W3P2 - Closed Economy ISLM

Question 1

Assume the following model of the economy, with the price level fixed at 1:
C = 500 + 0.8 (Y − T)
T = 1000
I = 800 − 20r
G = 1000
Ms = 1200 (30)
Md/P= 0.4Y − 40r

Write numerical formulas for the IS and LM schedules, showing Y as a function of
r alone in both cases

Answer 1

IS schedule:
Y=C+I+G -> Y=500+0.8(Y-T)+800-20r+G
Y=500+0.8(Y-1000)+800-20r+100
make y the subject:
Y=7500-100r
the partial derivative of income Y with respect
to the interest rate r is negative, indicating that the IS schedule is downward sloping

LM schedule:
Md/P=0.4Y-40r
make y the subject: Y=Md+40r/0.4
Using condition that Ms=Md in equilibrium
Y=Ms+40r/0.4 = 1200+40r/0.4
Y=3000+100r
the partial derivative of income Y with respect
to the interest rate r is positive indicating that the LM schedule is
upward sloping

Question 2

What is the IS schedule derived from?

Answer 2

the goods market

Y = C + I + G

Question 3

What is the LM schedule derived from?

Answer 3

the money market

Md/P

Question 4

Where does short-run equilibrium occur?

Answer 4

at the points where the IS and LM schedules intersect

Question 5

Assume the following model of the economy, with the price level fixed at 1:
C = 500 + 0.8 (Y − T)
T = 1000
I = 800 − 20r
G = 1000
Ms = 1200 (30)
Md/P= 0.4Y − 40r
IS = 7500 - 100r
LM = 3000 + 100r

What are the short-run equilibrium values of Y, r, Y − T, C, and I?

Answer 5

Equilibrium is where the IS and LM schedule intersect, thus the interest rate is LM=IS
-> 3000+100r=7500-100r
->r=22.5
Using this interest rates in either the IS or LM schedule gives for equilibrium income
Y = 7500 − 100r -> Y=5250
Investment is:
I=800-20r -> I=350
Disposable income (Y-T) is:
Yd=Y-T -> Yd=4250
Consumption is:
C=500+0.8(Y-T) -> C=3900

Question 6

Assume that G increases by 200. By how much will Y increase in short-run equilibrium? What is the government spending multiplier?

C = 500 + 0.8 (Y − T)
T = 1000
I = 800 − 20r
G is now = 1200
Ms = 1200 (30)
Md/P= 0.4Y − 40r
LM = 3000 + 100r

Answer 6

IS schedule is now Y=C+I+G
Y=500+0.8(Y-T)+800-20r+G
Y=500+0.8(Y-1000)+800-20r+1200
Make y the subject: Y =8500-100r (gives IS)
LM stays the same so the equilibrium rate (LM=IS) is:
3000+100R=8500-100r
r=27.5
in previous q, r=22.5
So that the equilibrium interest rate is increasing from 22.5 to 27.5.
Plugging the interest rate back into the IS or LM schedule gives income
Y=8500-100r = 5750
Income has increased from 5250 to 5750 (increase by 500 units), hence the gov multiplier is:
ΔY/ΔG=500/200=2.5
Which is lower than the value implied by the MPC of 0.8 that you would get in the Keynesian Cross model.