Chapter Twelve Uncertainty Uncertainty is Pervasive u

Chapter Twelve Uncertainty

Uncertainty is Pervasive u What is uncertain in economic systems? – tomorrow’s prices – future wealth – future availability of commodities – present and future actions of other people.

Uncertainty is Pervasive u What are rational responses to uncertainty? – buying insurance (health, life, auto) – a portfolio of contingent consumption goods.

States of Nature u Possible states of Nature: – “car accident” (a) – “no car accident” (na). u Accident occurs with probability a, does not with probability na ; a + na = 1. u Accident causes a loss of $L.

Contingencies u. A contract implemented only when a particular state of Nature occurs is state-contingent. u E. g. the insurer pays only if there is an accident.

Contingencies u. A state-contingent consumption plan is implemented only when a particular state of Nature occurs. u E. g. take a vacation only if there is no accident.

Preferences Under Uncertainty u Think of a lottery. Suppose U(x) = x. 5 u Win $100 with probability 1/2 and win $0 with probability 1/2. u U($100) = 10, U($0) = 0. u Expected utility is

Preferences Under Uncertainty u Think of a lottery. u Win $90 with probability 1/2 and win $0 with probability 1/2. u Expected money value of the lottery is

Preferences Under Uncertainty U($50) > EU risk-aversion. 10 U($50) MU declines as wealth rises. EU=5 $0 $50 $100 Wealth

Preferences Under Uncertainty 10000 U($50) < EU risk-loving. Example: U(x) = x 2. EU = 5000. U(50) = 2500 EU=5000 MU rises as wealth rises. U($50) $0 $50 $100 Wealth

Preferences Under Uncertainty U($50) = EU risk-neutrality. Example: U(x) = 4 x + 5 405 U($50)= EU=205 5 $0 MU constant as wealth rises. $50 $100 Wealth

Preferences Under Uncertainty u State-contingent consumption plans that give equal expected utility are equally preferred.

Choice Under Uncertainty u Q: How is a rational choice made under uncertainty? u A: Choose the most preferred affordable state-contingent consumption plan.

Competitive Insurance u Suppose entry to the insurance industry is free. u Expected economic profit = 0. o If price of $1 insurance = accident probability, then insurance is fair. o Even if insurance is ‘unfair’, a riskaverse person might buy some.

Diversification u Two firms, A and B. Shares cost $10. u With prob. 1/2 A’s profit is $100 and B’s profit is $20. u With prob. 1/2 A’s profit is $20 and B’s profit is $100. u You have $100 to invest. How?

Diversification u Buy only firm A’s stock? u $100/10 = 10 shares. u You earn $1000 with prob. 1/2 and $200 with prob. 1/2. u Expected earning: $500 + $100 = $600

Diversification u Buy only firm B’s stock? u $100/10 = 10 shares. u You earn $1000 with prob. 1/2 and $200 with prob. 1/2. u Expected earning: $500 + $100 = $600

Diversification u Buy 5 shares in each firm? u You earn $600 for sure. u Diversification has maintained expected earning and lowered risk. u Typically, diversification lowers expected earnings in exchange for lowered risk.