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1 ECO364 - International Trade Chapter 2 - Ricardo Christian Dippel University of Toronto Summer 2009 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

2 : The Ricardian Model Why do countries specialize in different commodities/goods? Is trade a good thing? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

3 The Ricardian Model: Definitions start with: Unit Labor Requirement: the amount of labor required to increase output by one unit. aj is the amount of labor needed to produce one unit of good j. With one factor (labor), 1/a j is the marginal product of labor. Arithmetically, if Y = F (L), then the unit labor requirement is 1 MPL = 1 Y L = L Y Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

4 The Ricardian Model: Motivating Example Suppose that Canada and China each have 100 workers and technology manifested by the following unit labor requirements: Table: Unit Labor Requirements Country Textiles Computers Canada 10 5 China 5 10 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

5 The Ricardian Model: Motivating Example Suppose that each country divides its labor force in half so that there are 50 workers in each sector... Table: Output Country Textiles Computers Canada 5 10 China 10 5 World Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

6 Examine two other possibilities. 1. Canada specializes in computers and China in textiles. 2. Canada specializes in textiles and China in computers. Canada: C, China: T Canada: T, China: C Country C T C T Canada China World Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

7 If countries specialize in the right sector, world output can increase. But how do we know what the right sector is? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

8 The Ricardian Model: Definitions Constant Returns to Scale (CRS): If one increases all inputs by some proportion, output increases by the same proportion. y=ouput and l= labor. y = f (l) is CRS if y = f (γl) = γf (l) where γ > 0. y = l is a CRS production function. y = l 0.4, y = l 1.1, and y = l + 5 are all not CRS production functions. Homothetic Preferences: The form of the utility function does not depend on income (linear Engels Curves). Autarky: When economies are closed and do not trade at all. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

9 The Ricardian Model: Assumptions Two countries, two goods, one factor (labor), Labor is immobile across countries and mobile across sectors, Constant returns to scale (CRS) production, Identical and homothetic preferences, Perfect Competition (all agents are price takers). Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

10 The Ricardian Model: Opportunity Costs Opportunity costs (OC) formalize the tradeoffs implicit in the unit labor requirements. Recall that an opportunity cost is the cost associated with forgoing one s next best option. The OC of production turns out to be the ratio of unit labor requirements. Table: Unit Labor Requirements Country Textiles Computers Canada 10 5 China 5 10 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

11 10 Canadian workers needed to produce 1 unit of textile and 5 needed to produce a computer. Consequently, the opportunity cost of producing a computer in Canada is the 0.5 of a textile that is forgone. 5 Chinese workers needed to produce one unit of textiles and 10 needed to produce a computer. Consequently, the opportunity cost of producing a computer in China is the 2 textiles that are forgone. Because the opportunity cost of producing a computer is lower in Canada than China, Canada has a comparative advantage in computers and China possesses a comparative advantage in textiles. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

12 An absolute advantage is when a country has a lower unit labor requirement than another country for a given good. Absolute advantage involves comparing unit labor requirements for a good across countries. Comparative advantage involves comparing unit labor requirements across countries and goods. This distinction is at the heart of Ricardian Theory. Do not confuse the two. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

13 More generally, rename Canada and China to be N(orth) and S(outh), With the same two goods, C(omputers) and T(extiles), the North will possess a comparative advantage in computers if and only if: ac N at N < as C a S T The South will possess a comparative advantage in computers if and only if: ac N at N > as C a S T Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

14 Is this confirmed in the earlier data? Country a T a C Canada 10 5 China 5 10 a Can. C a Can. T = 1 2 a China C a China T = 2 acan. C a Can. T < achina C at China and Canada has a comparative advantage in computers! Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

15 With only two goods, if a country possesses a comparative advantage in one good, the other country will possess the comparative advantage in the other good. With only two goods, a country cannot have a comparative advantage in both goods!! In the above example, suppose one country has a set of a j s that are lower for both goods. Are there still gains from specialization, if one country has an absolute advantage in which it possesses lower unit labor requirements in both sectors? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

16 Suppose that North possesses an absolute advantage in both sectors such that the structure of unit labor requirements is as follows: Table: Unit Labor Requirements Country Textiles Computers North 10 5 South For each good, the North has a lower unit labor requirement but which good is it more better at? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

