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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.