Name: __________________________
Date: _____________
Problem Set #5 (Due in Class on June 2, 2011)
1. The table below represents a demand and supply schedule for a small-country
producer of iron ore. It sells output in its home market and on the world market at
the world price of $70 per ton.
Table: Demand and Supply for Iron Ore
Price/Ton
$100
$90
$80
$70
$60
$50
$40
$30
$20
$10
a.
.
b.
c.
d.
e.
f.
Quantity Demanded Quantity Supplied
(Tons)
(Tons)
10
100
20
90
30
80
40
70
50
60
60
50
70
40
80
30
90
20
100
10
At the world price of $70 per ton, how many units will be sold domestically?
The table shows 40 tons.
At the world price of $70 per ton, how many units will it export?
Supply is 70 tons and home demand is 40 tons, so 30 tons are left over for
export.
Suppose that the country's government offers its iron ore producers an export
subsidy of $10 per ton. How many tons will the country now export?
With a $10 per ton export subsidy, the producer is receiving a price of $80
per ton, assuming the producer exports all production. Then, the producer
will charge $80 per ton for home demand. At $80 per ton, the producer
produces 80 tons. The subsidy is an export subsidy, so the producer charges
$80 per ton at home. This leads to home demand of 30 tons. Then, 80 tons
produced minus 30 tons demanded leaves 50 tons exported.
How many tons will be sold domestically when exporters receive a $10-per-ton
export subsidy?
From part (c), 30 tons sold domestically.
What price will domestic iron ore consumers pay for their iron ore purchases when
there is a $10-per-ton export subsidy?
From part (c), $80 per tons domestically.
What is the total value of the export subsidy that exporters receive?
The producer makes an extra $10 per ton for each ton exported, so for the 50
tons exported, the exporter makes $500.
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2. In the small country of Freedonia, the domestic demand for widgets is represented by P = 100 –
3Q; the home supply of widgets is represented by P = 1Q.
a. In the absence of trade, what is the equilibrium price and quantity in Freedonia's widget
market?
In the absence of trade, the equilibrium is when supply equals demand. Then demand would
be Q = (100 – P)/3 and supply would be Q = P. Equating gives (100 – P)/3 = P, and solving
for P gives, P = 25. We know that for supply, Q = P, so the equilibrium price = 25 and the
equilibrium quantity = 25.
b. Now suppose Freedonia engages in international trade in widgets. The world price is $40.
How many widgets will be consumed domestically and how many will be exported?
Supply will be determined by P = 1Q, so the total supply is 40. Domestic demand is Q =
(100 – P)/3, so substituting P = 40 gives domestic demand of 20. With total supply of 40 and
domestic demand of 20, exports will be the difference, exports will be 20.
c. Now let the government of Freedonia give a $15 per unit subsidy on each widget exported.
What will be the new price and quantity consumed in the Freedonia domestic market?
Adding $15 to the world price of $40 makes the new domestic price $55. Substituting
P = $55 into Q = (100 – P)/3, gives the new domestic quantity of 15.
d. Calculate the value of the deadweight losses with the $15 per unit export subsidy.
From part (b), consumption falls by 5 units and the subsidy is $15, so this part of the
deadweight loss is ½(5)(15) = 37.50, a reduction in consumer surplus. On the producer side,
the production increases from 40 units to 55 units, an increase of 15 units times the $15
subsidy, so the production loss is ½(15)(15) = 112.50, so the deadweight loss is the sum of
the consumption loss and the production loss, 37.50 + 112.50 = $150.
e. What is the value of total subsidy payments to Freedonia's widget exporters?
With supply of 55 units and domestic consumption of 15 units, exports are 40 units with a
subsidy of $15 each, for a total subsidy payment of $600.
f. Is the subsidy paid to Freedonias's widget exporters considered part of the deadweight losses
of the subsidy?
No, the subsidy is a redistribution of income within the Freedonian economy.
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3. The graph below shows the case for a tariff imposed by a large country.
a. How much will the home market firms produce and what will be the total demand
for the good if the world price of the product is $30?
Reading across the $30 price and down to the quantity the answer is 20 units.
b. What is the amount imported by the home market under free trade?
Continuing to read across the $30 price, demand is 100, so imports are 100–20=80.
c. What is the net loss in the world market if a tariff of $10 is imposed by the home
country?
Raising the price from $26 to $36 will apply to the triangle in the World market
graph. The area of the triangle is ½(40)(10) = 200.
d. What is the loss of consumer surplus in the home country?
The loss of consumer surplus in the home country is the area in dashed lines
between the $36 and $30 price lines. This is the rectangle that is 6 x 80 = 480 plus
the triangle that is 20 x 6 which is 60 for a total of 540.
e. What is the terms-of-trade gain and what is the deadweight loss?
