Question

Consider an economy described by the following equations:

Y =C+I+G+NX, Y =5,000,
G = 1, 000,
T = 1, 000,

C =250+0.75(Y −T), I = 1, 000 − 50r,

NX = 500 − 500ε, r = r∗ = 5

(a) In this economy, solve for national savings, investment, the trade balance, and the equilibrium exchange rate.

(b) Suppose that G rises to 1,250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.

(c) Now suppose that the world interest rate rises from 5 percent to 10 percent. (G is again 1,000.) Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.

Answer 1

(a). National saving is given by :

S = Y - C - G

= 5000- (250+0.75(5000-1000))-1000

=750

Investment depends inversely on interest rate, equals world rate r* of 5. Thus,

I = 1000 - 50*5

=750

Net exports = Savings - Investments

= 750-750

=0

Having solved for net exports, we can now find the exchange rate that clears the foreign exchange market:

NX = 500-500* ε

0 = 500-500 * ε

ε = 1.

(B). Same analysis with the new value of government spending we find :

S = Y - C - G

= 5000 - (250+0.75(5000-1000))-1250

= 500

I = 1000-50*5

= 750

NX = S- I

= 500- 750

= -250

NX= 500-500*ε

-250 = 500-500*ε

ε = 1.5.

The increase in government spending reduces national savings but with unchanged world real interest rate,investment remains same. Therefore domestic investmnets> domestic savings, so some of the investments must be financed by borrowings from abroad.This capital outflow is accomplished by reducing net exports, which requires that the currency appreciate.

(C). Same stepts with new interest rates.

S = Y - C - G

= 5000 - (250+0.75(5000-1000))-1000

= 750

I = 1000-50*10

= 500

NX = S- I

= 750- 500

= 250

NX= 500-500*ε

250 = 500-500*ε

ε = 0.5.

Savings are unchanged, butthe higher world interest rate lowers investment.This capital outflow is accomplished by running a trade surplus, which requires that the currency depreciate.