A car manufacturer can choose to locate a new plant in country A or country B. Your job is to determine where to locate this new plant. The only inputs used in car production are labor and capital, and the production function is Cobb-Douglas: F(L; K) = L½K½, where L is the labor input and K the capital input. In country A, labor costs $7 per unit and capital costs $7 per unit, while in country B, labor costs more ($8) but capital costs less ($6).
a. In which country should you locate the new plant so as to minimize cost per unit of output (i.e., average cost)?
b. Now assume that country A subsidizes labor so that labor costs $6 per unit in country A. Does it change the location decision of the firm?
c. Instead of subsidizing labor, suppose that country A subsidizes capital so that capital costs $6 per unit. Does it change the location decision of the firm?
d. What happens if both countries act identically in either taxing or subsidizing capital and labor? What would be the location decision of the firm? Has any country an incentive to alter its tax-subsidy choice, and if so, how?