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

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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 a b Q K L where Q , K , and L denote output and inputs of capital and labor, respectively, and 0 a and 0 b are constants with 1 a b . 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 1 1 1 * 1 1 1 1 1 ( , , ) b b b b a b a b a b a b a b K p r w a b p r w           and 1 1 1 * 1 1 1 1 1 ( , , ) a a a a a b a b a b a b a b L p r w a b p r w           a. Suppose now that the capital input is fixed in the short run at K K . Derive the firm's short run demand function for labor, ( , , ) S L p w K . b. Verify that * * ( , , ) [ , , ( , , )] S L p r w L p w K p w r . [Hint: the algebra is a bit messy; note that 1 (1 )(1 ) 1 1 (1 )(1 ) (1 )(1 ) 1 ab a b a b b 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)
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