Consumer Theory 8

# Consumer Theory 8 - Economics 21 Intermediate...

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Economics 21 Intermediate Microeconomics Topic 2: Consumer Theory (viii) Risk & Uncertainty

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I. Introduction We have so far assumed that the world is certain This is a bit … silly? This world is inherently uncertain The same people who insure their cars and houses also but lottery tickets and play bingo! Why?
II. Uncertainty Assume that there are two states of the world State 1: Wealth = w 1 State 2: Wealth = w 2 = w 1 - L where L > 0 occurs with probability p > 0 Expected wealth: w = 1- π ( 29 ϖ 1 + πϖ 2

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II. Uncertainty Expected wealth: ( 29 ( 29 ( 29 1 2 1 1 1 1 1 1 1 1 w p w pw w p w p w L w w pw pw pL w w pL = - + Þ = - + - Þ = - + - Þ = -
II. Uncertainty Individuals are not interested in wealth per se , but in the utility of wealth This is an important distinction; an increase in wealth of £100 is unlikely to change the utility of a prince (David Beckham? A-Rod?) and a pauper (me!) by the same amount Assume individual’s utility function is u = u ( w ) Individual’s objective is to maximise expected utility, not expected wealth!

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II. Uncertainty Utility function: We assume that total utility increases with wealth such that marginal utility is positive: u = υ ϖ ( 29 du dw = υϖ ( 29 0
II. Uncertainty Expected Utility: Add and subtract u ( w 2 ) ( 29 ( 29 ( 29 1 2 1 u p u w pu w = - + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 2 2 1 2 1 1 u u w p u w pu w u w u u w p u w u w = + - + - Þ é ù = + - - ë û

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II. Uncertainty
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## This note was uploaded on 07/16/2010 for the course ECON 21 taught by Professor Johng.sessions during the Summer '09 term at Dartmouth.

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Consumer Theory 8 - Economics 21 Intermediate...

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