11Breview1 - econ 11b ucsc ams 11b Review Questions 1...

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Unformatted text preview: econ 11b ucsc ams 11b Review Questions 1 Partial derivatives and applications. 1. Compute the indicated partial derivatives of the functions below. a. z = 3 x 2 + 4 xy- 5 y 2- 4 x + 7 y- 2 , z x = z y = b. F ( u,v,w ) = 60 u 2 / 3 v 1 / 6 w 1 / 2 ∂F ∂u = ∂ 2 F ∂w∂u = c. w = x 2 z ln( y 2 + z 3 ) w x = w y = w xx = w yz = w xyz = d. f ( x,y,z ) = 2 x 3 yz 2- 3 xy 3 z + 5 x 2 y 2- 7 yz 5 + 11 x- 1 f x = f y = f zx =. e. q ( u,v ) = u 2 v- 3 uv 3 2 u + 3 v ∂q ∂u = ∂q ∂v = 2. Suppose that z = 3 x 2 y 3 + 5 xy 2- 3 x + y- 1, where x = 3 t- 2 and y = 2 t + 1. Use the chain rule to compute dz dt t =0 . 3. The production function for a firm is given by Q = F ( K,L ) , where Q is the firm’s monthly output, K is the firm’s monthly capital input and L is the firm’s monthly labor input. Furthermore, the labor input L is given by L = 2 m (60 h- h 2 ) , where m is the number of the firm’s employees and h is the average number of hours each employee works per month. The firm’s profit function is given byeach employee works per month....
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This note was uploaded on 09/16/2011 for the course ECON 11B taught by Professor Binici during the Spring '08 term at University of California, Santa Cruz.

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11Breview1 - econ 11b ucsc ams 11b Review Questions 1...

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