Economics 4413
International Trade
Keith Maskus
Answers to Problem Set #4
Tariffs
1. Here is how to go about these kinds of problems. It really helps to do these step by step.
(a)
Tariff on car imports. Step 1: figure out the impacts on relative prices in the home
economy. A tariff on car imports will reduce imports, forcing up the price that domestic
producers of cars receive. Further, it will provide the same higher price for car consumers,
so there is no difference between consumer and producer prices. So we have:
pc = pc*(1+t), or pc > pc*
Meanwhile, no policy in toys means pt = pt*. Overall, then we have p > p*, where p (p*) is
the relative price of cars in home (the world).
Step 2: draw a PPF diagram and first show free trade (points Qf and Cf below).
Figure 1
T
p
p*
Qf
Qt
Cf
Ct'
Ct
p*
C
Step 3: work out where production and consumption must be with the tariff. Because the
import tariff raises the relative price of cars, p becomes steeper than p* and production
moves to a point like Qt. To determine consumption, recall that 2 things must be true:
1. Consumers face home prices p; 2. International trade must be balanced at world
prices p*. So draw a line parallel to p* from point Qt; this line is the constraint along which
trade must occur. Next draw a line parallel to p that is tangent to an indifference curve at a
point along p*. The point I've drawn at Ct then indicates the consumption point.
(Incidentally, take my word for it that it's a pain in several posterior spots to draw these
diagrams in Word. This explains the arrow depicting where point Ct is.) Note that if you
draw in the trade triangles the tariff on imports causes both imports and exports to fall but
welfare is reduced.
(b)
Subsidization of toy exports. Again, first work out the price impacts. Because toy
makers get to sell wine abroad at a fixed price, the subsidy simply raises their domestic
price (and consumers must also pay this higher price). So we have
pT = pT*(1 + s) and pc = pc*, or p = (pc*/pT*(1+s) < p* . Thus, the price impacts of
the export subsidy are the opposite of those of the import tariff (Note: you might want to
convince yourself that an import tariff and export tax would have similar impacts on
relative prices, and an import subsidy and export subsidy have similar impacts on prices,
but taxes and subsidies are opposites to each other, that is taxes restrict trade and subsidies
expand trade. As a result, the production point would move to Qs (see next diagram)
because p is flatter than p*, and the consumption point (which must be on p* line but also
tangent to p) to Cs. Note that welfare falls relative to free trade in this case also. Note also
that this policy doesn't even work in terms of the objective set out because production of
cars falls rather than rises.
Figure 2
T
p*
p*
Qs
Qf
p
Cf
p
Cs
C
(c)
Taxation of toy production. Here there will be a difference between consumer and
producer prices because consumers can buy at the given world price (no tax on imports)
and so toy producers have to absorb the full price decline from the tax. In Figure 1 above,
the consumer relative price remains at the world relative price: q = p*. But the producer
relative price of cars is higher (because relative price of toys is lower): p > p* (here we
assume the tax on toys raises the relative price of cars by the same amount as the tariff on
imports). Thus, production again moves to Qt and the trade constraint remains along p*
through that point. However, consumers get to consume at p*, so the consumption
equilibrium is at Ct'. Note that the production tax imposes lower costs on the economy than
the import tariff because prices to consumers are not distorted (though producer prices are
distorted).
(d) Subsidization of car production. You should convince yourselves that this policy has
the same price impacts as policy (c). Thus, the effects on production, consumption, and
prices are the same and final equilibrium points are Qt and Ct' in Figure 1.
The essential point of this problem is to show that a tax on imports or a subsidy to
exports generates higher welfare costs than a direct intervention in production (tax toys or
subsidize cars). Policies (a), (c), and (d) work to change production toward more cars, as
the policy desired. However, direct production subsidies or taxes are the lower-cost
policies. In terms of ranking the welfare effects of these policies, (c) and (d) are equivalent
to each other and both are better than (a). Policy (b) doesn't work and is, therefore, quite
stupid.
