The Keynesian
Cross Model, The
Money Market, and
IS/LM
Planned expenditure and actual
expenditure.
Constructing the Keynesian Cross
• Actual expenditure is Y and
planned expenditure is
E = C + I + G.
• I, G, and T are assumed
E
exogenous and fixed.
Y=E
• Our consumption function is
C = c(Y–T), where c is the
marginal propensity to
consume (mpc).
• Mapping out
•
•
E = c(Y–T) + I + G gives us…
The slope of E is the mpc.
In equilibrium planned
expenditure equals total
expenditure or Y=E.
E=C+I+G
E*
mpc
£1
Y*
Y
Constructing the Keynesian Cross
• Equilibrium is at the point
•
•
•
•
where Y = C + I + G.
If firms were producing at Y1
then Y > E
Because actual expenditure
exceeds planned
expenditure, inventory
accumulates, stimulating a
reduction in production.
Similarly at Y2, Y < E
Because planned expenditure
exceeds actual expenditure,
inventory drops, stimulating
an increase in production.
Inventory
accumulates.
drops.
E
Y=E
E=C+I+G
E*
mpc
£1
Y2
Y*
Y1
Y
Government expenditure and tax multipliers
• An increase of G by ΔG causes an
upward shift of planned expenditure
by ΔG.
• Notice that ΔY > ΔG. This is because
•
although ΔG causes an initial change
in Y of ΔG, the increased Y leads to
an increase in consumption and
triggers a multiplier effect.
Now suppose a decrease of T by ΔT
E2
that causes an upward shift of
E3
planned expenditure by mpc*ΔT.
• Notice again that ΔY > ΔT but that ΔY
is less than in the case with ΔG. This
is because ΔT causes no initial
change in Y as ΔG did, the decrease
in T simply leads to an increase in
consumption and triggers the
multiplier effect.
E
Y=E
ΔG
mpc*ΔT
E1
Y
Y1
Y3 Y2
Building the IS curve
E
E=Y
• The IS curve maps the
relationship between r and Y for
the goods market.
E=C+I(r1)+G
Let the interest rate
This decrease in
increase
So Y decreases
from r1 to from
r2
investment
The IS curve
causes
mapsthe
out this
reduce planned
Y1 toinvestment
Y2.
planned
relationship
expenditure
between the
from I(r1) to I(r2).
function
interest to
rate,
shift
r, and
down.
output
(or income) Y.
E=C+I(r2)+G
ΔI
Y2
r
r
r2
r2
r1
r1
I(r)
I
I(r2)
I(r1)
Y
Y1
IS
Y2
Y1
Y
Shifting the IS curve
E
• While changing r allows us to map
E=Y
out the IS curve, changes in G, T,
or mpc cause Y to change for any
level of r. This causes a shift in
the IS curve.
E=C+I+G2
E=C+I+G1
ΔG
Suppose an increase in G
causes planned
expenditure to shift up by
ΔG.
For any r the increase in G
causes an increase in Y of
ΔG times the government
expenditure multiplier.
Y1
Y
Y2
r
r1
Therefore, the IS curve
shifts to the right by this
amount.
IS´
IS
Y1
Y2
Y
A loanable funds market interpretation
• The IS curve maps the
relationship between r and Y for
the loanable funds market in
equilibrium.
• Suppose Y increases from Y1 to
• The IS curve maps out this
Y2. This raises savings from S(Y1)
to S(Y2) resulting in a lower
equilibrium interest rate.
relationship between the
lower interest rate and
increased income.
r
r
S(Y1)
S(Y2)
r1
r1
r2
r2
I(r)
I
IS
Y1
Y2
Y
A loanable funds market interpretation of fiscal policy
• While changing r allows us to map
out the IS curve, changes in G, T,
or mpc cause Y to change for any
level of r. This causes a shift in
the IS curve.
• Suppose again an increase in G.
• Therefore, for a given Y there is a
In the loanable funds market this
results in a decrease in S and an
increase in the interest rate.
higher level of r. So, the IS curve
shifts up by this amount.
r
r
S(G2)
S(G1)
r2
r2
IS´
r1
r1
I(r)
I
IS
Y1
Y
Building the LM curve
• The LM curve maps the
relationship between r and Y for
the money market.
Given money supply
and money demand
suppose an increase in
income raises money
demand.
r
The LM curve maps
out this relationship
between
r and Y.
r
(M/P)s
LM
r2
r1
r2
L(r,Y1) L(r,Y2)
r1
Real
Money
Balances
Y1
Y2
Y
Shifting the LM curve
• While changing money demand
money
supply
and
allows usGiven
to map
out the
LM curve,
Now
there
is
a
higher
real
changesmoney
in M ordemand
P causesuppose
r to
a
interest
rate
for
the
current
changedecrease
for any level
of money
Y. This stock
in the
causes a shiftlevel
in the
curve.
of LM
output.
The LM curve shifts
up so that at the same
level of output the
interest rate is higher.
shifts real money supply to
the left resulting in a higher
equilibrium interest rate.
r
(M2/P)s (M1/P)s
r
LM´
r2
r1
LM
r2
L(r,Y)
r1
Real
Money
Balances
Y
Y
IS=LM: The Short Run Equilibrium
• Given our IS and LM equation we
•
•
•
can now determine the short run
equilibrium interest rate and
output
By mapping out the relationship
between Y and r when the goods
market (or loanable funds market)
is in equilibrium we get the IS
curve.
By mapping out the relationship
between Y and r when the money
market is in equilibrium we get the
LM curve.
When we set IS=LM we can solve
for the equilibrium levels of r and
Y. This represents simultaneous
equilibrium in the goods market
(or loanable funds market) and the
money market.
r
LM
r*
IS
Y*
Y
Conclusion
• We constructed the IS curve from the goods
market and from the loanable funds market.
We discussed shifting factors for IS.
• We constructed the LM curve from the
money market and discussed shifting
factors for LM.
• Finally, we set IS=LM to achieve equilibrium
in all markets giving us short run
equilibrium r and Y.