The terms-of-trade gain is the rectangle bounded by the $26 and $30 price lines and
the 40 and 80 unit quantity lines. The area is 4 x 40, so the terms-of-trade gain is
160. The deadweight loss is the sum of the two triangles between the $26 and $30
price lines and the 20 to 40 and 80 to 100 quantity lines.
The area is 2(1/2)(20)(6) = 120.
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4. The demand and supply for Gloves is given in the following table:
Price
$1
$2
$3
$4
$5
$6
$7
$8
Quantity Supplied
5
6
7
8
9
10
11
12
Quantity Demanded
20
19
18
17
15
14
13
12
$9
13
11
$10
14
10
a. The United States can also import gloves from China at $4 per pair and from Mexico at $5
per pair. Currently, the United States imposes a specific tariff of $2 on its glove imports.
Suppose that the United States and Mexico form a free-trade area. How much trade in gloves
is created?
With the tariff, at $6, the US imports 4 pairs of gloves from China and without the tariff, at
$5, the US imports 6 pairs of gloves from Mexico. There are two additional pairs of gloves,
so the tariff reduction creates trade of 2 pairs of gloves.
b. The United States can also import gloves from China at $4 per pair and from Mexico at $5
per pair. Currently, the United States imposes a specific tariff of $2 on its glove imports.
How much trade in gloves is diverted in the U.S.-Mexican free-trade area?
At $6, the US could import 4 pairs of gloves from China, but in the free-trade area this trade
is diverted to Mexico because they are available from Mexico for $5. Therefore, there are
four pairs of gloves that are diverted.
c. The United States can also import gloves from China at $4 per pair and from Mexico at $5
per pair. Currently, the United States imposes a specific tariff of $2 on its glove imports. Is
the United States better off or worse off in its trade in gloves following the free-trade
agreement with Mexico?
The United States is worse off because trade diversion losses exceed trade creation gains.
d. The United States can also import gloves from China at $4 per pair and from Mexico at $5
per pair. Currently, the United States imposes a specific tariff of $2 on its glove imports.
Suppose instead that the United States negotiated a free-trade agreement with China. Will the
United States be better off or worse off as a result of its trade in gloves in the free-trade area
with China?
The United States is better off because there are no trade diversion losses.
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5. The Figure below represents U.S. Imports from Mexico and Asia.
a. The figure illustrates a customs union between the United States and Mexico. Under free
trade how much of the good will the United States will import from which country at what
price?
From the graph, the United States will import 250 units from Mexico at a price below
$150, and will import 350 units from Asia at a price of $150.
b. What will total imports be if the United States imposes a tariff of $100?
With the $100 tariff, United States import demand intersects the Asian supply line
(price) at 500 units.
c. With the $100 tariff, how much will the United States will import from Mexico and from
Asia?
From the graph, the United States will import 250 units from Mexico at a price below
$250, and will import 250 units from Asia at a price of $250.
d. The $100 tariff by the United States results in how much tariff revenue?
With the tariff of $100, imports are 500 units (part b) at a tariff of $100 per units for a total of
$50,000 in tariff revenue.
e. If the United States forms a customs union with Mexico, will it result in an increase or a
decrease in producer surplus for Mexico and how large will it be?
With the customs union, Mexico will export 400 units. Mexico will saving the rectangle
between the $150 and $250 price lines and the price axis and the 250 quantity line plus the
upper part of the rectangle (the triangle) between the $150 and $250 price lines and the 250
and the 400 quantity line. The rectangle is $25,000 and the triangle is $7,500 for an increase
in producer surplus of $32,500.
f. The combined welfare of the United States and Mexico will be higher or lower by what
amount?
g. The United States looses tariff revenue of $40,000 (400 units at $100 each) and Mexico gains
producer surplus of $32,500 (from part e), so the result is a $7,500 loss of combined welfare.
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6. Suppose that the U.S. government required U.S. firms to pay a “living wage” to workers in its
subsidiaries or contracting firms in developing countries.
a. What are the likely consequences of this requirement?
Wages will most likely rise and employment will fall.
b. How would one determine a living wage?
Presumably, a living wage is somewhat higher than the current market equilibrium wage.
However, it is difficult to determine how much higher. If set equal to U.S. average wages,
then firms are likely to close and employment will fall dramatically. It is also difficult to
compare living standards across countries. What U.S. workers consider a living wage may
allow them to own several automobiles, live in large homes, and avail themselves of the
latest technological gadgets. The U.S. living wage is inappropriate for developing countries
that find their comparative advantage in labor-intensive products where wages are expected
to be lower.
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