12章讲义

State-Contingent Budget Constraints
Cna
m The endowment bundle.
m L Cna Ca 1 1
slope
mL

1
Where is the most preferred state-contingent consumption plan?
Preferences Under Uncertainty
Expected utility function
Von-Neuman-Morgenstern utility function
EU a U(ca ) na U(cna )
Preferences Under Uncertainty
dEU a MU(ca )dca na MU(cna )dcna
dEU 0 a MU(ca )dca na MU(cna )dcna 0
Preferences Under Uncertainty
EU a U(ca ) na U(cna )
dEU a MU(ca )dca na MU(cna )dcna
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.
m L Ca

State-Contingent Budget Constraints
Cna
m The endowment bundle.
m L Cna Ca 1 1
slope
mL
Affordable plans

1
Where is the most preferred state-contingent consumption plan?
State-Contingent Budget Constraints
Buy
$K of accident insurance. Cna = m - K. （ K 为premium(保费)） Ca = m - L - K + K = m - L + (1- )K. So K = (Ca - m + L)/(1- ) And Cna = m - (Ca - m + L)/(1- ) m L I.e. Cna Ca 1 1
m L Ca

State-Contingent Budget Constraints
Cna
More preferred m Where is the most preferred state-contingent consumption plan?
mL
m L Ca

State-Contingent Budget Constraints
Preferences Under Uncertainty
EU a U(ca ) na U(cna )
dEU a MU(ca )dca na MU(cna )dcna
Preferences Under Uncertainty
EU a U(ca ) na U(cna )
Buy
$K of accident insurance. Cna = m - K. Ca = m - L - K + K = m - L + (1- )K. So K = (Ca - m + L)/(1- ) And Cna = m - (Ca - m + L)/(1- )
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.
Buy
$K of accident insurance. Cna = m - K. Ca = m - L - K + K = m - L + (1- )K. So K = (Ca - m + L)/(1- )
State-Contingent Budget Constraints
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.
m L Cna Ca 1 1
slope
mL

1
m L Ca

State-Contingent Budget Constraints
Cna
m The endowment bundle.
Байду номын сангаас
m L Cna Ca 1 1
slope
Uncertainty is Pervasive
What
are rational responses to uncertainty? – buying insurance (health, life, auto) – a portfolio of contingent consumption goods.
mL

1
Where is the most preferred state-contingent consumption plan?
m L Ca

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).
Cna
Most preferred affordable plan m
mL
m L Ca

State-Contingent Budget Constraints
Cna
Most preferred affordable plan m
State-Contingent Budget Constraints
$1 of accident insurance costs . Consumer has $m of wealth. Cna is consumption value in the noaccident state. Ca is consumption value in the accident state.
Chapter Twelve
Uncertainty
Structure
State
contingent consumption (依情 形而定的消费） State-contingent budget constraint Preferences under uncertainty Choice under uncertainty Risk aversion Diversification and risk spreading
State-Contingent Budget Constraints
Cna
m The endowment bundle.
m L Cna Ca 1 1
mL
m L Ca

State-Contingent Budget Constraints
Cna
m The endowment bundle.
dEU 0 a MU(ca )dca na MU(cna )dcna 0
a MU(ca )dca na MU(cna )dcna
dcna a MU(ca ) . dca na MU(cna )
Preferences Under Uncertainty
Cna Indifference curves EU1 < EU2 < EU3
dcna a MU(ca ) dca na MU(cna )
EU3 EU2 EU1
Ca
Choice Under Uncertainty
Q:
How is a rational choice made under uncertainty? A: Choose the most preferred affordable state-contingent consumption plan.
Each
State-Contingent Budget Constraints
Cna
Ca
State-Contingent Budget Constraints
Cna
A state-contingent consumption with $17 consumption value in the accident state and $20 consumption value in the no-accident state.