|Required Supplemental Problems for Homework
Supplemental Problem for HW #1 - There is a positive correlation
between international trade and economic growth, but correlation does
not prove causality. What are some of the alternative
interpretations of this statistical relationship? Using Google Scholar or the Knowledge Center's
subscription to EconLit,
look up three different papers published in economics journals since
2000, and in a paragraph each, explain how their findings compare to
the causality problem and the literature discussed in class.
Supplemental Problems for HW #2 -- Consider two countries, England and
producing two goods, sausages (S) and beer (B), with only one resource,
labor, constant returns, and perfect competition. Assume that England
has 40 million identical workers, and one worker can produce either
1500 kilos of sausages (per year) or 1200 liters of beer (that is, MPLs
= 1500 and MPLb=1200).
Germany has 60 million workers, and one worker there can produce
either 1200 kilos of sausages or 2000 liters of beer.
- In two separate diagrams, graph the PPFs for both England
and Germany, putting sausages (in billions of kilos) on the horizontal
axis, and beer (in billions of liters) on the vertical. What is the
autarky relative price ratio (Ps/Pb) in each
country? Which country has the higher real per-capita
- Assume that, at autarky, each country allocates 40% of its
labor to sausage production and 60% to beer. What is the autarky
production combination of S and B for each country? (Hint: first
figure out how much 10% of the workers in each country could produce of
each good.) Show these preferred combinations on your PPF graphs using
indifference curves, and label them (A) for autarky.
- Which country has the comparative advantage in which good?
What does the Ricardian Theorem predict would be the pattern of free
- Prove that in this example, total production of S and B
increases when each country specializes in its comparative advantage.
At what values of the terms-of-trade (Ps/Pb)
would each country be willing to specialize in its comparative
- Assume that the terms-of-trade for sausage are 4:3. Assume
fully specializes, and they then trade 36 billion kilos of
for 48 billion liters of beer. How much S and B will each country
consume? Show these new general equilibria on your PPF diagrams,
labeling the new production points (Q), the consumption point (C), and
the consumption possibility frontier (CPF).
- Using this spreadsheet,
you may check some of your answers. The model input goes in the
boxes, and the spreadsheet makes the calculations. This
assumes that each country has total effective money supply (money times
velocity) of $100 billion, and also calculates the nominal prices and
exchange rate, along with the real wage rate and the average utility
level. Note however that the spreadsheet uses the constant-shares
utility function. What is the
terms of trade and the amount of trade
predicted by this spreadsheet? Does trade make people in both
countries better off?
- Using this spreadsheet, how would the terms of trade, the
pattern of specialization, the pattern of trade (who exports which
product), the volume of trade, and the gains from trade (measured
as an increase in average utility) all change if:
- Germany's money supply doubled? (What changed?)
- Germany became more productive in beer production, and
MPLb rose to 2200?
- Germany became more productive in sausage
production, and MPLs
rose to 2000?
- Germany became much
more productive in sausage production, and MPLs rose
Supplemental Problems for HW #3
Assume that a country produces two goods, Crafts and Food, under
perfect market conditions. Craft production uses labor with a constant
(non-diminishing) marginal product, while Food
production requires specific farmland, so labor has diminishing
- Using the four-quadrant diagram, graph the production
functions and the labor allocation, and then show how to derive the PPF.
- Assume that Foreign has more significantly more labor,
while Home has much more land. Which PPF would be more bowed out?
- In two separate diagrams, graph
the PPFs for both countries, with Crafts on the horizontal axis, and
indifference curves to show the autarky equilibria. Assuming
preferences are identical, how does the
relative autarky price (PC/PF) differ
internationally? Which country has the comparative advantage in
- On your PPF diagrams, show how free trade would lead
to new equilibria. For each country, show the production
point Q and the consumption point C, and compare this to the autarky
- Using the labor allocation diagram for the Home country,
show how the optimal labor allocation and the wage rate is determined.
Assume that trade only affects PC, and nominal PF does
not change. Show what happens to the nominal income of workers in
each sector, and to landowners. Assuming workers buy an
of both goods, what happens to the real wage rate?
- Assume in #5 above that wages are rigid in the short-run.
