Econ 348 International Economics Fall 2011 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. Chapter 2, Problem 8. Please read the introduction to problem 8 and use the supply and demand equations provided, but answer the following three questions (not those in the text). Hint: you do not get “pretty numbers” a. Use the supply and demand equations to solve for autarky equilibrium price and quantity. Then use the equations and your results to provide a clear, well labeled graph of the US market for oil. b. Suppose that under free trade, the international price (world price) of oil is $67 per barrel. Mathematically determine the US quantity supplied and quantity demanded and number of imports. Clearly show these results on your graph in part (a). c. Construct a table that shows the welfare effects (consumer surplus, producer surplus, total welfare and gains from trade) under both autarky and free trade. To do this, you may need to use labels on your graph in part (a) to help you identify areas in your graph. Then use the results of your table to carefully explain who benefits/looses under autarky and who benefits/looses under free trade. Solutions: note due to rounding, your numerical answers may differ slightly – this fine! a. we have: Qd: P=291-40Qd and P=.05+35Qs In equilibrium we know that the prices must be equal and that Qs = Qd = Q. We can write: 291-40Q = 0.5 + 35Q Now use basic algebra to solve for equilibrium Q: 291 - 0.5 -40Q = 0.5-0.5 + 35Q 290.5 - 40Q = 35Q 290.5 - 40Q + 40Q = 35Q + 40Q 290.5 = 75Q 290.5/75 = 75Q/75 Q = 290.5/75 = 3.9 billion barrels Now you can plug Q into either your supply or demand equation to find the equilibrium price: Demand: P=291-40Qd = 291 - 40(3.9) = 136 $ per barrel Supply: P = 0.5 + 35Qs = .05 - 35(3.9) = 136 $ per barrel. Thus we have Q = 3.9 and P = 136 Alternatively we can re-arrange the original Supply and demand equations in terms of quantity: Qd: Qd = 7.275 - .025P and Qs:Qs = .02857P-.001429 Then: Qs = Qd ⇒ 7.275 - .025P = .02857P-.001429 Thus equilibrium price is about P=136 per barrel Then autarky equilibrium quantity Q*=Qd=Qs⇒ Qd = 7.275 - .025(135)=3.9 billion barrels produces and consumed.
Transcript
Econ 348 International Economics Fall 2011
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. Chapter 2, Problem 8. Please read the introduction to problem 8 and use the supply and
demand equations provided, but answer the following three questions (not those in the text). Hint: you do not get “pretty numbers” a. Use the supply and demand equations to solve for autarky equilibrium price and quantity.
Then use the equations and your results to provide a clear, well labeled graph of the US market for oil.
b. Suppose that under free trade, the international price (world price) of oil is $67 per barrel. Mathematically determine the US quantity supplied and quantity demanded and number of imports. Clearly show these results on your graph in part (a).
c. Construct a table that shows the welfare effects (consumer surplus, producer surplus, total welfare and gains from trade) under both autarky and free trade. To do this, you may need to use labels on your graph in part (a) to help you identify areas in your graph. Then use the results of your table to carefully explain who benefits/looses under autarky and who benefits/looses under free trade.
Solutions: note due to rounding, your numerical answers may differ slightly – this fine! a. we have: Qd: P=291-40Qd and P=.05+35Qs In equilibrium we know that the prices must be equal and that Qs = Qd = Q. We can write: 291-40Q = 0.5 + 35Q Now use basic algebra to solve for equilibrium Q: 291 - 0.5 -40Q = 0.5-0.5 + 35Q 290.5 - 40Q = 35Q 290.5 - 40Q + 40Q = 35Q + 40Q 290.5 = 75Q 290.5/75 = 75Q/75 Q = 290.5/75 = 3.9 billion barrels Now you can plug Q into either your supply or demand equation to find the equilibrium price: Demand: P=291-40Qd = 291 - 40(3.9) = 136 $ per barrel Supply: P = 0.5 + 35Qs = .05 - 35(3.9) = 136 $ per barrel. Thus we have Q = 3.9 and P = 136 Alternatively we can re-arrange the original Supply and demand equations in terms of quantity: Qd: Qd = 7.275 - .025P and Qs:Qs = .02857P-.001429 Then: Qs = Qd ⇒ 7.275 - .025P = .02857P-.001429 Thus equilibrium price is about P=136 per barrel Then autarky equilibrium quantity Q*=Qd=Qs⇒ Qd = 7.275 - .025(135)=3.9 billion barrels produces and consumed.
