Micro 33001 - Lecture 4

Name the three general problems with insurance

1) Adverse selection2) Moral hazard3) No diversification

Name the two assumptions we've made in the past about consumers, that can be violated.

1) Consumer faces no uncertainty. I.e., he knows everything about his world (including the price of everything) and knows how much he will like anything.2) Consumer is rational. More is always better, and preferences are transitive

With respect to the overconfidence issue, name the three types of consumers. Let's say the issue is when people pay $70 for a monthly gym membership and go only four times, when the average visit costs $10.

1) Rational/economists who don't make this mistake.2) Sophisticates - know they're bad at going to the gym, but they're paying $30 to motivate themselves. They know they have a problem. This is like the people who order the New Yorker but never read it. Prestige3) Naive people - thinkthey went a lot to the gym, but they didn't. Every month, they think they're getting a deal.As a gym operator or magazine owner, you'd like to know what % of your customers fall into each of these categories. For example, the New Yorker people might want to charge a lot for their magazines, because they know the sophisticates will want to tie their hands and buy the magazine.

Name the four forms of irrationality or consumer biases that consumers have.

1) Valuation of the future. Standard economic theory says that I value consumption tomorrow less than consumption today, and consumption two days from now less than consumption tomorrow. The difference in valuation is the sam. In practice, people value tomorrow or anything in the future WAY less than today, but two days from now and tomorow are the same. This is called hyperbolic discounting -- i.e., anything that happens in the future (i.e., future consumption) is worth a fraction of what it is right now, but when I think of two periods in the future, my preference for caring less about the futrue is smooth.2) Defaults. 3) Overconfidence 4) Knowledge over probabilities.

What are two ways insurance companies can deal with adverse selection?

1) have the company require everyone to carry insurance2) screen applicants

What does the CLASS Act kind of look like?

A savings account for LT care.

Being risk-averse means your marginal utility of additional income is (diminishing/steady/increasing).

Diminishing

Name two ways to reduce risk.

Diversification and insurance

Assume that Merck has offered you a job that pays a salary of $75k. Simultaneously, a small biotech startup has also offered you a job that will pay $120k so long as the startup gets the next round of financing. The probability of the startup getting financing is about 0.5. If you lose your job, the best job you can get on short notice pays $30k. Draw a graph of expected utility assuming you are risk-averse. Mark the risk-premium.

Draw a diminishing marginal utility graph with utility as the y-axis and consumption as the x.axis. Draw the points of $30k and $120k. Draw a line connecting the points of $30k and $120k ... the point on this straight line where c=75k is your expected utility from the start-up job. The point directly above that but on your utility curve is the point at which you'd be if you were at the Merck job. The difference is the extra utility you get from being certain of getting the 75k. The risk premium is the difference in x value between your EU on the straight line and the x value of the point with the same utility, but on the utility curve.

Assume that Merck has offered you a job that pays a salary of $75k. Simultaneously, a small biotech startup has also offered you a job that will pay $120k so long as the startup gets the next round of financing. The probability of the startup getting financing is about 0.5. If you lose your job, the best job you can get on short notice pays $30k. Calculate the risk premium.

Draw a graph with consumption on the x-axis and utility on the y-axis. Draw a straight line between the point on the utiliy curve with an x-value of 30k, and the point on the utility curve with an x-value of 120k. Mark the point on this straight line that has an x-value of $75k. The risk premium is the horizontal distance between this line and the point on the curve that has the same utility. To calculate this distance, we do the natural log of the expected utility equation: 0.50ln(120k) + 0.5ln(30k) = ln(x). The risk premium, therefore, is $75k - $60k = $15k.

Give two examples of hyperbolic discounting or valuing the present more.

Eating all foods at the start of the month. Obesity? Credit cards.

How would an office providing insurance under the CLASS Act price premiums?

Evaluate 5 years * Some premium = $50 per day * 365 days in a year * the number of years the average person lives.

Rick's current income is $16,000. However, Rick knows that there is a 1/3 chance that his hours will be cut on his job and he will make only $10,000 rather than $16,000. What is Rick's expected income?

