pset1_s10 - Economics 217 Spring 2010 Problem Set 1...

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Economics 217 Spring 2010 P r o b l e m S e t 1 (Answers to due in class Tuesday, Feb. 2nd, to be discussed Friday, questions 1-3 Feb. 5th; ) Please denote which recitation you plan to attend on Friday 1. (Nicholson, 2.2). Suppose a firm's total revenues depend on the amount produced ( ) according ; to the function: . Total costs also depend on : 3 . V œ (!;  ; ; G œ !;  ; ## a) What level of output should the produce in order to maximize profits ( )? What will VG profits be? b) Show that the second-order condition for a maximum is satisfied at the output level found in (a). c) Does the solution calculated in (a) obey the "marginal revenue equals marginal cost" requirement. Explain (with mathematical support). 2. Suppose a trucking firm produces deliveries ( ) using capital ( ) and labor ( ) according to the ;5 6 daily production function: . The firm rents capital and labor at rates and ; so ;œ5 6 < A "Î# "Î# total cost is given by: . Set up the firm's Lagrangian for cost subject to Gœ<5A 6 minimizing producing an output level . Write out the problem's first-order conditions. ; 3.
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pset1_s10 - Economics 217 Spring 2010 Problem Set 1...

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