Problem Set 3
Prof. Nordhaus and staff
Economics 122a: Fall 2010
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
a. Merchandise trade balance
b. Services
- $68,200
- $68,200
$0
II. Financial account [lending (-) or borrowing (+)]
a. Private borrowing or lending
b. Government
+$68,200
+$68,200
$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.
R
S – I1
S – I2
NX(R)
0
NX
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.
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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.
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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)
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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.
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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.
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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.
Market for Loanable Funds
r
Net Capital Outflow
r
S, I+CV
CF
R
Market for Foreign Exchange Rate
NX
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.