Expected Income = 2/3(16,000) + 1/3(10,000) = $14,000

True/False: State whether the underlined statement is true or false, taking the non-underlined information as given. Explain your answer. A bank has six tellers. The bank has found that customers prefer that the bank have one line that feeds into the next available teller rather than six separate lines, one for each teller. It is silly for people to express a preference for the one-line system, since the time in line should be the same on average under each system.

FALSE: If you take as given - as the problem asked you to do - that both systems lead to the same expected waiting time, then a risk-averse person should prefer the system with the least variance. If there are six lines, then there is variance which comes from the fact that you have to choose a line without knowing which teller is the fastest. If you choose a slow line then you might have to wait a long time. If you choose a fast teller, you will wait a short time. In the one-line system, a slow teller doesn't affect you as much because you go to the first teller available.

T/F Moral hazard also has the unraveling problem that adverse selection has.

False. This is because insurance companies can't address moral hazard with screening, because people haven't behaved recklessly yet.

T/F People have steady marginal utility from income.

False; people have diminishing marginal utility from income. The difference in your happiness levels between making $0 and $75k is much greater than the difference in your happiness levels between making $75k and $100k

What is the variance of the payoff to a risky investment that pays $40 25% of the time and $0 75% of the time?

First, find the expected value: EV = 0.25 * (40) + 0.75 * 0 =10Next, calculate the variance: 0.25 * (40-10)^2 + 0.75 * (0=10)^2. 0.25 * 900 + 0.75 * 100 = 225 + 75 =300

What does moral hazard mean? What can it result in?

Having auto insurance may cause you to change your behavior such that you are more likely to drive recklessy. If you have no insurance, you might drive less and you might drive more carefully. Because the insurance leads people to act recklessly, again the probability that the insurance company has to pay each consumer is greater than 0.005. The insurance company must tak this into account when setting rates. The insurance company cannot see what you plan to do, and what you do might depend on whether you own insurance. In some ways, moral hazard is worse than averse selection, since there is no way to price it.

What type of insurance can often face problems?

Insurance that provides annuities. People who own annuities tend to be those who are very long-lived. This creates a problem for insurance companies because the people live much longer than modeled.

What is the problem with the CLASS Act?

It is a classic example of where unraveling could occur. For example, if someone KNOWS he will get Parkinson's, the insurance is a great deal. He pays 5 years of premiums and could get 20 years of long term care.

Describe the CLASS Act.

Late part of the health care bill. Required the government to create a LT insurance product. To buy this insurance, people must pay premiums for about 5 years. If you then become disabled, the insurance pays $50/day in long term care until you die. This must pay for itself. This was an optional part of the health care bill. Coverage for home or nursing care, with no time or total amount limits. However, it needed to break even -- it needed to pay for itself over time and couldn't use additional taxpayer dollars. The pricing was only based on age. The office decides the premiums.

Rick's utility of different income levels is given below:Income U(income)10000 9911000 13012000 15713000 18114000 19815000 21116000 222Is Rick risk-averse, risk-neutral, or risk-loving?

Marginal Utility of Income is declining. Thus Rick is risk-averse.

Imagine you're selling LT care insurance, and you observe that relative to the general population, the people who own your insurance are more likely to enter a nursing home. Is this moral hazard or adverse selection? How can you tell? Why is it important?

Moral hazard: once I own the insurance, I act such that I'm more likely to go to the nursing home. Adverse selection: the kind of people who buy your insurance are predisposed to go into a nursing home, due to some disease, ailment or something else. More likely adverse selection. It is important to know what is causing this issue because you will need to address the problem in different ways if it is due to moral hazard, or to adverse selection.

Are most people risk averse based on evidence?

Most economists think so, at least when there's possibility for large losses. For example, most people buy insurance. They purchase insurance that is less than actuarially far. This means they pay a premium to avoid risk (this behavior is a characteristic of risk aversion).

Does it make sense to buy life insurance on kids or old people? Why or why not?

NO. You want insurance that protects your income in the relatively unlikely event that something bad happens. Kids and old people don't make money! Besides, older people are probably kind of expensive to take care of, anyway -- even more so than kids sometimes. Things that simply pay you when you're sad don't make sense from an economic perpsective!

Will a risk-averse person always avoid risk?

No. For example, let's say the start-up job now could possibly give you $1mm in the event that it goes public. Your EU with the start-up job will now be $515k, and you would likely pick the start-up job.

