Homework 6
UCDavis, 160a, Fall 2011
Prof. Farshid Mojaver
Economies of Scale and Imperfect Competition 2
1. The United States, France, and Italy are among the world’s largest producers. To answer the
following questions, assume that their markets are monopolistically competitive, and use the
gravity equation with B = 93 and n = 1.25.
a. Using the gravity equation, compare the expected level of trade between the United States and
France and between the United States and Italy.
Answer: The expected level of trade between the United States and France is
93(1,830 * 12,409) / 5,544125 = $44,146 billion. The expected level of trade between the United
States and Italy is 93(1,668 * 12,409) / 6,229125 = $34,785 billion.
(Note: These numbers are larger than is realistic because we are using the gravity equation
estimated on the United States and Canada state/provincial trade, rather than the equation
estimated on international trade.)
b. The distance between Paris and Rome is 694 miles. Would you expect more French trade with
Italy or with the United States? Explain what variable (i.e., country size or distance) drives your
result.
Answer: The expected level of trade between Italy and France is 93(1,830 * 1,668) / 694125 =
$79,694 billion. This number is so large because it reflects the short distance between the two
countries. In particular, this number is larger than the predicted amount of trade between the
United States and Italy, as calculated in part (a).
2. What evidence is there that Canada is better off under the free-trade agreement with the United
States?
Answer: Economist Daniel Trefler found that between 1988 and 1996 the productivity of
Canadian firms increased by as much as 15% in industries most affect by the tariff cuts. The
growth in productivity translates to an increase in real earnings of 3% over the 8-year period.
Moreover, Canadian consumers gained from the fall in prices and the rise in product variety.
WTO
1. Go to: http://www.wto.org/english/thewto_e/whatis_e/tif_e/org6_e.htm , and find out
how many countries belong to the WTO. Which countries joined most recently?
2. Which of the following actions would be legal under GATT, and which would not?
a. A U.S. tariff of 20 percent against any country that exports more than twice as much to
the United States as it imports in return.
While tariffs are legal, the United States is obliged to offer compensation for any unilateral
tariff increase by reducing other tariffs to compensate the affected exporting country.
b. A subsidy to U.S. wheat exports, aimed at recapturing some of the markets lost to the
European Union.
Export subsidies on agricultural products are legal under GATT.
c. A U.S. tariff on Canadian lumber exports, not matched by equivalent reductions on other
tariffs.
This is not legal under GATT because the United States is not offering compensating
reductions in other tariffs on Canadian goods. Interestingly, in the late 1980s, U.S. efforts to
protect the shakes and shingles industry were met with an outcry and Canadian threats of a
trade war. These protectionist efforts by the United States were rescinded.
d. A Canadian tax on lumber exports , agreed to at the demand of the United States to
placate U.S. lumber produces.
This is legal under GATT since the action is taken by Canada on its own exports.
e. A program of subsidized research and development in areas related to high-technology
goods such as electronics and semiconductors.
This is legal under GATT since it does not involve any direct export subsidies.
f.
Special government assistance for workers who lose their jobs because of imports
competition.
This is legal under GATT and, in fact, may help increase the benefits from trade.
Trade Policy 1: Tariffs and Quota
1. Consider a small country applying a tariff, t, to imports of a good.
a. Suppose that the country decides to reduce its tariff to t’. Draw the graphs for the
Home (with domestic supply and demand) and import markets (derived import demand
curve) to illustrate this change. What happens to the quantity of goods produced at Home
and their price? What happens to the quantity of imports?
Answer: The reduction of the tariff, and corresponding decrease in domestic price in the
small country, leads to a reduction in domestic production (to S3) and an increase in
domestic quantity demanded (to D3). The result is an increase in imports (to M3). See the
following figure.
b. Are there gains or losses to domestic consumer surplus due to the reduction in tariff?
Are there gains or losses to domestic producer surplus due to the reduction in tariff? How
is government revenue affected by the policy change? Illustrate these on your graphs.
