Chapter 2 Commodity Trade

Transcription

1 Chapter 2 Commodity Trade This chapter presents two models which stress international trade as the interaction between consumers: the standard two-good model and the varieties model. We can think of these models either as primitive worlds where no production takes place and nature determines consumers' endowments, or else as descriptions of a time period so short that firms cannot alter their production plans. In the standard two-good model, countries trade, and consumers are thus better off, only if autarky relative prices differ. Consumers' preferences and their endowments combine to determine autarky prices. Generally, these prices will differ across countries if either or both of the following hold: (i) preferences differ, and (ii) endowments differ. In the varieties model, consumers like variety. If countries' endowments differ in the varieties they contain, trade may occur even with identical relative prices. Trade makes consumers better off by giving them a wider choice of varieties. In autarky, a country's consumers trade with each other. While opening up to free international trade benefits some of these consumers and harms others, it is not a zero-sum game: As Section 2.4 shows, the winners gain enough that they could compensate the losers and still be better off than they were before international trade. This is the fundamental reason economists favor international trade. Of course, if no compensation takes place, the case for free trade is weaker, as it then implies sacrificing some individuals' welfare for others'. This problem is not unique to trade policy. Most public policy changes imply winners and losers, and, in the absence of compensation, may be hard to justify. For example, changes in monetary policy or government spending and taxation affect individuals differently. The demand that losers be compensated is often voiced much more loudly for changes in trade policy than it is for other public policy changes. Changes in monetary policy, for example, may affect more people but rarely ignite the sort of angry protests that occurred at the 1999 World Trade Organization meetings in Seattle. Although the chapter assumes that trade is balanced, that is, the value of exports equals the value of imports, the insight that trade reflects differences in endowments and/or preferences can be extended to trade over time. Thus a country wants to have a surplus on the balance of trade, i.e. it wants the value of its exports to exceed the value of its imports, if it desires to consume less today than it produces today in return for raising its consumption in some future period.

2 SHORT-ANSWER QUESTIONS 1. Which of the following statements is false? All budget lines are price lines. All price lines are budget lines. 2. Suppose the world market relative price of American-made IBM personal computers, which are exported to the Netherlands, falls. The terms of trade of the United States have (d) improved. deteriorated (worsened). Both of the above. Neither of the above. 3. Sweden and Norway trade extensively with each other. If Sweden's terms of trade with Norway improve, then Norway's terms of trade with Sweden must (d) improve. deteriorate (worsen). Both of the above. Neither of the above. 4. Define a balance of trade surplus. a balance of trade deficit. balanced trade. 5. Define "an increase in real income." 6. True or false: "The worst a country can do by opening up to trade is to remain at the autarky level of utility."

3 7. Consider two island nations that have agreed to use the French franc as their common currency. Suppose that a bottle of red wine costs two francs on Martinique and six francs on Corsica while a beret costs ten francs on Martinique and twenty francs on Corsica. Will there be any trade? Find the set of possible world (relative) prices of berets. What will be the pattern of trade if the trade route is opened between Corsica and Martinique? 8. In the following diagram an economy's endowment point is E and its initial consumption point is F when the world terms of trade (the relative prices on the world market) are given by line 1. Suppose a change in world prices causes the budget line to change to line 2 and that consumption is now at point F'. Has the relative price of food increased? Have this nation's terms of trade improved? 9. True or false: "A terms of trade improvement raises a country's real income."

4 10. In the following diagram, does the line labeled 1 or the line labeled 2 imply a higher relative price of food? 11. The consumer's preferences, i.e. the consumer's attitude towards different bundles of commodities, are reflected in the indifference curve map. Consider the following three possible shapes of indifference curves: The marginal rate of substitution of food for clothing at some point, say A, is defined as the negative of the slope of the line tangent to the indifference curve at point A. When you consider panel 2, what is the marginal rate of substitution of clothing for food at point Q? at point R? at point S? In panel 3, is the marginal rate of substitution of food for clothing smaller at point Qor R? The Law of Diminishing Marginal Rate of Substitution states that the marginal rate of substitution of food for clothing along a given indifference curve falls as more clothing is consumed. Which of the panels violates this rule?

5 12. The consumption possibilities set is defined as all the consumption bundles, i.e. the amounts of clothing and food that the consumer can obtain given the constraints he faces. Assuming that it is costless to throw any clothing or food away, illustrate Robinson Crusoe's consumption possibilities set when: There is nobody with whom to trade (i.e. autarky). Robinson can trade with a neighboring island at a relative price, p. 13. The consumer's choice problem is to find (and consume) the feasible bundle of goods that yields the highest utility. Diagrammatically, this implies that the consumer strives to reach the highest possible indifference curve. Illustrate the solution to Robinson Crusoe's choice problem when: (i) He cannot trade with anybody. (ii) He can trade at some relative price p. What is the significance of the marginal rate of substitution at the endowment point? What does it equal? 14. Define Pareto optimality.

