1. Consumer Choice With Uncertainty Part II: Examples
Agenda:
The Used Car Game
Insurance & The Death Spiral
The Market for Information
The Price of Risk

2. The Used Car Game Good used cars are worth $10,000
Bad used cars are worth $2,000
The market has both good and bad cars.
Sellers: If you sell a car for MORE than what it is worth you get a bonus point!
BUT If you sell a care for LESS than what it is worth you LOSE a bonus point.
Buyers: If you buy a car for LESS than what it is worth you get a bonus point!
BUT If you buy a care for MORE than what it is worth you LOSE a bonus point.

3. “The Market for Lemons: Quality Uncertainty and the Market Mechanism”
by George A. Akerlof (1970)
QJE 84(3)
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)?
Akerlof, Michael Spence and Joseph Stiglitz won the Nobel Prize in Economics in 2001 for their work on information asymmetry.
What are some of the things buyers and sellers of used cars do to overcome these problems?
What units?
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?

4. Market Failure!
Is your $10,000 car worth $10,000 if you can’t sell it?

5. Because we are risk averse we are willing to pay MORE than the expected loss to reduce risk!
→ gains from trade!!

6. MathTrick Square both sides!
Key Formula
Expected Utility WITH Risk = Expected Utility WITHOUT (with less) Risk
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?
MathTrick Square both sides!
Test yourself: What would you be willing to pay if you were risk neutral (U=M)?

7. 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?
healthy
sick .9 .1 .5 .5
$1,000
$640
$1,000
$640
Health: .9(sqrt(1000)) + .1(sqrt(1000 – 360)) = sqrt(1000 – X)
Sick: .5(sqrt(1000)) + .5(sqrt(1000 – 360)) = sqrt(1000 – X)
$39.62
$190

8. Willing to pay for insurance
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 - $ = $39.62
Willing to pay for insurance
25.30
What is the expected value: $964
What is the expected utility: 30.99
How much money for sure would make you equally happy as your expected utility?: $960.38
Difference is what you are willing to pay for insurance: $39.62
Test yourself: What is the utility of the expected value and where should it go on the graph?
$640
$960.38
$964
$1,000

9. 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
Math Trick
Multiply probabilities on each “branch” of the tree.
healthy
sick .9 .1 .5 .5
Health: .9(sqrt(1000)) + .1(sqrt(1000 – 360)) = sqrt(1000 – X)
Sick: .5(sqrt(1000)) + .5(sqrt(1000 – 360)) = sqrt(1000 – X)
$1,000
$640
$1,000
$640
$39.62
$190
What will happen to the market if they charge this? $0
$360 $0
$360
.5*.1*$ *.5*360 = $108
If a risk-neutral insurer could not tell who is in which group, what premium would it have to charge to cover expected losses?

10. People may be unwilling to pay 112.5. This is not market failure!
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
Quantity of
Medical Care
AFP for D2’& D3’: ½ * 0 + ¼*$50 + ¼*$200 = $62.5
AFP for D2 & D3 : ½ *$ 0+ ¼*$150 + ¼*$300 = $112.5
People may be unwilling to pay This is not market failure!
Forcing people to have insurance does not improve social welfare.

11. The Price of Information
You want to get into a top 10 MBA program because you will have an 80% chance of landing a job paying $100,000. In another program your chance of a $100,000 job is just 20%. You figure your odds of admission to a top program are Is it worth paying an “admissions coach” $5,000 to improve your chance of admissions to 75%? Consider just one year of salary (not present value of future lifetime income) with a lower salary of $45,000 if you don’t get the $100,000 job.
Yes! Utility with the coach = > utility without =
Make two double trees – one with the coach and one without the coach.
Compute the expected utility of each tree and compare them.
If you’re the coach, could you charge more if you only get paid if your client gets into the top school and lands the $100K job? Assume no time value of money.
Yes! You can charge $15,784
Test yourself: If you are the coach, what is your EXPECTED fee?

12. Top school .75 .25 Other School .8 .2 .2 .8
If you’re the coach, could you charge more if you only get paid if your client gets into the top school and lands the $100K job? Again, assume no time value of money.
Top school
.75
.25
Other School .8 .2 .2 .8

13. Signaling!
Test yourself: Can you come up with a question that determines how much a company would be willing to pay for “brand” identity? How about how much more a consumer would be willing to pay for a branded rather than generic item?

14. Management – Moral Hazard, Incentives and Transaction Costs
You own a bar, and you face the risk that your bartender will serve free drinks to his friends. You estimate that the probability of this is 50-50, and if he does the lost value to you will be about $10,000 per year. In addition, if he serves an underage friend you can face a $1 million liability. You think the risk of this is only 15% and independent of whether he serves friends generally. You can install a video security system to reduce both probabilities (independently) to 5% for $50,000. You are a risk-neutral business owner. Should you install the system?
Expected loss without the system:
.5*.85*$10, *.15*$1,010,000 = $80,000
Expected loss with the system:
.05*.95*$10, *.05*$1,010,000 = $3,000
$3,000 + $50,000 for the system < $80,000
Therefore YES, buy the system.
Think about it: What other management considerations might you have? How would you feel as a bartender if you knew you were being watched all the time? How would you feel as a customer? What other things might you be able to do to reduce the risk?

15. Uncertainty is everywhere!
Conclusion
Uncertainty is everywhere!
But we can deal with it!!
Expected Value
Expected Utility
Willingness to Pay to reduce risk!