International Trade: application exercises

1 Balance of Payments

Exercise 1.1 :CA is the current account, Sp the private savings, I investment, G the public

spending and T the taxes.

1. Show that CA = (Sp − I)− (G− T ). What does a surplus of the currentaccount mean?

2. Rewrite this equation and explain how private spending can be used fordifferent purposes.

Exercise 1.2 : (source GUILLOCHON B. and KAWECKI A. Economieinternationale. 4th edition. Dunod. Paris 2003)

Is a deficit of the current account compatible with a surplus of the officialsettlement balance (sum of the current account balance, the capital accountbalance, and the nonreserve portion of the financial account balance) ? What isthe sign of the balance of official reserve transactions? Have the official reservesincreased or decreased?

Exercise 1.3 :1. Explain how each of these transactions enters the balance of payments

and write them down in a simplified version of the balance of payments.

-a- French exports worth 2 milliards of euros, paid in foreign currency.- b- A firm residing in France buys for 1 milliard of euros financial services

to a firm residing in a foreign country.-c- An outflow of foreign direct investment worth 7,5 milliards of euros paid

in foreign currency.-d- An inflow of foreign direct investment worth 3 milliards of euros paid in

foreign currency.-e- The European commission pays a subsidy worth 0,45 milliard of euros.-f- A firm residing in France pays the wages of workers living in Switzerland,

equal to 0,15 milliard of euros.

2. Using the balance of payments, explain the relationship between thecurrent account and the evolution of the exchange rate (with the main economicpartners).

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2 The Ricardian model of trade

Exercise 2.1 :(source GUILLOCHON B. and KAWECKI A. Economie inter-nationale. 4th edition. Dunod. Paris 2003)

Consider two countries, North (N) and South (S). Both produce two goods,1 and 2, using labor L. aij is the cost, in terms of labor, of producing one unitof good i in country j. Set a1N = 2 ; a2N = 4 ; a1S = 3 and a2S = 12.Both countries are endowed with the following amount of labor: LN = 4000and LS = 9000. yij is the production of good i in country j and yj is thenational income of country j, measured in terms of good 1, which is chosen asthe numeraire. p is the price of good 2 in terms of good 1. Consumers in bothcountries have the same preferences: d1j = 0, 5yj and d2j = 0, 5(yj/p).

1. State the characteristics of each country in autarky. Illustrate graphically.

2. What is the comparative advantage of each country? If both countriesopen to trade, what is the free trade equilibrium price?

3. At this equilibrium price, how much do both countries produce, consumeand trade? Explain graphically. How can the gains from trade be evaluated?

4. Determine the wages in free trade in both countries. What is the rela-tionship between wages and labor productivities?

Exercise 2.2 :Consider two countries, Home (H) and Foreign (F). Both countries produce

two goods (1 and 2) using a single production factor, labor. Labor productivityin each country in each sector is equal to:

Home: a1H = 10λ a2H = 10λ with λ ≥ 0.8Foreign : a1F = 8 a2F = 2

Good 1 is chosen to be the numeraire: p, y, w are respectively the price ofgood 2, the national income and the minimum wage, all expressed in terms ofunits of good 1.

1. Compare the situation of both countries. Do they both have interest intrading? If yes, in which interval is the free trade equilibrium price ? Explaineach step of the answer.

2. How do the gains from trade appear for each country? Under whichconditions does free trade generate gains from trade for both countries?

3. Labor endowments for both countries are noted LH for Home and LF =4LH for Foreign. Consumers in both countries have the same preferences: d1j =0.5yj and d2j = 0.5yj/p (j = H,F ).

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Write the equilibrium free trade price, p, as a function of the parameterλ in the case where free trade generates gains from trade for both countries.Illustrate graphically the relationship between the equilibrium free trade priceand the parameter λ in the axis (λ, p). Provide an interpretation of the graph.

4. State the relationship between the ratio of wages in free trade, wH/wF ,the equilibrium free trade price and the parameter λ. Illustrate graphically thisrelationship in the axis (p, wH/wF ) for λ = 1.

5.“Competition from countries with low wages is an insurmountable handi-cap for the competitiveness of developed countries.” Discuss this assertion usingthe previous example.

