PS4-solutions

PS4-solutions - 2 vu ; this point is a Maximum b) First...

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Problem Set 4 Answer Key 8.4.6 a) dy dx 2 x + (1 = 3) x 2 = 3 y 1 = 3 2 y + (1 = 3) y 2 = 3 x 1 = 3 b) dy dx = 2 xy + y 2 + y x 2 + 2 yx + x c) dy dx = (3 =x ) 2 xy 2 2 x 2 y 4 d) @y @x = 3 x 2 + wy 3 w 3 y 2 + wx e) dy dx = y x (2 + y ) 9.1.6 A quadratic function has only one bend and is either concave or convex.The second derivative is constant because f&(x) is linear, therefore, there is no in±ec- tion point since the second derivative never changes sign. 9.2.10 ( w + b ) L The derivative of the pro²t function d dL = 1 ( w + b ) Optimal demand for labor is derived from setting d dL = 0 . L ± = ( w + b ) 1 1 In order to see how labor demand changes with b; we take the derivative of the optimal labor demand function with respect to b: dL db = 1 ± 1 ( w + b ) 2 1 < 0 1
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workers. 10.1.2 and 10.2.2 a) First order conditions: g u = 20 4 u 2 v = 0 g v = 16 2 v 2 u = 0 There±s a unique statinary point: ( u ; v ) = (2 ; 6) Second order Conditions: g u u = 4 g vv = 2 g uv = 2 g u u ± g vv > g
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Unformatted text preview: 2 vu ; this point is a Maximum b) First Order Conditions: g u = & 5 + 8 u + 8 v = 0 g v = & 9 + 10 v + 8 u = 0 There±s a unique stationary point ( u & ; v & ) = ( & 11 = 8 ; 2) Second order Conditions g u u = 8 g vv = 10 g uv = 8 g u u ± g vv > g 2 vu ; this point is a Minimum c) First Order Conditions g u = u 2 + 3 v + 2 = 0 g v = 3 u & 3 v = 0 There are two stationary points (-2,-2) and (-1,-1). Point (-2,-2) is a local maximum and the other point doesn±t satisfy the inequality for the second order condition. d) First Order Conditions: g u = 24 u ± 2 = 3 v 1 = 3 & 6 = 0 g v = 24 u 1 = 3 v ± 2 = 3 & 3 = 0 The stationary point is ( u & ; v & ) = (128 ; 256) . This point is a maximum. 2...
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This note was uploaded on 05/18/2008 for the course ECON 300 taught by Professor Cramton during the Spring '08 term at Maryland.

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PS4-solutions - 2 vu ; this point is a Maximum b) First...

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