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400exam1-10-soln - ECON 400 Winter 2010 ANSWERS FOR FIRST...

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ECON 400 Hartman Winter 2010 ANSWERS FOR FIRST EXAM 1.a. 3/4 1/4 2 0 p L K w and 1/4 3/4 2 0 p L K r . 1.b. 7/4 1/4 3 0 2 pL K , 1/4 7/4 3 0 2 pL K , and 2 7/4 1/4 1/4 7/4 3/4 3/4 2 3/2 3/2 3 3 1 2 0 2 2 2 pL K pL K pL K p L K    , so the (sufficient) second order conditions for a maximum are satisfied. 1.c * 2 3/2 1/2 4 L p w r and * 2 1/2 3/2 4 K p w r 1.d * 1/2 1/2 16 Q pw r 1.e. * 2 3/2 1/2 4 L p w r , * 2 1/2 3/2 4 K p w r , and * 1/2 1/2 16 Q pw r are homogeneous of degree zero in w , r , and p . This does not imply that the production function is homogeneous of degree one. 1.f. 1/ 2 Lr   2.a. 1 1 2 1 ( , ) 0 pf x x w and 2 1 2 2 ( , ) ( ) 0 pf x x C x 2.b 11 0 pf , 22 0 pf C  , and 11 12 2 2 11 22 12 21 22 ( ) 0 pf pf pf pf C p f pf pf C   . The (sufficient) second
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