International Trade: application exercises

International Trade: application exercises 1 Balance of Payments Exercise 1.1 : CA is the current account, S p the private savings, I investment, G the public spending and T the taxes. 1. Show that CA = (S p I) (G T ). What does a surplus of the current account mean? 2. Rewrite this equation and explain how private spending can be used for different purposes. Exercise 1.2 : (source GUILLOCHON B. and KAWECKI A. Economie internationale. 4th edition. Dunod. Paris 2003) Is a deficit of the current account compatible with a surplus of the official settlement balance (sum of the current account balance, the capital account balance, and the nonreserve portion of the financial account balance)? What is the sign of the balance of official reserve transactions? Have the official reserves increased 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 the current account and the evolution of the exchange rate (with the main economic partners). 1

2 The Ricardian model of trade Exercise 2.1 :(source GUILLOCHON B. and KAWECKI A. Economie internationale. 4th edition. Dunod. Paris 2003) Consider two countries, North (N) and South (S). Both produce two goods, 1 and 2, using labor L. a ij is the cost, in terms of labor, of producing one unit of good i in country j. Set a 1N = 2 ; a 2N = 4 ; a 1S = 3 and a 2S = 12. Both countries are endowed with the following amount of labor: L N = 4000 and L S = 9000. y ij is the production of good i in country j and y j is the national income of country j, measured in terms of good 1, which is chosen as the numeraire. p is the price of good 2 in terms of good 1. Consumers in both countries have the same preferences: d 1j = 0, 5y j and d 2j = 0, 5(y j /p). 1. State the characteristics of each country in autarky. Illustrate graphically. 2. What is the comparative advantage of each country? If both countries open to trade, what is the free trade equilibrium price? 3. At this equilibrium price, how much do both countries produce, consume and trade? Explain graphically. How can the gains from trade be evaluated? 4. Determine the wages in free trade in both countries. What is the relationship 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 productivity in each country in each sector is equal to: Home: a 1H = 10λ a 2H = 10λ with λ 0.8 Foreign : a 1F = 8 a 2F = 2 Good 1 is chosen to be the numeraire: p, y, w are respectively the price of good 2, the national income and the minimum wage, all expressed in terms of units of good 1. 1. Compare the situation of both countries. Do they both have interest in trading? If yes, in which interval is the free trade equilibrium price? Explain each step of the answer. 2. How do the gains from trade appear for each country? Under which conditions does free trade generate gains from trade for both countries? 3. Labor endowments for both countries are noted L H for Home and L F = 4L H for Foreign. Consumers in both countries have the same preferences: d 1j = 0.5y j and d 2j = 0.5y j /p (j = H, F ). 2

Write the equilibrium free trade price, p, as a function of the parameter λ in the case where free trade generates gains from trade for both countries. Illustrate graphically the relationship between the equilibrium free trade price and 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, w H /w F, the equilibrium free trade price and the parameter λ. Illustrate graphically this relationship in the axis (p, w H /w F ) for λ = 1. 5. Competition from countries with low wages is an insurmountable handicap for the competitiveness of developed countries. Discuss this assertion using the previous example. Exercise 2.3 : Consider a typical framework of the trade model with comparative advantages. Consider two countries, A and B, two goods, 1 and 2, and one production factor, labor L. c j i is the unit labor cost for sector i in country j. c A 1 = 4, c A 2 = 2, c B 1 = 1, c B 2 = 8 p is the relative price of good 2 in terms of good 1, y is the national income expressed in units of good 1. Demand functions are identical in both countries: ( ) y d 1 = by and d 2 = (1 b) p Labor endowments are respectively L A and L B. 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, L A and L B in the case free trade generates gains from trade for both countries. 4. Suppose both countries have the same size: L A = L B. -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 are the gains from trade maximum/equal to zero? -b- Interpret the preceding result by showing how demand affects the distribution of the gains from trade. 5. Suppose both countries have different sizes. Country B is larger than country A: L B = δl A, 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 countries benefit less from international trade than small countries. 3

3 The Heckscher-Ohlin model of trade 1 Exercise 3.1 : Consider the typical HOS setting: two goods, 1 and 2, are produced using two production factors: labor L and capital K. y i is the production of good i, and K i and L i are respectively the amounts of capital and labor used in sector i. Demand functions write: y 1 = K 0,2 1 L0,8 1 y 2 = K 0,8 2 L0,2 2 Good 1 is chosen as the numeraire. p is the price of good 2 in units of good 1. y is the national income in units of good 1. w is the wage and r is the capital reward, both expressed in units of good 1. k i is the capital intensity of sector i: k i = K i /L i. 1. Write the relationships that characterize the optimal allocations of ressources. Explain the different steps. Express k 1 as a function of w/r and k 2 as a function of 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 = 400 units of labor. What are the limit values of w/r? What are the limit values of k 1 and k 2? 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 by consumers to the consumption of good 1: d 1 = by. y is the national income in terms 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. Illustrate graphically. What are the values of w/r, k 1 and k 2 in autarky? 5. The country opens to free trade. The country is assumed to be a small country. 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 good chosen to be the numeraire? Exercise 3.2 : 1 These two exercices are from the course at the University Paris-Dauphine. B. Guillochon and A. Kawecki 4

