices increase and the interest rate level decreases.
The decrease in the interest rate level spurs investment demand, which increases
aggregate demand. In response to the increase in demand, firms increase prices. The
increase in the price level makes it profitable to hire the additional labor needed to
produce additional output so as to meet the additional demand. Analogous to the
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
explanation above, the increase in the price level will crowd out some investment
spending. However, in this case, investment does not decrease. Rather, the increase in
prices reduces the extent to which investment increases by reducing the extent to which
the interest rate decreases.
Overall, this results lead to the following “Keynesian” conclusions:

Expansionary monetary policy---i.e., an increase in the money supply---will tend to
generate inflation and decrease the real interest rate level.

Contractionary monetary policy---i.e., a decrease in the money supply---will tend to
be deflationary and increase the real interest rate level.

Expansionary monetary policy can be used to lift an economy out of a recession. It
will tend to increase employment, reduce unemployment, increase output, and
increases incomes.

Contractionary monetary policy can cause a recession. It will tend to decrease
employment, increase unemployment, decrease output, and decrease incomes.
Keynes was actually skeptical about the usefulness of expansionary monetary policy
during a economic downturn. The main problem, he said, is that investment tends not to
be very responsive to a change in the interest rate level, particularly when the economy is
in a depressed state. Notice that if Ir is small, then the multipliers dY/dM and dN/dM are
also small. Consequently, even if an increase in the money supply does decrease interest
rates, it need not have much of an impact on output and employment.
These results also indicate that expansionary monetary policy can be used to offset the
crowding out caused by expansionary fiscal policy.
The problem with expansionary
fiscal policy is that it increases the interest rate level, which leads to a decrease in
investment. The increase in the interest rate level occurs because an excess demand for
money is created. Expansionary monetary policy can directly eliminate this excess
demand so that the interest rate level does not increase. Thus, using this Keynesian
model as our view of how the world works, we are left with the impression that output
and employment can be increased to any level as long a government simultaneously
pursues expansionary fiscal policy and expansionary monetary policy.
8.5 The Classical View
At the end of chapter 2 of The General Theory, Keynes identifies three key postulates
of Classical economics:
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
1. the real wage is equal to the “marginal disutility of the existing employment”
level;
2. involuntary unemployment cannot occur; and
3. supply creates its own demand.
Keynes argued that these three assumptions are essentially equivalent in that any one
implies the other two.
Marginal
Disutility of
Employment
If involuntary unemployment does not exist, then labor supply and labor demand are
equal. None of the previous models in this chapter have distinguished labor supply from
labor demand. The variable N has been used to represent the employment level.
Equation (8.31) in the last model is the condition that employers will hire labor to the
point where the marginal product of labor is equal to the real wage. Thus, the variable N
has been representing labor demand. Because there is no condition that recognizes labor
supply, labor demand a labor supply need not be equal. Thus, in the Keynesian models
we have been examining, involuntary unemployment can occur
Now, consider labor supply. In chapter 5, we assumed labor supply Ns would depend
upon the real wage W/P and some other factors (e.g., population) represented by the
variable Z. Here, assume that an increase in the real wage entices additional people into
the labor force; i.e., assume the labor supply curve does not bend backwards. For a given
value of Z, we can define the marginal disutility of a particular labor supply level by the
inverse of the labor supply function
(8.41)
g ( N s , Z )  [ N s ]1 (W / P, Z )
so that
(8.42)
W / P  g(N s , Z ) ,
gN s  0 ,
gZ  0 .
Equation (8.42) can be thought of as the same labor supply function as was presented in
chapter 5. However, labor supply is given here implicitly rather than explicitly.
The marginal disutility of employment is the term Keynes used to describe the real
wage needed to attract a labor supply equal to the actual employment level. Assuming
employers always hire optimally so that the actual employment level is equal to the labor
demand level (N=Nd), the labor supply level is equal to the actual employment level if
and only if there is no involuntary unemployment---i.e., N=Nd and N=Ns if only if Ns=Nd.
That is, under the assumption that producers hire labor optimally, “Classical postulates” 1
and 2 are indeed equivalent. Assuming labor supply and labor demand each equal the
employment level N, equation (8.42) becomes
(8.43)
W / P  g(N , Z ) ,
gN s  0 ,
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gZ  0 ,
Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
which is equivalent to Classical postulate 1 above.
To consider Classical postulate 3, we now create a model by simply adding condition
(8.43) to the model presented in section 8.2. Doing so, we obtain the following
“Classical” model
Capital Market
(8.44) AD  C  I  G
(8.45) C  C(Y  T ) ,
0  C'  1
(8.46) I  I (r , ) ,
Ir  0 , I  0
(8.47) AE  Y
(8.48) AE  AD
Money Market
(8.49) PL( r,Y )  M
L' 0
Production Function
(8.50) Y  Y ( N , K)
YN  0 , YNN  0 , YK  0 , YKK  0
Labor Market
(8.51) W  PYN ( N , K)
(8.52) W / P  g( N , Z ) ,
gN s  0 ,
gZ  0 .
Endogenous (8): AD,C, I, AE, Y, N, r, P, W
Exogenous (6): , K, M, G, T, Z
The additional equation allows an additional endogenous variable to be determined.
Notice that we have assumed the nominal wage W is now endogenous.
This is
consistent with the notion that the nominal wage is wage adjusts to equate labor supply
and labor demand. Using (8.51) and (8.52), we find
(8.53) YN ( N , K )  g( N , Z ) .
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
The only endogenous variable in (8.53) is the employment level N. It follows that the
employment level depends only upon the capital stock level K and the (population level)
variable Z.
Taking the differential of (8.53) and solving for dN, we can see how the employment
level is affected by changes in the capital stock level and by changes in population:
YNN dN  YNK dK  gN dN  gZ dZ ;
(8.54) dN 
gZ
YNK
dZ 
dK .
YNN  gN
YNN  gN
The result (8.54) indicates that employment increases as population increases and as
capital stock increases. However, notice that employment is not affected by the money
supply, government purchases, net taxes. In other words, changes in monetary and fiscal
policy have no impact on employment. Moreover, the state of expectations with regard to
investment, which Keynes saw as being significant, also has no impact on the level of
employment.
With employment determined by equation (8.53), equation (8.50) then determines
output. Differentiating (8.50) and then using (8.54), we can see how the output level is
affected by changes in the capital stock level and by changes in population:
dY  YN dN  YK dK ;
 gZ

