A f x x2 2 b f x ln x 5 d f x 1 c f

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Unformatted text preview: rictly concave. 1 15 - 4 14 1 -12 15 - x -34 3 12 15 - x -74 f (x) = - x-32 - x - x 4 2 8 2 64 2 Solution: 4 (a) The first derivative is: The second derivative is: f (x) = (12)(x2 + 2)-12 (2x) (b) The first derivative is: Since f (x) > 0 for all x, the function is strictly convex. Not homogeneous. The second derivative is: f (x) = 1 x f (x) = (x2 + 2)-12 - x2 (x2 + 2)-32 (c) The first derivative is: 1 x2 For all x > 0, f (x) < 0 the function is strictly concave. The function is not homogeneous. f (x) = 2(x2 + x3 - 1)(2x + 3x2 ) f (x) = - The second derivative is: (d) The first derivative is: Neither strictly concave or strictly convex. For example f (0) = -4 whereas f (1) = 66. Not homogeneous. f (x) = 0 f (x) = 2(2x + 3x2 )2 + 2(x2 + x3 - 1)(2 + 6x) The second derivative is: Neither strictly concave nor strictly convex. Homogeneous of degree 0. 3. Let c(q) denote the total cost function of a firm. (a) Define marginal cost and average cost of production. (b) Using a graph, draw a "typical" total cost function an...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University, Canada.

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