l. Joe's coffee house operates under the production function Q (L, K) = L3/2K1/2, where L is the number of worker hours and K is the number of coffee machine hours. a. Does Joe's production function exhibit a diminishing marginal rate of technical substitution of labor for capital as he uses more worker hours and fewer machine hours, holding output constant? Mathematically justify using derivatives. (8 points) b. Does Joe's production function exhibit a diminishing marginal product of labor as he uses more labor, holding capital constant? Mathematically justify using derivatives. (8 points) c. Compare and contrast the phenomena of diminishing marginal product of labor and diminishing marginal rate of substitution of labor for capital. In your explanation, consider how MPL and MRTS both essentially measure how much an additional unit of labor is worth to production. Also consider what is held constant and what is changing for each as the firm uses more labor. (9 points)