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Suppose the production function for a car manufacturer is:
Q = 2K2L2
where Q is the number of cars produced, K is the number of machine hours used, and L is the number of worker hours used. Use calculus for the following:
a. to determine a function for the marginal product of labor
b. to determine a function for the marginal product of capital
c. to find the marginal rate of technical substitution
d. to discuss how MRTSLK changes as the firm uses more labor, holding output constant
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