17 Opportunity costs. (a N C /a N T )=0.5 (a S C /a S T )=2. Opportunity costs are the same as before even though Canada is 4 times as productive as before in both goods! Comparative advantage is not necessarily affected by shifts in Absolute Advantage. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

18 Are their gains from specialization? Suppose that the South wants an additional computer. The South can: 1. Forgo 2 textiles and produce the computer at home. Or, 2. Produce 0.5 textiles and then trade them to the North for, for example, 1 computer. (the North is willing to do this because 1 is less than its own opportunity costs of producing textiles). Clearly, the South prefers producing the good they have a comparative advantage in and the trading it relative to producing an additional unit of the good at which they are at a comparative disadvantage. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

19 Despite the fact that the North has an absolute advantage in both goods, the North has a comparative advantage in Computers and the South has a comparative advantage in Textiles. Why is it inefficient for the North to produce everything? Suppose they did... Both countries could always be better of by specializing and trading at a price that lies in between the two opportunity costs. The South should produce what it is good at and the North should produce what it is good at. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

20 What will the relative price of computers and textiles be? Remember that there is no money in this model. All prices are relative prices of goods. Assume that trade occurs. Assertion: In equilibrium, the world price of computers will be between 0.5 and 2 textiles per computer. Start with the result that Canada produces computers and China produces textiles. i.e. assume each country produces its comparative advantage good. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

21 Suppose that the world price of computers is less than 0.5 textiles per computer. Computers are cheap for China relative to autarky. China is happy but textiles are expensive for Canada relative to autarky. Canada is better off producing its own textiles the relative price cannot be less than 0.5 textiles per computer. Suppose that the world price of computers is more than 2 textiles per computer. Textiles are cheap for Canada relative to autarky. Canada is happy but computers are now expensive relative to autarky. China is better off producing its own computers the relative price cannot be more than 2. Consequently, the the relative price will be between 0.5 and 2. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

22 Can 1 (textile per of computer) be the equilibrium relative price? Canada produces computers. The one textile per computer it can obtain through trade is better than the 1/2 of a textile it could get if it produced its own textiles. China produces textiles. The one computer per textile it can obtain through trade is better than the 1/2 of a computer it could get if it produced its own computers. For yourself: verify that 0.75 and 1.5 are also both possible equilibrium relative prices. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

23 More generally, an equilibrium relative price must satisfy the following restriction where the North has a comparative advantage in good x and the South has a comparative advantage in good y. a North x a North y p x asouth x p y ay South This only pins down a possible range of equilibrium factor prices. To narrow this range, we introduce demand. First, let s think more deeply about the gains from trade in this Ricardian model. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

24 Conjecture: Suppose that the North has a comparative advantage in good x: If If a N x a N y = px p y < as x a S y trade and the South gains. a N x a N y < px p y = as x a S y South neither gains nor loses. then the North neither gains nor loses from then the North gains from trade and the Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

25 Can we illustrate this graphically? The North s Production Possibility Frontier (PPF) is as follows where L N is the amount of labor that the North possesses: a N C QN C + an T QN T LN Assuming full employment of all factors, simple arithmetic gives: Q N T = LN a N T an C a N T Q N C Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

26 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

27 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

28 A key insight is that in autarky, the PPF and the budget constraint will be the same line. In autarky, what you consume/purchase must be what you produce. With trade, you need not consume what you produce. Therefore, in a trading equilibrium, the budget constraint and PPF need not be the same line. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

29 Autarky Relative Prices w = P k MPL k = P k a k for k = {C, T } Because the same wage w is paid in both sectors, this implies P C P T = a C a T Autarky relative prices will be equal to the ratio of unit labor requirements in that country. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

30 Now introduce Trade a The PPF will look the same as before and will have a slope of N C. at N The budget constraint will now be based on the equation P C Q C + P T Q T Y and will have the slope P C P T. Let s examine the case where P C P T > an C. at N Does the North gain from trade if it specializes in computers? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

31 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

32 Now let s examine the Southern case. Let s examine the case where P C P T < as C. at S Does the South gain from trade if it specializes in textiles? Starting from autarky... Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

33 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

34 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

35 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

36 Suppose that (for either country) world relative prices more closely resemble autarky relative prices. The gains from trade will diminish until ( ) PC P T 0 = an C a N T At this point, utility will be the same as in autarky.. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

