ECON* International Trade Winter 2011 Instructor: Patrick Martin

Transcription

1 Department of Economics College of Management and Economics University of Guelph ECON* International Trade Winter 2011 Instructor: Patrick Martin MIDTERM 1 ANSWER KEY 1

2 Part I. True/False statements on the Gravity Model, the Ricardian model and Heckscher- Ohlin (H.O.) model from chapters 2, 3, and 4. Circle either T (true) or F (false) (1 1/2 points each 30 points total). (A statement is false if you can think of a counter example - you don t need to provide one on the exam however.) Suggested time 30 minutes 1. T F The gravity model predicts that a country s citizens will spend a fraction of their income, equal to the share of their trading partners income relative to world income, on imported goods. 2. T F The gravity model predicts that large economies will import export a larger fraction of domestic production than small economies. 3. T F Suppose country X has 10% of the world s GDP. Both large and small trading partners will import goods worth 10% of their own GDP from country X according to the gravity model. 4. T F In empirical tests of the gravity model borders are not as important as the distance between economies. 5. T F The gravity model discussed in class assumes balanced trade. 6. T F Both the Ricardian and Heckscher Ohlin model assume labour mobility within each country but not between countries. 7. T F Factor price equalization occurs given free trade in both the Ricardian and Heckscher Ohlin models of trade. 8. T F An increase in a country s endowment of labour in the Ricardian model cannot result in an increase in the relative price of that country s exported good. 9. T F An increase in unit labour requirement in the sector in which a country does not have a comparative advantage may result in a reversal of comparative advantage in the Ricardian model 2

3 10. T F The relative demand curve in the Ricardian model always exhibits a negative correlation between relative price and quantity. 11. T F Firms profits can be positive in the Ricardian model. 12. T F Factor markets are competitive in both the Ricardian and Heckscher Ohlin models of trade. 13. T F In the Ricardian trade model all firms in both countries will want to produce the same good if relative prices are less than, or greater than, the autarky relative price of both countries. 14. T F Given the assumptions of the Heckscher Ohlin model, if the relative price of a good increases the factor used intensively in its production will see its factor reward increase. 15. T F The Rybczynski theorem predicts the factor intensity of production changes if the endowment of one of the factors changes. 16. T F In both the Ricardian and Heckscher Ohlin models countries only trade with one another if both of them have a comparative advantage in production. 17. T F In the Ricardian and Heckscher Ohlin models we have so far assumed that net exports (value of exports minus the value of imports) are zero. 18. T F In the Ricardian model comparative advantage arises due to productivity differences whereas in the Heckscher Ohlin model comparative advantage arises due to difference in relative factor endowments. 19. T F In the Ricardian and Heckscher Ohlin models of trade production is characterized by diminishing marginal productivity. 20. T F In the Ricardian and Heckscher Ohlin models of trade production exhibits constant returns to scale. 3

4 Part II. (40 points) Suggested Time 60 minutes Suppose there are two countries, France and Canada, which are capable of producing two goods, Bread and Wine. The amount of labour in France is 360 and that in Canada is 240. The amount of labour needed to produce a unit of each commodity is given as Type of good Wine Bread Country France 4 3 Canada 1 2 a) Which country has a comparative advantage in the production of Wine? Circle either FRANCE, CANADA, or NEITHER. (No work required) (1 point) Canada has the comparative advantage in wine production as it gives up ½ unit of bread in producing 1 unit of wine compared to 4/3 of bread given up by France. b) What is the autarky price ratio P W /P B in each country assuming both goods are consumed? (Be careful that you don t write down P B /P W ). (No work required) (2 pts) Autarky prices are given by opportunity costs. Wine is half as expensive as bread in Canada and is 4/3 as expensive as bread in France Autarky price ratio, P W /P B, in FRANCE 4/3 Autarky price ratio, P W /P B, in CANADA 1/2 c) Assume that preferences (the same for all individuals in both countries) can be summarized by the utility function U = Q W 3/4 Q B 1/4. The marginal utility of Wine is (3/4)(Q B /Q W ) 1/4 while the marginal utility of Bread is (1/4)(Q W /Q B ) 3/4. Derive the relative demand curve. Show your work. (4 pts) From consumer theory individuals allocate their scarce income so that the additional utility per dollar spent is the same on all goods consumed. Hence MRS = MU W /MU B = P W /P B. MRS = (3/4)(Q B /Q W ) 1/4 /(1/4)(Q W /Q B ) 3/4 = 3 Q B /Q W = P W /P B The relative demand curve can be written as (P W /P B )( Q W /Q B ) = 3 or as (P B /P W )( Q B /Q W ) =1/3 4

