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ECMC41
Problems and Solutions About International Trade
This set of problems deals with the effects of tariffs and quotas on the welfare of
Canadians. A tariff is a tax on a particular imported good, often called a customs
duty. A quota is an annual limit on the number of units of a particular good that
may be imported into a country. Tariffs and quotas are measures a government
may use to try to protect its own producers from competitors in foreign
countries.
Problems (with solutions provided)
1. The market for graphic chips for computers is perfectly competitive in
Canada and there is no international trade. The demand curve for these
chips is given by P = 1000 – 0.1Q, where P is the price in dollars and Q is
number of chips traded per month. The domestic (i.e., from domestic
Canadian producers) supply is given by P = 100 + 0.05Q. What is the
equilibrium price, equilibrium quantity of computer chips traded per
month, and the amount of consumer surplus and producer surplus? What
is the overall welfare gain to society?
2. Now, international trade is opened between Canada and other countries
that produce graphic computer chips. Graphic chips are perfectly
elastically supplied on international markets at a price of $200. After
trade is opened up, what is the new equilibrium price of graphic chips in
Canada, and what is the equilibrium quantity of graphic chips traded?
How much of this quantity is imported, and how much is produced by
Canadian domestic suppliers of computer chips? What is the amount of
consumer surplus and producer surplus? Who is made better off and who
worse off by international trade? What is the overall welfare gain to
society?
3. Canadian domestic suppliers of graphic chips complain to the Canadian
government that they are being driven out of business by cheap foreign
imports and that there are job losses in politically sensitive regions of the
country. The Canadian government responds by levying a tariff of $200
per chip (or, what is equivalent, a tariff of 100% on the value of imported
chips). What is the effect of this tariff on equilibrium price and quantity in
this market in Canada? How many imports are there now each month?
What is the amount of consumer and producer surplus? Who is better off
and who is worse off? What is the overall gain to society of this new
arrangement? What is the deadweight loss to society?
4. Imagine now that the Canadian government is defeated in an election by
the Liberal party. Prime Minister Stephane Dion decides to get rid of the
100% tariff on computer chips and replaces it with a subsidy to Canadian
domestic graphic chip producers of $200 per chip. What is the effect of
this new policy – is it better or worse for Canadians? In particular, what is
the new equilibrium price and quantity of computer chips traded on the
Canadian market? What is the consumer surplus and producer surplus,
and how does it compare to the previous situation with the tariff? Taking
into account the cost of the subsidy to Canadian taxpayers, what is the
overall gain to society from the computer chip industry, and what is the
amount of deadweight loss?
A Couple of Extra Problems with No Solutions
5. What would the effect of a tariff be if the tariff was not large enough to
stop all trade? In particular, what would be the effect (on price, quantity,
imports, consumer surplus, producer surplus, deadweight loss, etc.) of a
tariff of $100 per chip (or a tariff of 50% on the value of a chip)?
6. What would be the effect of a quota that reduced imports of computer
chips by the same amount as this tariff of $100 per chip? Would all of the
effects be the same, or would some be different?
Answers to Problems
1. P = 1000 – 0.1Q = 100 + 0.05Q, so 0.15Q = 900 or Q* = 6000 per month.
Substituting into the demand curve, we get P* = 1000 - .1(6000) = $400.
That means consumer surplus is [(1000 – 400) x 6000]/2 = $1.8 million per
month and producer surplus is [(400 – 100) x 6000]/2 = $900,000 per
month. The total gain to society is the sum of consumer and producer
surpluses or $2.7 million per month.
2. With an international price of $200, the domestic Canadian equilibrium
price of $400 is no longer sustainable. Canadian consumers will buy from
some Canadian producers (those that can match this international price),
but will buy many imported computer chips. The new equilibrium price
will be $200. The new quantity traded will be where 200 = 1000 – 0.1Q, or
Q* = 8000. That means the new consumer surplus will be [(1000 – 200) x
8000]/2 = $3.2 million per month. Domestic production of computer
graphic chips will be where 200 = 100 + 0.05Q, or Qdom = 2000. Imports
will make up the difference or 8000 – 2000 = 6000 units per month. The
total producer surplus for domestic producers will now be [(200 – 100) x
2000]/2 = $100,000. Clearly consumers are better off from trade, while
Canadian domestic producers of computer chips are worse off. The
overall welfare gain to society from the production, consumption and
import of computer chips is CS + PS = $3.3 million per month.
