uncertainty risk
TRANSCRIPT
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Decision Making Under Uncertaintyand Asymmetric information
Expected Utility
Insurance Premium
Risk Return Analysis
Asymmetric information
Moral Hazard (Hidden action)
Adverse Selection (Hidden information)
http://cepa.newschool.edu/het/home.htm
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Utility Function for Risk Averse Individual
Wealth
( )WU ln=
WL WH
Utility
0
1
( )11
( ) HL WWEW 11 1 +=
( ) ( ) ( )HL WWEU ln1ln 11 +=
Expected utility
Expected wealth
EWCEW
ln(CEW)
InsurancePremium
ln(WH)
ln(WL)
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Utility Function for Risk Averse Individual
Wealth
( )WU ln=
WL WH
Utility
0
1 ( )11
( )( )( ) 0
1
1
1
'
''2
>=
== WW
W
WU
WUWr
Pratt(1964) Measure of risk aversion:
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WeU =
WHWL
Utility Function for Risk Loving Individual
0
Utility
( )11 1
( )( )
( )0
'
''2
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WaU .=
WHWL
Utility Function for Risk Neutral Individual
0
Utility
( )11 1
( )( )( )
00
'
''===
aWU
WUWr
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Wealth
Utility
Uncertainty and Expected Utility
010000 20000
( )WU ln=UH
UL
UEW
UCE
RiskPremium
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Wealth
Utility
Uncertainty and Expected Utility and Insurance Payment
010000 20000
( )WU ln=
5.01 = ( ) 5.01 1 =
EW=15000
9.903
9.616
9.201
9.557
14143
Risk premium15000-14143
= 857
Insurance
payment
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Preference of an Investor Toward Risks Returns
0p
Standard deviation of return to a portfolio
pR
R
eturnona
portfolio
Treasury Bill Stocks
BR
STR
( ) fmp RbbRR += 1
Risks
mRMarketreturn
fR risk freereturn
10
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Optimal Portfolio
0p
Standard deviation of return to a portfolio
pR
Expec
ted
Retur
nonaportfolio
BR
STR
p
m
mf
fp
RR
RR
+=
m
pb
=U1
U2
Not feasibleM
E
Optimal point
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111 2
1R
2R
p
m
mf
fp
RRRR
+=
Expec
ted
Retur
nonaportfolio
Standard deviation of return to a portfolio
U2
U1
Choices of Risk Averse vs Risk Lover in a Financial Market
Risk averse investor.
Risk loving investor.
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Asymmetric information
Equilibrium is affected when someeconomic agents have more information
than others. Market of used cars
Plums: good cars
Lemons: bad cars
Seller knows his quality of cars but buyersdoes not
Market for good cars disappear becauseof existence of bad cars in the market
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Akerlofs Model of Asymmetric Information
SHSL
DL
DH
DM
250 500
10
7.5
DL
DM
500 750
5
7.5
Markets for good carsMarkets for bad carsP
P
Q Q
5
200
Sellers know exactly quality of cars but buyers do not.
Demand for high quality car falls and that for low quality rise, ultimately allLow quality cars remain in the market.
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Signalling for high quality
Warranty and Guarantee
Providing warranty less costly for highquality carsThey last long.
warranty is costly for low quality cars asthey frequently break down.
Principal agent problem
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Adverse Selection (hidden information) Problem
Uncertainty about the quality of good low quality items crowd out high quality items;
Theft insurance; health insurance; risky vs. gentle borrowers in the financialmarket.
Healthy people are less likely to buy health
insurance, people from safe area are less likely to buy
theft insurance
honest borrowers less likely to borrow athigher interest rates.
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Moral hazard (hidden action):
People who have theft insurance are likely
to have easy to break locks in their bicycle(car) and most likely to claim insurances.
Probability of event is affected by theaction of the person
Remedy: deductible amount; to ensurethat some customers take care in security.
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Impacts of Asymmetric information
Equilibrium if inefficient relative to full
information Government can improve the market by
setting high standards Signalling: Warranty
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Education as a signal of quality of workers:
Type 1 is less productive than type 2
worker but an employer cannot distinguish
off-hand.
The marginal productivity of type 1 is less
than that of type 2, 11 aa