Answer to Question #323746 in Macroeconomics for Fisagogos

Question

A small open economy can be described as follows: Y=C+ I + G + NX, Y = 5 000,

G = 1 000, T = 1 000, C = 250 + 0.75(Y - T), I = 1 000 - 50*r, NX = 500 - 500*€, r

=r* = 5 %.

a) Estimate the total national saving, investment, the trade balance and the

equilibrium exchange rate.

b) Estimate the impact on national saving, investment, trade balance and

equilibrium exchange rate, if government increases the purchases of goods

and services by 250?

c) Estimate the change in national saving, investment, trade balance and

equilibrium exchange rate, if the world interest rate increases up to 10 %. (G

= 1 000)

Answer 1

a.In this economy, solve for national saving, investment, the trade balance, and

the equilibrium exchange rate.

National saving is the amount of output that is not purchased for current

consumption by households or the government. We know output and

government spending, and the consumption function allows us to solve for

consumption. Hence, national saving is given by

S = Y – C – G

= 5,000 – (250 + 0.75(5,000 – 1,000)) – 1,000

= 750

Investment depends negatively on the interest rate, which equals the world rate

r* of 5. Thus,

I = 1,000 – 50(5) = 750

Net exports equals the difference between saving and investment. Thus,

NX = S – I = 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. Suppose now that G rises to 1,250. Solve for national saving, investment, the

trade balance, and the equilibrium exchange rate. Explain what you find.

Doing the same analysis with the new value of government spending we find:

S = Y – C – G

= 5,000 – (250 + 0.75(5,000 – 1,000)) – 1,250= 500

I = 1,000 – 50 × 5= 750

NX = S – I = 500 – 750= –250

NX = 500 – 500ε

–250 = 500 – 500ε

ε = 1.5

The increase in government spending reduces national saving, but with an

unchanged world real interest rate, investment remains the same. Thus,

domestic investment now exceeds domestic saving, so some of this investment

must be financed by borrowing from abroad. This capital inflow is

accomplished by reducing net exports, which requires that the currency

appreciate.

c. Now suppose that the world interest rate rises from 5 to 10 per cent, G is again

1,000. Solve for national saving, investment, the trade balance, and the

equilibrium exchange rate. Explain what you find.

Repeating the same steps with the new interest rate,

S = Y – C – G

= 5,000 – (250 + 0.75(5,000 – 1,000)) – 1,000= 750

I = 1,000 – 50(10) = 500

NX = S – I = 750 – 500 = 250

NX = 500 – 500 ε

250 = 500 – 500 ε

ε = 0.5

Saving is unchanged from part (a), but the higher world interest rate lowers

investment. This capital outflow is accomplished by running a trade surplus,

which requires that the currency depreciate.