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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 ) y f(x 1 ,x 2 ). Take the output level y 0 as given 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: i min , x x w x w x 1 2 0 1 1 2 2 + subject to f x x y ( ) 1 2 = , . 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 c w w y w x w w y ( , , ) ( , , ) * 1 2 1 1 1 2 = w x w w y ( , , ). * 2 2 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- , the $100 iso cost line has the equation w x w x 1 1 2 2 100 + = . 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. w x w x 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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