Exercise 2.3 :Consider a typical framework of the trade model with comparative advan-

tages. Consider two countries, A and B, two goods, 1 and 2, and one productionfactor, labor L. cj

i is the unit labor cost for sector i in country j.

cA1 = 4, cA

2 = 2, cB1 = 1, cB

2 = 8

p is the relative price of good 2 in terms of good 1, y is the national incomeexpressed in units of good 1. Demand functions are identical in both countries:

d1 = by and d2 = (1− b)(

y

p

)Labor endowments are respectively LA and LB .

1.What are the comparative advantages of both countries?

2. In which interval is the equilibrium free trade price situated?

3. Express the equilibrium free trade price as a function of the parameters b,LA and LB in the case free trade generates gains from trade for both countries.

4. Suppose both countries have the same size: LA = LB .-a- Illustrate graphically the relationship between p and b. How d the gains

from trade in country A vary with the parameter b? For which values of b arethe gains from trade maximum/equal to zero?

-b- Interpret the preceding result by showing how demand affects the distri-bution of the gains from trade.

5. Suppose both countries have different sizes. Country B is larger thancountry A: LB = δLA, with δ > 1.

-a- Illustrate graphically the relationship between p and δ for b = 1/2.-b- Interpret this result by discussing the following assertion: “Large coun-

tries benefit less from international trade than small countries”.

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3 The Heckscher-Ohlin model of trade1

Exercise 3.1 :Consider the typical HOS setting: two goods, 1 and 2, are produced using

two production factors: labor L and capital K. yi is the production of good i,and Ki and Li are respectively the amounts of capital and labor used in sectori. Demand functions write:

y1 = K0,21 L0,8

1

y2 = K0,82 L0,2

2

Good 1 is chosen as the numeraire. p is the price of good 2 in units of good1. y is the national income in units of good 1. w is the wage and r is the capitalreward, both expressed in units of good 1.

ki is the capital intensity of sector i: ki = Ki/Li.

1. Write the relationships that characterize the optimal allocations of ressources.Explain the different steps. Express k1 as a function of w/r and k2 as a functionof w/r. Illustrate graphically.

2. Write the relationships between p and w/r. Illustrate graphically.

3. The country is endowed with K = 800 units of capital and with L = 400units of labor. What are the limit values of w/r? What are the limit values ofk1 and k2? What are the values of p for which the countries specializes entirely?Explain. Illustrate graphically.

4. Let b be the share of national income, in terms of good 1, allocated byconsumers to the consumption of good 1: d1 = by. y is the national income interms of good 1 (0 < b < 1). In autarky, is can be showed that

w

r=

[0, 2(1− b) + 0, 8b

0, 8(1− b) + 0, 2b

]K

L

Suppose b = 0, 75. What are the values of w/r, k1 and k2 in autarky?Illustrate graphically.

5. The country opens to free trade. The country is assumed to be a smallcountry. The world price p is equal to 0.6. State the Stolper-Samuelson theorem.Is the theorem verified here? Explain why. Does the result depend on the goodchosen to be the numeraire?

Exercise 3.2 :1These two exercices are from the course at the University Paris-Dauphine. B. Guillochon

and A. Kawecki

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Consider two countries A and B, two goods 1 and 2, two production factors,capital K and labor L.

Good 1 is chosen to be the numeraire. p is the price of good 1. Yj is thenational income of country j, wj the wage in country j and rj the capital rewardin country j.

Production functions are :

y1 = K0,251 L0,75

1

y2 = K0,752 L0,25

2

Labor endowments are:

KA = 80; LA = 80; KB = 30;LB = 70

1. Explain the relationship between p and w/r.

2. Suppose the demand functions are identical: D1j = 0, 5Yj and D2j =0, 5Yj , j = A,B. What is the good exported by country A in free trade? Dothese specializations follow the law of factor proportions ?

3. Suppose that the two countries trade freely, however the demand functionsare now different. In each country, demand functions are: D1A = 0, 25YA

and D1B = 0, 9YB . Which country exports which good? Is the law of factorproportions verified? Explain why.

4. Both countries refuse to trade goods. However, capital flows betweencountries is allowed. Labor is still immobile. Demand functions are the onesdescribed in question 2. Knowing that capital flows towards the location withthe highest reward, characterize the equilibrium situation for each country interms of w/r and p. Discuss the result.

4 The standard model of trade

Exercise 4.1:Brazil increases its production of coffee because of an extension in the land

suitable for cultivation. Depending on the reaction of the world price of coffee,explain why this increase in coffee production may increase/decrease welfare inBrazil. Illustrate graphically.

