Solution: Cobb-Douglas production function The output Q of
Chapter 12, Problem 74(choose chapter or problem)
Cobb-Douglas production function The output Q of an economic system subject to two inputs, such as labor L and capital K, is often modeled by the Cobb-Douglas production function Q1L, K2 = cLaKb. Suppose a = 13 , b = 23 , and c = 1. a. Evaluate the partial derivatives QL and QK. b. Suppose L = 10 is fixed and K increases from K = 20 to K = 20.5. Use linear approximation to estimate the change in Q. c. Suppose K = 20 is fixed and L decreases from L = 10 to L = 9.5. Use linear approximation to estimate the change in Q. d. Graph the level curves of the production function in the first quadrant of the LK@plane for Q = 1, 2, and 3. e. Use the graph of part (d). If you move along the vertical line L = 2 in the positive K-direction, how does Q change? Is this consistent with QK computed in part (a)? f. Use the graph of part (d). If you move along the horizontal line K = 2 in the positive L-direction, how does Q change? Is this consistent with QL computed in part (a)?
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