Answer: Consumer surplus increases because consumers now buy a greater quantity of
products at a lower price. Domestic producer surplus, on the other hand, decreases
because producers sell a smaller quantity of products at a lower price. Government
revenue changes from the rectangle S2D2PWPW + t to the rectangle S3D3PWPW + t’. Notice
that the area of the rectangle does not necessarily decrease when the tariff is lowered
because, although the tax per import is less, the amount of imports has increased.
c. What is the overall gain or loss in welfare due to the policy change?
Answer: The overall welfare gain from the reduction in the tariff is illustrated by the
decrease in total deadweight loss. On our graphs this is the reduction in the size of the
striped triangles; after the reduction in the tariff, total deadweight loss is represented by
the smaller solid triangles.
2. Consider a large country applying a tariff, t, to imports of a good.
a. How does the export supply curve in panel (b) compare with that in the small country
case? Explain why these are different.
Answer: The export supply curve is upward-sloping in the large-country case (it was
horizontal in the small-country case). In the small-country case, a horizontal export
supply curve means that the supply of exports from the rest of the world is infinitely
elastic. This corresponds to the price taking assumption in perfect competition. In
contrast, an upward-sloping export supply curve means that the price of exports from the
rest of the world responds when the large country changes its import demand. For
instance, if the large-country importer applies a tariff that decreases its demand for
imports, the price charged by foreign exporters falls.
b. Explain how the tariff affects the price paid by consumers in the importing country,
and the price received by producers in the exporting country. Use graphs to illustrate how
the prices are affected if (i) the export supply curve is very elastic (flat), or (ii) the export
supply curve is inelastic (steep).
Answer: In the small-country case (flat export supply curve), a tariff increases the
amount that consumers pay by exactly the amount of the tariff and foreign exporters are
paid the original world price, P*; the difference is collected by the domestic government
as tax revenue. Refer to Figure 8-7: With an upward-sloping export supply curve (in the
large-country case) foreign exporters reduce their price due to a tariff; that is, foreign
exporters receive less than they did prior to the tariff. Domestic consumers pay more than
before, but by less than the full amount of the tariff. Again, the difference between what
consumers pay and what Foreign exporters receive is the amount of the tariff, t, collected
by the domestic government. In the large-country case, the incidence of the tariff is
shared by domestic consumers and foreign producers. Moreover, a steeper foreign export
supply curve implies that foreign exporters absorb more of the price increase due to the
tariff.
3. Consider a large country applying a tariff, t, to imports of a good. How does the size of
the terms-of-trade gain compare with the size of the deadweight loss when (i) the tariff is
very small, and (ii) the tariff is very large?
Use graphs to illustrate your answer.
Answer: As the size of the tariff increases, the export supply curve shifts upward by
more, M2 decreases by more (relative to M1), and the size of the triangle with area b+ d
increases relative to rectangle e. That is, consumer deadweight losses get larger relative
to terms-of-trade gains due to the tariff. We can interpret this as meaning that for small
tariffs the welfare gains from terms of-trade improvements outweigh consumer
deadweight losses, but the opposite is true for tariffs that are sufficiently large.
4. Consider the following scenarios:
a. If the foreign export supply is perfectly elastic, what is the optimal tariff Home should
apply to increase welfare? Explain.
Answer: This is the small-country case. Because the incidence of the tariff is shouldered
completely by consumers and there is no terms-of-trade gain to applying a tariff, the
optimal tariff is zero.
b. If the foreign export supply is less than perfectly elastic, what is the formula for the
optimal tariff Home should apply to increase welfare?
Answer: This is the large-country case. The optimal tariff is determined as: t=1/E*X,
where E*X is the Foreign export supply elasticity.
c. What happens to Home welfare if it applies a tariff higher than the optimal tariff?
Answer: For a tariff higher than the optimal tariff, welfare declines because deadweight
losses increasingly outweigh terms-of-trade gains. For a sufficiently high tariff, welfare
can go as low as the autarky level.
5. Rank the following in ascending order of Home welfare and justify your answers. If
two items are equivalent, indicate this accordingly.
a. Tariff of t in a small country corresponding to the quantity of imports M.
b. Tariff of t in a large country corresponding to the same quantity of imports M.
c. Tariff of t’ in a large country corresponding to the quantity of imports M’> M.
