Six per page _ Week8 Part I_Econ2101_S1_2010

Six per page _ Week8 Part I_Econ2101_S1_2010 - The Problem...

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1 Costs 1. Cost Minimization (Ch 20) 2. Cost Curves (Ch 21) The Problem ± Production function: y = f(x x ) Production function: y f(x 1 ,x 2 ). ± Take the output level y 0 as given Take the output level y 0 as given. ± Given the input prices w 1 and w 2 , the cost of an input bundle (x 1 ,x 2 ) is w 1 x 1 + w 2 x 2 . WEEK 8 Part I ECON2101 S1 2010 2 The Problem (contd.) ± For given w 1 , w 2 and y, the firm’s cost-minimization problem is: min , xx wx 12 0 11 22 + subject to x x y 1 2 = f x ( , ) . WEEK 8 Part I ECON2101 S1 2010 3 Solution ± Variable: x1, x2 ± Parameters: w1, w2, y ± x 1 *= x 1 *(w 1 ,w 2 ,y), x 2 * = x 2 *(w 1 ,w 2 ,y) x (w x (w ± The (smallest possible) total cost for producing y output units is therefore cw w y wx w w y ( , ,) * 1 112 = (,, ) . * 22 1 2 + WEEK 8 Part I ECON2101 S1 2010 4 Diagrammatically Speaking ± ISOCOST LINE: A curve that contains all of the input bundles that cost the same amount is an iso-cost curve. ± E.g., given w 1 and w 2 , the $100 iso- cost line has the equation 100 += . WEEK 8 Part I ECON2101 S1 2010 5 Iso-cost Lines ± Generally, given w 1 and w 2 , the equation of the $c iso-cost line is i.e. c 1 1 2 2 + = x w x c 2 1 1 = − + ± Slope is - w 1 /w 2 . w w 2 2 = . WEEK 8 Part I ECON2101 S1 2010 6
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2 Iso-cost Lines x 2 Slopes = -w 1 /w 2 . 200 w 1 x 1 +w 2 x 2 100 w 1 x 1 +w 2 x 2 x 1 WEEK 8 Part I ECON2101 S1 2010 7 The y’-Output Unit Isoquant x 2 All input bundles yielding y’ units All input bundles yielding y units of output. Which is the cheapest? f(x x ) y’ x 1 f(x 1 ,x 2 ) y WEEK 8 Part I ECON2101 S1 2010 8 The Cost-Minimization Problem x 2 All input bundles yielding y’ units All input bundles yielding y units of output. Which is the cheapest?
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This note was uploaded on 05/17/2011 for the course ECON 2103 taught by Professor No during the Fall '10 term at DeVry NJ.

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Six per page _ Week8 Part I_Econ2101_S1_2010 - The Problem...

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