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Unformatted text preview: Lecture 3: Utility Maximization Optimization Principle Agents choose to allocate their fixed income in such a way as to maximize their utility. To maximize utility, given a fixed amount of income, an individual will buy the goods and services: that exhaust total income (or at least dont exceed total income) Individuals exhaust income if were not considering the future, for which people might want to save for which the MRS is equal to the rate at which goods can be traded for one another in the marketplace The Budget Constraint Assume that 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 FOCs for a Maximum We can add the individuals utility map to show the utilitymaximization process Utility is maximized where the indifference curve is tangent to the budget constraint ( if this tangency exists ). Quantity of x Quantity of y U 1 A The individual can do better than point A by reallocating his budget U 3 C The individual cannot have point C because income is not large enough U 2 B Point B is the point of utility maximization FOCs for a Maximum Quantity of x Quantity of y U 2 B constraint budget of slope...
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.
 Spring '08
 Govel
 Utility

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