Answer: a < c < b. For the same quantity of imports, M, Home welfare is greater in the
large-country case relative to the small-country case because (assuming an optimal tariff)
the terms-of-trade gain partially offsets the deadweight losses due to the tariff; thus, a< b.
A larger quantity of imports implies that t’< t. Therefore, in the large-country case with
optimal tariff t, the welfare associated with a tariff of t’ is somewhere in between the
small-country case and the large country case; thus, a < c < b.
6. Rank the following in ascending order of Home welfare and justify your answers. If
two items are equivalent, indicate this accordingly.
a. Tariff of t in a small country corresponding to the quantity of imports M.
b. Quota with the same imports M in a small country, with quota licenses distributed
to Home firms and no rent seeking.
c. Quota of M in a small country with quota licenses auctioned to Home firms.
d. Quota of M in a small country with the quota given to the exporting firms.
e. Quota of M in a small country with quota licenses distributed to rent-seeking
Home firms.
Answer: d = e < a = b = c. A tariff t corresponding to imports M, and a quota on M units
of import corresponding to tariff t are equivalent in terms of welfare so long as proceeds
from quota rents remain in the Home country and are not squandered by rent-seeking
activities: a = b = c. When quota rents are either given away to Foreign firms or are
squandered completely by Home firms seeking access to rents, Home welfare diminishes
by an equal amount (the amount of the quota rents):
d = e < a = b = c.
6. Suppose Home is a small country. Use the graphs below to answer the questions.
a. Calculate Home consumer surplus and producer surplus in the absence of trade.
Answer: Total surplus in the absence of trade is 35.
Consumer surplus without tariff:
Producer surplus without tariff:
CS = 0.5 . 5 .(18 - 9)
PS = 0.5 . 5 . (9 - 4)
CS = 22.5
PS = 12.5
b. Now suppose that Home engages in trade and faces the world price, P*= $6.
Determine the consumer and producer surplus under free trade. Does Home benefit from
trade? Explain.
Answer: Home is better off with trade because total surplus increases by 15 (i.e., total
surplus under trade is 50).
Consumer surplus under free trade: Producer surplus under free trade:
CS = 0.5 . 8 .(18 - 6)
PS = 0.5 . 2 . (6 - 4)
CS = 48
PS = 2
c. Concerned about the welfare of the local producers, the Home government imposes a
tariff in the amount of $2 (i.e., t = $2). Determine the net effect of the tariff on the Home
economy.
Answer: The net effect on Home welfare is -8.
Consumer surplus with tariff:
Producer surplus with tariff:
CS = 0.5 . 6 . (18 - 8)
PS =0.5 . 4 . (8 - 4)
CS = 30
PS = 8
Government with tariff:
Government = (6 - 4) . (8 - 6)
Government = 4
Fall in consumer surplus:
-18
Rise in producer surplus:
+6
Rise in government revenue:
+4
Net effect on Home welfare:
-8
7. Refer to the graphs in problem 8. Suppose that instead of a tariff, Home applies an
import quota limiting the amount foreign can sell to 2 units.
a. Determine the net effect of import quota on the Home economy if the quota licenses
are allocated to local producers.
Answer: An import quota of 2 units has the same net effect on Home welfare as an
equivalent tariff of $2 when the quota licenses are allocated to local producers as long as
the firms do not participate in rent-seeking activities.
Fall in consumer surplus:
Rise in producer surplus:
Rise in government revenue:
Net effect on Home welfare:
-18
+6
+4
-8
b. Calculate the net effect of the import quota on Home’s welfare if the quota rents are
earned by foreign exporters.
Answer:
Fall in consumer surplus:
-18
Rise in producer surplus:
+6
Net effect on Home welfare:
-12
c. How do your answers to parts (a) and (b) compare with part (c) of problem 8?
Answer: With an import quota of 2 units the net effect on Home welfare is equivalent to
that of a tariff of $2 (i.e., the net effect on Home welfare is -8) when the quota licenses
are allocated to local producers. If the quota rents are earned by foreign exporters, Home
welfare falls further so that the net effect is -12.