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Problem Set 3 Solutions Question a


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Problem Set 3 Economics 122a: Fall 2010

Prof. Nordhaus and staff
Problem Set 3 Solutions
Question 1.a.
The financial account balance represents the net financial inflows into a country. Assets owned abroad and borrowing are positive contributions or credits (financial inflow). Domestic foreign-owned assets and lending are negative contributions (financial outflows) or debits.

Question 1.b.
We will construct the personal balance of payments in dollars.
Exchange rate = 0.733 Euros/Dollar

50,000 Euros = $68,200


I. Current account - $68,200

a. Merchandise trade balance - $68,200

b. Services $0
II. Financial account [lending (-) or borrowing (+)] +$68,200

a. Private borrowing or lending +$68,200

b. Government $0
III. Sum of Current and Financial Account $0

Question 1.c.
Yes, the current account balances the financial account because, by definition, when you buy something, you must either pay for it or borrow for it.

Question 2.
To meet the goal of adopting a fiscal plan that will halve the deficit by 2013 and stabilize or reduce the debt-to-GDP ratio by 2016, the small open economy will need to either reduce government purchases (G) or increase taxes (T) or both.
To determine how this will affect domestic interest rates, net capital outflow, real exchange rate, and net exports, we need to first determine how this affects national savings.
Domestic Interest Rate:

For a small open economy, we assume that domestic interest rates are given by the world interest rate. So the domestic fiscal policy will not affect the real domestic interest rate.


rd = rw = r*
Net Exports and Real Exchange Rate:

Net exports in the small open economy, however, are determined by a combination of national saving and the real interest rate. Since the interest rate is given, the change in net exports will be driven by changes in saving. Public saving is a function of taxes and government purchases:


Spub = T – G
So whether the country raises taxes or cuts back on purchases, or both, public saving will go up, causing national saving to go up. The increase in national saving moves the saving – investment curve to the right, causing a fall in the real exchange rate and thus an increase in net exports, as when the exchange rate falls the domestic currency weakens and domestic goods become relatively cheaper than international goods.

Net Capital Outflows:

Because Net Exports increased, the country will be selling more goods abroad, leading to more capital flowing into the economy. As a result, net capital outflow will fall.



Question 3.a.
National saving is the amount of output that is not purchased by households or the government.

S = Y – C – G

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

S = 750.


Investment

I = 1,000 – 50 x 5

I = 750

Net exports

NX = S – I

NX = 750 – 750

NX = 0


Exchange rate

NX = 500 – 500 R

0 = 500 – 500 R

R = 1
Question 3.b.


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

Saving

S = Y – C – G

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

S = 500


Investment

I = 1,000 – 50 x 5

I = 750

Net exports

NX = S – I

NX = 500 – 750

NX = –250



Exchange rate

NX = 500 – 500 R

–250 = 500 – 500R

R = 1.5
The increase in government spending reduces national saving, but with an unchanged world real interest rate, investment remains the same. Therefore, 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.



Question 3.c.
We can do the same analysis, but we must first adjust the real interest rate with the risk premium:

Real Interest Rate

rd = rw + δ

rd = 5 + 5

r* = 10


Saving

S = Y – C – G

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

S = 750


Investment

I = 1,000 – 50 x 10

I = 500

Net exports

NX = S – I

NX = 750 – 500

NX = 250


Exchange rate

NX = 500 – 500R

250 = 500 – 500R

R = 0.5
Saving is unchanged from part (a), but the higher interest rate due to the risk premium lowers investment. This capital outflow is accomplished by running a trade surplus, which requires that the currency depreciate.



Question 4.a.


















An increase in government purchases reduces national saving. This reduces the supply of loans and raises the equilibrium interest rate. This causes both domestic investment and net capital outflow to fall. The fall in net capital outflow reduces the supply of dollars to be exchanged into foreign currency, so the exchange rate appreciates and the trade balance falls.



Question 4.b.












The increase in demand for exports shifts the net exports schedule outward. Since nothing has changed in the market for loanable funds, the interest rate remains the same, which in turn implies that net capital outflow remains the same. The shift in the net exports schedule causes the exchange rate to appreciate. The rise in the exchange rate makes U.S. goods more expensive relative to foreign goods, which depresses exports and stimulates imports. In the end, the increase in demand for American goods does not affect the trade balance.



Question 4.c.
c)



The U.S. investment demand schedule shifts inward. The demand for loans falls, so the equilibrium interest rate falls. The lower interest rate increases net capital outflow. Despite the fall in the interest rate, domestic investment falls; we know this because I + CF does not change, and CF rises. The rise in net capital outflow increases the supply of dollars in the market for foreign exchange. The exchange rate depreciates, and net exports rise.



Question 4.d.





The increase in saving increases the supply of loans and lowers the equilibrium interest rate. This causes both domestic investment and net capital outflow to rise. The increase in net capital outflow increases the supply of dollars to be exchanged into foreign currency, so the exchange rate depreciates and the trade balance rises.



Question 4.e.








The reduction in the willingness of Americans to travel abroad reduces imports, since foreign travel counts as an import. This shifts the net exports schedule outward. Since nothing has changed in the market for loanable funds, the interest rate remains the same, which in turn implies that net capital outflow remains the same. The shift in the net exports schedule causes the exchange rate to appreciate. The rise in the exchange rate makes U.S. goods more expensive relative to foreign goods, which depresses exports and stimulates imports. In the end, the fall in Americans’ desire to travel abroad does not affect the trade balance.



Question 4.f.















The net capital outflow schedule shifts in. This reduces demand for loans, so the equilibrium interest rate falls and investment rises. Net capital outflow falls, despite the fall in the interest rate; we know this because I + CF is unchanged and investment rises. The fall in net foreign investment reduces the supply of dollars to be exchanged into foreign currency, so the exchange rate appreciates and the trade balance falls.




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