Demand and Supply of Health Insurance

1. Demand and Supply of Health Insurance Folland et al chap 8

2. Outline • What Is Insurance? • Risk and Insurance • The Demand for Insurance • The Supply of Insurance • The Case of Moral Hazard • Health Insurance and the Efficient Allocation of Resources • How to limit Moral Hazard • Conclusions

3. WHAT IS INSURANCE?A Simple Example Consider a club with 100 homogeneous members. It seems that about once a year one of the 100 members gets sick and incurs health care costs of $5,000. The incidence of illness seems to be random. Club members, worried about potential losses due to illness, decide to collect $50 from each member and put the $5,000 in the bank for safekeeping and to earn a little interest. If a member becomes ill, the fund is used to pay for the treatment. This, in a nutshell, is insurance. The members have paid $50 to avoid the risk or uncertainty, however small, of having to pay $5,000.

4. Desirable Characteristics of an Insurance Arrangement • The number of insured should be large, and they should be independently exposed to the potential loss. • The losses covered should be definite in time, place, and amount. • The chance of loss should be measurable. • The loss should be accidental from the viewpoint of the person who is insured.

5. Insurance vs. Social Insurance INSURANCE Insurance is provided through markets in which buyers protect themselves against rare events with probabilities that can be estimated statistically. SOCIAL INSURANCE The government programs are insurance programs with the government as insurer and are distinguished by two features: • Premiums (the amounts paid by purchasers) are heavily and often completely (as in the case of Medicaid) subsidized. • Participation is constrained according to government-set eligibility rules.

6. Insurance Terminology • Premium, Coverage—When people buy insurance policies, they typically pay a given premium for a given amount of coverage should the event occur. • Coinsurance and Copayment—Manyinsurance policies, particularly in the health insurance industry, require that when events occur, the insured person share the loss through copayments. This percentage paid by the insured person is the coinsurance rate. With a 20 percent coinsurance rate, an insured person, for example, would be liable (out of pocket) for a $30 copayment out of a $150 charge. The insurance company pays the remainder.

7. More Insurance Terminology • Deductible—With many policies, some amount of the health care cost is paid by the insured person in the form of a deductible, irrespective of coinsurance. In a sense, the insurance does not apply until the consumer pays the deductible. Deductibles may be applied toward individual claims, or, often in the case of health insurance, they may be applied only to a certain amount of total charges in any given year. • Exclusions—Services or conditions not covered by the insurance policy, such as cosmetic or experimental treatments.

8. Still More Insurance Terminology • Limitations—Maximum coverages provided by insurance policies. For example, a policy may provide a maximum of $3 million lifetime coverage. • Pre-Existing Conditions—Medical problems not covered if the problems existed prior to issuance of insurance policy. Examples here might include pregnancy, cancer, or HIV/AIDS. • Pure Premiums—The actuarial losses associated with the events being insured. They do not include any loading for commission, taxes and expenses. • Loading Fees—General costs associated with the insurance company doing business, such as sales, advertising, or profit.

9. RISK AND INSURANCEExpected Value • Suppose Elizabeth considers playing a game in which a coin will be flipped. If it comes up heads, Elizabeth will win $1; if it comes up tails, she will win nothing. • With an honest coin, the probability of heads is one-half (0.5), as is the probability of tails. The expected value, sometimes called the expected return, is: ER = (probability of heads) x (return if heads, $1) + (probability of tails) x (return if tails, $0) = $0.50

10. In General With n outcomes, expected value E is written as: E = p1R1 + p2R2 + … + pnRn where • piis the probability of outcome i, (that is p1or p2, throughpn) • Riis the return if outcome ioccurs. • The sum of the probabilities pi equals 1. • The expected value of any game is the sum of all possible outcomes weighted by their respective probabilities.

11. Actuarially Fair Insurance Policy • An actuarially fair game is one with an expected value equal to zero or one that costs its expected value for the right to play. In other words, a fair game is one in which: – The weighted sum of the outcomes equals zero, or – To play, a person must pay an amount equal to the positive expected value or receive an amount equal to the negative expected value of the game. • Π are the probabilities • x is the return if outcome i occurs

12. Actuarially Fair Insurance Policy • When the expected benefits paid out by the insurance company are equal to the premiums taken in by the company the insurance policy is called an actuarially fair insurance policy. • In reality, insurance companies must also cover additional administration and transaction costs to break even, but the definition of an actuarially fair policy provides a benchmark in talking about insurance.