2. In the diagram below, H imports X. H's tariff raises home price and reduces imports but
improves its terms of trade from p* to p1 (that is, a lower foreign price), which allows for
the potential improvement in welfare. For H, the loss in "import surplus" (area below
excess demand curve and above price) is -(pHp*AB). The gain in tariff revenue is
+(pHp1CB). The net gain or loss is -(BDA) + (p*p1CD). Here, the first effect is the loss
from reducing the VOLUME OF TRADE, so it's called the volume of trade effect. It is
also the deadweight losses caused by distorting consumption and production. The second
effect is the net gain from forcing down the import price; it is called the terms of trade
effect. Retaliation by F would involve an export tax, shifting its excess-demand curve in
the left half of the figure up (fewer exports at every price) and offsetting the initial terms of
trade change, resulting in, say, price p2 somewhere near p*. The net effect is lower trade
volumes (causing distortionary welfare losses) and little effect on the terms of trade, so
both H and F are likely to be worse off.
p
pH
p*
B
A
D
C
p1
Exp. X
EH
EHt = EH/(1+t)
X* Xt
Xt X*
EF
Imp. X
3. I'll show this for the case of a PPF diagram. Revenues were already shown above in
question 2 for an excess-demand curve diagram.
Y
p*
p
Qf
p*
p
Cf
Qt
Ct
Z
V
X
The tariff on X raises domestic price of X so p > p*. This shifts production to Qt and
consumption to Ct (recall our equilibrium conditions for consumption and trade).
Exports of Y are the distance QtZ and total imports of X are the distance ZCt. But
note that, while exports of QtZ buys imports of ZCt at world prices p*, those same
exports are only worth ZV units of X at domestic prices p. Thus, the difference, VCt,
gives tariff revenue in terms of good X.
A prohibitive tariff cuts off imports altogether, meaning that tariff revenues would be
zero.
4. Here is the diagram for a small country, which faces a horizontal (perfectly elastic)
world supply curve S* and so can import all it wants at fixed p*.
px
Sx
A
B
px*(1+t)
px*
Sx*(1 + t)
C
Q0
D
E
F
Q1
C1
C0
Sx*
Qx
The tariff of t raises domestic price to px*(1+t), causing output to rise from Q0 to Q1
and consumption to fall from C0 to C1. The loss in consumer surplus is the area
px*(1+t) px*FB. The gain in producer surplus is area px*(1+t) px*CA. The tariff
revenue is ADEB. There is a net loss of - (ACD + BEF). ACD is the producer
deadweight loss and BEF is the consumer deadweight loss.
5. The diagram for a large country is below. If the country is large, a tariff will drive
down the world price to px*', which is a terms of trade gain for H.
px
Sx
A
B
px*'(1+t)
px*
C
px*'
Q0
D
E
G
H
Q1
C1
F
C0
Qx
In this case, domestic price rises to px*'(1+t), and consumer surplus loss is px*(1+t)
px*FB. The gain in producer surplus is area px*'(1+t) px*CA. The tariff revenue is now
AGHB, reflecting the reduction in world price to px*'. The net effect is -(ACD + BEF) +
(DGHE). The first term is the deadweight losses ("volume of trade effect") and the
second term is the net gain in tariff revenue ("terms of trade effect").
6*. A small country exporting good X would face a perfectly elastic world demand curve
at fixed price px* as shown below. Because that price is fixed, the home exporters would
have to absorb the tax fully in a lower price, as shown by the distorted world demand
curve Dx*/(1+t).
px
Dx
Sx
A
E
F
B
px*
px*/(1+t)
Dx*
C
D
C0 C1
Q1
Dx*/(1+t)
Q0
Qx
Because the tax drives down the domestic price, the gain in consumer surplus is
px*{ px*/(1+t)}CA and the loss in producer surplus is px*{ px*/(1+t)}DB. Note that because
this is an export good there is more domestic production than consumption. The tax causes
consumption to rise and production to fall. The tax revenue is ECDF. The net welfare loss
is -(ACE + FDB), which consists of deadweight consumer and producer losses.
Quotas
7. Here is the diagram with excess-demand curves. Note that a small country can import
the product at a fixed price p*, which is given by the perfectly elastic world supply curve
EX*.
p
Z
ph
B
A
p*
EX*
C
EXh
EXh/(1+t)
EXhQ
Exp. X
X1
X*
Imp. X
The tariff shifts the home excess demand curve down to EXh/(1+t). This raises domestic
price to ph but has no impact on p* (because country is small). Equilibrium in home
moves from A to B, with import volume falling from X* to X1. The loss in "import
surplus" (which is the difference between consumer surplus loss and producer surplus
gain in H) is the area php*AB. The gain in tariff revenue for H is php*CB. Net welfare
loss is area BCA.
Set the quota to the same level of imports as under the tariff, X1. Then this quota has no
effect on the H excess-demand curve from Z to B, at which point it becomes vertical.
Thus, ZB EXhQ is the H excess-demand curve under the quota. Impacts on "import
surplus" are the same as with tariff. The rectangle php*CB is now quota rents. If they go
to domestic importers without any rent-seeking costs, then these rents would be
considered a welfare gain for H. Thus, the welfare impacts of tariff and quota would be
the same, with the only difference being who gets the revenues. However, if some
portion of the rectangle is wasted as rent-seeking the welfare losses would be larger by
the amount of the rent-seeking.
