Question

In: Economics

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,

IS: ______________________________________

LM: _______________________________________

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

d) What is the budget multiplier for this economy?

d) What is the exchange before and after the increase of government expenditures? Does the currency depreciate or appreciate?

Expert Solution

(a)

(I) In goods market equilibrium,

Y = 400 - 1000r + 0.75(Y - 300 - 0.1Y) + 240 - 4000r + 850 + 800 - 0.075Y - 120(1.25 + 10r)

Y = 2290 - 1000r + 0.75(0.9Y - 300) - 4000r - 0.075Y - 150 - 1200r

Y = 2140 - 6200r + 0.675Y - 225 - 0.075Y

0.4Y = 1915 - 6200r

Y = 4787.5 - 15500r.........(IS equation)

(II) In money market equilibrium,

MD = MS

840 + 0.4Y - 1000r = 2540

0.4Y = 1700 + 1000r

Y = 4250 + 2500r.........(LM equation)

(b)

Setting IS = LM,

4787.5 - 15500r = 4250 + 2500r

18000r = 537.5

r = 0.03 (= 3%)

Y = 4250 + 2500 x 0.03 = 4250 + 75 = 4325

(c)

When G = 1000, Increase in G = 150

0.4Y = (1915 - 6200r) + 150

0.4Y = 2065 - 6200r

Y = 5162.5 - 15500r.........(New IS equation)

It means that IS curve shifts rightward by (5162.5 - 4787.5) = 375 units.

Setting New IS = LM,

5162.5 - 15500r = 4250 + 2500r

18000r = 912.5

r = 0.05 (= 5%)

Y = 4250 + 2500 x 0.05 = 4250 + 125 = 4375

In following graph, IS0 and LM0 are initial IS & LM curves intersecting at point A with initial interest rate r0 and output Y0. When G increases, IS0 shifts right to IS1, intersecting LM0 at point B with higher interest rate r1 and higher output Y1.

(d)

Budget multiplier = Increase in Y / Increase in G = (4375 - 4325) / 150 = 50 / 150 = 0.33

Rahul Sunny answered 2 years ago

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