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# PS 08 - 3 If w P L L = is the solution to the firm’s...

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Dr. Steven Waters Econ 380 Page 1 of 1 Problem Set #8 Profit Maximization 1) Calculate the profit maximizing amount to produce given the following: The firm’s inverse demand function: q p 8 360 = The firm’s cost function: q TC 4 160 + = Verify the second order conditions for maximization. 2) Calculate the profit maximizing amounts of K and L to hire given the following: The firm’s production function: 3 / 1 3 / 1 9 L K q = Labor costs \$5 and Capital costs \$15 per unit The firm can sell all the output it produces at \$5 per unit.
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Unformatted text preview: 3) If ) , ( * w P L L = is the solution to the firm’s profit maximization problem wL L F P L − ⋅ ) ( max , what is the formula for w w P L ∂ ∂ ) , ( ? (Hint: Think about the Implicit Function Theorem and assume that ) ( ' ' L F is always negative.) 4) Let ) , , ( * w v P q q = be the solution to the firm’s profit maximization problem ) , , ( max w v q TC q P q − ⋅ Derive the formula for P w v P q ∂ ∂ ) , , ( in terms of (among other things) q w v q MC ∂ ∂ ) , , ( ....
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