# ps4_f04 - Econ 313.1 Wissink Fall 2004 PS#4 XtraQ DUE...

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1) Suppose the production function for x is: x = L a K b with 0 < a <1 and 0 < b < 1 and a + b = 1. a) Show that each input, L and K, has a positive marginal product. b) Show that each input, L and K, has diminishing marginal productivity. c) Show that the marginal rate of technical substitution, the MRTS, depends only on the kapital to labor ratio, that is, on K/L, but not on the scale of production. 2) Compare and contrast the concepts of diminishing returns to scale and diminishing returns to a factor of production. Dream up a Cobb-Douglas production function that exhibits
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Unformatted text preview: increasing returns to scale and at the same time, diminishing returns to BOTH factors of production. 3) Given a common wage rate for labor, w, and rental rate for kapital, r, how would the long run total cost function for the production function: x = K + L compare with the long run total cost function for the production function z = (K + L) 2 ? Find and graph them both. Econ 313.1 - Wissink - Fall 2004 PS#4 - XtraQ DUE: Friday Oct 22 at the start of class....
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