ISLM Question?

Question

a. Consider this economy: C = 200 + 0.75 (Y-T) and I = 200 - 25r.

Government purchases and taxes are both 100. Graph the IS curve for r ranging from 0 to 8.

b. The money demand is (M/P)^d = Y - 100r. The money supply M is 1,000 and price level P is 2. Graph the LM curve for r ranging from 0 to 8.

c. Find the equilibrium interest rate r and the equilibrium level of income Y.

d. Suppose that government purchases increase from 100 to 150. How much does the IS curve shift? What are the new equilibrium interest rate and level of income?

e. Suppose instead that the money supply is raised from 1,000 to 1,200. How much does the LM curve shift? What are the new equilibrium r and level of income?

f. With the initial values for monetary and fiscal policy, suppose that the price level rises from 2 to 4. What happens? What are the new equilibrium r and level of income?

g. Derive and graph an equation for the aggregate demand curve. What happens to it if monetary/fiscal policy changes, as in part d?

Answer 1

a)

Y=C+I+G+NX

T=100

C=200+0.75Y-75 = 125+0.75Y

Y=125+0.75Y+200-25R+100

0.25Y=425-25R

Y=1700-100R = Is Curve Equation

IS Curve Graph:

r      0     1          2       3           4      5 6        7        8

Y  1700 1600   1500 1400    1300 1200   1100 1000   900

b)

1000/2=Y-100R

Y=500+100R   LM Curve equation

LM Curve Graph:

r      0     1      2        3          4 5          6          7        8

Y  500 600   700    800 900     1000   1100   1200 1300

c)

Equilibrium LM=IS

1700-100R = 500+100R

1200 = 200r

Answ: equilibrium R=6% Y=1'100

d)

Change 150-100=+50

Old Y:

0.25Y=425-25R

New Y:

0.25Y=425-25R+50

0.25Y=475-25R

Y=1900-100R  =  New IS Curve Equation

New equilibrium:

1900-100R=500+100R

1400=200R

R=7%

Y=1'200

e)

1200/2=Y-100R

100R=Y-600

R=0.01Y-6

Y=100R+600   New LM Curve Equation

New equilibrium:

100R+600=1'700-100R

200R=1'100

R=5.5%

Y=1'150

f)

1000/4=Y-100R

250=Y-100R

Y=100R+250 (new LM curve)

Y=1700-100R (Old IS curve)

IS=LM

100R+250=1'700-100R

200R=1'450

R= 7.25%

Y= 975

Answ: R will increase to 7.25% (by 7.25-6=+1.25% percentage points) and Y will fall by -125 (975-1'100=-125) to 975. LS will shift up for +1.25% (by R axis)

g)

Initial IS curve Y=1700-100R (this one is fixed)

Rearrange to: 100R=1700-Y

Parts of LM curve (variable):

M/D=1000/P

1000/P=Y-100R

Y=100R+1000/P

Put IS curve into LM curve (100R)

Y=1700-Y+1000/P

2Y=1700+1000/P

Y=850+500/P

500/P=Y-850

P=500/(Y-850)

Answ: Aggregate demand equation:

Y=850+500/P or P=500/(Y-850)

IS curve (from part "d")

Y=1900-100R

Parts of LM curve:

M/D=1000/P

1000/P=Y-100R

100R=Y-1000/P

Put in into IS curve (100R)

Y=1900-Y+1000/P

2Y=1900+1000/P

Y=950+500/P

500/P=Y-950

P=500/(Y-950)

Answ: Aggregate demand equation:

Y=950+500/P or P=500/(Y-950)

Changes from initial aggregate demand: (from Y=850+500/P to Y=950+500/P) - AD will shift right for +100 (by Y axis)

Answer 2

a)

Y=C+I+G+NX

NX=0 (closed economy)

T=100

C=200+0.75Y-75 = 125+0.75Y

Y=125+0.75Y+200-25R+100

0.25Y=425-25R

Y=1700-100R

100R=1700-Y

IS curve: R=17-0.01Y

..8|_.R %

....|..\__

....| ......\__

....|............\__

.6.|...........| .....\__ IS - Curve

....|...........|...........\__

....|...........|................\__

.4.|...........|.................... |\__

....|...........|.................... |.....\__

....|...........|.................... |.........\__

....|.......... |.....................|.... .........\__

.2.|-----------|-------------------- |--.------------ |...\__

....|...........|.................... |............... |.......\__

....|...........|.................... |.............. .|............\__

.0.|.______|_____.  _____ |_________ |_________\____> Y

...900 ...1100........... 1300........... 1500........... .1700

R%........Y

0.......1'700

1.......1'600

2.......1'500

3.......1'400

4.......1'300

5.......1'200

6.......1'100

7.......1'000

8.........900

b)

1000/2=Y-100R

Y=500+100R

100R=Y-500

R=0.01Y-5

LM curve: R=0.01Y-5

R%.......Y

8.......1'300

7.......1'200

6.......1'100

5.......1'000

4.........900

3.........800

2.........700

1.........600

0.........500

c)

Equilibrium LM=IS

0.01Y-5=17-0.01Y

0.02Y=22

Y=1'100

R=1'100*0.01-5 = 11-5=6%

Answ: equilibrium R=6% Y=1'100

d)

Change 150-100=+50

Old Y:

0.25Y=425-25R

New Y:

0.25Y=425-25R+50

0.25Y=475-25R

Y=1900-100R

R=19-0.01Y

New IS R=19-0.01Y

Old IS: R=17-0.01Y

Shift:

Y(new)=0 R=17

R(old)=17

So: 19-0.01Y=17

2=0.01Y

Y=200

Answ: IS will shift right by +200 (on Y axis)

New equilibrium:

1900-100R=500+100R

1400=200R

R=7%

Y=1900-100*7=1900-700=1'200

e)

1200/2=Y-100R

100R=Y-600

R=0.01Y-6

Y=100R+600

New equilibrium:

100R+600=1'700-100R

200R=1'100

R=11/2=5.5%

Y=100*5.5+600=550+600 =1'150

LM will shift down by  -0.5%=5.5%-6.0% (on R axis)

Answ: New equilibrium R=5.5% Y=1'150

f)

1000/4=Y-100R

250=Y-100R

Y=100R+250 (new LM curve)

Y=1700-100R (Old IS curve)

IS=LM

100R+250=1'700-100R

200R=1'450

R=7.25%

Y=100*7.25+250= 725+250=975

Answ: R will increase to 7.25% (by 7.25-6=+1.25% percentage points) and Y will fall by -125 (975-1'100=-125) to 975. LS will shift up for +1.25% (by R axis)

g)

Initial IS curve Y=1700-100R (this one is fixed)

Rearrange to: 100R=1700-Y

Parts of LM curve (variable):

M/D=1000/P

1000/P=Y-100R

Y=100R+1000/P

Put IS curve into LM curve (100R)

Y=1700-Y+1000/P

2Y=1700+1000/P

Y=850+500/P

500/P=Y-850

P=500/(Y-850)

Answ: Aggregate demand equation:

Y=850+500/P or P=500/(Y-850)

IS curve (from part "d")

Y=1900-100R

Parts of LM curve:

M/D=1000/P

1000/P=Y-100R

100R=Y-1000/P

Put in into IS curve (100R)

Y=1900-Y+1000/P

2Y=1900+1000/P

Y=950+500/P

500/P=Y-950

P=500/(Y-950)

Answ: Aggregate demand equation:

Y=950+500/P or P=500/(Y-950)

Changes from initial aggregate demand: (from Y=850+500/P to Y=950+500/P) - AD will shift right for +100 (by Y axis)