lect9

# lect9 - Review for Final Exam Intermediate Microeconomics...

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Review for Final Exam Intermediate Microeconomics Amy Brown University of California, Los Angeles September 8, 2008 A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 1 / 20

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Outline of Lecture 1 Review for Final Exam, Wednesday, September 10, 2008 2 Overview of topics 3 Break 4 Answers to Practice Final Exam A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 2 / 20
Important Assumptions of Course Scarcity of Resources Principle of Rationality Ceteris Paribus A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 3 / 20

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Mathematical Tools Constrained Optimization L = f ( x , y ) + λ ( g ( x , y )) where f ( x , y ) is the objective function and g ( x , y ) ° 0 is our constraint. Implicit Function Theorem ± dy dx = f ( x , y ) x f ( x , y ) y ° ° ° ° ° ° f ( x , y )= k Homogeneity of degree k f ( tx , ty ) = t k f ( x , y ) Duality of Constrained Optimization Problems Envelope Theorem (Shephard°s Lemma and Roy°s Identity) A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 4 / 20
Consumer Choice Opportunity Cost Utility, as de±ned by axioms of rational choice Completeness Transitivity Continuity Convexity Monotonicity Budget set A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 5 / 20

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Method of Solution General MRS xy = p x p y M = p x x + p y y Perfect Complements U ( x , y ) = min f ax , by g ax = by M = p x x + p y y Perfect Substitutes U ( x , y ) = ax + by a b > p x p y = ) x = M p x a b < p x p y = ) y = M p y a b = p x p y = ) M = p x x + p y y A. Brown (UCLA) Econ 11 Lecture 9 09/08/08 6 / 20
Demand Function 1 Solve constrained optimization problem for generic prices and level of constraint function, i.e. p x , p y , M , p x , p y , U or v , w , q . 2 Resulting equations give you optimizing demand at every price and level of constraint function.

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