Model assumes certainty, but the consumer actually does face uncertainty, in the form of risk.

OK

Assume that Merck has offered you a job that pays a salary of $75k. Simultaneously, a small biotech startup has also offered you a job that will pay $120k so long as the startup gets the next round of financing. The probability of the startup getting financing is about 0.5. If you lose your job, the best job you can get on short notice pays $30k. Which offer will you take, and why?

Offer 1: EV = 75K, variance = 0Offer 2: EV=75k, variance equals about 2.025mmI would generally take Job 1 since it has the same EV but lower variance/risk.

Draw the utility functions for risk-neutral, risk-loving, as well as risk-averse people.

On the curve, the x-axis is consumption and the y-axis is utility. The slope of the risk-loving individual gets larger and larger over time. The slope of the risk-neutral person stays steady, and the slope of the risk-averse person decreases over time.

Harry Potter faces a probability of 0.5 that his boss, Severus Snape, will fire him. If he is fired, Harry will remain unemployed for a year, earning nothing. His yearly salary is $36,000. Now suppose he would be willing just to take a pay cut of $20k per year from his current income of $36k in exchange for a guarantee of not being fired; what might be a reason why employers, like Severus Snape, would choose not to offer an employment guarantee like this?

One reason that Severus Snape would not choose to offer the guaranteed employment is that once Snape guarantees Harry $16,000 no matter what, Harry might choose not to work hard. The fear of being fired is a strong incentive. Once Snape gives up that incentive, Harry may be likely to shirk his responsibilities. We call the change of Harry's effort, or his actions, in response to the offer of insurance (or reduction of risk) - moral hazard.

What does adverse selection mean? What can it result in?

People who are more likly to have a traffic accident, for example, may be more likely to buy auto insurance. So, for example, let's say the average driver has a 0.004 chance of acidentally killing someone. You may be more likely to buy insurance if your probability is higher than the average. The insurance company has to take this into account when it sets rates, and it's one reason why mandatory auto insurance makes sense. Adverse selection is a result of hidden information -- when one side of the market has information that the other side doesn't. Adverse selection results in unraveling ... e.g., people with a greater likelihood of getting into an acceident theoretically buy insurance, then the insurance rates get higher, then only the people with an even greater likelihood of getting into an accident buy insurance, etc.

Rick's current income is $16,000. However, Rick knows that there is a 1/3 chance that his hours will be cut on his job and he will make only $10,000 rather than $16,000. What is the maximum amount that Rick will pay for an insurance contract that pays him $6000 if his hours are cut?

RICK'S INCOME IN DIFFERENT STATES OF THE WORLD Rick's Hours Are Cut Rick's Hours Are Not CutNo Insurance 10,000 16,000Insurance 10,000 + 6,000 - P 16,000 - Pwhere P is the premium Rick pays for the insurance.The question asks you to find the P that makes Jake's expected utility equal from buying insurance and not buying insurance.EU(No Insurance) = 2/3 U(16,000) + 1/3 U(10,000)= 2/3 (222) + 1/3 (99) = 181EU(Insurance) = 2/3 U(16,000 - P) + 1/3 U(16,000 - P)= U(16,000 - P)Set these two equal:181 = U(16,000 - P)U(13,000) = U(16,000 - P)13,000 = 16,000 - PP = $3,000A common answer is that Rick would be willing to pay $1,000 for the insurance. It is true that the Risk Premium is $1,000, and that this is how much Rick is willing to pay to get rid of the risk. But, the insurance policy does more than reduce the risk. It also increases Rick's expected income by $2,000. So, Rick pays $1,000 to get rid of the risk, and $2,000 for the extra $2,000 in expected income. Altogether, he is willing to pay $3,000.

Give the formula for the variance. Why do we square part of it? Why do we measure variance?

Sigma of p(X-Xbar)^2We square part of it to make sure the number is positive. This can also be thought of as the distance from the average.We measure variance because it is a way to measure/gauge risk. We take the square root of variance to get the standard deviation.

What are potential solutions to the CLASS Act?

Since the provider HAS to provide insurance and pricing is based ONLY on age, the government could make this mandatory in theory. Second, they could charge old people much more relative to what they charge young people.

