L12Optimisation - Introduction to Microeconomics More...

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1 Introduction to Microeconomics Lecture 12 More Differentiation and Optimization Simon Cowan Outline z more economic applications z cost functions z profit maximization th d t l th i f ti l d th z the product rule, the inverse function rule and the chain rule z economic applications z elasticity and revenue z the monopolist’s inverse elasticity rule Cost Functions N N 2 Fixed Cost Variable Cost ( ) 9 C Q Q = + z How do we find marginal cost? z How do we find average cost? Marginal and Average Cost 2 ( ) 9 for 0 ( ) ( ) 2 C Q Q Q MC Q C Q Q = + 9 ( ) C AC Q Q Q Q = = = = + Relationship of Marginal cost to Minimum Average Cost z Let’s show algebraically that the marginal cost function passes through the average cost function at the minimum AC MC Finding the Minimum Average Cost 1 9 ( ) 9 C AC Q Q Q Q Q Q = = + = + 2 2 2 9 1 9 1 0 9 3 ( 3 is ruled out) dAC Q dQ Q Q Q = = = = =
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