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# microbook_3e-page90 - o how much should it produce o how...

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Profit Maximization with Two Inputs x In a perfectly competitive industry: o firms are price takers in both input output markets, o firms cannot affect the price of their product, nor can they affect the price of inputs (wages, rental rate on kapital) . x Assume that a firm produces X with kapital and labor and that its production function is given by: X = K 2/3 *L 1/3 x Assume also that: o price of the firm’s output is \$1 o wage rate and rental rate are both \$0.53 x So its profits are given by: Ȇ = p x X – r*K – w*L = \$1* K 2/3 *L 1/3 – \$0.53*K – \$0.53*L X x and firm should hire labor until MPL x p w Profit Maximization with Two Inputs x If the firm has 20 units of kapital on hand (this is the short-run) : o how much labor should it hire?
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Unformatted text preview: o how much should it produce? o how much profit will it make? Output of X Kapital Labor MPL 14.74 20 8 0.61 15.33 20 9 0.57 15.87 20 10 0.53 16.39 20 11 0.50 16.87 20 12 0.47 x In the case depicted, the firm: o would hire 10 labor units o would produce 15.87 units of X o would make zero profit … (I’m foreshadowing Lecture 8 a little here) Ȇ * = \$1* 15.87 – \$0.53*20 – \$0.53* 10 = \$0 x Hiring more labor or less labor would lower profit: Ȇ 8 = \$1* 14.74 – \$0.53*20 – \$0.53* 8 = – \$0.14 Ȇ 9 = \$1* 15.33 – \$0.53*20 – \$0.53* 9 = – \$0.07 Ȇ 11 = \$1* 16.39 – \$0.53*20 – \$0.53* 11 = – \$0.03 Ȇ 12 = \$1* 16.87 – \$0.53*20 – \$0.53* 12 = – \$0.06 Page 90...
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