400ps4-11 - ECON 400 Winter 2011 Problem Set IV (for...

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ECON 400 Hartman Winter 2011 Problem Set IV (for Monday, January 24) 1. A price taking firm's production function is ab QKL where Q , K , and L denote output and inputs of capital and labor, respectively, and 0 a and 0 b are constants with 1 . The output price and the prices of the capital and labor inputs are p , r , and w , respectively. In Problem Set III you showed that the firm's long run demand functions are 11 1 * 1 (,,) bb b b Kp rw a b p r w  and 1 * 1 aa a a Lp rw a b p r w a. Suppose now that the capital input is fixed in the short run at KK . Derive the firm's short run demand function for labor, (,, ) S LpwK . b. Verify that ** [,, (,,) ] S Lprw LpwK pw r . [Hint: the algebra is a bit messy; note that 1( 1 ) ( 1 ) 1 1 ( 1) ( 1 )( ( 1 ) 1 ab a b a a b b a b a b  .] 2. (This is problem 4 after section 4.6 of the text.) There are several definitions of complementary and substitute factors in the literature, among which are: (i) Factor 1 is a substitute (complement) for factor 2 if the marginal product of factor 1 decreases (increases) as factor 2 is increased.
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400ps4-11 - ECON 400 Winter 2011 Problem Set IV (for...

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