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Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
1
Please use complete sentences when answering all questions. Also in your written answers, you must
explicitly refer to your labels on your graph when possible.
Basic Theory of Trade Using Supply and Demand
1. Assume that Australia and the UK are the only producers wine in a perfectly competitive market.
Below are domestic supply and demand equations and their corresponding autarky equilibrium price
and quantity of wine.
Australia UK
Qs = 3,500 + 100P Qs = 50P
Qd = 9,500 – 100P Qd = 6,000 – 50P
a. Australia: Solve for autarky equilibrium price and quantity.
b. UK: Solve for autarky equilibrium price and quantity
c. Now assume that both countries opened their boarders to free trade. Based on your answers in part
(a) and (b), which country will import and which country will export wine?
d. Use the supply and demand equations above to derive the equation for import demand and the
equation for export supply of wine.
e. Use your equations for import demand and export supply found in part (d) to solve for the
international equilibrium price and quantity traded.
f. Consider just The UK’s market for wine. Add labels (and figures found above) to the graphs below
to illustrate UK’s trade with Australia (include the export supply curve or import demand curve for
the UK in the right graph). Then add letters to the spaces in the graph in order to complete the table
of welfare effects under autarky and free trade (you do not need to mathematically calculate the area
of each space).
Autarky Free Trade
Consumer Surplus:
Producer Surplus:
Total welfare:
Consumer Surplus:
Producer Surplus:
Total welfare:
Gains from trade:
SUK
DUK
UK Wine UK Import Demand
Or
Export Supply
PUK
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
2
Solutions
a. Australia:
Qs = Qd
3500 + 100P = 9500 – 100P
200P = 6000
PA = 30
Qs = 3500 + 100PA = 3500 + 100(30) = 6500
Qd = 9500 – 100PA = 9500 – 100(30) = 6500
Qs = Qd = Q* = 6500
b. UK:
Qs = Qd
50P = 6000 – 50P
100P = 6000
PUK = 60
Qs = 50P = 3000
Qd = 6000 – 50P = 3000
Qs = Qd = Q* = 3000
c. Since the price of wine is higher in the UK (PUK = 60), the UK will import and Australia will export.
d.
Import Demand for UK
Dm = Qd – Qs
Dm = 6000 – 50P - (50P)
Dm = 6000 – 100
Export Supply for Australia
Sx = Qs - Qd
Sx = 3500 + 100P – (9500 – 100P)
Sx = - 6000 + 200P
e.
Import Demand for UK = Export Supply for Australia
Dm = Sx
6000 – 100P = - 6000 + 200P
12000 = 300P
Pw = 40
Dm = 6000 – 100P = 6000 – 100(40) = 2000
Sx = - 6000 + 200P = -6000 + 200(40) =
2000
X = M = 2000
f.
Autarky Free Trade
Consumer Surplus: A
Producer Surplus: BE
Total welfare: ABE
Consumer Surplus: ABCD
Producer Surplus: E
Total welfare: ABCDE
SUK
DUK
UK Wine UK Import Demand
Pw=40
MD,UK
A
B
CD C+D
E
PUK = 60
QUK
3000
QS QD M Quantity of Imports
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
3
Gains from trade: CD
2. Suppose there are only two countries: Mali and Algeria. Both countries can produce shirts.
a. The Mali supply curve for shirts is: Qs = 1/2P. The Mali demand curve is: Qd = 12 - P. Use the
supply and demand equations to solve for autarky equilibrium price and quantity. Draw the
corresponding graph for Mail.
b. The Algerian supply can be described by Qs = P and Algerian demand is Qd = 9 - P. Use the supply
and demand equations to solve for autarky equilibrium price and quantity. Draw the corresponding
graph for Algeria.
c. Assume the international price of shirts is Pw = 3, what is the quantity traded on the world market? Is
it possible that Pw = 3 is a world equilibrium price if there are no barriers to world trade? Briefly
explain.
d. Use your supply and demand equations for each country to derive the equations for import demand
(excess demand) and export supply (excess supply). Then use these equations to find the equilibrium
international price and quantity trade.
e. Support your answer in (d) with a corresponding diagram of the international market.