YNK
dY  YN 
dZ 
dK   YK dK
YNN  gN
 YNN  gN

(8.55)
dY 
YN gZ
Y Y  YK g N  YN YNK
dZ  K NN
dK .
YNN  gN
YNN  g N
This result indicates that output, like employment, increases as population increases and
as capital stock increases.
These results are the foundation for Say’s Law---the idea that supply creates demand
rather than vice versa.
Because the three equations (8.50)-(8.52) determine the
equilibrium employment, output, and nominal wage levels with having to use equations
(8.44)-(8.49), the Classical model presented here is said to “dichotomize.” Equations
(8.50)-(8.52) represent the supply-side of the economy, while equations (8.44)-(8.49)
represent the demand-side. The supply of output is determined independently from the
demand for output. The level of aggregate demand determined by the demand-side must
adjust to the output level determined on supply-side. Hence, supply creates its own
demand.
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
The reason supply is independent of demand is because it is assume the nominal wage
adjusts to generate full employment. That is, the output level in this Classical model is
always the full employment output level or potential output level. If the nominal wage is
sticky over shorter time intervals, as captured by the Keynesian model presented in the
last section, then the economy may not be producing at its potential. Over longer time
intervals, it is more likely that nominal wages will be able to adjust so as to eliminate any
surpluses or shortages of labor. Consequently, many economists like to view the
Classical model as a long run model, while the Keynesian model is viewed as a short run
model.
Keynes defended his model by noting that, “In the long run we’re all dead,”
which focuses on the fact that people tend to be most concerned about their immediate
future. Nonetheless, the Classical model is useful because it gives us information about
the long run and about the economy’s potential.
We can again reduce the demand side equations (8.44)-(8.49) to an IS equation and an
LM equation. Doing so and differentiating, we obtain
Supply-side
(8.56)
dY  C' dY  C' dT  I r dr  I d  dG
Demand-side
and
(8.57) PLr dr  PLY dY  LdP  dM .
Solving (8.56) for dr and using (8.54) to eliminate dY, we obtain
(8.58) dr 
C'
I
1
1  C'  YN gZ dZ  1  C' YKYNN  YK gN  YN YNK dK
dT   d  dG 




Ir
Ir
Ir
I r  YNN  gN 
Ir 
YNN  gN

This result tells us how changes in the economic environment affect the real interest rate
level. Solving (8.57) for dP and using (8.54) and (8.58) to eliminate dY and dr, we
obtain
(8.59) dP 
1
PL C
PL
PL I
dM  r r dT  r dG  r  d
L
LI r
LI r
LI r
 PL
 Y g 
 PL
  Y Y  YK gN  YN YNK 
PL
PL
  Y  Y [1  C']  N Z dZ   Y  Y [1  C']  K NN
dK
LI r
LI r
YNN  gN
 L
  YNN  gN 
 L


