Econ 342 International Trade Problem Set 1...

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


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


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


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


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


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


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


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


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


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


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


Fall 2018

Problem Set 1

Solutions

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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.

Econ 342 International Trade Problem Set 1...

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