What kind of person SHOULD get life insurance?

Someone who makes income or provides childcare and has dependents.

Describe the issue of probabilities when it comes to consumer behavior.

Standard economic theory posits that people understand probabilities and make choices based on them. In practice, however, people have no idea what the probability of anything is, and are especially bad at small and large probabilities. They consistently OVER-estimate small probabilities (e.g., winning the lottery or dying in an airplane crash) and UNDER-estimate large ones.

T/F and explain with a paragraph. Pay-per-view movies are an inferior good for Karen. Karen consumes only pay-per-view movies and gasoline. If the price of gasoline rises, Karen will purchase less gasoline.

TRUE: The price change for gasoline will have an income and a substitution effect. The substitution effect will tend to make Karen purchase less gasoline. The sign of the income effect depends on whether gasoline is a normal or an inferior good. Since pay-per-view movies are inferior, and since there are only two goods in Karen's budget, gasoline must be normal. Thus, the income effect will also tend to make Karen purchase less gasoline (the price increase makes Karen feel poorer). Both effects work in the same direction. Thus, the total effect must be for Karen to purchase less gasoline.

True/False: State whether the underlined statement is true or false, taking the non-underlined information as given. Explain your answer. Local government has the problem of attempting to reduce the number of people who park illegally. A perennial question is whether it should increase the probability that illegal parkers will get caught, or whether it should raise the fine that is imposed once an illegal parker is caught. If lawbreakers are risk averse, it follows that a 10 percent increase in the fine will have a greater disincentive effect than a 10 percent increase in the probability of getting caught.

TRUE: You can show that a 10 percent increase in the fine and a 10 percent increase in the probability of getting caught will lead to the same expected fine.Thus, a risk-averse parker will compare the variances and show more dislike for the option with the higher varianceFirst let's show that the effect on the Expected Fine is the same for both options:Fo = original finepo = original probability of being caughtEVsuboriginal = psub0 * Fsub0 + (1-p) * 0 = psub0Fsub0EVsubincreaseF = psub0 * (1.1 * Fsub0) = 1.1*psub0 *Fsub0EVsubincreaseP = 1.1 * psub0 * Fsub 0 When the fine is bigger, it is riskier because you have a smaller chance of paying a larger fine. Think of the logical extreme. Raising the probability to 1 and paying a fine of $1, versus lowering the probability to .001 and raising the fine to $1000. In both cases, you pay an expected fine of $1, but it is clear that the .001 chance of paying a $1000 fine is riskier.You can choose values for the original probability and fine and show that the variance is higher when you increase the fine.

Harry Potter faces a probability of 0.5 that his boss, Severus Snape, will fire him. If he is fired, Harry will remain unemployed for a year, earning nothing. His yearly salary is $36,000. Now suppose he would be willing just to take a pay cut of $20k per year from his current income of $36k in exchange for a guarantee of not being fired; what is his risk premium?

The Risk Premium is defined as the Expected Value minus the Certainty Equivalent.The Certainty Equivalent is the amount of money Harry would be willing to take for sure that would give him the same expected utility as the risky gamble. Since Harry is willing to take a $20,000 paycut, his Certainty Equivalent is $16,000. Therefore:RP = EV - CE = $18,000 - $16,000 = $2,000

Define risk premium. How does one calculate it?

The amount of money someone who is risk averse would pay to avoid taking a risk.

Harry Potter faces a probability of 0.5 that his boss, Severus Snape, will fire him. If he is fired, Harry will remain unemployed for a year, earning nothing. His yearly salary is $36,000.If Harry prefers earning $18k with a guarantee of employment to his current situation of receiving $36k, then what can we say about Harry's preferences toward risk?

The expected value of Harry's earnings is 0.5 * 36,000 + 0.5 * 0 = $18,000. Because Harry prefers getting the expected value for sure to taking the risk, he must be risk-averse.

If everyone is risk-averse, how does anyone find someone to sell them insurance?

The insurance company can diversify some of its risk. It still bears some risk, but sells some of the company to investors and diversifies its assets. It also charges a risk-premium.

What is true about insurance holders in practice?

