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Unformatted text preview: UNCERTAINTY 5 Econ 100A Mortimer Uncertainty and Consumer Behavior 1. We will quantify risk. 2. We will examine people’s preferences toward risk. 3. We will see how people can sometimes reduce or eliminate risk. We will study the ways that people can compare and choose among risky alternatives, and how they may able to reduce or eliminate risk. Econ 100A Mortimer DESCRIBING RISK Probability ● probability Likelihood that a given outcome will occur. Subjective probability is the perception that an outcome will occur. ● expected value Probabilityweighted average of the payoffs associated with all possible outcomes. Expected Value ● payoff Value associated with a possible outcome. The expected value measures the central tendency — the payoff or value that we would expect on average. Econ 100A Mortimer Coin toss: Heads with a probability of 0.5 > $100 Tails with a probability of 0.5 > $0 Expected value or payoff: EV = 0.5 x $100 + 0.5 x $0 = $50 More generally, EV = p 1 X 1 +p 2 X 2 +… p n X n where p i is the probability of outcome i and X i is the return (or payoff) in the event of outcome i (Note that p 1 +p 2 +….+ p n = 1) DESCRIBING RISK Variability ● variability Extent to which possible outcomes of an uncertain event differ. ● deviation Difference between expected payoff and actual payoff. Healthy Getting Ill Probability Wealth ($) Probability Wealth ($) Expected Wealth ($) Illness 1: Illness 2: .5 .8 10,000 10,000 8,000 5,000 .5 .2 9,000 9,000 Probability of Getting Sick and Wealth ● standard deviation Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values. Econ 100A Mortimer 2000 = 4000000 = ) 16000000 ( 2 . + ) 100000 ( 8 . = ) 000 9 5000 ( 2 . + ) 9000 10000 ( 8 . 1000 = 1000000 = ) 00 90 8000 ( 5 . + ) 9000 10000 ( 5 . 2 2 2 2 Illness 1: Illness 2: ] E(X)) [(X p + ] E(X)) [(X p = 2 2 2 2 1 1 σ DESCRIBING RISK Variability Illness 2 has a greater standard deviation and is more risky. A risk averse person would be less concerned about Illness 1 that has a lower standard deviation (let’s set aside physical pain and discomfort – we are just focusing on money here). What if Illness 2, although it has a higher standard deviation, does not cost as much as $5,000 so that an individual is left with a higher expected wealth? e.g., If it costs $3,000 to treat, the expected wealth is $9,400 (=0.8x$10,000+0.2x$7,000) and the standard deviation is $1,200 (=sqrt[0.8($600) 2 +0.2($2,400) 2 ]) One cannot eliminate the risk of illness but can mitigate financial risk by purchasing health insurance. purchasing health insurance....
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This note was uploaded on 04/24/2009 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at Berkeley.
 Spring '08
 Woroch

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