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400ps5-11-soln

# 400ps5-11-soln - ECON 400 Winter 2011 Solutions for Problem...

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ECON 400 Hartman Winter 2011 Solutions for Problem Set V 1. The fact the demand and supply functions are homogeneous of degree zero in prices implies that 3 a , 2 b   , and 1 c   . The fact that * * / / K w L r   implies that 4 2 3 4 2 3 6 p r w np r w   so 6 n , and the fact that * * / / K p Q r   implies that 3 2 2 3 2 2 12 p r w mp r w so 12 m . 2.a. The first order conditions are 1 1 1 2 ( , ) 0 p wg y y and 2 2 1 2 ( , ) 0 p wg y y . The second order sufficient conditions are 11 1 2 ( , ) 0 wg y y , 22 1 2 ( , ) 0 wg y y , and 11 12 2 2 11 22 12 21 22 [ ( ) ] 0 wg wg w g g g wg wg . 2.b. Since the * 1 y and * 2 y are given implicitly by the first order conditions, and since the first order conditions can be written as 1 1 1 1 2 ( , ) p tp g y y w tw and 2 2 2 1 2 ( , ) p tp g y y w tw for any 0 t , both * 1 y and * 2 y are homogeneous of degree zero in prices. 2.c. Solve the first order conditions for * 1 1 1 2 ( , , ) y y p p w and * 2 2 1 2 ( , , ) y y p p w , substitute these back into the first order conditions to get identities, and differentiate through the identities with respect to 1 p to get the following system: * * * * * * 1 2 11 1 2 12 1 2 1 1 * * * * * * 1 2 21 1 2 22 1 2 1 1 ( , ) ( , ) 1 ( , ) ( , ) 0 y y wg y y wg y y p p y y wg y y wg y y p p   Use Cramer's rule to solve for * 1 1 / y p ; this gives 12 * 22 1 22 2 2 11 12 1 11 22 12 21 22 1 0 0 [ ( ) ] wg wg y wg

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400ps5-11-soln - ECON 400 Winter 2011 Solutions for Problem...

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