3. The tariff of $200 (on top of the international price of $200) will raise the
price of imported chips to $400 per chip. Since Canadian domestic
suppliers can supply the entire Canadian demand at a price of $400, there
will be no incentive for anyone to import chips from international sources.
There will be no imports of computer chips into Canada. The result of this
tariff would return us to the situation in Question #1. In other words,
there would be, compared to the situation with free international trade, a
transfer of $800,000 from consumer surplus into producer surplus
(received by Canadian domestic producers), and there would be an
overall reduction of consumer surplus from $3.2 million to $1.8 million (a
reduction of $1.4 million). The overall gain to society would be $2.7
million (as in Question #1). In other words, the deadweight loss from
imposing this tariff would be $600,000. Note that normally we do
deadweight loss calculations by comparing welfare gains under some
other market arrangement to the ideal, which is perfect competition. Once
we consider the effects of international trade, perfect competition without
trade (in one country) is not the ideal. Instead, perfect competition with
international trade becomes the ideal standard (because the gains to
society are larger).
4. A subsidy is like a negative tax. A tax on suppliers will shift the supply
curve upwards; a subsidy to suppliers will shift the supply curve
downwards. A subsidy of $200 per chip will mean that the effective
supply curve of the domestic Canadian producers is not P = 100 + 0.05Q,
but is P = -100 + 0.05Q. A subsidy to domestic producers does not halt
international trade; international suppliers will still produce and sell
computer chips at $200 each. At this price, domestic suppliers will now be
able to sell more chips: 200 = -100 = 0.05Q, so Qdom = 6000 units. Since, as
calculated above, the total purchases of chips by Canadians at a price of
$200 will be 8000 units, this implies that imports are 8000 – 6000 or 2000
units per month.
Although the new supply curve (with the subsidy taken into account)
represents the prices consumers will have to pay to domestic suppliers,
the production costs paid by these suppliers are still given by the old
supply curve. In order to calculate producer surplus, we need to use this
old supply curve. Producer surplus is defined as the difference between
price and the marginal costs paid by suppliers. Part of the supply curve
(which represents marginal costs) is below the price (and therefore
contributes positively to producer surplus), but part of it is above the price
(and is subtracted from producer surplus). For instance, we can calculate
that when Qdom = 6000, 100 + 0.05(6000) = $400, so marginal costs are $200
above the price. In addition, producers receive revenue from the subsidy
that must be included in the measure of producer surplus. Therefore,
producer surplus is {[(200 – 100) x 2000]/2} - {[(400 – 200) x (6000 –
2000)]/2} + (200 x 6000) = $100,000 - $400,000 + $1,200,000 = $900,000.
The consumer surplus is [(1000 – 200) x 8000]/2 = $3.2 million per month.
The cost to taxpayers for the subsidy to domestic producers is (200 x 6000)
= $1.2 million. The overall welfare gain to society will therefore be $3.2
million + $900,000 - $1.2 million or $2.9 million. If we compare this to the
situation with free international trade (no restrictions and no subsidies),
the welfare gain with the subsidy to Canadian producers is $400,000 less.
Therefore, the deadweight loss is $400,000.
How does this compare to the use of a tariff to protect Canadian
producers? Note that in both cases, Canadian producers produce 6000
chips per month, and, in both cases, the amount of producer surplus
received is $900,000. So, Canadian domestic producers are equally well
off. However, with the subsidy, the overall welfare gains to society are
$2.9 million, rather than $2.7 million. This results from a much larger
consumer surplus ($3.2 million, rather than $1.8 million), offset by $1.2
million in costs to taxpayers for the subsidy. Still, the gain to society is
higher; in other words, the deadweight loss is lower with the subsidy
($400,000), rather than with the tariff ($600,000).