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Unformatted text preview: “The myth of unlimited production brings war in its train as inevitably as clouds announce a storm.” –Albert Camus ECON 410 Production Fundamentals 2 Class 14  Preferences Over Risk Risk Averse An individual is Risk Averse if 1. Intuitively, the individual would avoid a 50/50 even bet where possible. 2. Intuitively, the individual dislikes risk and would pay to avoid it. 3. u(x) is strictly concave (diving board), where u(x) is the individual’s vNM utility over money. 4. u’’(x) < 0 3 Class 14  Preferences Over Risk Risk Neutral An individual is Risk Neutral if 1. Intuitively, the individual is indifferent to a 50/50 even bet. 2. Intuitively, the individual is indifferent to risk and would not pay to avoid it. 3. u(x) is linear where u(x) is the individual’s vNM utility over money. 4. u’’(x) =0 4 Class 14  Preferences Over Risk Risk Loving An individual is Risk Loving if 1. Intuitively, the individual would take a 50/50 even bet where possible. 2. Intuitively, the individual likes risk and would pay for a gamble. 3. u(x) is convex (skate ramp) where u(x) is the individual’s vNM utility over money. 4. u’’(x) >0 GroupClicker Question (P) An individual’s vNM utility function over money is u(x)=x2/3+ 2. If I offered the individual a 50/50 bet over $5 (they win $5 if its heads and they lose $5 if its tails), would they take it? 1. Yes 2. No 6 Class 14  Preferences Over Risk 7 Class 14  Preferences Over Risk Wealth vNM Utility GroupClicker Question (P): What is the expected utility of a lottery that gives you a wealth of $1 with 50% probability and a wealth of $5 with 50% probability when your vNM utility function is as shown? 1. 2.5 2. 3 3. 3.7 9 Class 14  Preferences Over Risk Wealth vNM Utility 10 Class 14  Preferences Over Risk Wealth vNM Utility EU 11 Class 14  Preferences Over Risk Wealth vNM Utility EU 12 Class 14  Preferences Over Risk Wealth vNM Utility EU 13 Class 14  Preferences Over Risk Wealth vNM Utility EU 14 Class 14  Preferences Over Risk 15 Class 14  Preferences Over Risk 16 Class 14  Preferences Over Risk Risk Premium Consider a risk averse individual with vNM utility for money, u(x). The Risk Premium of a particular lottery with expected value, EV, is 1. The amount less than EV she would accept in exchange for the lottery. 2. Intuitively, the “fee” paid to avoid the risk inherent to the lottery. 3. The value, r, such that u(EVr)=EU where EU is the expected utility of the lottery. 17 Class 14  Preferences Over Risk Wealth vNM Utility EU r EV EVr 18 Class 14  Preferences Over Risk Wealth vNM Utility EU r EV EVr 19 Class 14  Preferences Over Risk Risk Premium 3. The value, r, such that u(EVr)=EU...
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 Fall '07
 Codrin
 Risk premium, vNM utility

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