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?
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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 = -
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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
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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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Consumer Theory 8 - Economics 21 Intermediate...

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