5 d) How much wine and bread is produced and consumed in Canada in autarky (no trade) given the preferences in part (c) if both goods are consumed. (BE CAREFUL and THINK you were not asked to do this on the assignment.) Show your work. (4 points) In Canada the autarky (no trade) price from part (b) is P W /P B = ½ so that from part (c) MRS = MU W /MU B = P W /P B = 1/2 MRS = (3/4)(Q B /Q W ) 1/4 /(1/4)(Q W /Q B ) 4/5 = 3 Q B /Q W = ½ or Q B = (1/6) Q W Substituting this into Canada s production possibility frontier equation, L = (a LW) Q W + (a LB) Q B we get 240 = 1Q W + 2 Q B = 1Q W + 2 (1/6) Q W = (4/3)Q W Solving, Q W = 240((3/) = 180 and so Q B = (1/6) Q W = (1/6)180 = 30. In autarky production equals consumption. Quantity of wine produced 180; Quantity of wine consumed 180 Quantity of bread produced 30; Quantity of bread consumed 30 e) On the graph below determine the intercepts of the RS curve on the vertical and horizontal axis and record your answers on the three lines. What is the equilibrium world price ratio and relative supply? Explain how you arrived at the equilibrium world price and show your calculation for the horizontal intercept of the vertical portion of the curve I will give full credit for whatever RD curve you found in part (c) if used correctly. (6pts) P W /P B 4/3 RS 1/2 RD 2 9/4 (Q W +Q* W )/(Q B + Q* B ) 5

6 The vertical intersects for the horizontal portions of the RS curve are the autarky prices while the horizontal intercept of the vertical portion of the RS curve is the production ratio if both countries specialize in the good in which they have a comparative advantage (wine Canada, bread France from part (a). Canada produces L/(a LW) = 240/1 = 240 units of wine and France produces L*/(a LB) = 360/3 = 120 units of bread Relative demand curve used above (P W /P B )( Q W /Q B ) = 3 Equilibrium world price P W /P B = 4/3 World relative supply (Q W +Q* W )/(Q B +Q* B ) = 9/4 f) Based on your answer for the world price ratio in part (e) determine relative wages, w F /w C, between France and Canada. (Hint: write down the expressions for wages in each country before you take their ratio.) Show your work. (3 pts) With competitive factor markets wages are just equal to the price of the good times the marginal product of labour (the reciprocal of the unit labour requirement). So w C = P W (1/a LW ) and w F = P B (1/a LB *) = P W (1/a LW *) as both goods are produced in France (the foreign country) w F /w C = P W (1/a LW *)/P W (1/a LW ) or P B (1/a LB *)/P W (1/a LW ) In either case the relative wage w F /w C = 1/4 g) What share of world production does Canada consume? Explain or show your work (I m not asking for the amount consumed just the share or percentage - an easier calculation) (3 pts) From (f) we know that the Canadian worker has 4 consumption shares for every 1 consumption share of the French worker. As there as 240 Canadian workers and 360 Foreign workers there are 960 (4x240) Canadian consumption shares and 360 (1x360) French consumption shares for a total of 1320 consumption shares. Hence Canada consumes 960/1320 or 24/33 (approximately.73) of world production of both goods. Share of world production consumed by Canada 960/1320 or 24/33 (approximately.73) 6

7 h) Suppose that Canada sees its productivity in wine and bread production fall in half (that is it now takes 2 workers to produce a unit of wine and 4 workers to produce a unit of bread.) (Circle one of the three capitalized words in each of the four statements below.) (Hint: Redraw the RS curve and the unchanged RD curve on the diagram provided below.) (8pts) P W /P B 4/3 RS 1/2 RD 1 9/4 (Q W +Q* W )/(Q B + Q* B ) As a result of equally proportional decline in productivity in Canada opportunity cost and comparative advantage are unchanged. The amount of wine Canada produces falls in half to 120 and so the vertical section of the RS curve shifts to the right. As preferences are unchanged RD is unchanged as well. The relative world price remains unchanged (see above.) However the relative wage in Canada falls as the marginal product of labour falls in half (since the unit labour requirements double.) Recall that wages are equal to the value of the marginal product of labour. Canada has a comparative advantage producing WINE, BREAD, NEITHER GOOD The equilibrium world price P W /P B FALLS, INCREASES, REMAINS THE SAME France produces ONLY WINE, ONLY BREAD, BOTH GOODS The relative wage in Canada has FALLEN INCREASED, REMAINED THE SAME, 7

8 For the next two parts assume that Wine and Bread are always consumed in the ratio 1 to 2 (i.e. 1 unit of Wine for each 2 units of Bread). i) Draw your original RS curve (in part (e) above) on the graph below along with the new RD curve given the description of preferences in the previous sentence. Find the new equilibrium relative price and supply. (5pts) P W /P B 4/3 RD RS 1/2 1/2 2 (Q W +Q* W )/(Q B +Q* B ) Given that wine and bread are now perfect complements in consumption the relative demand curve is invariant with respect to the relative price. It is just a vertical line at 1/2. The equilibrium world price falls to that of Canada in Autarky (= 1/2) and the relative supply is just the horizontal intercept of the relative demand curve, coincidentally 1/2 as well. Equilibrium world price P W /P B = 1/2 World relative supply (Q W +Q* W )/(Q B +Q* B ) = 1/2 j) Using your graph in part (i) above suppose that in France population doubles. Circle one of the three capitalized words in each of the statements below. (4pts) If the population of France doubles from 360 to 720 the production of bread increase to 240 units and the vertical portion of the relative supply curve has a horizontal intercept of 1 rather than 2. Canada still produces both goods and the world relative price remains the same. Canada produces ONLY WINE, BOTH GOODS, ONLY BREAD The equilibrium world price P W /P B FALLS, INCREASES, REMAINS THE SAME 8

