Chapter20 - (a increasing returns to scale implies...

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Chapter 20 - Cost Minimization 1. Cost minimization problem (a) minimize cost to produce some given level of output: min w 1 x 1 + w 2 x 2 s.t. f ( x 1 ,x 2 ) = y (b) geometric solution: slope of isoquant equals slope of isocost curve. (see figure 20.1. in the textbook) (c) equation is: w 1 /w 2 = MP 1 /MP 2 (d) in words: the technical rate of substitution should equal the factor price ratio (e) optimal choices of factors are the conditional factor demand functions x i ( w 1 ,w 2 ,y ) - not to be confused with the factor demand functions x i ( w 1 ,w 2 ,p ) obtained from profit maximization ! (f) optimal cost is the cost function c ( w 1 ,w 2 ,y ) (g) examples if f ( x 1 ,x 2 ) = x 1 + x 2 , then c ( w 1 ,w 2 ,y ) = min { w 1 ,w 2 } y if f ( x 1 ,x 2 ) = min { x 1 ,x 2 } , then c ( w 1 ,w 2 ,y ) = ( w 1 + w 2 ) y can calculate other answers (e.g. Cobb-Douglas) using calculus (La- grangian Method) 2. Returns to scale and the cost function
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Unformatted text preview: (a) increasing returns to scale implies decreasing AC (b) constant returns implies constant AC (c) decreasing returns implies increasing AC 3. Long-run and short-run costs (a) long run: all inputs variable • c s ( y, x 2 ) = w 1 x s 1 ( w 1 ,w 2 , x 2 ,y ) + w 2 x 2 (b) short run: some inputs Fxed • c ( y ) = w 1 x 1 ( w 1 ,w 2 ,y ) + w 2 x 2 ( w 1 ,w 2 ,y ) 4. ±ixed and quasi-Fxed costs (a) Fxed: must be paid, whatever the output level • there are no Fxed costs in the long-run ! (b) quasi-Fxed: only paid when output is positive (heating, lighting, etc.) (c) sunk costs : costs that cannot be recovered 1...
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