Exercise 4.2: (source Krugman P. and Obstfeld M. International Trade.6th edition. De Boeck)

1. Under what conditions does an international transfer between countriesdeteriorate the terms of trade of the donor?

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2. In reality, an important share of international aid for developing countriesis conditional. For example, France may finance an irrigation project in Africa,under the condition that the pumps, pipelines and other building materials bebought to French producers. How does this conditionality affect the impact ofinternational transfers on each country’s terms of trade? Is this conditionalityimportant for the donor? Can you imagine a situation in which the conditionalaid deteriorates the situation of the developing country?

5 Location theory

Exercise 5.1:A firm must choose the location of its production plant. The firm can pro-

duce in Morocco, or in France, or in both countries. France is the main market,with a demand worth 40. The Moroccan demand is worth 5. Morocco has lowerproduction costs: 6 for each unit produced, and 7 in France. The price of thegood is equal to 10 in both countries. A fixed cost equal to 30 must be paid foreach production plant. If the firm sells locally, she does not pay any transactioncosts. However, in order to sell abroad she must pay t per unit sold on theforeign market.

1. Show that the profit of the firm is equal to 80 if she produces in bothcountries.

2. Show that if the firm chooses to concentrate her production in France,she sill have a profit equal to 105− 5t, and equal to 150− 40t if she locates inMorocco.

3. Suppose Morocco and France do not share any trade agreement. Tradecosts are thus high: 6 per unit sold. Show that the firms prefers to produce inboth countries. Explain why.

4. Morocco and France sign a free trade agreement, which decreases theinternational trade costs to 2 per unit sold abroad. Show that the firm prefersto concentrate production in France and export to Morocco. Explain why.

5. If Morocco and France decrease their trade costs to 1 per unit sold abroad,show that the firm prefers to locate its production in Morocco. Explain why.

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6 Monopolistic Competition

Exercise 6.1: (source Krugman P. and Obstfeld M. International Trade. 6thedition. De Boeck)

Consider the automobile industry in country A. There are n symmetric firms,selling annually a total of 900000 cars. Demand addressed to a given car pro-ducer can be written as:

X = S[

1n −

(P−P∗)30000

]X is the number of cars sold by the firm, S the total sales of the industry,

P the price set by the firms and P ∗ the average price of other producers. Firmsare assumed to consider the price of competitors as given. Total cost is givenby C = 750000000 + 5000X.

1. What is the name of this market structure? Show that the firms produceunder increasing returns to scale.

2. Show that the more there are producing firms, the higher the cost toproduce one unit. Illustrate graphically the average cost as a function of n.

3. Write the inverse demand function. Get the marginal revenue of therepresentative firm. Write the profit maximization condition. What is theequilibrium price ? Illustrate the price graphically on the preceding graph.Note: This is equivalent to showing that the more there are firms, the lower theequilibrium price.

4. What is the equilibrium number of firms and the equilibrium long termprice?

5. Consider country B in which the annual total sales of cars is equal to 1,6millions automobiles. As for country A, give the equilibrium number of firmson the market and the equilibrium long term price in the automobile industryin country B.

6. Suppose both countries can trade cars without trade costs. The newintegrated market thus has total sales equal to 2.5 millions of cars. What arethe consequences of the creation of the integrated market? Summarize theeffects on the equilibrium number of firms and the equilibrium price in a tablecomparing each national market with the integrated market.

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7 Trade policy

Exercise 7.1 :Suppose the demand and supply functions for a good i in a country j are

given respectively by

Qdi = 140− 20pi et Qs

i = 20pi − 20

where pi is the price in monetary units.

1. Illustrate graphically the demand and supply curves of good i. Indicatethe equilibrium price and the quantities produced and consumed without trade.

2. Suppose the country enters free trade. The world price is pi = 2. Theworld supply of good i is infinitely elastic at pi = 2. There are no trade costs.

-a- What is the equilibrium price in the country ?-b- What are the amounts of good i produced, consumed and traded?-c- Calculate the value of the consumer and producer surplus.

3. The government of country j sets an ad-valorem tariff of 50% on itsimports of good i.

-a- Give the definition of an ad-valorem tariff.-b- Determine graphically the new equilibrium price in country j. Give the

impact of the tariff on consumption, production, trade and income.-c- On what do these effects depend?-d- Calculate the level of tariff for which there would be no imports.-e- Calculate and show graphically the consumer and producer surplus

4. The government sets a quota on imports equal to 40 units of good i.-a- Evaluate and discuss the consequences of the quota on the different

agents.-b- Compare with the effects of the tariff.