With a VER set at the same level of imports, X1, the H excess-demand curve is the same
as with the quota. In this case, however, the rents from the trade restriction go to foreign
exporters and the area php*CB is a welfare loss to Home (consider it a terms of trade loss
because H has to pay a higher price to foreign exporters). In this case the total welfare
loss is php*AB.
8. This problem is most easily analyzed with a partial-equilibrium diagram for good X.
Suppose there is a single domestic producer and that the economy is small so it can buy
the good from abroad at fixed price p*. The diagram for the import market looks like
this:
px
MC
Z
pQ
MR
B
pt
p*
S*(1+t)
S*
D
A
F
D
Qt
Qm Q*
Ct
C*
Qx
In this diagram, MC is the marginal cost curve for the single home firm. Free trade is at
point A, with consumption level C* and production level Q* (imports are Q*C*) Note
that the monopoly home firm must act as a perfectly competitive firm and only gets price
p*. The tariff distorts the world supply curve up to S*(1+t), causing home price to rise to
pt. This causes consumption to fall to Ct, output to rise to Qt, and imports to fall to QtCt
(= AF = DB). The quota requires that supply level AF come in from abroad but then any
additional demand must be satisfied by the home firm. Thus, the home demand curve
with the quota is ZFAD. This yields a marginal revenue curve for the home monopolist
as shown, causing it to choose quantity Qm and set a higher price pQ. Thus, output is
lower, consumption is lower (show this), price is higher, and imports are the same under
the quota as the tariff. Clearly this is better for the monopolist but worse for consumers.
Overall the quota is worse for the country in welfare terms.
9. See the text's discussion. Essentially the impacts on consumer and producer prices in
the US are the same but with a tariff the revenue goes to the US government while with
an export tax the revenue goes to the Canadian government. Any idea why the US
government would agree to this?
10. Consider a small economy importing good X. With an increase in domestic supply
capacity for good X, the economy's excess-demand curve will shift toward the origin
(become smaller) because the economy would produce more X at home. The diagram is
shown below.
p
EXh'
h
p
h
p
2
EXh'/(1+t)
1
EX*
EXh
EXh/(1+t)
p*
EXhQ
Exp. X
Xt'
XQ' = Xt
Imp. X
Initially the tariff (curve EXh/(1+t)) and quota (curve EXhQ) cut imports by the same
amount (to XQ' = Xt) and raise domestic price by the same amount (to ph1). Welfare
effects are the same if rents go to domestic interests and there is no rent-seeking. Now
suppose the excess-demand curve falls to EXh' because of higher domestic production
capacity in X. Because the tariff remains a fixed tax rate, there will be a correspondingly
lower excess-demand curve with the tariff (EXh'/(1+t)). As a result, the quantity of
imports falls to Xt' but the domestic price remains the same at ph1 = p*(1+t). Note that
revenue falls because the revenue rectangle is unambiguously smaller with the lower
import demand. But with the quota fixed at XQ' the domestic price falls to ph2 even
though imports remain the same. In simple terms, there is lower demand but the same
competition from imports, so home price must fall. So consumers are made better off in
this case than under the tariff.
The essential point here is that a tariff is a tax but does not prevent quantities from
changing. So market shifts with a tariff in place will change imports but not domestic
prices. A quota is a limit on quantity, not a restriction on price. So market shifts with a
quota in place will change price but not imports.
11. Up to you. See discussion in text and class notes.
Strategic Trade Policy
12. This is not going to be an easy one to draw on the computer, but here goes. In the
Cournot-Nash story in section 17.2, there are 2 symmetric firms (home and foreign)
selling in a third market as duopolists. Their reaction curves are shown below, where X
indicates sales by F and H in the third market. By the way, did you notice that this is the
diagram on the front of the textbook?
XF
45o line
RCH
RCF
N
S
XH
At the Cournot-Nash equilibrium, point N, both firms sell the same amount and each is
on its own reaction curve. N is a stable equilibrium and neither firm would deviate from
it for that would lower its profits. But if the home firm could expand its sales and push
foreign down its reaction curve to point S, home's profits would be the highest possible
level. This can be accomplished by a subsidy from H government to exports of this good
by the home firm to the third market. To answer the questions:
A.
