Consider the production functions given below: a. Suppose that the production function faced by a 30-weight ball bearing producer is given by Q = 4K^0 · 5 L^0 · 5 , where MPK = 2K^0.5 x L^0.5 and MPL = 2K^0 · 5 L^ –0.s_ Do both labor and capital display diminishing marginal products? Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = MPL/MP K) Does this production function display a diminishing marginal rate of substitution? b. Suppose that the production function faced by a 40-weight ball bearing producer is given by Q = 4KL, where MP K = 4L and MP L = 4K. Do both labor and capital display diminishing marginal products? Find the marginal rate of technical substitution for this production function. Does this production function display a diminishing marginal rate of substitution? c. Compare your answers to (a) and (b). Must labor and capital display diminishing marginal products in order for the MRTS to diminish?
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