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Unformatted text preview: Keep track of the patterns. Greg Schulz ECON 410 CostMinimization (Mathematical) 1 1 2 2 1 2 ( , ) ( ) w x w x q f x x + + L 2 Class 18  Cost Minimization (Mathematical) 3 Labor Capital Class 18  Cost Minimization (Mathematical) q =1 wK=$1 wL=$2 D 4 CostMinimizing Input Blend If a firms production underlying production set is convex, displays strict free disposal, and the firm is operating efficiently, then if the firm is using both input goods its costminimizing input blend to produce a specified level of output will be at a point such that the slope of the firms isoquant is identical to the slope of the isocost line passing through that point. Class 18  Cost Minimization (Mathematical) 1 1 2 2 f w f w = 5 C r o s s M u l t i p l y 2 1 2 1 w f f w = 1 1 2 2 f w f w = Class 18  Cost Minimization (Mathematical) 6 L K L K w f f w = Class 18  Cost Minimization (Mathematical) 7 Labor Capital Class 18  Cost Minimization (Mathematical) q =1 slope of isocost K L w w 8 L K L K w f f w = Class 18  Cost Minimization (Mathematical) CostMinimization Management Principle As prices and technologies change, a manager needs to always balance the costminimizing best response and the cost of process disruption. Corollary Beware of process paralysis. 9 Class 18  Cost Minimization (Mathematical) The Innovators Dilemma When New Technologies Cause Great Firms to Fail , Clayton M. Christensen 10 Class 18  Cost Minimization (Mathematical) 11 Class 18  Cost Minimization (Mathematical) 12 Class 18  Cost Minimization (Mathematical) 13 Labor Capital Class 18  Cost Minimization (Mathematical) q =1 14 Meals Books I 1 I 2 I 3 I 4 I 5 Class 18  Cost Minimization (Mathematical) 15 Class 18  Cost Minimization (Mathematical) 16 Meals Books I 4 Class 18  Cost Minimization (Mathematical) 17 Class 18  Cost Minimization (Mathematical) Utility Maximization Problem Generates Marshallian demand curves Expenditure Minimization Problem Generates Hicksian demand curves 18 Meals Books I 4 Class 18  Cost Minimization (Mathematical) 19 Class 18  Cost Minimization (Mathematical) Good 1 Good 2 I 2 I 3 xorig Iori g BLne w xnew BLcompe xsubs S I 20 Meals Books I 4 Class 18  Cost Minimization (Mathematical) Hicksian demand curves have no Income Effect 21 Labor Capital Class 18  Cost Minimization (Mathematical) q =1 The CostMinimization Problem has no Income Effects 22 Class 18  Cost Minimization (Mathematical) 23 Class 18  Cost Minimization (Mathematical) 1 2 1 1 2 2 , ) ( ( ) x I p x p x U x = + L 24 Class 18  Cost Minimization (Mathematical) 1 2 1 1 2 2 , ) ( ( ) x I p x U p x x =  + L 25 Class 18  Cost Minimization (Mathematical) How can a firm minimize cost, given that it must produce q units of output? GroupClicker Question (P): A firm is trying to minimize its costs when producing a specific amount of output, q. It uses x1 units of Good 1 and x2 units of Good 2 to produce the output according to the...
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This note was uploaded on 01/05/2012 for the course ECON 410 taught by Professor Codrin during the Fall '07 term at UNC.
 Fall '07
 Codrin

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