Use the labor allocation diagram to show how free trade could
Supplemental Problems for HW #4
Consider an model of trade between China and the USA, in which the only
resources are labor (L) and capital (K). Suppose the USA has 150
million workers and $12 trillion in capital, while China has 600
million workers and $1 trillion in capital. Each country produces only
machines (M) and textiles (T) under perfect market conditions, using
both labor and capital with constant returns to scale and diminishing
marginal returns, though machine production is relatively
capital-intensive. Assume preferences and available technologies are
identical, and factors are equally productive between the two countries.
- In two separate diagrams, graph
the PPFs for both countries, with M on the horizontal axis, and use
indifference curves to show the autarky equilibria. How does the
relative autarky price (PM/PT) differ
- Under perfect free trade between
the two countries, what would the Heckscher-Ohlin theorem predict would
be the pattern of trade? How would this affect relative prices in
- According to the Stolper-Samuelson theorem, how would free
affect the wage-rental (W/R) ratio in each country, and how would this
in turn affect the (K/L) ratios in each sector, in each country?
- On your PPF diagrams, show the
free trade equilibria. How does free trade affect overall welfare
in each country?
- Use an Edgeworth box to show how free trade affects the
allocation of capital and labor for the USA.
- Use an Edgeworth box to show that specialization increases
the total production of M and T, while trade leads to a Pareto-optimal
- Assume instead that preferences are not identical, but
instead each country
had a strong preference bias for the good of its comparative advantage.
How might this change your answers to the first three questions?
- Assume that in the very short-run, neither factor (K,L) is
mobile between sectors (M,T). How would this affect your answers
to the first three questions (assuming preferences were still
- In words, not graphs, explain how your predictions would be
different if labor in the USA was five times as productive as in China.
HW #5 -- Assume that Spain and Portugal both have many producers of
(sherry), with free entry and exit, but product differences, brand-name
recognition, and economies of scale keep the two markets from being
perfectly competitive. Assume that Spanish and Portuguese sherry
producers have similar cost structures, but that Spain is a much larger
- Explain how the number of firms
in this hybrid case of “monopolistic competition” would
affect the price of sherry. Explain how the number of firms and the
size of the market would affect the average cost of production. Explain
how free entry and exit would affect producer profits in the long-run.
- How would Spain and Portugal
have differed, under autarky, in the number of producers and the price
- How would free trade between the two affect the price of
sherry in each, the total number of producers, and the number of brands
available to consumers? Show your predictions using the
Krugman-Obstfeld monopolistic competition pricing (PP) and cost (CC)
HW #8 -- Consider a country we shall call
“Home” that produces only two goods, X and Y, with only
capital and labor resources under standard Heckscher-Ohlin production
functions. Assume Home is perfectly competitive and relatively
capital-abundant, and good X is
- Use a model of intertemporal trade (i.e., PPFs and
indifference curves) to show the autarky amount of savings and
investment for Home. Assuming its marginal rate of return (R) on
investment is higher at Home than in foreign countries, explain how
savings would flow, and what would happen to domestic savings,
investment, and future output at Home? What would happen to Home's
trade balance? What would then happen in the future?
- Assume Home has perfect competition. Home
very much, however, and borrows savings from the rest of the world.
- Use a standard trade model with a PPF and indifference
curves, with X on the horizontal axis, to show how this inward
transfer affects Home’s
consumption in the current period (remember this is not an
intertemporal model). How this must affect Home’s trade
balance? Assume the transfer does not affect the terms-of-trade.
- Use the model to show how Home’s consumption,
and its trade balance,
will be affected in the future, when Home has to repay its borrowing
- Assume that Home decides to use
this borrowing to finance investment in its capital stock, instead of
increasing its consumption. Show how this investment would change
its PPF in the future.
- If Home uses its foreign
borrowing to finance investment instead of consumption, is it possible
that Home will be able to consume more in the future than it could have
without the borrowing? Show this, if possible.
- Using a supply and demand model for Home’s market for
foreign exchange (Forex):
- Why do we typically assume Forex
supply is more elastic than demand? How would these elasticities change
over time? How is the direct exchange rate E related to the value of
- How would a transfer of savings
from the foreign country to Home affect E and the trade balance?
- How would a transfer of savings
from Home back to the foreign country affect E and the trade balance?
