18_CostMinimization_Mathematical_ToPost-1

# 18_CostMinimization_Mathematical_ToPost-1 - “Keep track...

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Unformatted text preview: “Keep track of the patterns.” –Greg Schulz ECON 410 Cost-Minimization (Mathematical) 1 1 2 2 1 2 ( , ) ( ) w x w x q f x x λ + +- L 2 Class 18 - Cost Minimization (Mathematical) 3 Labor Capital Class 18 - Cost Minimization (Mathematical) q =1 wK=\$1 wL=\$2 D 4 Cost-Minimizing Input Blend If a firm’s 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 cost-minimizing input blend to produce a specified level of output will be at a point such that the slope of the firm’s 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) Cost-Minimization Management Principle As prices and technologies change, a manager needs to always balance the cost-minimizing best response and the cost of process disruption. Corollary Beware of process paralysis. 9 Class 18 - Cost Minimization (Mathematical) “ The Innovator’s 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 Cost-Minimization 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 λ = +-- L 24 Class 18 - Cost Minimization (Mathematical) 1 2 1 1 2 2 , ) ( ( ) x I p x U p x x λ = - +-- L 25 Class 18 - Cost Minimization (Mathematical) “How can a firm minimize cost, given that it must produce q units of output?” Group-Clicker 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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18_CostMinimization_Mathematical_ToPost-1 - “Keep track...

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