Solutions
a.
b.
c. First consider Mali, Pw = 3 <Pmali=8. Thus Mali would import shirts. How much? Qs=1/2(3)=1.5 and
Qd=12-3=9. Thus M=Qd – Qs = 9-1.5=7.5.
Now consider Algeria, Pw = 3 < Palgeria = 4.5. Thus Algeria would import shirts. How much?
Qs = P = 3, Qd = 9-3 = 6. Thus M = Qd –Qs = 6-3 = 3.
So both Algeria and Mali would both want to import at Pw = 3, but in a two country world, this is not
Qs = 1/2P and Qd = 12-P. ps=2qs
At equilibrium, Qs = Qd , therefore
1/2P = 12-P
3/2P = 12
Pmali = 8
Qs =1/2Pmali = ½(8) = 4
Qd = 12 - Pmali = 12 – 8 = 4
Qmali= 4
Pmali = 8
Qs = P Qd = 9-P.
At equilibrium, Qs = Qd , therefore
P=9-P
2P=9
Palgeria=4.5
Qs= Palgeria = 4.5
Qd=9 - Palgeria = 4.5
Qalgeria = 4.5
Palgeria = 4.5
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
4
possible. Because we are assuming these two countries are the world (so one imports the other’s exports),
this price is not an equilibrium price if there are no barriers to world trade. Until the two countries agree
on a mutually beneficial price, the quantity of shirts traded on the world market would be 0.
d. Looking at the autarky price of shirts in both countries, Algeria will export shirts to Mali because its
price of shirts is lower.
Xs = Qs- Qd Xs= Md Md = Qd- Qs
=(P)- (9-P) 2P – 9 = 12 – 3/2P = (12 – p) – (1/2P)
=P-9 + P 7/2 P= 21 = 12 –3/2 P
=2P - 9 P = 6, Q = 3
3. In this problem, you need to think about how trade is affected by changes that occur to a domestic
market. Assume only two countries in the world produce motorcycles (US and Germany). The
figure below, illustrates a case of free trade, where the US imports 50 motorcycles from Germany at a
price of $1000.
Now assume that US experiences a change in technology that increases domestic productivity of
motorcycles.
a. What is the direct effect on the US domestic motorcycle market? That is, what happens to US
supply/demand/autarky equilibrium? Show this on the graph above and refer to your labels in a brief
explanation. (You don’t need to find numbers.)
b. What is the direct effect on the US import demand curve? Show this on the graph above and refer to
your labels in a brief explanation.
c. What is the effect on the new world equilibrium price? What happens to US imports of motorcycles?
What happens to Germany exports of motorcycles? Show this on the graph above and refer to your
labels in a brief explanation. (You don’t need to find numbers.)
Solutions
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
5
a. The supply curve SUS shifts to the right.
b. The right shift in supply causes the U.S. import demand curve Dm, US shifts to the left.
c. As a result, the equilibrium international price decreases below 1,000—it is shown by the
intersection of the new U.S. Dm, US curve and the original Sx. G curve. Imports from the world
market fall below 50 to M2 and exports from Germany also fall to X2
4. Optional - Suppose there are only two countries in the world that produce coffee: Colombia and
Guatemala. The following present the supply and demand equations for each country:
Supply for coffee Demand for coffee
Colombia Qs = ½ P + 1 Qd = 10 - P
Guatemala Qs = P + 1 Qd = 10 - 2P
g. Colombia: Solve for autarky equilibrium price and quantity.
h. Guatemala: Solve for autarky equilibrium price and quantity
i. Based on your answers in part (a) and (b), which country will import and which country will export
coffee?
j. Use the supply and demand equations above to derive the equation for import demand and for export
supply of coffee.
k. Use your import demand equation and export supply equation from part (d) to find the international
equilibrium price and quantity traded.
l. Sketch a graph of this market.
m. Construct a table that shows the welfare effects (consumer surplus, producer surplus, total welfare
and gains from trade) under both autarky and free trade for Columbia. To do this, you may need to
use labels on your graph in part (c) to help you identify areas in your graph. Then explicitly refer to
the results of your table in a brief explanation of who in Columbia benefits/loses under free trade.
Solutions
a.
Qs = ½ P + 1 ½ P + 1 = 10 - P Qs = ½ P* + 1 = ½ (6) + 1 = 4
Qd = 10 - P 1 ½ P = 9 Qs = Qd=Q* = 4
Qs = Qd P* = 6
b.
