Download Choice with uncertainty examples from 2-17 File

Consumer Choice With Uncertainty
Part II: Examples
Agenda:
1. Market for Lemmons
2. Insurance & The Death Spiral
“The Market for Lemons: Quality Uncertainty
and the Market Mechanism”
by George A. Akerlof (1970)
QJE 84(3) 488 - 500
http://en.wikipedia.org/wiki/The_Market_for_Lemons
If a good car is worth $10,000 and a “lemon”
car is worth $2,000 how much would you be
willing to pay for a car if you think 20% of cars
are lemons and your utility = sqrt(M)?
.8 10, 000  .2 2, 000  X
What units?
7911  X
Test Yourself: If you owned a “good” car would you be willing to sell it for the
“market” price? If you want to buy a car and know this (owners of good cars
won’t sell) then how much would you be willing to pay?
Market Failure!
Is your $10,000 car worth $10,000 if you can’t sell it?
Because we are risk averse we are
willing to pay MORE than the
expected loss to reduce risk!
→ gains from trade!!
Key Formula
Expected Utility WITH Risk = Expected Utility WITHOUT (with less) Risk
N
N
 pU (M )   p U (M
i 1
i
i
j 1
j
j
 X)
What we are willing to pay!
Example: (U = sqrt(M))
Your car is worth $3,000. You have a 10% chance of having it stolen
without recovery. How much would you pay for insurance that
would pay 100% of your car’s value if stolen?
.9 3000  .1 0  3000  X
49.295  3000  X
2430  3000  X
X  570
Test yourself: What would you be willing to pay if you were risk neutral (U=M)?
Insurance – Adverse Selection & “The Insurance Death Spiral”
Assume there are two groups in the population: healthy people have a 10%
chance of having $360 in expenses and sick people have a 50% chance of having
$360 in expenses. If everyone starts with $1000 in wealth and U = sqrt(M), what
is the most each group would be willing to pay for insurance?
sick
healthy
.9
$1,000
.1
.5
$640
$1,000
.9 1, 000  .1 640  1000  X
$39.62
.5
$640
.5 1, 000  .5 640  1000  X
$190
Healthy people have a 10% chance of having $360 in expenses. If they start with $1000 in
wealth and U = sqrt(M), what is the most healthy people would be willing to pay for insurance?
What is the expected value (amount of money in the bank with risk)?
What is the expected utility (happiness with risk)?
How much money for sure (without risk) would make you as happy as your expected utility?
31.62
30.99
$1,000 - $960.38 = $39.62
Willing to pay for insurance
25.30
Test yourself: What is the utility
of the expected value and where
should it go on the graph?
$640
$960.38 $964 $1,000
Insurance – Adverse Selection & “The Insurance Death Spiral”
Assume there are two groups in the population: healthy people have a 10%
chance of having $360 in expenses and sick people have a 50% chance of having
$360 in expenses. If everyone starts with $1000 in wealth and U = sqrt(M), what
is the most each group would be willing to pay for insurance?
.5
.5
sick
healthy
.9
.1
.5
.5
$1,000
$640
$1,000
$640
$39.62
$190
$360
$0
$0
$360
.5*.1*$360 + .5*.5*360 = $108
What will happen to
the market if they
charge this?
If a risk-neutral insurer could not tell who is in which group, what premium would
it have to charge to cover expected losses?
Mark Pauly The Economics of Moral Hazard: Comment
The American Economic Review 58(3):1968
Price of Medical Care
D2’: mild illness
D3’: serious illness
D2’ and D3’: Inelastic demand
no change in quantity at any price
D2
D3’
D2 and D3: Elastic demand
Lower price, higher quantity
Marginal cost
1
Efficiency
Loss
Efficiency
Loss
50
150
200
300
AFP for D2’& D3’: ½ * 0 + ¼*$50 + ¼*$200 = $62.5
Quantity of
Medical Care
AFP for D2 & D3 : ½ *$ 0+ ¼*$150 + ¼*$300 = $112.5
People may be unwilling to pay 112.5. This is not market failure!
Forcing people to have insurance does not improve social welfare.