Economics 309

Public Finance

Mark Witte

Northwestern University

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Insurance

New source of market failure from “Information asymmetries”

• We are familiar with classical market failures like externalities, public goods, and failures of competition
• Another kind of market failure has to do with information asymmetries
• Sometimes one party to a trade knows much more than the other, and there's no credible way to communicate that information
• Suppose Antiques Roadshow offers to pay $1,000 for an old lamp you have….
• How do you react?
• Asymmetric information advantages can mess up markets
• This has been the justification for government to become “an insurance company with tanks”

Market failure from “Information asymmetries”

• Sometimes one party to a trade knows much more than the other, and there's no credible way to communicate that information
• Asymmetric information advantages can mess up markets
• Consider the market for used cars
• “The Market for Lemons” (1970), George Akerlof, 2001 Nobel Prize

Biblical Adverse Selection

And Jesus said, Behold, two men went forth each to buy a new car.

And the car of the first man was good and served its owner well; but the second man’s was like unto a lemon, and worked not.

But in time both men grew tired of their cars, and wished to be rid of them. Thus the two men went down unto the market, to sell their cars.

The first spoke to the crowd that had gathered there, saying honestly, My car is good, and you should pay well for it;

But the second man went alongside him, and bearing false witness, said also, My car is good, and you should pay well for it.

Biblical Adverse Selection II

Then the crowd looked between the cars, and said unto them, How can we know which of ye telleth the truth, and which wisheth falsely to pass on his lemon?

And they resolved themselves not to pay for either car as if it were good, but to pay a little less than this price.

Now the man with a good car, hearing this, took his car away from the market, saying to the crowd, If ye will not pay full price for my good car, then I wish not to sell it to you;

But the man with a bad car said, I will sell you my car for this price; for he knew that his car was bad and was worth less than this price.

Biblical Adverse Selection III

But as the first man left, the crowd returned to the second man and said, If thy car is good, why then dost thou not leave to keep the car, when we will pay less than it is worth? Thy car must be a lemon, and we will pay only the price of a lemon.

The second man was upset that his deception had been uncovered; but he could not gainsay the conclusion of the market, and so he sold his car for just the price of a lemon.

And the crowd reasoned, If any man cometh now to sell his car unto us, that car must be a lemon; since we will pay only the price of a lemon.

And Lo, the market reached its Nash equilibrium.

Asymmetric information: Used cars

• Sellers know more about the car they want to sell than does the potential buyer
• People are willing to pay a price that matches the quality of a car, but don’t want to pay a lot for a car that’s bad
• It’s hard for a potential buyer of a used car to tell if the car is any good or not, so all used cars, good and bad, tend to sell for the price of a bad one, which means that cars that aren’t bad, don’t get sold, even though the owner might prefer to sell for a reasonable price and buy a new car

Asymmetric information: Used cars

• Suppose that someone has a car that she values at $5,000, but would be happy to sell it for more than that
• If the car is good, a buyer would be glad to pay $7,000 for the car
• Since $7,000-$5,000 = $2,000, this would generate $2,000 in gains divided between the buyer and seller
• Problem:  The buyer can't trust the seller, and doesn't know if the car is any good or not
• Result:  The trade doesn't happen and the $2,000 social gain is lost

Value to potential buyer = $7,000

Value to potential seller = $5,000

Deeper used car example

• Cars can be either good (worth $15,000) or a worthless lemon.
• 2/3rds of cars are good
• 1/3 are lemons
• Each seller knows the type of his or her own car
• Prospective buyers cannot know the quality of any individual car.
• Buyers are willing to pay what they believe to be the average value of cars on the market.
• What price would that be?
• Could the market price be 2/3 * $15,000 + 1/3 * $0 = $10,000?
• Yes, if…

...cars on the market were a representative sample of the population.

• Would that be true? Why or why not?

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Problems with asymmetric info and insurance

• Suppose good cars are worth $15,000 and bad cars are worth $0, and we can’t tell them apart at the time we would buy them, but the sellers can
• This is asymmetric information
• If we are willing to pay $10,000, then….
• We are going to see a lot of $0 value cars for sale
• And very few (maybe zero) $15,000 cars for sale
• This is adverse selection
• We are more likely to observe bad outcomes because those with the information advantage choose to dump them on us

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However, no one really cares very much that the market for used cars doesn’t work very well. The real issue is….

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Why do people like insurance?

• Classical economics: Diminishing marginal utility of consumption or wealth
• Behavioral economics: Loss aversion, expected regret
• Probably a truer explanation of human behavior
• Let’s go with diminishing marginal utility here
• It’s easier to model
• We get less marginal utility from a given increase in income than we lose from the same drop in income
• If so, then our utility function is concave and we are risk averse
• If we valued gains and losses equally, then our Utility Curve would be a straight line
• We would be risk neutral
• If utility curves up, we would be risk loving

How do people feel about risks?

• How much would you value holding a lottery ticket that would pay you either z₁ with probability p or or z₂ with probability (1-p)?
• Let the expected value of this ticket be E(z) = p*z₁ + (1-p)z₂
• What sure payment (“certainty equivalent”) would you be willing to trade that ticket for?
• C(z) is the certainty equivalent for holding the gamble that pays off either z₁ or z₂

Risk aversion and the insurance industry - Pat Ryan!!

• Risk aversion means that we are willing to trade something with a higher expected value, E(z), but some risk for something with a lower expected value, C(z), with now risk
• We as individuals care a lot about our idiosyncratic risk
• Insurance companies pool a lot idiosyncratic risks, reducing the expected range of possible outcomes
• Paying less than the expected value and then pooling is very profitable

Many insurance markets

• Health insurance is clearly huge, and something we will talk about
• Government also often provides insurance in markets where payouts are highly correlated
• If I breaking my leg or crash my car, it does not raise the probability that you broke your leg or crashed our car (unless I crashed into you)
• These kinds of idiosyncratic risks can be pool and diversified
• Bigger problem when the payoffs to insurance are highly correlated
• For example….

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Correlated insurance payouts

• Bigger problem when the payoffs to insurance are highly correlated
• For example….
• Flood insurance
• Crop failure insurance
• Earthquake insurance
• Unemployment insurance
• Deposit insurance

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Hard for a private party to have enough liquidity against such rare, big events

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Other reasons governments involved in insurance

• Paternalism
• Concern about ability to pay for people who have bad outcomes
• Insurance may be a “merit good”
• Something that’s good for society if people have it

Annuities

• Our productive lives are often shorter than our actual lives
• We need to build up savings while we work to cover our needs in retirement
• We risk outliving our assets
• Granted, this is better than dying young
• We could buy insurance in the form of an “annuity” that would pay us some level of income for the rest of our lives
• However, these tend to be very expensive
• Usually: Price >> Actuarially fair premium, expected future payoffs
• Why are annuities so expensive?

Asymmetric information and Annuities

• Why are annuities so expensive?
• People who know they are likely to die young don’t buy them
• People with good genes and boring lifestyles will have high demand for such assets
• Jeanne Calment lived to be 122, and you would not want to sell annuities to her or her descendants!
• Insurers can’t differentiate between these two groups, and so must treat everyone as if they were going to live to 100
• (Also, buying annuities reduces the resources to give bequests, in case we die young.)
• Problem: This will mean that some old people will end up in poverty
• Also, sometimes the economy goes to hell and a lot of people end up unlucky with their savings wiped out

This leads us to….

• Social Security