Qs = P + 1 P + 1 = 10 - 2P Qs = P* + 1 = (3) + 1 = 4
Qd = 10 - 2P 3 P = 9 Qs = Qd=Q* = 4
Qs = Qd P* = 3
c. Since the price of coffee is cheaper in Guatemala, Guatemala will export and Colombia will import.
Q
Pri
ce
65
DUS
SUS
US Mkt for motorcycles
2000
15
1000
Q
Pri
ce
Dm, US,
World Mkt for motorcycles
50 Q
Pri
ce
50
DG
SG
German Mkt for motorcycles
75 25
Sx,G
700
40
SUS
DM, US M2 =X2
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
6
d.
Colombia import
demand:
Dm = QD - Qs
Dm =(10 – P) – (½ P + 1)
Guatemala
export supply
Sx = QS – QD
Sx = (P + 1) – (10 - 2P )
Dm = 9 - 1 ½ P Sx = 3P - 9
e.
Dm = 9 - 1 ½ P 9 - 1 ½ P = 3P - 9 Dm = 9 - 1 ½ P* = 9 - 1 ½ (4)=3
Sx = 3P - 9 4 ½ P = 18 Dm = Sx = 3
Dm = Sx P* =4
f.
Thus in Colombia, the country as a whole benefits because total welfare rises by area (D). However,
consumers gain welfare and benefit more by opening the border to low cost imports from Guatemala.
They receive the opportunity to purchase more at a lower price. Firms in Colombia may be harmed
because they must now sell less and receive a lower price for their product.
Absolute Advantage and Comparative Advantage
5. The Ricardian Model of Trade suggests that differences in labor productivity (due to technology) may
be a source of comparative advantage. Assume Australia and the UK are the only producers of wine
and medicine and behave according to the standard assumptions of the Ricardian Model of Trade
(including constant opportunity cost of production) In one day: one UK worker can produce 15
bottles of wine or 30 bottles of medicine; one Australian worker can produce 30 bottles wine or 10
bottles of medicine.
Q
P Columbia coffee market
Sc
Dc
6
Dm
M=X=3 Qd1 Qs1
International coffee market
M=3
4
Sg
Dg
Sx
Guatemala coffee market
3
Q Qs1 Qd1
X=3
a
b
c
d d e
f
g
h h
4 4 Q imports &
exports
Colombia
Welfare Before Trade
• Consumer surplus: A.
• Producer surplus: B + C.
• Total surplus: A + B + C.
Welfare After Trade
• Consumer surplus: A + B + D. (Gain B+D)
• Producer surplus: C. (Loose B)
• Total surplus: A + B + C + D
Changes in Welfare
• Gains from trade: D
• Consumer surplus changes by: +(B + D)
• Producer surplus changes by: –B.
• Transfer of B from producers to consumers
Guatemala
Welfare Before Trade
• Consumer surplus: E+F.
• Producer surplus: G.
• Total surplus: E+F+G.
• Welfare After Trade
• Consumer surplus: E (loose F)
• Producer surplus: F+G+H (gain F+H)
• Total surplus: E+F+G+H
• Changes in Welfare
• Gains from trade: H
• Consumer surplus changes by: -(F)
• Producer surplus changes by: +(F+H).
• Transfer of F from consumers to producers
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
7
a. Given the assumptions above, complete and label each country's PPF for one worker in one day.
b. What is the opportunity cost (domestic relative price ratio) of each good for each country?
Opportunity cost of 1 bottle medicine Opportunity cost of 1 bottle wine
UK
Australia
c. Explicitly refer to your numerical answers in (b) in an explanation of who has a comparative
advantage in each of the two goods, who will export which good and where on your graph in part (a)
will each country produce under this scenario?
• Medicine:
• Wine:
d. The UK and Australia agree to an international terms of trade ratio of 2 wine for 1 medicine (2 w/m).
Draw this trade line on your diagram. If 10 bottles of medicine are traded for 20 bottles of wine, how
much of each good will each countries consume?
Consumption of medicine Consumption of wine
UK
Australia
e. Explain how each country gains from trade, explicitly referring to your graph.
