profitmaxspring06 - Profit Maximization - Example Suppose f...

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Pro f t Maximization - Example Suppose f ( L, K )=4 L 1 4 K 1 2 .Let prices be p =1 ,w L =2 and w K . Method 1 (direct long run pro f t maximization) max L,K ³ 4 L 1 4 K 1 2 w L L w K K ´ s.t. L 0 ,K 0 In an interior solution, FOC: 4 × 1 4 L 3 4 K 1 2 4 × 1 2 L 1 4 K 1 2 Dividing one condition by the other we f nd 1 2 K L K =4 L. Substitute into the f rst condition and solve for L: 4 × 1 4 L 3 4 (4 L ) 1 2 L K L y L 1 4 K 1 2 =8 . Pro f tequa ls π = AL 1 4 K 1 2 w L L w K K 2 × 1 4=2 . Method 2 Step 1- f nd cost function. Step 2 fond pro f t maximizing output. Step 1: The long run cost is the solution to: min L,K (2 L + K ) s.t. L 0 0 and 4 L 1 4 K 1 2 = y. When y> 0 the solution must be interior. If one of the inputs is zero the quantity produced is zero. In an interior solution we know that TRS = w L w K and f ( L, K )= y K 2 L 4 L 1 4 K 1 2 = 1
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We solve the system. The f rst equation implies that K =4 L. Substituting
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This note was uploaded on 02/23/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).

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profitmaxspring06 - Profit Maximization - Example Suppose f...

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