solution1 - L Karp International Trade March 2008 Solutions...

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LKarp International Trade March 2008 Solutions to problem set 1 1. As a result of the productivity increase, the world production possi- bility frontier shifts to the dashed line in Figure 1. (Compare to f gure 4 of Notes1.) Remember that the "real wage" has two de f nitions: it is either an index number that tells me how many "consumption bundles" that a worker can exchange for one unit of labor, or it is the number of "utils" (units of utility) that a worker can exchange for one unit of labor. To use either of these de f nitions, I need to specify what constitutes a "consumption bundle", or to specify the utility function. However, I know that the real wage un- ambiguously increases if and only if the worker can buy more of everything with one unit of labor. That possibility requires that both w/p 1 and w/p 2 increase. (What are the units of these ratios?) A. If the initial equilibrium is in region A, where the US is completely specialized and Canada is unspecialized, the US welfare increases and Cana- dian welfare is unchanged. The world relative commodity price ( p 2 p 1 )isg iven by the Canadian autarkic price, which is unchanged by technological change in US umbrella manufacturing. Canada receives no bene f ts from trade - before or after the technological improvement. We can normalize by setting p 1 =1 (any other normalization is OK). The free trade equilibrium relative price p 2 p 1 (and therefore p 2 ) is unchanged by the change in U.S. technolgoy. Therefore the nominal wage in Canada, w c , is unchanged, as is the Cana- dian real wage. The nominal wage in US is given by the 0 pro f tcond it ion p 2 = w u a u 2 .S i n c e a u 2 has decreased, the nominal US wage must have in- creased. Since nominal commodity prices are unchanged, real US wage has increased. (Both w u /p 1 and w u /p 2 increase.) C. If the initial equilibrium is in region C, where only Canada is special- ized, the world price under trade equals the autarkic US price. The world relative price of corn increases (i.e., the relative price of umbrellas falls) as a result of technological improvement in umbrella sector). If I normalize by setting
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the nominal price of corn, must have increased. Zero pro f ts in the Canadian corn sector requires p 1 = w c a c 1 , so the nominal Canadian wage increases. Since w c /p 1 is unchanged, but w c /p 2 increases, the real Canadian wage (and therefore Canadian welfare) increases. Given my normalization p 2 =1 ,the 0pro f t condition in US umbrella sector implies that the nominal US wage, w u ,ha sinc rea sed ,a sha s w u /p 2 .T h e0p r o f t condition in US corn sector requires p 1 = w u a u c ,o r 1 /a
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solution1 - L Karp International Trade March 2008 Solutions...

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