Download 1. Various shocks on a small open economy

Problem Set 3
Prof. Nordhaus and Staff
Econ 122a: Fall 2013
Due: In class, Wednesday, September 25
Problem Set 3 Solutions
Sebastian is responsible for this answer sheet. If you have any questions about the solutions,
please email him at [email protected].
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1. Various shocks on a small open economy
Assume for the purpose of this question that the United States is a small classical open
economy (Mankiw 141-142). Use the model in Chapter 6 to predict what would happen
to the US trade balance (NX) in response to the following events:
a. Wages in developing countries exporting to the U.S. rise sharply.
Net exports unchanged. We assume that the U.S. is importing labor-intensive products
from developing countries. An increase in foreign wages will make these products more
expensive, leading the U.S. to reduce its imports from the developing countries. Since
neither domestic savings nor domestic investments change, the S-I schedule stays
unchanged and the real exchange rate appreciates to offset the reduced demand for foreign
goods. This causes exports to decline, and overall net exports stay unchanged. See diagram.
b. Americans decide that they want to reduce their carbon footprint and reduce their
consumption sharply.
Net exports increase. The reduction in consumption leads to an increase in domestic
savings, since S = Y – C – G. This increases net exports. Intuitively, the country doesn’t
need to borrow as much from abroad and therefore imports less, or can lend more to
foreigners and exports more. The figure illustrates the case where consumption falls so much
that net exports become positive.
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Note also that the real exchange rate depreciates, making domestic goods cheaper relative to
foreign goods and supporting the expansion of exports.
c. The Congress puts a large tariff on imports from developing countries to punish
countries with low wages and to reduce the trade deficit.
Net exports unchanged. The tariff reduces imports from foreign countries, since their
products are now more expensive. This sets in motion the same mechanism as in part a., and
net exports remain unchanged.
d. The US Congress cuts federal military purchases to reduce the budget deficit.
Net exports increase. The reduction in military purchases leads to a fall in government
spending, G, and hence an increase in domestic savings. As illustrated in part b., this
implies an increase in net exports. As before, the real exchange rate falls.
2. Lilliputian economics
Lilliputia is a small open economy, described by the following set of equations:
Y = C + I + G + NX
Y = 5000, G = 1000, T = 1000
C = 250 + 0.75 (Y-T)
I = 1000 – 50r
NX = 500 – 500R
r = r* = 5% per year
In these equations, R is the real exchange rate, and r* is the world interest rate.
Suppose that a large number of foreign countries begin to subsidize investment, but
Lilliputia does not institute such an investment subsidy.
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a. Solve for Lilliputia’s national saving, investment, the trade balance, and the
equilibrium exchange rate before the investment subsidy.
We have that C = 250 + 0.75(5000-1000) = 3250. Then national saving is S = Y – C – G =
5000 – 3250 – 1000 = 750.
Investment is I = 1000 – 50*5 = 750. It follows that NX = S – I = 0.
The real exchange rate is therefore R = 1.
b. How will the investment subsidy of the foreign countries influence foreign
countries’ investment demand function (as a function of the interest rate)? What
happens to the world interest rate? Draw a hypothetical world supply and demand
for savings and investment.
The investment subsidy will increase the foreign countries’ investment at any interest rate.
Therefore, the investment curve in the S-I diagram for the world shifts upward. This is
illustrated in the diagram. Since the world supply of savings is assumed fixed, the subsidy
will just lead to an increase in the world interest rate to r**.
Note that r* would also increase if we assumed that savings were not perfectly inelastic (i.e.,
the savings curve is not vertical, but with finite positive slope). In that case investment and
savings expand, and so the rise in r* would not be as large as in the perfectly inelastic case.
c. Assume that as a result of the investment subsidies, r* rises to 10%. How is
investment in Lilliputia affected by this change in the world interest rate?
Investment is now I = 1000 – 50*10 = 500. Intuitively, investment has declined because
firm now have to pay higher interest rates to finance their projects.
d. What happens to Lilliputia’s trade balance (NX) and the real exchange rate (R) after
the investment subsidies? Interpret.
Assuming that S did not change, we now have NX = S – I = 750 – 500 = 250. Thus,
Lilliputia is now running a trade surplus. Its excess savings are exported (capital exports),
and are used to finance other countries’ imports of Lilliputia’s goods. Since the supply of
Lilliputia’s currency has increased, the real exchange rate depreciates to R = 0.5.
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3. A large open economy prepares for war
(You will need to study the Appendix to Chapter 6 for this question.) We now
realistically assume that the US is a large classical open economy. It faces the prospect
of military conflict.
For each of these events, describe the effect on the US national savings, domestic
investment, the trade balance, the US interest rate, and the exchange rate of the dollar.
To keep things simple, consider each of the following effects separately.
a. Negotiations in the Mideast break down. The US, fearing it may need to engage in
prolonged hostilities, increases its purchases of military equipment.
Government expenditures G increase. This lowers US national savings since S = Y – C – G.
Reduced savings lead to excess demand in the market for loanable funds and raise the US
interest rate to equilibrate supply and demand. Higher interest rates mean that domestic
investments fall, and furthermore the net flow of capital to other countries declines.
Consequently foreign countries receive less US currency and the dollar appreciates. Net
exports fall. See diagram.
b. Other countries worry about their own security. As a result, they increase their
purchases of high-technology weapons, which are a major export of the United
States.
Foreign governments increase their expenditures, leading them to reduce government
savings. This leads to excess demand for savings abroad and raises the foreign interest rate.
The rise in the foreign interest rate increases the net flow of capital, which means that less
capital is available domestically. This raises the domestic interest rate. Domestic investment
falls, but this fall just mitigates the interest rate rise and is not enough to offset it. Domestic
savings are unaffected. The net outflows of capital increase the supply of dollars, which
depreciates the real exchange rate. Net exports increase.
c. The prospect of war frightens US consumers, and they increase their savings rate in
response.
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The mechanics are just the reverse as in part a. The domestic savings rate increases. This
leads to an excess supply of savings and reduces the domestic interest rate. Therefore,
domestic investment and the net flow of capital to other countries increase. This reduces the
real exchange rate and raises net exports.
d. Investors around the world also get frightened and move massive quantities of
their financial portfolios into good old safe US Treasury securities.
The capital inflows lead to a reduction of the net flow of capital (CF). This increases the
supply of capital in the US and depresses the domestic interest rate. Note that while this in
turn tends to raise capital outflows again, this is only a partial effect and therefore the net
flow of capital still falls. Domestic savings remain unchanged, while the decline in the
interest rate raises domestic investment. The reduced level of capital outflows lowers the
supply of US dollars and appreciates the foreign exchange rate, which reduces net exports.
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