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Lecture01-2000

# Lecture01-2000 - AEB 6182 Lecture I Professor Charles Moss...

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AEB 6182 Lecture I Professor Charles Moss 1 Expected Utility Lecture I I. Basic Utility A. A typical economic axiom is that economic agents (consumers, producers, etc.) behave in a way that maximizes their expected utility. The typical formulation is: ( 29 Y x p x p st x x U x x + 2 2 1 1 2 1 , , max 2 1 where x 1 and x 2 are consumption goods and Y is monetary income. In decision making under risk, we are typically interested in the utility of income U(Y). How do these concepts relate? B. The linkage between these two concepts is the indirect utility function which posits optimizing behavior by the economic agent. Specifically, assuming an Cobb-Douglas utility function the general utility maximization problem can be rewritten as: Y x p x p st x x x x + 2 2 1 1 2 1 , 2 1 max b a Due to the concavity of the utility function, the inequality can be replaced with an equality. The maximization problem can then be reformulated as a Lagrangian: ( 29 2 2 1 1 2 1 x p x p Y x x L - - + = l b a The first order conditions are then: 0 0 0 2 2 1 1 2 2 2 1 2 1 1 2 1 1 = - - = = - = = - = x p x p Y L p x x x x L p x x x x L l l b l a b a b a Taking the ratio of the first two first order conditions yields 2 1 1 2 p p x x a b = Substituting this result into the third first order condition yields the demand for x 1 as a function of prices and income ( 29

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