Question

In a small open economy which has a national income identity as the following.

Y= C + I + G + NX

Where C = 400-1000r +0.75 (Y-T)

I = 240-4000r

G= 850

T= 300 + 0.1 Y,

NX= 800-0.075 Y-120 e

Where e= foreign currency/ domestic currency, and initially set at

e = 1.25 + 10r

The money demand function is Md = 840 + 0.4 Y-1000 r

and Money supply is set by the Central Bank at 2540.

a) Derive the IS and LM curves for the economy,

b) Calculate the equilibrium level of GDP and the interest rate

c) The government increases its expenditures by 150 to 1000, show the shift of the diagram and figure out the new equilibrium level of GDP and interest rate based on the new IS curve and initial LM curve?

New IS after increasing government spending by 150,

IS: _____________________________________

New equilibrium GDP and interest rate

Answer 1

Solution:

a):-

• Deriving Equation for LM:-

IS Equation -

Y = C + I + G + NX

Y = 400 - 1000r + 0.75(Y - T) +240 - 4000r + 850 + 800 - 0.075Y -120e

where T = 300 + 0.1Y and e = e = 1.25 + 10r

Y = 2290 - 5000r + 0.75(Y - 300 - 0.1Y) -0.075Y - 120(1.25 + 10r)

Y = 2290 - 5000r + 0.75(0.9Y - 300) - 0.075Y - 120(1.25 + 10r)

Y = 2290 - 5000r + 0.675Y - 225 - 0.075Y - 150 - 1200r

Y = 2290 - 6200r + 0.6Y - 375

Y - 0.6Y = 1915 - 6200r

Y = (1915 - 6200r)/0.4

Y = 4787.5 - 15500r

• Deriving Equation for LM:-

Md = 840 + 0.4Y - 1000r

Ms = 2540

For money market to be in equilibrium:

Ms = Md

2540 = 840 + 0.4Y - 1000r

1700 = 0.4Y - 1000r

0.4Y = 1700 + 1000r

Y = 4250+ 2500r

b) :-

Equlibrium GDP & rate :

In Equilibrium

IS = LM

4250 + 2500r =4787.5 - 15500r

2500+ 15500r = 4787.5 - 4250

18000r = 537.5

r = 537.5/18000 = 0.0298 ~ 2.98%

Equlibrium Rate

Y = 4250 + 2500(0.02986) = 4250 + 74.652 = 4324.652

Equlibrium GDP = 4324.652

c) :-

Now, IS equation(new) :-

Y = 400 - 1000r + 0.75(Y - T) +240 - 4000r + 850 + 800 - 0.075Y -120e + 150

where T = 300 + 0.1Y and e = e = 1.25 + 10r

Y = 2440 - 5000r + 0.75(Y - 300 - 0.1Y) -0.075Y - 120(1.25 + 10r)

Y =2440 - 5000r + 0.75(0.9Y - 300) - 0.075Y - 120(1.25 + 10r)

Y = 2440 - 5000r + 0.675Y - 225 - 0.075Y - 150 - 1200r

Y = 2440 - 6200r + 0.6Y - 375

Y - 0.6Y = 2065 - 6200r

Y = (2065 - 6200r)/0.4

Y = 5162.5 - 15500r

Similarly, LM equation(new)

Y = 4250 + 2500r

In equlibrium -

IS = LM

4250 + 2500r = 5162.5 - 15500r

15500r +2500r = 5162.5 - 4250

18000r = 912.5

r = 912.5/18000

r = 0.05069

New Equilibrium Rate = 0.05069 ~ 5.069%

Y = 4250 + 2500r = 4250 + 2500(0.05069) = 4250 + 126.725 = 4376.725

New Equilibrium GDP = 4376.725