Econ 348 International Economics Fall 2011
Solutions
2
Graphically we have: US market for oil
b. With free trade at $67 per barrel: Domestic production Qs: Qs = .02857(67)-.001429=1.9 billion barrels Domestic consumption Qd: Qd = 7.275 - .025(67)=5.6 billion barrels. Number of Imports: Qd – Qs = 5.6-1.9 = 3.7
US market for oil
c. Autarky Free Trade Consumer Surplus: a Producer Surplus: bc Total welfare: abc Gains from trade: - not relevant
Consumer Surplus: abde Producer Surplus: c Total welfare: abcde Gains from trade: de
Price ($/barrel)
136
1.9 3.87 5.6 Quantity (billions of barrels)
SUS
o i l
DUS
67
Price ($/barrel)
136
1.9 3.87 5.6 Quantity (billions of barrels)
SUS o i l
DUS
67
a
b d e
c
Econ 348 International Economics Fall 2011
Solutions
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If the US moves from autarky to free trade, consumer’s gain by an area of (bde), d is welfare transferred from producers to consumers and de are new gains from trade. Producers loose areas b. But society as a whole gains areas de. If the US stops all imports and moves from free trade to autarky, consumers loose areas bde, while producers gain welfare area b. Society as a whole looses de. 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 3, what is the Q traded on the world market? Is this an 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. Support your answer with a corresponding diagram of the international market.
Solutions
a.
b. c. First consider Mali, Pw = 3 <P*=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 < P* = 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 have to import shirts from a third party since this price is less than both of their autarky prices. 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.
3. Chapter 2, Question 10. For this problem, please draw a well labeled diagram of figure 2.3
from your text. In your careful explanation of your answers to the questions, explicitly refer to the labels on the diagram you have drawn.
solutions
The supply curve SUS shifts to the right, causing the U.S. demand-for-imports curve Dm shifts to the left. As a result, the equilibrium international price decreases below 1,000—it is shown by the intersection of the new U.S. Dm curve and the original Sx curve. Imports from the world market fall below 50 to M2.
Q
Pric
e
65
DUS
SUS US Mkt for motorbikes
2000
15
1000
Q
Pric
e
Dus,m,
World Mkt for motorbikes
50 Q
Pric
e
50
DROW
SROW
ROW Mkt for motorbikes
75 25
Sx,ROW
700
40
SUS
Dus,m, M2
Econ 348 International Economics Fall 2011
Solutions
5
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
a. Colombia: Solve for autarky equilibrium price and quantity. b. Guatemala: Solve for autarky equilibrium price and quantity c. Based on your answers in part (a) and (b), which country will import and which country will export
coffee? d. Use the supply and demand equations above to derive the equation for import demand and for export
supply of coffee. e. Use your import demand equation and export supply equation from part (d) to find the international
equilibrium price and quantity traded. f. Sketch a graph of this market. g. 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 careful 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* = 3 c. Since the price of coffee is cheaper in Guatemala, Guatemala will export and Colombia will import. 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.
Econ 348 International Economics Fall 2011
Solutions
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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 boarder 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 1. Chapter 3, Problem 8. Please refer to the introduction, table of labor productivity and
endowment of labor hours for each country provided. Then use this information to answer the following questions (not those in the text). Be sure to carefully explain your answers in complete sentences, explicitly referring to any tables/graphs when possible. a. Use the table to explain which country has the absolute advantage in wine? In cheese? b. Use the data to construct a carefully labeled diagram of each country’s production
possibility frontier (place wine on the y-axis). Assume that under autarky Vintland consumes 1.5 million kilos of cheese and Moonited Republic consumes 3 million kilos of cheese.
c. 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 wine? In cheese?