13. Marginal Utility of Wealth and Risk Aversion • The foregoing example implies that Elizabeth is indifferent to risk. That is, for her the incremental pleasure of winning $0.50 (the gain of $1 less the $0.50 she paid to play) is exactly balanced by the incremental displeasure of losing $0.50 (the gain of zero less the $0.50 paid to play). • Suppose that the coin flip in the previous example is changed so that the coin flip yields $100 or nothing, but Elizabeth is now asked to pay $50 to play. • This is an actuarially fair game but Elizabeth may choose not to play because the disutility of losing money may exceed the utility of winning a similar amount.

14. Marginal Utility of Wealth and Risk Aversion

15. Marginal Utility of Wealth and Risk Aversion

16. Utility of Wealth • Suppose that Elizabeth’s wealth is $10,000. That wealth gives her a utility level of U1 = 140 and allows her to buy some basic necessities of life. This can be denoted as point A. • Suppose her wealth rises to $20,000. Will her utility double? • It is hard to know for certain, but it is plausible that the next $10,000 will not bring her the incremental utility that the first $10,000 brought. Thus, U2 will likely be less than twice U1. Suppose, for example, that U2 = 200. This is denoted as point B. • Do all of the points on the utility function between U1 and U2 lie on a straight line? If they do, this is equivalent to saying that the utility from the 10,001st dollar is equal to the utility from the 19,999th dollar, and hence the marginal utility is constant. This also is unlikely. Because the marginal utility of earlier dollars is likely to be larger than that of later dollars, the utility curve is likely to be bowed out, or concave, to the x-axis.

17. Utility of Wealth • The marginal utility of wealth refers to the amount by which utility increases when wealth goes up by $1. • The utility of wealth function pictured to the right exhibits diminishing marginal utility and describes an individual who is risk averse, that is, will not accept an actuarially fair bet. Figure 8-1 Total Utility of Wealth and the Impact of Insurance

18. Utility of Wealth • With wealth of $20,000, Elizabeth understands that if she becomes ill, which may occur with probability 0.10, her expenses will cause her wealth to decline to $10,000. If this occurs, she can calculate her expected wealth, E(W), and expected utility, E(U):

19. Purchasing Insurance • Suppose that Elizabeth can buy an insurance policy costing $1,000 per year that will maintain her wealth irrespective of her health. • Is it a good buy? We see that at a net wealth of $19,000, which equals her initial wealth minus the insurance premium, her certainty utility is 198. • Elizabeth is better off at point D than at point C, as shown by the fact that point D gives the higher utility. • If insuring to get a certain wealth rather than facing the risky prospect makes Elizabeth better off, she will insure. Figure 8-1 Total Utility of Wealth and the Impact of Insurance

20. Purchasing Insurance • The distance FC reflects Elizabeth’s aversion to risk. • At point F, Elizabeth would be willing to pay up to $4,000 (that is, initial wealth of $20,000, less $16,000 at point F) for insurance and still be as well off as if she had remained uninsured. If, for example, she were able to purchase the insurance for $3,000, she would get $1,000 in consumer surplus.

21. What Does this Analysis Tell Us? • Insurance can be sold only in circumstances where the consumer where there is diminishing marginal utility of wealth (or income)—that is, is risk averse. • Expected utility is an average measure. Elizabeth either wins or loses the bet. If she is exposed to risk, Elizabeth will have wealth and hence utility of either $20,000 (with utility of 200), or $10,000 (with utility of 140), and a risky expected wealth of $19,000. • Insurance will guarantee her wealth to be $19,000. If she does not fall ill, her wealth will be $20,000 less the $1,000 insurance premium; if she falls ill, her wealth will be $10,000 plus the $10,000 payment for the loss of health, minus the $1,000 premium—again $19,000. • If insurance companies charge more than the actuarially fair premium, people will have less expected wealth from insuring than from not insuring. Even though people will have less wealth as a result of their purchases of insurance, the increased well-being comes from the elimination of risk. • The willingness to buy insurance is related to the distance between the utility curve and the expected utility line.

22. THE DEMAND FOR INSURANCEHow Much Insurance? • We address Elizabeth’s optimal purchase by using the concepts of marginal benefits and marginal costs. Consider first a policy that provides insurance covering losses up to $500. • The goal of maximizing total net benefits provides the framework for understanding her health insurance choice.

23. How Much Insurance? Suppose that Elizabeth must pay a 20 percent premium ($100) for her insurance, or $2 for every $10 of coverage that she purchases. This worksheet describes Elizabeth’s wealth if she gets sick.