This result tells us how changes in the economic environment affect the price level.
8.6 Fiscal Policy in a Classical Economy
125
Full
Employment
Output Level
Potential Output
Level
Long Run
Short Run
Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
An change in the budget deficit can occur either due to a change in government
purchases or a change in net taxes. Using equations (8.54) and (8.55), we know that
neither of these changes affects either the employment level or the output level.
However, the composition of output---i.e., the allocation of output among consumption,
investment, and government purchases---is affected.
Consider first an increase in the budget deficit caused by an increase in government
purchases. The increase in government purchases increases aggregate demand, creating
an excess demand for output. However, because the economy is already at full
employment, the output level cannot increase to meet the additional demand.
When
there is an excess demand for output, there must also be an excess demand for saving.
(The reader should be able to show this.) The Classical view of the adjustment process is
that the interest rate level will increase in response to the excess demand for saving, as is
indicated by the positive coefficient on dG in (8.58). The increase in the interest rate
level eliminates the excess demand by decreasing investment and consequently aggregate
demand.
Composition of
Output
In this model, crowing out is complete, meaning each additional dollar of government
purchases results in a one dollar decrease in investment. To understand this, remember
that AS=AD must hold in equilibrium. This implies Y=C+I+G must also hold. Because
Y is unaffected by a change in G, it follows from the last equation that an increase in G
implies a decrease in either C or I. Because consumption depends only upon disposable
income in this model, and disposable income does not change, C does not change as G
changes. Thus, each additional dollar of government purchases must crowd out one
dollar of investment spending. The bottom line is that the increase in government
purchases shifts the composition of output away from investment toward government
purchases.
Like an increase in government purchases, a decrease in net taxes---which can occur
due to a tax cut or transfer payment increase---increases the budget deficit and creates an
excess demand for output. However, with a tax cut (or transfer payment increase), the
increase in aggregate demand stems from an increase in consumption. The tax cut
increases disposable income which promotes consumption. As indicated by the negative
coefficient on dT in (8.58), a tax cut will increase the interest rate level, just like an
increase in government purchases. The primary difference between a tax cut and an
increase in government purchases is in the affect on the composition of output. As
before, investment spending is crowded out by the increase in interest rate. However,
with the tax cut, investment spending is being crowded out by an increase in consumption
spending rather than by an increase in government spending. The bottom line is that a
decrease in net taxes shifts the composition of output away from investment toward
consumption.
Both a tax cut and an increase in government purchases lead to an increase in the
interest rate level. The increase in the interest rate reduces the demand for money,
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
creating an excess supply of money. Classical monetary theory holds that money is
primarily used to make transactions---i.e., to purchase goods and services. As the excess
supply of money is spent on goods and services, the price level increases, as indicated by
the positive coefficient on dG in (8.59).
Expansionary fiscal policy refers to a fiscal policy which increases aggregate demand,
whereas contractionary fiscal policy refers to a fiscal policy which decreases aggregate
demand. Using these definitions and the results above, we can draw the follwing
conclusions about the effects of fiscal policy changes in this Classical economy.

Expansionary fiscal policy increases the real interest rate level and is
inflationary.



When the only policy change is an increase in government purchases,
the budget deficit increases and the composition of output shifts away
from investment toward government purchases.
When the only policy change is an decrease in net taxes, the budget
deficit increases and the composition of output shifts away from
investment toward consumption.
Contractionary fiscal policy decreases the real interest rate level and is
deflationary.


When the only policy change is an increase in government purchases,
the budget deficit decreases and the composition of output shifts away
from government purchases toward investment.
When the only policy change is an decrease in net taxes, the budget
deficit increases and the composition of output shifts away from
consumption toward investment.
If the Classical model is viewed as an appropriate model for long term analysis, these
results indicate that fiscal policy determines the composition of output for the economy
over longer periods of time. Government can use this knowledge to select any desirable
composition. If a proportionate increase in consumption is desired, then a tax cut is the
appropriate policy. This policy will crowd out investment.
However, by decreasing
government purchases along with net taxes---i.e., down-size government, the model
indicates that it is possible to increase consumption without crowding out investment.
Thus, after having decided that an increase in consumption is desirable, it would also be
wise to decide whether it is more desirable to obtain the relative increase in consumption
at the expense of investment or at the expense of government purchases. Such decisions
are value judgments.
If a proportionate increase in investment is desired, the a reduction in the budget
deficit is appropriate, either through a decrease in government purchases, an increase in
net taxes, or both. Focusing on a net tax increase would favor investment at the expense
127
Expansionary
Fiscal Policy
Contractionary
Fiscal Policy
Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
of consumption, while focusing on a government purchases decrease would favor
investment at the expense of government purchases. Again, the ultimate decision is a
value judgment.
Finally, if a proportionate increase in government purchases is desired, then an
increase in government purchases is the appropriate policy. By simultaneously increasing
net taxes so that the budget deficit does not increase, the increase in government
purchases is obtained primarily at the expense of consumption. Alternatively, if the
budget deficit increases because net taxes are not simultaneously increase, the increase in
government purchases is obtained primarily at the expense of investment.
8.7 Monetary Policy in a Classical Economy
Notice that there is no dM term in conditions (8.54), (8.55), and (8.58). This indicates
that a change in the money supply has no impact on the employment level, the output
level, or the real interest rate level. If none of these variables change, then consumption
and investment also do not change. Money neutrality refers to this situation---one in
which a change in the money supply has no impact on any real economic variable.
The positive coefficient on (8.59) indicates that a change in the money supply will
affect the price level. To be precise, setting dT=dG=d=dK=dZ=0, (8.59) reduces to
dP 
1
dM
L
dP M dM

