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Chapter Twelve

Chapter Twelve. Uncertainty. Uncertainty is Pervasive. 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. What are rational responses to uncertainty?

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Chapter Twelve

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  1. Chapter Twelve Uncertainty

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

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

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

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

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

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

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

  10. Preferences Under Uncertainty U($50) < EU  risk-loving. Example: U(x) = x2. EU =5000. U(50) = 2500 10000 MU rises as wealth rises. EU=5000 U($50) $0 $50 $100 Wealth

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

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

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

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

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

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

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

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

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