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The Keynesian Cross
vs
the “Classical” Cross
Alfred Marshall
John Maynard Keynes
A Telling Exercise
in Comparative Frameworks
Roger W. Garrison
2010
EXPENDITURES
a = 2,000
b = 0.75
I = 1,250
I
a
45O
Y=E
E=C+I
Combining
Expenditures
Spending
In
The
a wholly
primary
on
private
“Y=E”
consumption
playing
on of
the
with
economy,
economy’s
field
“E=C+I”
for
goods
theand
The
intersection
“E=C+I”
with
output
is
only
taking
Keynesian
a stable
other
into
become
component
function
account
macroeconomics
0 line
the allowing
income
of
C’sincome.
ofrelationship
spending
paid
has
The
“Y=E”
(the
45
income
to
linear
is
the
investment
workers
Ymeasured
relationship
allows
and
us
spending
tovertically
of
toother
allows
INCOME
calculate
(“I”),
factors
for
some
(Y)
this
of as
C = a + bY with
to
bedimensions
as which
well
1
production.
consumption
is
economy’s
and
simply
EXPENDITURES
added
equilibrium
“Y
(“a”)
= vertically
E”even
constitutes
income.
(E).
when
to
all
horizontally)
identifies
the
circularb
possible
income
consumption
iscircular-flow
(temporarily)
spending
(“C”)
zero.
1
flow equilibrium
point equilibria.
for
thisto get
1
total
Y
= Espending
and E
= C(“E”).
+I
particular
economy.
An upward slope (“b”) that is less
So,
=C+
I, where
C when
= a + bY
thanYone
means
that
people
Combining:
Y = a + bY
+ Ispend
earn more income,
they
Yeq = 13,000
more
but that
theyasave
more,
Suppose
= 2,000;
b =too.
0.75;
INCOME (Y)
and I = 1,250.
We can now write:
C = 2,000 + 0.75Y
And Y = 2,000 + 0.75Y + I,250
If dollar magnitudes are in billions
of dollars, then equilibrium income
is Yeq = $13,000 billion.
Or: Y – 0.75Y = 2,000 + I,250
Simplifying: 0.25Y = 3,250
Finally: Y = 13,000
EXPENDITURES
a = 2,000
b = 0.75
I = 1,250
I
a
45O
Y=E
E=C+I
The low
For
income-expenditure
levels of income, graph
consumption
tracks
consumption
spending
spending
exceeds
(C)
income;
totalsaving
spending
in this
(C+I)
lowasrange
these
C = a + bY and
(shown in red)
magnitudes
relate
is negative.
to income.
Indirectly, this graph keeps track of
For higher levels of income,
saving, too.
consumption spending is less than
Saving (S),
income;
saving
which
in this
simply
range
means
not spending
(shown
in green)
some
is positive.
part of income
can be written: S = Y – C.
Where red and green meet, saving
INCOME (Y)
Graphically,
is
neither negative
S is thenor
vertical
positive.
distanceare
People
between
neitherCsaving
and Y.nor
dissaving. Rather, S = 0 or,
equivalently, C = Y.
EXPENDITURES
Y=E
E=C+I
The saving
We’ve
First,
we
seen
track
function
that
saving
the is
equality
(“S”)
derived
asofit
income from
depends
directly
and
on expenditures
income.
the definition means
of
that the(S
economy
= Y – C)isand
in a the
circularC = a + bY saving
The “a” in the upper panel, which
flow equilibrium.
consumption
function (C = a + bY):
is consumption spending with no
We can now
income,
becomes
show“-a”
thatinthe
theequality
lower
S=Y–C
between
panel,
Now,
for
which
what
saving
indicates
level
andofinvestment
Y“dissaving.”
is S = 0?is
C =alternative
a + bY
an
condition for a
The
red-green
boundary in the
S
= – a + (1 – equilibrium.
b)Y
circular-flow
Combining: S = Y – (a + bY)
upper
panel marks the point in the
S = – 2,000 + (1 – 0.75)Y
Distributing:
S=Y–
a – bYis zero.
lower
panel where
saving
a = 2,000
b = 0.75
I = 1,250
I
a
45O
SAVIING (S)
INVESTMENT (I)
INCOME (Y)
the saving function.
