The Keynesian Cross Model, The Money Market, and IS/LM (Junior_ Economist)

1. THE KEYNESIAN
CROSS MODEL, THE
MONEY MARKET,
AND IS/LM
PLANNED EXPENDITURE AND ACTUAL
EXPENDITURE.

2. CONSTRUCTING THE KEYNESIAN
CROSS
• ACTUAL EXPENDITURE IS Y AND
PLANNED EXPENDITURE IS
E = C + I + G.
• I, G, AND T ARE ASSUMED
EXOGENOUS AND FIXED.
• 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… Y
E
E=C+I+G
Y=E
£1
mpc
Y*
E*
• The slope of E is the mpc.
• In equilibrium planned
expenditure equals total
expenditure or Y=E.

3. CONSTRUCTING THE KEYNESIAN
CROSS
Y
E
E=C+I+G
Y=E
• Equilibrium is at the point where Y
= C + I + G.
mpc
Y*
E*
Y2 Y1
Inventory
accumulates.
Inventory
drops.
£1
• 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.
• If firms were producing at Y1
then Y > E

4. GOVERNMENT EXPENDITURE AND TAX
MULTIPLIERS
• AN INCREASE OF G BY ΔG CAUSES
AN UPWARD SHIFT OF PLANNED
EXPENDITURE BY ΔG.
Y
E
GΔ
Y=E
Y1
E1
E2
• 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
that causes an upward shift of
planned expenditure by mpc*ΔT.
Y2
• 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.
Y3
E3
mpc* TΔ

5. BUILDING THE IS CURVE
• THE IS CURVE MAPS THE
RELATIONSHIP BETWEEN R AND Y
FOR THE GOODS MARKET.
IS
Y
E
Y2 Y1
r
I
I(r)
ΔI
Y2 Y1
r2
r1
r2
r1
I(r1)I(r2)
E=Y
E=C+I(r1)+G
E=C+I(r2)+G
Let the interest rate increase
from r1 to r2 reduce planned
investment from I(r1) to I(r2).
This decrease in investment
causes the planned
expenditure function to shift
down.
So Y decreases
from
Y1 to Y2.
Y
r
The IS curve maps
out this relationship
between the
interest rate, r, and
output (or income)
Y.

6. SHIFTING THE IS CURVE
• 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.
IS
Y
E
Y1 Y2
ΔG
Y1 Y2
r1
E=Y
E=C+I+G2
E=C+I+G1
Suppose an increase in G
causes planned expenditure to
shift up by ΔG.
Y
r
For any r the increase in G
causes an increase in Y of ΔG
times the government
expenditure multiplier.
Therefore, the IS curve
shifts to the right by this
amount.
IS´

7. A LOANABLE FUNDS MARKET
INTERPRETATION
• THE IS CURVE MAPS THE
RELATIONSHIP BETWEEN R AND Y
FOR THE LOANABLE FUNDS
MARKET IN EQUILIBRIUM.
IS
r
I
I(r)
Y2Y1
r2
r1r1
r2
S(Y2)
Y
r
S(Y1)
• Suppose Y increases from Y1 to Y2. This
raises savings from S(Y1) to S(Y2) resulting
in a lower equilibrium interest rate.
• The IS curve maps out this
relationship between the lower
interest rate and increased
income.

8. 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.
IS
r
I
I(r)
Y1
r2
r1r1
S(G1)
Y
r
r2
S(G2)
IS´
• Suppose again an increase in G. In
the loanable funds market this
results in a decrease in S and an
increase in the interest rate.
• Therefore, for a given Y there is a
higher level of r. So, the IS curve
shifts up by this amount.

9. BUILDING THE LM CURVE
• THE LM CURVE MAPS THE
RELATIONSHIP BETWEEN R AND Y
FOR THE MONEY MARKET.
LM
r
Real
Money
Balances
L(r,Y2)
Y1
r2
r1r1
Given money supply and
money demand suppose
an increase in income
raises money demand.
Y
r
r2
(M/P)s
L(r,Y1)
The LM curve maps
out this relationship
between
r and Y.
Y2

10. SHIFTING THE LM CURVE
• WHILE CHANGING MONEY DEMAND
ALLOWS US TO MAP OUT THE LM
CURVE, CHANGES IN M OR P
CAUSE R TO CHANGE FOR ANY
LEVEL OF Y. THIS CAUSES A SHIFT
IN THE LM CURVE.
r
Real
Money
Balances
r2
r1
Given money supply and
money demand suppose a
decrease in the money stock
shifts real money supply to
the left resulting in a higher
equilibrium interest rate.
(M1/P)s
L(r,Y)
Now there is a higher real
interest rate for the current
level of output.
(M2/P)s
The LM curve shifts up so
that at the same level of
output the interest rate is
higher.
LM
Y
r2
r1
Y
r
LM´

11. IS=LM: THE SHORT RUN EQUILIBRIUM
• GIVEN OUR IS AND LM EQUATION
WE CAN NOW DETERMINE THE
SHORT RUN EQUILIBRIUM
INTEREST RATE AND OUTPUT
LM
Y*
r*
Y
r
IS
• 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.

12. 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.
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