P PL M
(8.60)
dP dM

P
M
Equation (8.60) indicates that, if the only change in the economic environment is a
change in the money supply, then the economy’s inflation will be equal to the economy’s
rate of economic growth.
Money
Neutrality
A change in the money supply will also affect the nominal wage level. To get the
precise relationship between the two, we can use either equation (8.51) or (8.52). We
already know that the employment level N will not change unless either the capital stock
K changes or the population level Z changes. Differentiating either equation (8.51) or
equation (8.52) under the assumption that dK=dZ=0, we obtain
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
W 
d    0,
P
1
W
dW  2 dP  0
P
P
W dW W dP

0
P W
P P
(8.61)
dW dP

W
P
That is, the nominal wage growth rate must equal the inflation rate.
From the Classical perspective, the bottom line for monetary policy is that it is
impotent in that it cannot affect the “real” path the economy follows over time. Rather, it
can only be used to govern the economy’s inflation rate and rate of nominal wage growth.
8.8 Change in the State of Expectations with Regard to Investment
Keynes stressed that the demand for investment goods is subject to sudden, rather
unpredictable changes due to sudden changes in the expected profitability of investment.
Keynes viewed such fluctuations in investment as a primary cause of fluctuations in
employment and output. The inclusion of the exogenous variable  in the investment
function allows us to examine the effects of such a change in expectations.
Contrary to Keynes’ theory, the absence of a d term in (8.54) and (8.55) indicate that
a change in the expected profitability of investment affects neither the employment level
nor the output level in this Classical model. Why does the Classical model generate this
result? Let us answer this question by telling a “Classical story” about how a change in
expectations works its way through the economy.
Suppose, for whatever reason, the expected profitability of investment decreases; i.e.,
 decreases so that d is negative. Our investment function indicates that investment
will decrease, which will decrease aggregate demand. The decrease in aggregate demand
implies an excess supply of output in the product market and an excess supply of saving
in the capital market. In response to the excess supply of saving, the interest rate level
decreases. Thus, as indicated by the positive coefficient on d in equation (8.58),
worsening expectations leads to a declining interest rate level. The decrease in the
interest rate level increases investment demand and, consequently, aggregate demand. To
eliminate the surplus of saving (or the surplus of output), the interest rate level must
decrease enough so that the increase in investment caused by the declining interest rate
level just offsets the decrease in investment caused by the change in expectations.
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
The decrease in the interest rate level increases money demand and creates an excess
demand for money. As people spend less on goods and services so as to increase their
money holdings, the price level decreases. Thus, as indicated by the positive coefficient
on d in equation (8.59), worsening expectations lead to a decrease in the price level.
A decrease in the price level makes employing labor less profitable. As employers lay
off workers in response to this decline in profitability, an excess supply of labor is
created. This increase in involuntary unemployment is what Keynes expected to arise
from the negative change in expectations. As employment falls, output would also fall,
meaning the economy enters a recession. However, the distinguishing feature of
Classical model is that the nominal wage level will adjust in response to either a surplus
or shortage of labor. In this case, the labor surplus would lead to a decrease in the
nominal wage level until the economy moved back to the full employment level---the
employment level where the economy was prior to the change in expectations.
Thus, the reason why the change in employment does not lead to the results predicted
by Keynes is because the nominal wage level is assumed to adjust so as to maintain full
employment. With full employment maintained by the adjusting nominal wage, the
change in expectations does not affect the economy’s output level because it does not
affect the economy’s ability to produce. If the wage adjustment assumption is taken
away, then the results predicted by Keynes appear. Thus, we see that the essence of The
General Theory is the assumption that the nominal wage is “sticky.”
Key Words: Chapter 8
The General Theory
Marginal Propensity to Save
Marginal Propensity to Consume
Crowding Out
Supply-side
Full Employment Output Level
Long Run
Composition of Output
Contractionary Fiscal Policy
Effective Demand
Autonomous Spending Multiplier
Say’s Law
Marginal Disutility of Employment
Demand-side
Potential Output Level
Short Run
Expansionary Fiscal Policy
Money Neutrality
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Chapter 8: The Essence of The General Theory: Relaxing the Classical Tradition
131