S = – a + (1 – b)YY = 20/0.25 = 8,000
YS=0 = 8,000
[YS=0); S = 0]
–a
S = – 2,000 + 0.25Y
Rearranging:
S = the
–a+
Y – bY
We
now connect
(negative)
S
= – of
2,000
+ 0.25Y
=0
level
saving
when
and the
Factoring:
S=–
a + (1Y=0
– b)Y
level
of income
when S=0 to depict
– 2,000
= – 0.25Y
INCOME (Y)
1-b
[Y = 0;1 S = – a]
EXPENDITURES
a = 2,000
b = 0.75
I = 1,200
Y=E
E=C+I
The income ranges of dissaving
(red) and saving (green) are more
C = a + bY obvious with S graphed by itself.
Now, we show that investment (I)
does not depend on income.
I
a
45O
SAVIING (S)
INVESTMENT (I)
INCOME (Y)
S
I
I
–a
INCOME (Y)
We note that the equality of saving
and investment occurs at the
same level of income at which
income equals expenditures.
Notice also that all the information
contained or implied in the Y=E
graph is also contained or implied
in the S=I graph.
THE “CLASSICAL” CROSS
The Keynesian Cross, featuring the
intersection of Y and E or of S and I,
is fundamental to Keynesian theory.
The Keynesian Cross stands in
contrast to the “Classical” Cross,
whose relevance presuppose that
markets work.
SAVIING (S)
INVESTMENT (I)
Its relevance presupposes that labor
markets and output markets are
dysfunctional and that the interest
rate is out of play.
S
I
I
INCOME (Y)
RATE OF INTEREST
THE KEYNESIAN CROSS
S
D
SAVIING (S)
INVESTMENT (D)
SAVIING (S)
INVESTMENT (I)
And that’s good: if saving were to
shift upward, income spirals
downward until the equilibrium level
of saving, once again, equals the
unchanged level of investment.
This is Keynes’s
Paradox of Thrift.
S
I
INCOME (Y)
Marshall argued that the supply
and demand for loanable funds
are fully functional.
If saving shifts rightward,
the interest rate falls,
stimulating an increased
level of investment.
RATE OF INTEREST
Keynes argued that the saving curve
doesn’t shift. The parameters “a” and
“b” don’t change.
S
D
SAVIING (S)
INVESTMENT (D)
We can identify significant similarities and differences between Keynesian
theory and classical theory by responding to a few revealing questions.
Al, you’re
YES
YES….
Income
No.
The
Only
government
–with
adjusts.
by
just
“equilibrium”
accident
anThe
should
old or
understood
economy
design
fuddy-duddy!
is this
stimulus
spirals
asequality
apackages
balance
up or
between
down
consistent
to
supplement
untilincome
with
saving
spending
full
and
is
expenditures.
brought
employment.
and
driveinthe
lineeconomy
with
to
investment.
full
employment.
S
I
INCOME (Y)
YESinterest
YES….
The
Yes.
About
The
–with
what??
wage
“equilibrium”
rate
There
rate
adjusts,
adjusts,
is no
understood
moving
too,
need
infor
the
up
stimulus
face
or
asdown
aofbalance
packages.
shortages
in
between
response
or
The
surpluses
government
loanable
to shortages
of labor.
should
fundsorget
supplied
surpluses
Where
out
of the
did
and
market’s
of
you
loanable
demanded.
learnway
your
funds.
and
microeconomics,
let
it work. LaissezMaynard?
faire!
RATE OF INTEREST
SAVIING (S)
INVESTMENT (I)
Just
Is
Does
What
thehow
“equilibrium”
the
equality
should
is
market
this
the
ofadjustment
saving
itself
government
entail
bring
and
an made
about
equality
do in
investment
of
a
about
market
saving-investment
saving
it?economy?
and
consistent
investment?
equality?
with
maintaining full employment?
S
D
SAVIING (S)
INVESTMENT (D)
The Keynesian Cross
vs
the “Classical” Cross
Alfred Marshall
John Maynard Keynes
A Telling Exercise
in Comparative Analytical Frameworks
Roger W. Garrison
2010