321_19 - ECON 321 Spring 2011 Lecture 19 Chapter 23...

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ECON 321 Spring 2011: Lecture 19 Chapter 23: Industry Supply and Chapter 24: Monopoly
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Another Algorithm Just as in utility maximization we have a step-by-step process to minimize costs subject to an output constraint.
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Step 1 Is the technology linear? i.e. is it of the form: No: move to step 2 Yes: Perfect Substitutes. Try both corners and choose the one with the lowest cost: i.e. check: 2 1 2 1 ) , ( bx ax x x f + = ) / ( * ) / ( * 2 1 b y w and a y w
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Step 2 It wasn’t linear, is it a minimum function? i.e. is it of the form: No: go to step 3 Yes: set the expressions on either side of the comma equal to each other. i.e. the optimality condition is: } , min{ ) , ( 2 1 2 1 bx ax x x f = y bx ax = = 2 1
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Are the isoquant curves convex? Yes: Optimality condition is: Solve for one variable in terms of the other and plug into the output constraint. ( 29 ( 29 2 1 (.) (.) 2 1 2 1 2 1 : . . : . . w
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321_19 - ECON 321 Spring 2011 Lecture 19 Chapter 23...

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