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. Y j is the national income of country j, w j the wage in country j and r j the capital reward in country j. Production functions are : Labor endowments are: y 1 = K 0,25 1 L 0,75 1 y 2 = K 0,75 2 L 0,25 2 K A = 80; L A = 80; K B = 30; L B = 70 1. Explain the relationship between p and w/r. 2. Suppose the demand functions are identical: D 1j = 0, 5Y j and D 2j = 0, 5Y j, j = A, B. What is the good exported by country A in free trade? Do these specializations follow the law of factor proportions? 3. Suppose that the two countries trade freely, however the demand functions are now different. In each country, demand functions are: D 1A = 0, 25Y A and D 1B = 0, 9Y B. Which country exports which good? Is the law of factor proportions verified? Explain why. 4. Both countries refuse to trade goods. However, capital flows between countries is allowed. Labor is still immobile. Demand functions are the ones described in question 2. Knowing that capital flows towards the location with the highest reward, characterize the equilibrium situation for each country in terms 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 in Brazil. 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 countries deteriorate the terms of trade of the donor? 5

2. In reality, an important share of international aid for developing countries is conditional. For example, France may finance an irrigation project in Africa, under the condition that the pumps, pipelines and other building materials be bought to French producers. How does this conditionality affect the impact of international transfers on each country s terms of trade? Is this conditionality important for the donor? Can you imagine a situation in which the conditional aid 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 produce 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 lower production costs: 6 for each unit produced, and 7 in France. The price of the good is equal to 10 in both countries. A fixed cost equal to 30 must be paid for each production plant. If the firm sells locally, she does not pay any transaction costs. However, in order to sell abroad she must pay t per unit sold on the foreign market. 1. Show that the profit of the firm is equal to 80 if she produces in both countries. 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 in Morocco. 3. Suppose Morocco and France do not share any trade agreement. Trade costs are thus high: 6 per unit sold. Show that the firms prefers to produce in both countries. Explain why. 4. Morocco and France sign a free trade agreement, which decreases the international trade costs to 2 per unit sold abroad. Show that the firm prefers to 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. 6

6 Monopolistic Competition Exercise 6.1: (source Krugman P. and Obstfeld M. International Trade. 6th edition. 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 producer can be written as: [ ] 1 X = S n (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. Firms are assumed to consider the price of competitors as given. Total cost is given by C = 750000000 + 5000X. 1. What is the name of this market structure? Show that the firms produce under increasing returns to scale. 2. Show that the more there are producing firms, the higher the cost to produce one unit. Illustrate graphically the average cost as a function of n. 3. Write the inverse demand function. Get the marginal revenue of the representative firm. Write the profit maximization condition. What is the equilibrium price? Illustrate the price graphically on the preceding graph. Note: This is equivalent to showing that the more there are firms, the lower the equilibrium price. 4. What is the equilibrium number of firms and the equilibrium long term price? 5. Consider country B in which the annual total sales of cars is equal to 1,6 millions automobiles. As for country A, give the equilibrium number of firms on the market and the equilibrium long term price in the automobile industry in country B. 6. Suppose both countries can trade cars without trade costs. The new integrated market thus has total sales equal to 2.5 millions of cars. What are the consequences of the creation of the integrated market? Summarize the effects on the equilibrium number of firms and the equilibrium price in a table comparing each national market with the integrated market. 7

7 Trade policy Exercise 7.1 : Suppose the demand and supply functions for a good i in a country j are given respectively by Q d i = 140 20p i et Q s i = 20p i 20 where p i is the price in monetary units. 1. Illustrate graphically the demand and supply curves of good i. Indicate the equilibrium price and the quantities produced and consumed without trade. 2. Suppose the country enters free trade. The world price is p i = 2. The world supply of good i is infinitely elastic at p i = 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 its imports 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, the national production increases from 5 to 6 millions tons and national consumption decreases from 9 to 8 millions tons. The price for the American consumer is now equal to 480 dollars a ton, while it is equal to 280 dollars a ton on world markets. 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? 8

3. Evaluate the loss for American consumers (in millions of dollars) generated 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,...) in order 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 demand function is equal to p(y ) = 5 Y, with Y the aggregate consumption. The firms in country 1 has the following cost function: C A (y A ) = 1 + c a y A. The cost function of the competing firms is C B (y B ) = 1 + c b y B. Competition on the local market The 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 not export). Set the following costs: c a = 1 et c b = 1/2 1. When firm B sells on both markets, does she set identical prices on both markets? 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 of country 1 anymore? 6. If there is trade between countries, does country 1 gain or loose from trade? Competition on a third market Suppose 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 to p(y ) = 5 Y. 9

1. Write the reaction functions of both firms. Illustrate graphically. What are the equilibrium conditions? 2. The government of country 1 sets a subsidy s for firms A for each unit exported. Show the effects of this subsidy on firm A s market share and on its profit. 3. Country 1 and the third country sign a trade agreement which decreases trade costs from τ to τ < τ for firm A. Evaluate the effects of the trade agreement. 4. Progress in technology reduces the production cost for firm A: c a = 1/δ. Evaluate the effects of this change. 5. Discuss the consequences of a production subsidy, a trade policy, and a subsidy for research and development. Exercise 8.2 : (source GUILLOCHON B. and KAWECKI A. Economie internationale. 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 y are the respective numbers of airplanes produced by Boeing and Airbus. Both firms 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 and what 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 of dollars) per airplane exported to the Asian market. Assume s < 75. What are the new reaction functions of both firms? In equilibrium, how much is produced? Give the equilibrium produced quantities and the price as a function of s. Discuss the results and illustrate graphically. 4. Is there profit shifting? To the benefit of which firm? Has the aggregate profit (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 the collective welfare G. The collective welfare G is the profit of Boeing after subsidy minus 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 of equilibrium in this case and compare with the case of the optimal subsidy. Do the consumers gain or loose? 10