Trade_LN3_2011 - International Trade Lecture Note 3 Erzo...

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International Trade° Lecture Note 3 Erzo G.J. Luttmer Department of Economics University of Minnesota Spring 2011 1. Introduction The following describes a static economy with two countries and two traded ±nal goods. These goods are produced using labor-only technologies. Labor cannot be traded across borders and labor productivities may di/er across countries. This provides a motive for trade in ±nal goods. The pattern of trade is determined by ²comparative advantage.³ There is no intertemporal trade and there are no transfers, and hence the trade balance is zero by construction. Productivity di/erences and the inability of labor to move also provide an explanation for di/erences in wages across countries. This model of trade was proposed by David Ricardo in his ²Principles of Political Economy and Taxation³(1817). In his chapter On Foreign Trade, Ricardo describes the pattern of trade between England and Portugal and introduces comparative advantage to explain why England exports cloth and Portugal wine. 2. The Ricardian Technology Consider a world with two countries indexed by i 2 f H ; F g . The aggregate labor supply in country i is L i > 0 . There are two consumption goods, indexed by ! 2 f 0 ; 1 g , that can be produced using linear labor-only production technologies. The labor productivities are z !;i > 0 . Labor can only be used in its country of origin. Consumption goods can be shipped costlessly from one country to another. 2.1 The World PPF If it was possible for labor to migrate or otherwise supply its services anywhere in the world, then relatively unproductive technologies would never be used. For example, if z !; H > z !; F , then all production of good ! would make use of the home-country 1
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technology. The set of all possible combinations of output of good 0 and good 1 would be 8 < : ( y 0 ; y 1 ) : 0 ° y ! ° max f z !; H ; z !; F g l ! , X ! 2f 0 ; 1 g l ! ° L H + L F 9 = ; : This is just like a budget set with prices 1 = max f z !; H ; z !; F g and income L H + L F . But labor is not mobile in a Ricardian economy. This means that the production possibility set is really Y = 8 < : ( y 0 ; y 1 ) : 0 ° y ! ° z !; H l !; H + z !; F l !; F , 0 ° l !;i , X ! 2f 0 ; 1 g l !;i ° L i 9 = ; : What does this look like? Suppose we want to produce as much of good 0 as possible. There is only one way to do this: allocate all labor everywhere to the production of good 0 . World output would be z 0 ; H L H + z 0 ; F L F units of good 0 , and nothing of good 1 . Similarly, the most the world can produce of good 1 is z 1 ; H L H + z 1 ; F L F , and this would imply no output of good 0 . The question is now: how should labor be allocated in the two countries if we want to produce some amount of good 0 , and given that amount, as much as possible of good 1 ? 2.1.1 Comparative Advantage Start out with everyone producing good 0 . Suppose we want to produce one unit of good 1 in the home country. This requires 1 =z 1 ; H units of labor that has to taken from the production of good 0 . The cost of 1 unit of good 1 is thus z 0 ; H =z 1 ; H units of good 0 in the home country. Similarly, the cost of 1 unit of good 1 is z 0 ; F =z 1 ; F units of good 0 in the foreign country. Suppose that z 0 ; H z 1 ; H
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