24. How Much Insurance? • Her marginal benefit from the $500 from insurance is the expected marginal utility that the additional $400 ($500 minus the $100 premium) brings. • Her marginal cost is the expected marginal utility that the $100 premium costs. • If Elizabeth is averse to risk, the marginal benefit (point A) of this insurance policy exceeds its marginal cost (point A’). Figure 8-2 The Optimal Amount of Insurance

25. How Much Insurance? • The marginal benefits of the next $500 in insurance will be slightly lower (point B) and the marginal costs slightly higher (point B’). • Total net benefits will be maximized by expanding insurance coverage to where MB = MC, at q’ (the optimum insurance purchase) Figure 8-2 The Optimal Amount of Insurance

26. In formula…

27. Graphically… Marginal utility of insurance Costs Marginal utility of insurance Benefits

28. The Effect of a Change in Premiums on Insurance Coverage Suppose the premium rises to 25% instead of 20%.

29. Increase in Premium • Elizabeth’s marginal benefit from the $500 from insurance is now $375 rather than the previous value of $400, so point C lies on curve MB2 below the previous marginal benefit curve, MB1. • Similarly, Elizabeth’s marginal cost is the expected marginal utility that the (new) $125 premium costs her. This exceeds the previous cost in terms of foregone utility, so point C lies on curve MC2 above the previous marginal cost curve, MC1. • Elizabeth’s marginal benefit curve shifts to the left to MB2 and the marginal cost curve shifts to the left to MC2. • Elizabeth’s insurance coverage will fall to q’’. Figure 8-3 Changes in the Optimal Amount of Insurance

30. Effect of a Change in the Expected Loss Back to the original example, with a premium of 20%, how will Elizabeth’s insurance coverage change if the expected loss increases from $10,000 to $15,000, if ill?

31. Increase in Expected Loss • Her wealth, if healthy, is $19,900, so nothing changes with respect to marginal cost. Elizabeth remains on curve MC1. • As before, the insurance gives her a net benefit of $400. However, this net benefit increments a wealth of $5,000 rather than $10,000. If we assume that an additional dollar gives more marginal benefit from a base of $5,000 than from a base of $10,000, then the marginal benefit curve shifts upward because of the increased expected loss. • Elizabeth’s marginal benefit curve shifts to the right at MB3 but the marginal cost curve remains unchanged at MC1. • Elizabeth’s insurance coverage will increase to q’’’. Figure 8-3 Changes in the Optimal Amount of Insurance

32. Effect of a Change in Wealth Suppose Elizabeth was starting with a wealth of $25,000 instead of $20,000.

33. Increase in Wealth • At the higher level of wealth, the same insurance policy provides a smaller increment in utility, so the marginal benefit curve shifts down from MB1 to MB2. • However (for the same expected loss), the $100 premium costs less in foregone marginal utility relative to the increased wealth, a downward shift of MC1 to MC3 • The marginal benefit curve will shift to the left to MB2 and the marginal cost curve will shift to the right to MC3 and Elizabeth’s insurance coverage will be identified with point W, which could end up being to the right or left of q’. Figure 8-3 Changes in the Optimal Amount of Insurance

34. THE SUPPLY OF INSURANCECompetition and Normal Profits • In a perfectly competitive market, insurers will earn zero excess profit. • Profit = Total Revenue – Total Cost • Elizabeth sought to buy insurance in blocks of $500, and her insurer was charging her $100 for each block of coverage, or an insurance premium of 0.20 ($100 as a fraction of $500). • Following the previous example, revenues are $100 per policy.

35. What Would the Insurer’s Costs Be? • For those who do not get sick (90% of the policies), the only cost would be the cost of processing the policy payments, say $8 per policy. • For those who do get sick (10% of the policies), the cost would be the $500 payment plus the $8 processing cost, or $508.

36. Insurer’s Profit Profit = $100 - (probability of illness X cost if ill) - (probability of no illness X cost if no illness) Profit = $100 – (0.10 X $508) – (0.90 X $8) Profit = $100 - $50.80 - $7.20 Profit = $42

37. Role of Competition • These are positive profits, and they imply that another similar firm (also incurring costs of $8 to process each policy) might enter the market and charge a lower premium, say, 15 percent, to attract clients. • Such entry into the market would continue until all excess profit was competed away.

38. Competitive Premium • Profits = Revenues – Costs • Revenue is equal to a*q where • a is the premium (in fractional terms) • q is insurance covering loss (payout) • Cost is equal to p*(q+t) – (1-p) t where p is the probability of payout t is the processing cost (unrelated to the size of the policy) With perfect competition profits must be equal 0, so: 0 = a*q – p*(q+t) – (1-p) t Solving for the competitive premium a: a = p + (t/q) • The competitive premium will be equal to the probability of illness, p, plus the processing (or loading) costs as a percentage of policy value, q, or t/q.