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Unformatted text preview: Expected Utility: Lecture X Charles B. Moss September 10, 2010 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 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? B. The linkage between these two concepts is the indirect utility function which posits optimizing behavior by the economic agent. Specifically, assuming an CobbDouglas utility function the gen eral utility maximization problem can be rewritten as max x 1 ,x 2 x 1 x 2 s . t .p 1 x 1 + p 2 x 2 Y (2) 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 1 x 2 + ( Y p 1 x 1 p 2 x 2 ) ( 3 ) The first order conditions are then 1 AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture X Fall 2010 L x 1 = x 1 x 2 x 1 p 1 = 0 L x 2 = x 1 x 2 x 2 p 2 = 0 L = Y p 1 x 1 p 2 x 2 = 0 (4) Taking the ratio of the first two first order conditions yields x 2 = x 1 p 1 p 2 (5) Substituting this result into the third first order condition yields...
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This note was uploaded on 02/01/2012 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.
 Fall '08
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