37 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

38 If world relative prices equal autarky relative prices for one country, that country does not gain from trade. The other country does gain from trade. If world relative prices are in between autarky relative prices, both countries gain from trade. The more different a country s ratio of unit labor requirements are from world relative prices, the more a country gains from trade. If both countries have the same opportunity costs there is no comparative advantage Then there is no gains from trade for either country. Even though there might still be absolute advantage. Large differences mean larger gains from specialization. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

39 Let s introduce demand... Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

40 We are going to use the following graph to solve for equilibrium (relative) output and prices (note the axes labels!!). Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

41 The vertical axis gives the price of good X relative to Y. The horizontal axis gives the relative World quantities where the World is simply to aggregation of the North and South. Recall that the equilibrium relative price of goods X and Y must lie between the autarky relative prices/unit labor requirements of the two countries. Assume that the North has a comparative advantage in good x, therefore the South possesses a comparative advantage in good y. Arithmetically, an x a < as y n x a. y s We can represent this graphically as... Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

42 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

43 Now suppose that px p y = as x. ay S The North completely specializes in good x because it can produce x and then trade for y at better terms than if it produced its own y. Consequently X N = L N /a n x and Y N = 0. The South is indifferent between specializing in Y (and then trading for X ) and producing both X and Y. The South will produce some combination of (X S, Y S ) that satisfies Consequently, when px p y segment. 0 < X S Y S < = as x, the relative quantity supplied will be a ay S Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

44 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

45 Suppose that px p y = an x. ay N The South completely specializes in good y because it can produce y and then trade for x at better terms than if it produced its own x. Consequently X S = 0 and Y S = L S /a s y. However, we cannot say how much the North will specialize because the North is indiffernt indifferent between specializing in X (and then trading for Y ) and producing both X and Y. Consequently, when px p y segment... = an x, the relative quantity supplied will be a ay N Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

46 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

47 Now suppose that an x a N y < px p y < as x. ay S Complete specialization where the North specializes in X and the South specializes in X. Note that any set of relative prices between the two autarky price ratios will support this outcome. The relative supply curve will be vertical at this point. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

48 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

49 At this point... The North prefers specializing in X and trading for Y to producing both. Consequently, X N = L N /a N X and Y N = 0. The South prefers specializing in Y and trading for X to producing both. X S = 0 and Y S = L S /a S Y. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

50 Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

51 The structure of demand determines the equilibrium. This is done by introducing a relative demand curve As the relative price of a good rises, relative demand increases. Reflects substitution effects. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

52 Figure: Demand for X is high relative to Y Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

53 The North specializes in X and the South produces both X and Y. Why? World demand for X is sufficiently high that the North cannot produce enough X to satisfy high World demand for X. The South satisfies for the remaining demand for X. Because relative prices for the South are the same as in autarky, the South does not gain from trade but the North does. In sum, the World gains. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

54 Figure: Demand for Y is high relative to X Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

55 The South specializes in Y and the North produces both X and Y. Why? World demand for Y is sufficiently high that the South cannot produce enough Y to satisfy high World demand for Y. The North must provide for the remaining demand for Y. Because prices for the North are the same as in autarky, the North does not gain from trade but the South does. In sum, the World gains. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

56 Figure: Demand for X and Y is Relatively Even. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

57 The North specializes in X and the South specializes in Y. Because relative world prices are between autarky unit labor requirements, both countries gain from trade General Rule in this model: a country that does not specialize does not gain from trade! Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

58 This analysis suggests that a country will produce more of its comparative advantage good than its comparative disadvantage good (specialization). One country produces a lot of one good, the other country produces a lot of the other. If preferences are sufficiently similar (which we have assumed), they will demand the same goods. A country will export its comparative advantage good and import its comparative disadvantage good. See an upcoming problem set for concrete examples. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

59 Relative Wages Some commentators argue that high relative wages in the North relative to the south are evidence of Northern exploitation of Southern workers. Does the Ricardian model have anything to say about this? Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

60 Relative Wages Start with the profit maximizing condition that nominal wages equal the marginal revenue product of labor. w = p MPL Now suppose that Northern workers specialize in computers and Southern workers specialize in textiles. This gives us two equilibrium conditions: w N = p C a N C w S = p T a S T Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

61 Relative Wages These conditions can be combined to give the following expression w N w S = as T p C ac N p T = MPLN C p C MPL S p T T Northern relative wages are determined by labor productivity and the relative prices of the two goods. If the two goods have the same price, labor productivity alone determines relative wages. If the two goods do not have the same price, the relative wage is higher in the country that produces the relatively valuable good, holding labor productivity constant. But wages in both North and South are always higher under Trade than under Autarky. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

