A U.S. electronics firm is considering moving its production abroad. Its production function is q = L0.5K0.5 (based on Hsieh, 1995), so its MPL = 0.5 (K0.5/L0.5) and its MPK = 0.5 (L0.5/K0.5). The U.S. factor prices are w = r = 10. In Mexico, the wage is half that in the U.S. but the firm faces the same cost of capital: w* = 5 and r* = 10. What are the optimal values of L and K for each country and what is the total cost of producing q = 100 units for each country?

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A U.S. electronics firm is considering moving its production abroad. Its production function is q = L0.5K0.5 (based on Hsieh, 1995), so its MPL = 0.5 (K0.5/L0.5) and its MPK = 0.5 (L0.5/K0.5). The U.S. factor prices are w = r = 10. In Mexico, the wage is half that in the U.S. but the firm faces the same cost of capital: w* = 5 and r* = 10. What are the optimal values of L and K for each country and what is the total cost of producing q = 100 units for each country?

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