PS3-Solutions

PS3-Solutions - Econ 300 Spring Semester 2008 Solutions to...

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Unformatted text preview: Econ 300 - Spring Semester 2008 - Solutions to Problem Set 3 - Julien Bengui 7.2.2 (a) d f ( x ) d x = 2( x 2- 1)- (2 x + 7)2 x ( x 2- 1) 2 = 2 x 2- 2- 4 x 2- 14 x ( x 2- 1) 2 =- 2 x 2- 14 x- 2 ( x 2- 1) 2 (b) d f ( x ) d x = (3 bx 2 + 2 cx + 1) x- ( bx 3 + cx 2 + x- 4) x 2 = 3 bx 3 + 2 cx 2 + x- bx 3- cx 2- x + 4 x 2 = 2 bx 3 + cx 2 + 4 x 2 (c) d f ( x ) d x = 2 e 2 x x 2- e 2 x 2 x x 4 = 2 xe 2 x- 2 e 2 x x 3 = 2 e 2 x ( x- 1) x 3 (d) d f ( x ) d x = 2(3 x + 2) x- (3 x + 2) 2 x 2 = (3 x + 2)(2 x- 3 x- 2) x 2 =- (3 x + 2)( x + 2) x 2 7.2.8 First write Q ( t ) as a function of A ,K ,L and t : Q ( t ) = A K α L 1- α e [ c + αf +(1- α ) g ] t . Then write this expression in natural logarithms to get: ln Q ( t ) = ln( A K α L 1- α ) + [ c + αf + (1- α ) g ] t. Finally, differentiate this last expression with respect to t to get the growth rate of output dln Q ( t ) d t = c + αf + (1- α ) g....
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PS3-Solutions - Econ 300 Spring Semester 2008 Solutions to...

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