Question

The following equations are those for a small open economy, which takes the world real rate of interest ( r w ) as given. In particular:

M/P = 24 + 0.8Y - 400r

C =2+0.8(Y-T) - 200r

I =30 - 200r

NX =24-0.1Y - 2e
Y =C +I +G+NX

You are given the following values for various variables: rw = 0.05; M/P = 100;G = 10 and the budget is balanced. Using the model, find the values for Y, e and the components of demand. Verify that the values you found for consumption, investment and net exports satisfy the goods-market equilibrium condition, given the value of G. Finally, suppose that the nominal exchange rate ( enom ) is 0.8 and the foreign price level ( PFor ) is 1.0. Use this information to find the domestic price level and the nominal value of the money supply (M).

Suppose that the foreign price level ( PFor ) rose from 1 to 1.25: you can think of this as a foreign inflation shock. What would happen to the economy in the short and long run? Would the domestic price level be affected? What would happen to the components of demand?

Answer 1

Y = C + I + G + NX

G = T = 10 (Balanced budget means G = T

rw = 0.05

For a small open economy world real rate of interest = Domestic real rate of interest r

C = 2 + 0.8 (Y- 10) - 200 x0.05

C = 2 + 0.8Y - 8 - 10 = 0.8Y - 16

I = 30 - 200x 0.05

I = 20

M/P = 100 = 24 + 0.8Y - 400r

100 - 24 + 400x0.05 = 0.8Y

Y = 96/0.8

Y = 120

C = 0.8x120 - 16

C = 80

NX = Y- C - G -I

NX = 120 - 80 - 10 - 20

NX = 10

NX = 24 - 0.1Y - 2e

10 = 24 - 0.1x120 -2e

2e = 12-10

e = 1

Y = 120

C = 80

G = T = 10

I = 20

NX = 10

e = 1%

r = 0.05%