The kind of people who buy life insurance are those who are otherwise more cautious than people who don't buy insurance. Furthermore, people who own insurance are actally less likely to die than people who don't. For example, the people who own life insurance are typically rich people with a lot to protect, who use their seatbelt, don't smoke, aren't fat, and are otherwise trying really hard not to die.

Describe consumer behavior with respect to overconfidence.

The standard economic theory is that people can accurately forecast their desire to engage in activities in the future. In practice, people overestimate their future interest in activities which are costly now but have long-term payoffs. For example, with goign to the gym or buying vegetables from Peapod.

Describe the consumer behavior re: defaults.

The standard economic theory states that, when faced with a choice, people evaluate all the possible options and choose the one that is best. In practice, however, people are very responsive to (i.e., favor) whatever option is the default, even when it's obviously not beneficial to them. For example, employers will default people into the no match 401K plan. People might be lazy, aren't aware, etc. A business application of this is home delivery of pharmaceuticals -- a company saved money if people chose home delivery of pharmaceuticals. When the company made home delivery the default, people in the program switched from 20% to 90%.

Describe the diversification problem of insurance.

There are some kinds of insurance such as earthquake insurance or flood insurance where it's difficult to diversity. When the insurance company needs to pay, it likely has to pay out all at once. Therefore, it needs to hold a lot of money in reserve.

T/F It is possible to see risk-averse behavior below a certain threshold of income, which changes into risk-seeking behavior above that threshold of income.

True

T/F: Most people are risk-averse.

True

T/F: A risk-neutral person would only look at expected utility of an option, disregarding which is the riskier option.

True. If a risk-neutral person were given the option of getting $50 for sure or a 50% chance of getting $0 and a 50% chance of getting $100, that person would be indifferent between the two options.

T/F Any investment that is less than perfectly correlated with your income (or your current investments) will reduce risk.

True. The more negatively correlated the investment, the more it reduces your overall risk.

How might you figure out the source of the problem for the LT care insurance?

Try to figure out how much private information people have (for adverse selection), or observe people before/after they get insurance (for moral hazard)

T/F and explain with a paragraph. Jake, as a New York Yankees season ticket holder, has the right to purchase two World Series tickets at a price of $150 per ticket. Bert, a Yankees fan, but not a season ticket holder, can purchase two World Series tickets from a season ticket holder on the black market for $500 per ticket. Since Bert has to pay more to get World Series tickets, Jake is more likely to go to the World Series.

UNCERTAIN or FALSE: The opportunity cost of going to the World Series for Jake is the difference between what he can get by selling his ticket and what he has to pay explicitly to get the ticket. So, the total economic cost of attending the World Series for Jake is $500--$150 explicit cost + $350 foregone profits—the same as the economic cost of attending the World Series for Bert. If you do not see this, consider what Jake gives up by attending the World Series: he gives up the $500 he could get from selling the ticket on eBay.Since both face the same economic cost, whoever values attending the World Series more than $500 will attend the game.Note that the second half of the underlined sentence is UNCERTAIN, and the first half of the underlined sentence is FALSE.

How can healh insurance companies deal with moral hazard?

Via co-pays, deductibles, and rising premiums. These are companies' ways of incentivizing people against acting worse when they have insurance. It makes people internalize some of the payment.

What could you do to solve the nursing home problem if the problem is due to AS versus MH?

adverse selection: screen better the people you give insurance to, and price based on type (expensive). moral hazard: provide some kind of incentives not to enter nursing homes -- i.e., you get some money back if you don't

Give the four reasons why some companies require their employees to invest in them.

e.g., private equity, where people are heavily invested in their funds.1) to align their incentives (but it's not clear this is the best method to align incentives)2) marketing pitch3) taxes (if you work at a PE fund and much of your income is carry, that is taxed at capital gains tax (12.5%) and your marginal $ of income is taxed at 40%). Oster thinks in those industries in particular, you can pay people a lot more if you pay carry that's taxed at 12.5% vs. that taxed at 40%4) more money for investing.Other than the tax issue, from an employee's standpoint, people might prefer NOT to invest in the company in which they work, in order to diversity risk.

Since risk averse individuals have a higher marginal utility of income when their income is low than when their income is high, they would ______ ....

like to figure out some way to take money from when they are rich to when they are poor. For example, take on credit card debt or loans.