Solutions:
a. Given the assumptions above, complete and label each country's PPF for one worker in one day.
medicine
win
e
win
e
medicine
UK Australia
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
8
b. What is the opportunity cost (domestic relative price ratio) of each good for each country?
Opportunity cost of 1 bottle medicine Opportunity cost of 1 bottle wine
UK ½ bottle wine 2 bottle medicine
Australia 3 bottle wine 1/3 bottle medicine
c. Explicitly refer to your numerical answers in (b) in an explanation of who has a comparative
advantage in each of the two goods, who will export which good and where on your graph in part (a)
will each country produce under this scenario?
• Medicine: The UK has a comparative advantage in medicine because it only costs the ½ bottle of
wine to produce one unit, while it costs Australia 3 bottles of wine. The UK will export medicine.
It will completely specialize production of wine at point (P)
• Wine: Australia has a comparative advantage in wine because it only costs them 1/3 bottle of
medicine to produce, while it costs the UK 2 bottles of medicine. Australia will export wine.
Australia will completely specialize production at point (P)
d. The UK and Australia agree to an international terms of trade ratio of 2 wine for 1 medicine (2 w/m).
Draw this trade line on your diagram. If 10 bottles of medicine are traded for 20 bottles of wine, how
much of each good will each countries consume?
Consumption of medicine Consumption of wine
UK 20 20
Australia 10 10
e. Each country gains from trade. Each is able to consume combined quantities of wine and medicine
that are beyond its ability to produce domestically. The free trade consumption point is outside of the
production possibility curve.
6. The maximum amount of steel and aluminum that Canada and France can produce if they fully use
all the factors of production at their disposal with the best technology available is shown the
following table:
Steel and Aluminum Production
Canada France
Steel (tons) 500 1,200
Aluminum (tons) 1,500 800
medicine
win
e
win
e
medicine
UK Australia
15
30 10
30
P
P
X = 10 20
M =
20
20
X =
20
M=10
10
tt = 2 w/m tt = 2 w/m
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
9
Assume that production occurs under constant opportunity costs assumption of the Ricardian model of
trade.
a. Use the data to construct a carefully labeled diagram of each country’s production possibility
frontier (place aluminum on the x-axis). Assume under autarky, Canada produces and consumes
600 tons of aluminum and 300 tons of steel and that France produces and consumes 400 tons of
aluminum and 600 tons of steel.
b. Use the data and your diagram to help you construct a table of each country’s opportunity cost
(equivalently relative price) for each good. Use this table to explain which country has the
comparative advantage in the production of steel? In aluminum?
c. Suppose both countries open their borders to international trade. Within what range will the
international equilibrium price ratio lie? Suppose Canada and France agree to a terms of trade
ratio of 1:1 ( 1 ton of steel = 1 ton of aluminum). Use this information to construct the terms of
trade (trade line) on your graph in part (b).
d. Explain what your results from part (c) results imply about which country will export which
good if opened to international trade? Where on your graph in part (b) will each country produce
under this scenario?
e. Suppose that 500 tons of steel are traded for 500 tons of aluminum. How much of each good will
both countries consume? Show this point on your graph.
f. Explain how each country gains from trade, explicitly referring to your graph.
Solutions
a.
b. We can use the slope of the PPF to identify each country’s opportunity cost of production. The
slope of the PPF for Canada is 1/3, or Canada can produce 1 unit of aluminum by giving up 1/3 unit
of steel. While the slope of the PPF for France is 3/2. Thus France can produce one unit of aluminum
by giving up 3/2 unit of steel.
Opp cost of aluminum Opp cost of steel
Canada 1/3 tons of steel 3 tons of aluminum
France 3/2 tons of steel 2/3 tons if aluminum
Thus Canada has a CA in the production of aluminum since the opportunity cost of aluminum is less
for Canada than for France. France has a CA in the production of steel since the opportunity cost of
steel is less in France than in Canada.
c. For steel, the international terms of trade ratio for one ton of steel will be between 2/3 tons of
aluminum to 3 tons of aluminum. For aluminum, the international terms of trade ratio will be between
1/3 and 3/2 tons of steel.
aluminum 600
500
stee
l
aluminum 800
1200
stee
l
France PPF
Slope=500/1500=1/3 Slope=1200/800=3/2
Canada PPF
300
1500 400
600
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
10
If the terms of trade ratio is 1:1, Canada specializes in the production of aluminum while France
specializes in the production of steel. Complete specialization occurs in each country.
