Slides10-2010

# Slides10-2010 - Outline Basic Utility Expected Utility...

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Outline Basic Utility Expected Utility Expected Utility: Lecture X Charles B. Moss September 10, 2010 Charles B. Moss Expected Utility

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Outline Basic Utility Expected Utility Basic Utility Marshallian Demand Indirect Utility Function Expenditure Function Expected Utility Charles B. Moss Expected Utility
Outline Basic Utility Expected Utility Marshallian Demand Indirect Utility Function Expenditure Function Basic Utility I A typical economic axiom is that economic agents (consumers, producers, etc.) behave in a way that maximizes their expected utility. The typical formulation is max x 1 , x 2 U ( x 1 , x 2 ) s . t . p 1 x 1 + p 2 x 2 Y (1) 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? Charles B. Moss Expected Utility

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Outline Basic Utility Expected Utility Marshallian Demand Indirect Utility Function Expenditure Function I The linkage between these two concepts is the indirect utility function which posits optimizing behavior by the economic agent. SpeciFcally, assuming an Cobb-Douglas utility function the general utility maximization problem can be rewritten as max x 1 , x 2 x α 1 x β 2 s . t . p 1 x 1 + p 2 x 2 Y (2) I 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 L = x α 1 x β 2 + λ ( Y p 1 x 1 p 2 x 2 )( 3 ) Charles B. Moss Expected Utility
Outline Basic Utility Expected Utility Marshallian Demand Indirect Utility Function Expenditure Function I The frst order conditions are then L x 1 = α x α 1 x β 2 x 1 λ p 1 =0 L x 2 = β x α 1 x β 2 x 2 λ p 2 L ∂λ = Y p 1 x 1 p 2 x 2 (4)

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## This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Slides10-2010 - Outline Basic Utility Expected Utility...

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