- How would a tariff by the Home country on its imports
affect E and the trade balance?
- Assume that Home’s government imposes a tariff
on all of its imports.
- Use a PPF and indifference
curves to show how the tariff would affect Home’s welfare,
assuming Home was a small economy. Why is the terms-of-trade not
tangent to either the PPF or the indifference curve?
- If Home were a large economy,
how would this tariff affect its terms-of-trade? Is it possible
for the tariff to improve Home’s welfare? Show this.
- Use a graph for the supply and demand of Forex, from
Home's point of view, and assume (for simplicity) that the only reason
for trade in currencies is trade in goods and services. How would
the tariff's effect on import demand affect the demand for Forex?
How would this affect E? How would this affect exports?
- Suppose Home decided to impose this tariff to address its
international trade imbalance. Would this policy work? Why
or why not?
- Suppose Home puts a $2 tariff on a single good, imported
toys. Domestic production rises in response to the higher price,
from 3 million to 5 million toys, while domestic consumption falls
from 15 million to 12 million toys.
- What is the amount of the change in producer and consumer
surplus? How much does government receive in tariff revenue from
domestic consumers? No graph is necessary, and you should assume supply
and demand are linear functions.
- Suppose our tariff lowered the price of toys on the
international market by $1 (i.e., the tariff is actually $3, but we
paid only $2 of it). Does the tariff improve or worsen our domestic
welfare overall, and by how much?
HW #9 -- Suppose that the world price for oil was only $70 per barrel,
that price the U.S. would produce 3 billion barrels (per year) and
consume 10 billion barrels. Suppose there is an external cost of $60
barrel consumed in the U.S., and a new administration decides to
finally do something about it.
a) Suppose that the U.S. government
adds a $30 tariff to each barrel of imported oil, and the U.S. is a
small part of the world oil market. This then raises the
domestic petroleum price to $100 per barrel, increases domestic
production to 4 billion barrels, and decreases consumption to 8 billion
barrels. Show, calculate and explain the effects of this tariff
on domestic producer surplus, domestic consumer surplus, and the
government budget (all in billions of dollars per year). In the absence
of an externality, would this tariff improve or worsen
efficiency? Adding in the savings from the reduced external cost,
would the tariff improve or worsen efficiency?
b) Suppose that the U.S. government
instead puts a $30 tax on the consumption of each barrel of oil,
regardless of whether the oil is imported or
domestically-produced. Because we assume we are a price-taker,
this would not affect the before-tax
price of oil, but by making the effective after-tax price equal to
$100, it would reduce consumption exactly as the tariff does. Calculate
the effects of this consumption tax on domestic producer surplus,
domestic consumer surplus, the government budget, and the consumption
externality. Would this tax improve or worsen our net national welfare,
relative to the $30 tariff?
c) Now make the same comparison between a tariff and a consumption tax
of $60, assuming that the effects are linear, e.g., at a price of $130,
domestic producers would supply 5 billion barrels per year and
consumption would fall to 6 billion barrels.
c) How much is the optimal
consumption tax? Is the optimal tariff greater than or less than the
optimal consumption tax? Which is more efficient, the tariff or
the consumption tax?
HW#10 -- In part due to pressure from French Farmers, the European
import restrictions on food imports from the rest of the world, through
its Common Agricultural Policy (CAP) and its Common External Tariff
- Suppose this import restriction takes the form of a
tariff. Assume that this tariff has a significant effect on the world
price of food, use a supply and demand diagram to show the effects of
this tariff on European food markets. Carefully labeling areas,
how much does this change producer
surplus, consumer surplus, and the government budget? Can the
tariff improve overall welfare in the EU? How much does it affect
the net welfare of the rest of the world?
- Consider the effect of the above tariff on a small economy
the EU, and still imports food from the rest of the world (but not from
the rest of the EU).
- Show the effects of this tariff on the small economy.
- Show the effects of an
equivalent import quota. What are the quota rents, and who gets
them? If at first glance the quota is equivalent to the tariff,
what are some of the reasons that economists consider quotas to be much
- Show the effect of a production
subsidy that has the same effect on farmers. How much does this
change producer surplus, consumer surplus, and the government
budget? How does the production subsidy compare to the tariff?