Exercise 7.2 :The United-States set a quota on their imports of sugar. The following

numbers are real, however approximated for simplicity. After the quota, thenational production increases from 5 to 6 millions tons and national consumptiondecreases from 9 to 8 millions tons. The price for the American consumer isnow equal to 480 dollars a ton, while it is equal to 280 dollars a ton on worldmarkets.

1. What is the quota equal to?

2. Illustrate the situation graphically by showing the effects of the quota.Why does the quota increase the price of sugar within the United-States?

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3. Evaluate the loss for American consumers (in millions of dollars) gener-ated by the quota.

4. Evaluate the gain (in millions of dollars) for American sugar producers.How much would these producers be ready to pay (in terms of lobbying, ...) inorder to keep the benefit of the quota ?

5. Calculate the level of the rent of the quota. Who benefits from it?

8 Strategic trade policy and reciprocal dumping

Exercise 8.1 :Consider two firms A and B from two different countries (respectively 1 and

2). Both firms produce a homogenous good. In country 1, the inverse demandfunction is equal to p(Y ) = 5− Y , with Y the aggregate consumption.

The firms in country 1 has the following cost function: CA(yA) = 1 + cayA.The cost function of the competing firms is CB(yB) = 1 + cbyB .

Competition on the local marketThe unit transport cost from country 1 to country 2 is τ (τ > 0). Both firms

compete in Cournot competition on the market of country 1 (Firm 1 does notexport). Set the following costs: ca = 1 et cb = 1/2

1. When firm B sells on both markets, does she set identical prices on bothmarkets ?

2. Who incurs the trade cost?

3. Determine the reaction functions of both firms. Illustrate graphically.

4. Characterize the Cournot equilibrium on the market of country 1.

5. Is there a limit value of τ for which firm B does not sell on the market ofcountry 1 anymore?

6. If there is trade between countries, does country 1 gain or loose fromtrade?

Competition on a third marketSuppose both firms export on a third market. Both firms incur the same

transport cost τ . The inverse demand function in the third country is equal top(Y ) = 5− Y .

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1. Write the reaction functions of both firms. Illustrate graphically. Whatare the equilibrium conditions?

2. The government of country 1 sets a subsidy s for firms A for each unitexported. Show the effects of this subsidy on firm A’s market share and on itsprofit.

3. Country 1 and the third country sign a trade agreement which decreasestrade costs from τ to τ∗ < τ for firm A. Evaluate the effects of the tradeagreement.

4. Progress in technology reduces the production cost for firm A: ca = 1/δ.Evaluate the effects of this change.

5. Discuss the consequences of a production subsidy, a trade policy, and asubsidy for research and development.

Exercise 8.2 : (source GUILLOCHON B. and KAWECKI A. Economieinternationale. 4th edition. Dunod. Paris 2003 )

Boeing and Airbus sell airplanes in Asia. The demand for airplanes is p =100− 0, 25(x + y), with p the price of an airplane in millions of dollars. x and yare the respective numbers of airplanes produced by Boeing and Airbus. Bothfirms compete under Cournot competition (competition on quantities).

1. Total cost for each firm writes: C(x) = 500 + 25x and C′

y = 500 + 25y.What are the reaction functions for both firms? How much is produced andwhat is the equilibrium price? Illustrate graphically in the axis (x, y).

2. What are the equilibrium costs and profits?

3. The American government gives to Boeing a subsidy s (in millions ofdollars) per airplane exported to the Asian market. Assume s < 75. Whatare the new reaction functions of both firms? In equilibrium, how much isproduced? Give the equilibrium produced quantities and the price as a functionof s. Discuss the results and illustrate graphically.

4. Is there profit shifting? To the benefit of which firm? Has the aggregateprofit (of both firms) increased? Do the consumers in Asia gain of loose ?

5. Write the optimal subsidy for Boeing, i.e. the subsidy that maximizes thecollective welfare G. The collective welfare G is the profit of Boeing after subsidyminus the cost of subsidy incurred by the American consumer: G = π − sx.

6. Give all the characteristics of equilibrium in the case of an optimal subsidy.Illustrate graphically.

7. What happens if the subsidy reaches 75 ? Give the characteristics ofequilibrium in this case and compare with the case of the optimal subsidy. Dothe consumers gain or loose?

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