# chapter3 - L Karp International Trade November 14, 2007 3...

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LKarp International Trade November 14, 2007 3 The Ricardo-Viner Model The Ricardo-Viner or “Sector-Specific Factors”model assumes that both commodities require asec to rspec ific input (e.g. land for corn and machines for umbrellas) as well as a mobile factor. In contrast, the Ricardo model assumes that there is a single factor of production, which is mobile across sectors. The Heckscher-Ohlin-Samuelson (HOS), studied in the next section, assumes that there are two or more factors of production, all of which are mobile across sectors. We can interpret HOS as a long run model and the Ricardo-Viner model as a medium run model. I first outline the model and discuss its comparative statics properties. Then I use the model for two second-best applications: (i) trade in the presence of imperfect property rights and (ii) trade in the presence of a minimum wage. I close this chapter by studying an “intermediate” model in which the sector-specific factors can adjust slowly across sectors. This extension serves as a bridge between the Ricardo-Viner and the HOS models. 3.1 Equilibrium in the basic model The basic building block in this model is the optimality condition that the value of the marginal product of labor (the mobile factor) is equal to the wage, i.e. the price of labor. Since labor can move freely from one sector to the other, the wage in the two sectors must be equal (as in the Ricardo model). Since producers maximize profits by setting the value of marginal product of labor equal to the wage, so these values of marginal product must be equal in the two sectors. Let K c and K u be the amount of sector-specific capital in the corn and umbrella sector; L c and L u are the stocks of labor in the two sectors. Let C ( K c ,L c ) and U ( K u u ) be the sectoral production functions, and denote partial derivatives using subscripts, so C L and U L are the marginal products of labor in corn and umbrellas. (To conserve notation, I do not use subscripts on the subscripts, but the meaning should be clear from the context.) These marginal products are functions of the labor and the amount of capital in the sector. I assume that the production function in each sector is concave in labor and that the inputs are technical substitutes, i.e. that an increase in either factor in a sector increases the marginal product of the other factor in that sector. For the corn sector, for example, these assumptions mean: C LL < 0 and C LK = C KL > 0 . (40) 53

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We also assume that production is concave in inputs, which implies C LL C KK C LK C KL > 0 . (41) (We have analogous expressions for the other sector.) Let W be the nominal wage. The optimality conditions are p c · C L = W p u · U L = W. It is convenient to work with relative prices, so define p = p c /p u and w = W/p u . I choose umbrellas as the numeraire. Notice that the units of w are units of umbrellas/labor, so w tells how many umbrellas exchange for a unit of labor.
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## This note was uploaded on 08/01/2008 for the course ARE 201 taught by Professor Karp during the Fall '07 term at University of California, Berkeley.

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chapter3 - L Karp International Trade November 14, 2007 3...

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