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 ** // KwL r  implies that 42 3 6 prw n   so 6 n , and the fact that Kp Qr implies that 32 2 12 p rw m p rw so 12 m . 2.a. The first order conditions are 11 1 2 (, ) 0 pw gyy and 22 1 2 g y y . The second order sufficient conditions are 11 1 2 (, )0 wg y y  , 22 1 2 wg y y , and 11 12 11 22 12 21 22 [( ) ] 0 wg wg wgg 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 112 (, ) p tp wt w  and 212 p tp w 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 2 (, ,) y yppw and * 1 2 y yppw , 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: 12 11 1 2 12 1 2 2 2 (,) 1 0 yy wg y y wg y y pp w g yy w Use Cramer's rule to solve for * / y p ; this gives 12 * 22 2 11 12 1 2 2 1 2 21 22 1 0 0 ) ] wg wg yw g wg wg g g g wg wg   by the second order conditions.
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This note was uploaded on 04/04/2011 for the course ECON 400 taught by Professor Ellis,g during the Spring '08 term at University of Washington.

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

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