ch04 - Chapter 4 UTILITY MAXIMIZATION AND CHOICE 1 Our...

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1 Chapter 4 UTILITY MAXIMIZATION AND CHOICE
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2 Our Consumption Choices Our decisions can be divided in two parts We have to determine all available choices, given our income: BUDGET CONSTRAINT Of all the available choices we choose the one that we prefer: PREFERENCES, UTILITY FUNCTIONS, and INDIFFERENCE CURVES
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3 The Budget Constraint • If an individual has I dollars to allocate between good x and good y p x x + p y y I Quantity of x Quantity of y The individual can afford to choose only combinations of x and y in the shaded triangle If all income is spent on y , this is the amount of y that can be purchased y p I If all income is spent on x , this is the amount of x that can be purchased x p I
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4 First-Order Conditions for a Maximum • Utility is maximized where the indifference curve is tangent to the budget constraint Quantity of x Quantity of y U 2 B constraint budget of slope y x p p y U x U dx dy U constant curve ce indifferen the of slope MRS dx dy p p U y x constant - MRS y U x U p p y x
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5 Second-Order Conditions for a Maximum • The tangency rule is only necessary but not sufficient unless we assume that MRS is diminishing – if MRS is diminishing, then indifference curves are strictly convex • If MRS is not diminishing, then we must check second-order conditions to ensure that we are at a maximum
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Second-Order Conditions for a Maximum • Example in which the tangency condition is satisfied but we are not at the optimal bundle Quantity of x Quantity of
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This note was uploaded on 01/11/2011 for the course ECON 11 taught by Professor Cunningham during the Fall '08 term at UCLA.

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ch04 - Chapter 4 UTILITY MAXIMIZATION AND CHOICE 1 Our...

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