d. From part b-c, we know that Canada will completely specialize in aluminum and produce 1500 tons
because they have a CA in aluminum. We also know that France will completely specialize in steel,
producing 1200 tons.
e. If 500 tons of aluminum are traded for 500 tons of steel, we know that Canada will produce 1500
tons of aluminum, export 500 tons (which France will import) and consume 1000 tons of aluminum;
France will consume 500 tons of aluminum. Then France will produce 1200 tons of steel, export 500
tons (which Canada will import) and consume 700 tons of steel and Canada will consume 500 tons of
steel.
aluminum steel
Production Consumption Production Consumption
Canada 1500 1000 0 500
France 0 500 1200 700
f. The obvious gains from trade are that consumers in both countries can produce beyond their PPF.
Also note with this example that there are production gains from trade and complete specialization.
Under the autarky points, the maximum output of steel was 1100 tons; under complete specialization,
total output (produced by France) is 1200. For aluminum under autarky, total output was 1000, but
under complete specialization, Canada produces 1500 tons.
7. (Optional) The Economist reported that Australia has some of the most efficient cattle breeders in the
world, suggesting that labor productivity may be a source of their comparative advantage.1 Assuming
the Ricardian model of international trade, there are 2 countries (Australia and Indonesia) and 2
goods (cattle and fabric), and each country has 100 workers. In one week, one Australian worker can
produce 12 cattle or 4 pounds of fabric; one Indonesian worker can produce 6 cattle or 4 pounds of
fabric.
a. Given the assumptions, complete and label each country's PPF for a week.
1 The Economist “A row over cows: Indonesia curbs beef imports.” February 17, 2011. To help you make sense of
your equilibrium results, cattle are sold per kilogram. Thus, the price is per kilogram in Australian dollars.
aluminum 600
500
stee
l
aluminum 800
1200
stee
l
France PPF
Slope=1
Canada PPF
300
1500 400
600
1500
Slope=1
1000 500
700
1200
X = 500 M = 500
M =
500
X =
50
0
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
11
b. What is the opportunity cost (relative price ratio) of each good for each country?
fabric cattle
Australia
Indonesia
c. Use your numerical answers in (b) explain why each country has the comparative advantage in
which product.
d. Suppose Indonesia and Australia agree to an international terms of trade ratio of 2 cattle for one
pound of fabric or (2 c/f). Draw this trade line on your diagram. If 600 cattle are traded for 300
pounds of fabric, how much of each good will both countries consume?
fabric cattle
Australia
Indonesia
e. Use the given import/export data and international terms of trade ratio to explain why trade is
balanced.
Solutions
a.
b.
fabric cattle
Australia 3 cattle 1/3 fabric
fabric
Cat
tle
Cat
tle
fabric
fabric
Cat
tle
Cat
tle
fabric
Australia 1200
400 400
600
Indonesia
600
800
300
600
100
X =
60
0
M =
600
X = 300 M = 300
Econ 342 International Trade
Fall 2018
Problem Set 1
Solutions
12
Indonesia 1.5 cattle 2/3 fabric
c. Australia has the comparative advantage in cattle because the opportunity cost (1/3 units of fabric) is
lower than Indonesia’s opportunity cost of 2/3 units of fabric. Indonesia has a comparative
advantage in fabric because they have a lower opportunity cost (1.5 cattle for Indonesia is less than 3
cattle for Australia).
d.
fabric cattle
Australia 300 600
Indonesia 100 600
e. For balanced trade, we need that the value of imports are equal to the value of exports or for
Australia we have (Pc x Xc) = (Mf).
• The price of cattle is Pc = ½ (f/c)
• Exports of cattle are Xc = 600c
• Imports of fabric are Mf = 300f
• ½(f/c) x (600c) = 300f
• 300f = 300f Thus trade is balanced.
For Indonesia we have Pf x Xf = Mc
• The price of fabric is Pf = 2 (c/f)
• Exports of fabric are Xf = 300f
• Imports of cattle are Mc = 600c
• 2(c/f) x 300f = 600c
• 600c = 600c Thus trade is balanced.