9 Part III. Answer all four parts 30 points. Suggested time 30 minutes Assume a Heckscher Ohlin (H-O) for this problem. Four problems test your knowledge of the main results of the H-O model. In each problem state which of the four main trade theorems (0 points off for spelling errors) of the H-O model of trade best pertains to the problem. Work/Discussion/Graphs are not required expect for part (c) (but are required for any partial credit.) a) Like many small developing countries Sri Lanka has experienced a dramatic increase in the number of skilled men and women in the labour force over the past decades. Suppose that skilled labour is used intensively to produce electronic equipment while the production of clothing uses unskilled labour. Sri Lanka s economy is only.08% of its trading partners and can be considered a small country. Circle one of the capitalized terms in the first three statements below to make them consistent with an increase in Sri Lanka s skilled workforce. (8 points) Assuming that a change in production in Sri Lanka arising from an increase in the skilled labour force doesn t affect world prices (given that Sri Lanka constitutes less than 1/10 of 1 percent of world GDP), the impact on production of both goods is given by the Rybczynski theorem. An increase in skilled labour with relative good prices unchanged increases the goods, electronic equipment, that uses skilled labour intensively and decreases the production of the other good, clothing. As good prices are unchanged, factor prices, and factor intensities in the production of both goods are unchanged as well. The amount of clothing produced in Sri Lanka INCREASES, REMAINS UNCHANGED. DECREASES, The factor intensity (skilled to unskilled workers) in the production of electronic equipment in Sri Lanka INCREASES, DECREASES, DOESN T CHANGE. The relative wage rate of skilled to unskilled workers in Sri Lanka INCREASES, DECREASES, DOESN T CHANGE. Relevant trade theorem used in answering problem Rybczynski. 9

10 b) Suppose the production of rice requires water and land as does the production of wheat. Assume that rice production uses water more intensively than wheat production. Suppose that two large countries, India and the United States, produce both goods and the United States is relatively well endowed with water compared to India. (8 points) The Heckscher Ohlin theorem tells us that countries export the commodity that uses its relatively abundant factor intensively. The problem statement sets out the conditions, relative factor abundance and factor intensities in production, that allow the application of the H-O theorem. The Factor Price Equalization theorem tells us that is the assumptions of the H-O model hold factor prices are equalized through trade and so neither country will have factor prices that differ. Exported Commodity from India Wheat Relevant trade theorem used in answering the above Heckscher Ohlin Country with higher water prices Neither Relevant trade theorem used in answering the above Factor Price Equalization c) Determine the equilibrium prices of bread and wine if the rental rate of land in Canada is $5 and the wage rate of labour in the US is $2. Assume it takes 2 units of land and 2 units of labour to produce 1 unit of wine in Canada and in the US it take 3 units of land and 1 unit of labour to produce bread. Canada and the US are trading partners. SHOW YOUR WORK (7 points) Prices and factor prices are equalized through trade. The assumption of zero economic profits means that the expenditure on inputs equal the price of each good. We have two equations (let r equal the rental rate of land and s equal the price of capital) and knowing factor prices in either country, along with unit factor requirements, allows us to determine good prices. Note technology is identical in each country the factor inputs needed to produce 1 unit of each good are the same in both coutries (so a ij = a ij * for i = Land (L), Capital (K), and j = Wine (W), Bread (B)) P W = a LW r + a KW s = 2x$5 + 2x$2 = $14 P B = a LB r + a KB s = 3x$5 + 1x$2 = $17 Solving, we find that Price of Wine = $14 Price of Bread = $17 Relevant trade theorem used in answering problem Factor Price Equalization 10

11 d) Smaller countries often stand to greatly benefit from trade as the equilibrium world relative price is often substantially different from their autarky price ratio. Suppose Peru is relatively well endowed with land (used intensively in potato production) compared to skilled labour (used intensively in producing computers) in relation to their trading partners. Circle one of the capitalized terms in the first two statements below. (7 points) From the Heckscher Ohlin theorem we know that Peru has a comparative advantage in the production of potatoes and will export that good. With trade Peru will obtain a higher price for potatoes than producers in Peru are able to obtain with no trade. The Stolper Samuelson theorem tells use that an increase in the price of a good (in this case potatoes) leads to an increase in the factor reward (i.e. price) received by the factor used intensively in producing potatoes. As the price of land increases firms in Peru substitutes away from its use and the land to labour ratio in potato production falls (the labour to land ratio rises) Trade results in an INCREASE, DECLINE, NO CHANGE in land rents in Peru. Potato production uses labour LESS INTENSIVELY, AT THE ORIGINAL INTENSITY after trade. MORE INTENSIVELY, Relevant trade theorem used in answering problem Stolper Samuelson and Heckscher Ohlin (extra 1 point if both are written down) 11