lecture12kg - Introduction to Microeconomics Lecture 12...

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Unformatted text preview: Introduction to Microeconomics Lecture 12 More Differentiation and Optimization Kathryn Graddy Outline More Economic Applications Cost Functions Profit Maximization The Product Rule and The Chain Rule Economic Applications Elasticity and Revenues The Monopolists Inverse Elasticity Rule Cost Functions What are the variable and fixed costs? How do you find marginal cost? How do you find average cost? 2 ( ) 9 C y y = + Marginal and Average Cost 2 ( ) 9 ( ) '( ) 2 9 ( ) C y y MC y C y y C AC y y y y = + = = = = + Relationship of Marginal cost to Minimum Average Cost Lets show algebraically that the marginal cost function passes through the average cost function at the minimum AC MC Finding the Minimum Average Cost 1 2 2 2 9 ( ) 9 9 1 9 1 9 3 (or -3) C AC y y y y y y dAC y dy y y y-- = = + = + =- =- = = = How do You Know this is a Minimum? 2 2 3 2 1 9 18 dAC y dy d AC y d y-- =- = Does the marginal cost function pass through the average cost function at its minimum?...
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This note was uploaded on 04/12/2010 for the course ECON DEAM taught by Professor Vines during the Spring '10 term at Oxford University.

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lecture12kg - Introduction to Microeconomics Lecture 12...

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