62 Relative Wages We can also offer strong rebuttals to common criticisms of free trade if the Ricardian model possesses substantial validity. 1. Free Trade is beneficial only if your country is strong enough to stand up to foreign competition. 2. Foreign competition is unfair and hurts other countries when it is based on low wages. 3. Trade exploits a country and makes it worse off if its workers receive much lower wages than workers in other nations. Krugman and Obstfeld, pp Krugman Ricardo s Difficult Idea. (optional). Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

63 Relative Wages Free Trade is beneficial only if your country is strong enough to stand up to foreign competition. Comparative and not absolute advantage is sufficient for gains from trade Foreign competition is unfair and hurts other countries when it is based on low wages. Low foreign wages are caused by low productivity. Trade exploits a country and makes it worse off if its workers receive much lower wages than workers in other nations. If wages are based on productivity, they will be low even if there is no trade. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

64 Conclusions 1. Each country exports the good at which it possesses a comparative advantage. 2. Each country imports the good at which it possesses a comparative disadvantage. 3. In this setting, each country possesses a comparative advantage in some good. 4. If free trade relative prices lie between autarky unit labor requirements, both countries gain from trade. 5. If free trade relative prices equal the autarky price ratio for one country, that country is no worse off from trade and the other country is better off. 6. Increased utility comes from increased consumption possibilities that allow consumer/workers to attain a higher indifference curve. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

65 The Multi-Good Extension Let s make the model more realistic by allowing more than one good. This will also allow us to introduce the important notion of the the intensive and extensive margin of trade. Suppose there are N goods produced, indexed by i = 1,2,N. The domestic countrys unit labor requirement for good i is a i, and that of the foreign country is a i Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

66 The Multi-Good Extension Goods will be produced wherever it is cheaper to produce them. Let w represent the wage rate in the domestic country and w* represent the wage rate in the foreign country. If wa 1 < w a1 then only the domestic country will produce good 1, since total wage payments are less there. < w w Equivalently, good i is produced in Home only if a 1 a1 technology advantage is larger than its cost disadvantage) Let s consider an example: (if Home s Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

67 The Multi-Good Extension Figure: Demand for X and Y is Relatively Even. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

68 The Multi-Good Extension Home has high productivity in apples, bananas, and caviar. That gives Home a cost advantage. Suppose Foreign has low wages. That gives it a cost advantage, despite its low productivity. How is the equilibrium relative wage determined? the relevant equilibrium is equality of the relative supply and relative (derived) demand of labor services. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

69 The Multi-Good Extension As domestic labor becomes more expensive relative to foreign labor, goods produced in the domestic country become more expensive, and demand of these goods and therefore derived demand for the labor to produce them falls. At certain threshold-levels, comparative advantage shifts from Home to Foreign so that fewer goods will be produced in Home, further reducing the demand of domestic labor services. The relative (derived) demand of domestic labor services therefore falls when w/w* rises. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

70 The Multi-Good Extension The Intensive and Extensive Margin of Trade The intensive margin refers to a country exporting or importing a larger quantity of the same goods The extensive margin refers to a country exporting or importing new goods In later chapters, the intensive margin can also refer exporting firms exporting more while the extensive margin refers to non-exporting firms becoming exporters. Suppose w/w* increases from 3 to 3.99: Home produces the same goods but at higher prices so that the demand for these goods and the labor to produce them falls (intensive margin). Suppose w/w* increases from 3.99 to 4.01: The caviar industry now moves to Foreign, causing a discrete drop in the demand of domestic labor (extensive margin). Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

71 The Multi-Good Extension Figure: Demand for X and Y is Relatively Even. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

72 Empirical Evidence What is the empirical evidence for technology-differences-based comparative advantage? Do countries export those goods in which their productivity is relatively high? The ratio of U.S. to British exports in 1951 compared to the ratio of U.S. to British labor productivity in 26 manufacturing industries suggests yes. At this time the U.S. had an absolute advantage in all 26 industries, yet the ratio of exports was low in the least productive sectors of the U.S. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

73 Empirical Evidence Figure: Demand for X and Y is Relatively Even. Christian Dippel (University of Toronto) ECO364 - International Trade Summer / 73

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