Foreign firm's profits at S are lower than at N (it's on a lower iso-profit curve and
sells less). B. Because more total sales are made in the third market (see if you can
convince yourself that the increase in XH sales is larger than the cut in XF sales), the
price is lower there, raising consumer surplus. Since neither firm is owned by people in
this third market, that country would not care about the profit shifting. So its only
welfare effect is the gain in consumer surplus and the country is better off.
13. An export subsidy for perfectly competitive markets was shown in question 1b.
above. Another way to see this is with a partial-equilibrium diagram below, as follows.
The economy exports good X and (suppose this is a small economy) can sell in world
markets at p*. The subsidy to exports raises the domestic price to producers and
consumers to p*(1+s). Thus, there is lower consumption, more production, and higher
exports (C1Q1). Consumer surplus loss is -(px*(1+s) px*CA). Producer surplus gain is +
(px*(1+s) px*DB. The cost of the subsidy to taxpayers is -(ABGH). Thus, the total loss
in welfare is -(GCA + DBH). These triangles are the deadweight loss of the export
subsidy. Note the "double whammy" here on citizens. They have to pay higher prices as
consumers and also pay taxes to cover the subsidy costs. It's a wonder that consumers in
Europe are willing to do this on behalf of their farmers.
px
Dx
Sx
A
E
F
B
px*(1+s)
px*
Dx*(1+s)
G
C
D
H
C1 C0
Q0
Q1
Dx*
Qx
As for the case of increasing returns to scale, the answer to problem 12 will be good
enough, since these duopoly firms exist due to increasing returns to scale. You could
also use the analysis of Figure 17.6 and 17.7 in the textbook.
14. The idea is that by protecting domestic firms that have declining marginal costs, the
tariff can expand domestic production enough that costs go down sufficiently to make the
firms globally competitive. This is essentially the old infant industry argument dating
back at least to Alexander Hamilton. The modern phrase is that "learning by doing" or
"learning by producing" causes costs to fall in this way.
Preferential Trade Areas
15. Suppose that Chile, a small country, joins NAFTA. Assume that for Chile's import
product NAFTA is a higher-cost producer than Japan. However, Chile itself is a higher-cost
producer than NAFTA. Analyze the welfare effects (in terms of trade creation and trade
diversion) for Chile. Under what circumstances might we expect Chile to be better off as a
result of joining NAFTA, in terms of trade creation and trade diversion?
This diagram shows the case for Chile's import good. Chile is small and can import the good
from Japan at price pJ* or from NAFTA at pN*, where pJ* < pN*. Before joining NAFTA,
Chile has the same tariff on the good coming from either source, so consumers buy it from
Japan and the domestic price in Chile is pJ*(1+t).
px
S
A
pJ*(1+t)
pN*
pJ*
B
C
E
G
F
H
D
Q1
Q0
C0
C1
SJ*(1+t)
SN*
SJ*
X
This is Chile's market for imported good X. Initially imports are Q0C0 (= AB) from
Japan at tariff rate t. After the tariff is removed against NAFTA but not Japan,
consumers can get the product from NAFTA at price pN*, which then becomes the new
domestic price in Chile. Imports expand to Q1C1, but they are from NAFTA and there is
no tariff revenue. In welfare terms we have:
Gain in consumer surplus = +( pJ*(1+t) pN*DB).
Loss in producer surplus = - ( pJ*(1+t) pN*CA).
Loss in tariff revenue = - (AGHB).
Net gain or loss = + (ACE + BFD) - EGHF.
The first two terms are efficiency gains from expanding trade. They are called "trade
creation" because the extra imports come from NAFTA, which is a lower-cost producer
than Chile. The last term is a loss in the terms of trade. It is called "trade diversion"
because it comes from imports that are now arriving from NAFTA, which is higher cost
than Japan.
I'll let you think about conditions under which Chile would gain from joining NAFTA.
16. Discussed in text and class.
17. Discussed in text and class.
Administered Protection
18. Discussed in text and class.
19. Discussed in text and class.
20. Forget this one; I'm too tired to draw the picture and it's too complicated anyway.
The basic point is that the export subsidy drives down the world price of the country's
export good, which is a loss in the terms of trade. But this means imports become
cheaper in the importing country, where consumer gains exceed producer losses, at
least in a static sense. This description is quite accurate about the effects of EU and
US export subsidies in agriculture on prices in developing countries that import such
goods. Prices are lower (this is a source of subsidization to urban consumers in poor
countries), which tends dramatically to reduce incomes and incentives for farmers in
poor countries.
21. Up to you. Hint: consider impacts of perfect competition versus imperfect
competition.
22. Discussed in text and class.
MNE's and FDI
23. Discussed in text and class; see also that paper I wrote.
24. I'll leave this one to you.