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Econ_181_HW2_S13_solution

# answer an increase in capital shifts the capital

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Unformatted text preview: produced and both factors fully used. (Hint: setting price equal to marginal cost for each good gives you two linear equations in two unknowns. Solve these equations for factor prices.) Show how an increase in the price of food will affect factor prices. Answer: The marginal costs of production are respectively: MC! = 3w + 2r MC! = 3r + 2w Because of perfect competition, we have P! = MC! = 3w + 2r P! = MC! = 3r + 2w 3P! − 2P! w= 5 3P! − 2P! r= 5 An increase in the price of food (the capital intensive good) leads to an increase in the real return on capital and a decrease in real wage. So w/r ratio decreases. d) Assume that two countries (the US and Mexico) have identical tastes and technology, but assume the US has more capital and Mexico has more labor. Assuming the relative demand (ratio of demand for cloth to demand for food) is independent of income, show how autarky good prices and factor prices differ between the two countries, then show how trade will affect factor prices in each country. Will factor prices be equalized between the two countries? Does free trade benefit everybody in each country? Answer: As shown above, given prices, an increase in the supply capital increase output of capital intensive good and decreases output of labor intensive good. Because the US is capital abundant, it will have lower relative supply of clothing to food at a given price. Because we have the assumption of identical tastes, the autarky relative price of clothing will be higher in the US than in Mexico. According to the analysis in part (c), this implies that the wage rate will be higher in the US and return on capital will be higher in Mexico. Thus, with trade, the US will export food and import clothing. As a result of trade, P! /P! falls in the US and increases in Mexico. From (c), this implies that wage rate falls in the US and rises in Mexico, which the return on capital rises in the US and falls in Mexico. Finally, if free trade equalizes commodity prices and both goods are produced in both countries, it much equalize factor prices (see equations determining factor prices in (c)), provided technology is the same in two countries....
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