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
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
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
Econ 348 International Economics Fall 2011
Solutions
7
d. Suppose both countries open their boarders to international trade and the resulting equilibrium price ratio (terms of trade) is ½ bottle of wine per kilo of cheese. Use this information to construct the terms of trade (trade line) on your graph in part (b).
e. Explain what your results from part (c) results imply about which country will export which good under free trade international trade? Where on your graph in part (b) will each country produce under this scenario?
f. Suppose that 2 million kilos of cheese and 1 million bottles of wine are traded. How much of each good will both countries consume? Show this point on your graph.
g. Explain how each country gains from trade, explicitly referring to your graph. Solutions: a. Moonited Republic has an absolute advantage in wine—it takes fewer labor hours to produce
a bottle (10<15). Moonited Republic also has an absolute advantage in producing cheese—it takes fewer labor hours to produce a kilo (4<10). Thus Moonited has an absolute advantage in both goods!
b. Recall that Vintland has 30 million labor hours and Moonited Repbulic has 20 million labor
hours. The table gives us labor hours per bottle, and we need bottles per labor hour. Consider Vintland and wine: It takes 15 labor hours to produce 1 bottle of wine. Thus in 1 labor hour, Vintland can produce 1/15 = .0666 bottles of wine. Multiplied by 30 million labor hours, 2 million bottles of wine. Continuing this way we have: Bottles of wine per hour Kilos of cheese per hour Vintland .0666 .1 Moonited .1 .25 Total bottles produced Total kilos produced Vintland (30 mil labor hours) 2 million 3 Moonited (20 mil labor hours) 2 5
Thus we have the following PPF:
1.5 3
1
2
Wine Vintland
NV
Cheese
Wine
2
0.8
3 5
NM
Cheese
MoonitedRepublic
c.
Opp cost of Wine Opp cost of Cheese Vintland 3/2 kilo of cheese 2/3 bottle of wine
Econ 348 International Economics Fall 2011
Solutions
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Moonited 5/2 kilo of cheese 2/5 bottle of wine First consider wine: Vintland has a CA in wine because the opportunity cost in terms of cheese is lower than in Moonited (3/2 < 5.2) Second consider cheese: Moonited has a CA in cheese because the opportunity cost in terms of wine is lower than in Vintland (2/5 < 2/3) Moonited Republic has a comparative advantage in cheese.
d. 3
1
2
Wine Vintland
NV
Cheese
Wine
2
3 5
NM
Cheese
MoonitedRepublic
2
TV TM1
e. When trade is opened, Moonited Republic exports cheese because it has a CA in the
production of cheese and Vintland exports wine because it has a CA in wine. If the equilibrium free trade price ratio is 1/2 bottle per kilo, Moonited Republic will specialize completely in producing cheese, and Vintland will specialize completely in producing wine.
f. With free trade Moonited Republic produces 5 (=20/4) million kilos of cheese. If it exports 2 million kilos, then it consumes 3 million kilos. It consumes the 1 million bottles of wine that it imports. With free trade Vintland produces 2 (=30/15) million bottles of wine. If it exports 1 million bottles, then it consumes 1 million bottles. It consumes the 2 million kilos of cheese that it imports.
3
1
2
Wine Vintland
NV
Cheese
Wine
2
3 5
NM
Cheese
MoonitedRepublic
2
TV TM1
Econ 348 International Economics Fall 2011
Solutions
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g. Each country gains from trade. Each is able to consume combined quantities of wine and cheese that are beyond its ability to produce domestically. The free trade consumption point is outside of the production possibility curve.
2. Read the box in the text entitled, “Focus on Labor: Absolute Advantage Does Matter” on p.
42-43 of the text. According to the author, what is the role of absolute advantage and comparative advantage in helping us understand basic controversies over international trade? Based on this reading and/or other readings you may have done on your own, what solutions can be derived?
Solutions. This is an open ended question thus answers will vary.
Econ 348 International Economics Fall 2011
Solutions
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3. 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
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 steel on the y-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 boarders 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.
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 348 International Economics Fall 2011
Solutions
11
Opp cost of steel Opp cost of aluminum Canada 3 tons of aluminum 1/3 tons of steel France 2/3 tons if aluminum 3/2 tons of steel 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. 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. Then France will produce 1200 tons of steel, export 500 tons (which Canada will import) and consume 700 tons. 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.
4. (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
aluminum 600
500
stee
l
aluminum 800
1200 st
eel
France PPF
Slope=1
Canada PPF
300
1500 400
600
1500
Slope=1
1000 500
700
1200
Econ 348 International Economics Fall 2011
Solutions
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advantage.1
a. Given the assumptions, complete and label each country's PPF for a week.
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.
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.
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.
fabric
Cat
tle
Cat
tle
fabric
Econ 348 International Economics Fall 2011
Solutions
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b.
fabric cattle Australia 3 cattle 1/3 fabric
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.
