北京大学：《微观经济学》Chapter Twelve Uncertainty 不确定性

Chapter twelve Uncertainty 不确定性

Chapter Twelve Uncertainty 不确定性

Structure State contingent consumption(依情 形而定的消费) Preferences under uncertainty Attitudes toward risk State-contingent budget constraint Choice under uncertainty Diversification and risk spreading

Structure State contingent consumption (依情 形而定的消费） Preferences under uncertainty Attitudes toward risk State-contingent budget constraint Choice under uncertainty Diversification and risk spreading

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 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? buying insurance(health, life, auto a portfolio of contingent consumption goods

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

States of Nature Possible states of nature: car accident(a) “ no car accident”(na) Accident occurs with probability n does not with probability Tna j a na Accident causes a loss of sl

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

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

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

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

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

Preferences Under Uncertainty 2 states of nature At probability Ta consumption is a At probability Tna, consumption is na +兀=1 Utility is U(ca, Cna, Tay Tna)

Preferences Under Uncertainty 2 states of nature: –At probability a , consumption is ca –At probability na , consumption is cna – a + na = 1. Utility is U(ca , cna, a , na)

Preferences Under Uncertainty Expected utility function Von-Neuman-Morgenstern utility function EU=U(C)+IU(Cn) Positive affine transformation vu=au+b, a>0

Preferences Under Uncertainty EU U(c ) U(c ) = +   a na a na Expected utility function Von-Neuman-Morgenstern utility function Positive affine transformation v(u)=au+b, a>0

Preferences Toward risk Risk averse Risk neutral Risk loving

Preferences Toward Risk Risk averse Risk neutral Risk loving