6 PROBLEMS 1. Homothetic Preferences: A family of indifference curves is defined as homothetic when the slopes of the indifference curves (i.e. the marginal rates of substitution) are identical along a ray from the origin. The indifference curves drawn below are homothetic. Assume homothetic preferences. Determine whether countries will trade in each of the following circumstances: (d) (e) Countries have identical preferences and identical endowments. Countries have identical preferences, their endowments differ and their endowments are not in the same ratio of food to clothing. Countries have identical preferences, their endowments differ but the ratio of food to clothing is the same in the two countries. Countries have identical endowments but different preferences. Countries have both different preferences and different endowments. 2. Autarky Prices in the Exchange Model: Consider a country blessed with an endowment of food and clothing. Explain how autarky (relative) prices are determined. In particular, how are prices affected by the country's preferences? By the country's endowment? (To answer this question in a systematic way, you might want to consider prices when preferences are the same but endowments differ, and then prices when endowments are the same but preferences differ.) Suppose this country opens up for international trade and that it imports food. Draw its budget line (you may choose some world relative price) and indicate the trade triangle in your diagram.

7 3. Causes of Higher Welfare: Is the following statement true or false? "If a small country is initially trading but stops doing so after being assigned a new endowment point, then real income of its single resident must have fallen." (Hint: You can prove/disprove the statement by theuseofasinglediagram.) 4. The Edgeworth Box Diagram: In each of the situations below, some of many indifference curves have been drawn. Identify the region of mutual advantage. the contract curve. the pattern of trade. (You may have to draw in some indifference curves yourself.)

8 5. Autarky Prices and the Gains From Trade : Prove that if relative autarky prices differ, then: there are mutual gains to be made from trading. free trade leads to a Pareto-optimal equilibrium. 6. International Trade Does Not Have to Hurt: Show that the individual who gains from free trade can compensate the loser from free trade and still be better off from the trade than in autarky. Draw the diagrams for both the gainer and the loser.

9 7. Walras' Law: Exercise 6 in the textbook proves a very useful result called Walras' Law, named after the French economist Leon Walras. It states: "In a two-good model, if the world market for one good is in equilibrium (in other words, if the world supply of that good equals the world demand for that good), then the world market for the other good is in equilibrium as well." (More generally, if, in an n-good model, world markets for n-1 goods are in equilibrium, then the world market for the remaining good is in equilibrium.) The two-good result hinges upon the fact that there is only one relative price even though there are two absolute prices. The result greatly facilitates any analysis of the two-good model since we need only worry about one market. The proof of Walras' Law involves adding the two countries' budget constraints to get the world budget constraint, and then making use of the assumption that one of the markets clears. If the market for the other good clears as well, the proof is complete. Suppose there are two goods produced in the world, A and B. constraint for the home country can be written as The budget pa DA + pb DB = pa xa + pb xb. In words, the value of the home country's purchases must equal the value of the home country's sales of A and B. Similarly for the foreign country pa D + pb D = pa x + pb x. Show that when pa and pb are the world equilibrium prices of A and B and the market for A clears (that is, the world supply of A equals the world demand for A), the market for B must clear as well. Show that the following condition implies that the home country's spending equals the value of its endowment. (pa / pb) ( DA - xa) = (D - x)

10 8. Gains From Trade in Varieties: Suppose that Robinson Crusoe and Friday have identical preferences and that they have preferences for variety. They have identical endowments of the homogeneous good, clothing, say five units of each, and the same number of units of food, which however comes in different varieties. Specifically, Robinson has four units each of three different varieties, whereas Friday has four units each of three other distinct varieties. (d) Will Robinson and Friday trade? If your answer to was affirmative, what will be the trade pattern and what will be the terms of trade of, say, Robinson? In the following diagram illustrating this situation, is it possible to indicate gains from trade? Suppose that the endowments of the homogeneous good, clothing, are instead such that Robinson has four units and Friday has two units. Will Robinson and Friday now trade and if so, what will be the pattern of trade? 9. Trade over Time: Chapter 2 considers only the case of balanced trade in the sense that the value of the consumption bundle is equal to the value of the endowment for a single period of time. To relax this assumption, we can redefine the simple exchange model in terms of consumption and endowment bundles at different points in time. Let C(today) be the consumption bundle consumed by the home country today, and C(tomorrow) be the bundle consumed tomorrow. The starred variables refer to the foreign country. The endowments and the pattern of trade are shown in the following diagram.

11 What do we call the relative price between today and tomorrow? Given the trade pattern shown in the diagrams, who is the borrower and who is the lender? Which country runs a trade surplus in period 1? (d) Which country runs a trade deficit in period 2? (e) In setting up this problem, we assumed that neither country could save on its own; that is, neither country can store its endowment today to get a larger endowment tomorrow. Suppose we now let the countries store their endowments but at different rates of efficiency. Now, for each unit of Ctoday stored, the home country receives (1 + R) Ctoday in the next period, and the foreign country receives (1 + R*) C*today. Show that if R does not equal R*, there still remain gains from trade. What does this imply about interest rates across countries if borrowing and lending is permitted?

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