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ps1_solution - Econ 101: International Trade (Fall 2011)...

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Unformatted text preview: Econ 101: International Trade (Fall 2011) problem set #1 Axis-intersection for the production possibility frontiers and the opportunity costs Calculations for Home: Calculations for Foreign: Home has an absolute advantage both in cheese and wine production, because and Home has a comparative advantage in wine and Foreign has a comparative advantage in cheese production, because (b) see the graphs of #1.(a) Calculation of the relative price of cheese in terms of wine for Home with : Calculation of the relative price of cheese in terms of wine for Foreign with : and and (c) relative Supply: Foreign starts to produce cheese, when the relative world price is greater than its opportunity costs of cheese in terms of wine and Home starts to produce cheese, when the relative world price is greater than its opportunity costs of cheese in terms of wine . When Home specializes in wine and Foreign specializes in cheese, they produce the relative supply of World consumers relative demand function: Page 1 of 9 Econ 101: International Trade (Fall 2011) problem set #1 The relative supply curve’s y-axis intercept is The intercept of the relative supply curve and the relative demand function is Because , the quantities are: ; This pattern of production states about the pattern of trade, that both countries specialize in the goods, they have a comparative advantage in. Thus Home only produces and exports wine and imports cheese and Foreign only produces and exports cheese and imports wine. The wages differ across the countries, because labor productivity is higher in Home in all sectors. ; (d) World consumers relative demand function: ; for all positive quantities Because , the quantities are: ; ; Thus is no trade because both countries produce and consume only the wine, they have produced on their own. World consumers relative demand function: There will be no trade which as motivated by the same argument that for the consumers demand function above. Page 2 of 9 Econ 101: International Trade (Fall 2011) problem set #1 (e) Axis-intersection for the production possibility frontiers and the opportunity costs. Calculations for Home: Calculations for Foreign: World consumers relative demand function: When Home specializes in wine and Foreign specializes in cheese, they produce the relative supply of The demand curve interlaces the relative supply curve at The intercept of the relative supply curve and the relative demand function is: Because the , the quantities are: ; ; The pattern of production only chances in quantities. Both countries still specialize in the same goods that they have specialized in before the international migration. Because the relative wage was greater than 1 on the previous labor allocation, labor has moved from Foreign to Home and because of that the relative wage has decreased in comparison to the previous labor allocation. 2. (a) Calculation of the relative home productivities: Home has the strongest comparative advantage in tools and the least comparative advantage in cheese because it has the greatest relative productivity in tools and the smallest relative productivity in cheese: (b) Under the assumption, that we can neglect the relative size of the labor force, Home will specialize in tools and wine because its relative productivities in both goods are smaller than the relative wage rate: Page 3 of 9 Econ 101: International Trade (Fall 2011) problem set #1 (c) Gains from trade: That trade benefits both countries can be shown in two ways: First, one can think of trade as an indirect method of production. Instead of producing a good for itself, a country can produce another good and trade it for the desired good. The model shows that whenever a good is imported it must be true that this indirect "production" requires less labor than direct production so that there are different world prices than in autarky. This will lift the customer to a strict preferred consumption bundle Second, trade enlarges a country's consumption possibilities, implying gains from trade. (d) Assumption: The wage rate is Calculation of the total costs of the foreign goods to a home consumer by adding 50% to the unit labor requirements of foreign goods: Home Foreign Tools Wine Cheese Home has the smallest relative productivity in cheese. Because the relative wage rate is smaller than , Home will still import cheese from Foreign and because the relative wage rate is greater than and , Home will still produce tools and wine on their own. Calculation of the total costs of the home goods to a foreign consumer by adding 50% to the unit labor requirements of home goods: Home Foreign Tools Wine Cheese Foreign has the smallest relative productivity in tools. Because the relative wage rate is smaller than , Foreign will still import tools from Home. Foreign will produce Cheese on their own and they are indifferent between importing wine from Home or producing wine on their own because the relative productivity equals the relative wage rate. Therefore not all goods have to be traded but can be traded. In this example with transport costs it is possible that wine would become a non-traded good. This usually happens, if both countries would have a greater relative productivity in this good than the relative wage rate. Page 4 of 9 Econ 101: International Trade (Fall 2011) problem set #1 3. Given: ; ; ; (a) Derivation of the marginal products of labor: (b) Calculation of the equilibrium wage rate in autarky with mobile labor: ( c) Assumption: the price of flowers is fixed ( ) and the price of machinery will increase ( Page 5 of 9 ) Econ 101: International Trade (Fall 2011) problem set #1 When increases, labor employment shifts from the flower sector to the machinery sector and the output of machineries rises while that of flowers falls. The wages in both sectors will increase by less than the increase in the price of machinery because when the machinery employment rises, the marginal product of labor in that sector falls. (d) A machinery and a food firm maximize their profits by maximizing the equations: These equations follow after differentiate the firm’s profit-equation with respect to labor and using the general labor demand relationship: Because the wages are the same, these formulas can be equalized and it follows: (e) Quantities before trade: Quantities after trade: Page 6 of 9 Econ 101: International Trade (Fall 2011) problem set #1 Gains from trade: The result of a rise in price of the K-intensive sector is that owners of the factor K are better off, workers experience an ambiguous shift in their position, and owners of the T-factor are worse off. In our example, workers are also better off. But if those who gain from trade would compensate those who lose, that everybody would be better off! 4. (a) From this it follows that the straight line for foot virtually starts at : Calculation of the resources’ allocation: ; ; ; (b) From this it follows that the straight line for foot virtually starts at : Calculation of the resources’ allocation: ; ; ; From this it follows that the straight line for foot virtually starts at Calculation of the resources’ allocation: Page 7 of 9 : Econ 101: International Trade (Fall 2011) problem set #1 ; ; ; Thus an increase in the economy's supply of labor will, holding prices constant, lead to a fall in the output of the land-intensive good. The land and labor that is no longer used in food production is now used in the cloth sector, whose output has risen more than proportionately to the increase in labor supply. (Biased expansion of production possibilities). (c) If labor supply would increase beyond 1200hours, there would be unemployment, because there would not be any land left where workers can produce cloth (or food). Because unemployment is not allowed in the world equilibrium maybe prices of the goods will change (According to the TA in the Review Session). 5. (a) Given: ; ; ; When the price ratio rises, the wage ratio increases in squared terms. When the wage ratio rises, the land is now relatively cheaper, than the ratios of land to labor employed in the production of cloth and food would therefore increases in linear terms. Page 8 of 9 Econ 101: International Trade (Fall 2011) problem set #1 (b) For example, the land to labor ratio will rise in both industries, when the wages have increased because of a higher relative clothing price: The relatively land-intensive sector loses relatively more land than workers compared to the economy’s average but carries relatively more land than workers compared with its previous situation. The relatively labor-intensive sector hires relatively more workers than land compared to the economy’s average but gains relatively more land than workers compared with its previous situation. when the food sector shrinks. when the cloth sector expands. (c) Page 9 of 9 ...
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This note was uploaded on 10/27/2011 for the course ECON 101 taught by Professor Jacobson during the Fall '03 term at UCSD.

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