Chapter 20 Cost Minimization

# Chapter 20 Cost Minimization - Chapter 20 Cost Minimization...

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Chapter 20 Cost Minimization 20.1) Cost Minimization a) Let (w 1 ,w 2 ) be the prices for inputs (x 1 ,x 2 ) for given level of output y. b) Minimize: w 1 x 1 +w 2 x 2 such that f(x 1 ,x 2 )=y c) Cost function : c(w 1 ,w 2 ,y), the solution to the minimization. d) Isocost lines: w 1 x 1 +w 2 x 2 =C e) For cost minimization, TRS=factor price ratio ( *, *) ( *, *)= *, *=- MP1 x1 x2 MP2 x1 x2 TRSx1 x2 w1w2 f) Conditional factor demand functions (derived factor demands): x 1 (w 1, w 2 ,y) and x 2 (w 1, w 2 ,y) g) Conditional factor demands give the cost minimizing choices for a given level of output, profit maximizing factor demands give the profit maximizing choices for a given price of output. 20.2) Revealed Cost Minimization a) Weak Axiom of Cost Minimization: Given two sets of prices (w 1 t ,w 2 t ) and (w 1 s ,w 2 s ) and associated choices (x 1 t ,x 2 t ) and (x 1 s ,x 2 s ) Then: Δw 1 Δx 1 + Δw 2 Δx 2 ≤0. If Δw

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Chapter 20 Cost Minimization - Chapter 20 Cost Minimization...

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