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

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