1. Chapter Twelve Uncertainty

2. 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.

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

4. 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.

5. 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.

6. 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.

7. 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

8. 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

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

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

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

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

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

14. 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 risk- averse person might buy some.

15. 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?

16. 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

17. 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

18. 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.