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lecture08

# lecture08 - Main topics 1 2 3 4 5 6 Consumption under risk...

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Main topics 1. Consumption under risk 2. Decision-making under uncertainty 3. Gambling and avoiding risk 4. Demand for insurance 5. Value of information 6. Behavioral Economics

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Probability distribution relates probability of occurrence to each possible outcome first of two following examples is less certain fig. 1
Calculations Expected values Variance Concepts/Terms Fair bet Risk averse vs. risk neutral vs. risk loving Value of information You should know…

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Fair bet wager with an expected value of zero flip a coin for a dollar: [½ M (1)] + [½ M (-1)] = 0
Gambling Why would a risk-averse person gamble when the bet is unfair? enjoys the game makes a mistake: can’t calculate odds correctly has Friedman-Savage utility fig. 5

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Avoiding risk just say no: don’t participate in optional risky activities obtain information diversify risk pooling diversification can eliminate risk if two events are perfectly negatively correlated
LOTTERIES A “lottery” is the prospect with known (monetary) payoffs, each one with a known probability of occurring Can represent a lottery by a list of payoffs and their corresponding probabilities * payoffs given by: X n , n = 1,…,N * probabilities given by: pr n , n = 1,…,N where 0 < pr n < 1 such that: pr 1 + … + pr N = 1

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A REAL LOTTERY CALIFORNIA MEGA MILLIONS LOTTERY “Match” Prize Odds / Probabilities Prob*Prize -------------------------------------------------------------------------------------------------------------------------------------------- 5+Mega Ball Grand Prize 1 in 175,711,536 (e.g., \$10M) 0.0000000057 \$0.0 5 \$175,000 1 in 3,904,701 0.0000002561 \$0.04 4+Mega Ball \$5,000 1 in 689,065 0.0000014512 \$0.01 1 \$150 1 in 15,313 0.0000653040 \$0.01 3+Mega Ball \$150 1 in 13,781 0.0000725637 \$0.01 2+Mega Ball \$10 1 in 844 0.0011848341 \$0.01 3 \$7 1 in 306 0.0032679739 \$0.02 1+Mega Ball \$3 1 in 141 0.0070921986 \$0.02 Mega Ball \$2 1 in 75 0.0133333333 \$0.03 Nothing \$0 97.5 in 100 0.9749820794 \$0.00 Expected Prize \$0.21 Note: payoffs are made at one time or over many years. Source: www.calottery.com Expected payoff = Expected Prize – Cost of ticket = \$0.21 - \$1.00 = - \$0.79
A LITTLE STATISTICS RANDOM VARIABLE - Takes on values X n with probabilities pr n - Frequency distribution, e.g., bell-shaped grade distribution Probability 1.0 .90 .80 .70 .60 .50 .40 .30 .20 .10 0

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A LITTLE STATISTICS
EXPECTED UTILITY

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Utility of Income
RISK PREFERENCES Q. Is the decision maker willing to take a “fair bet”?

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