Chapter 10

Health Insurance

10.1INTRODUCTION

10.2DEMAND FOR HEALTH INSURANCE

10.2.1 Individual Demand for Insurance

Assumptions:

· Consumer Tastes. If wealth has diminishing MU for one individual, that individual is said to be risk averse, i.e., for a given wealth level, a loss of given amount is of greater importance (utility) to the person than would be a gain of an equal amount.

· Level of wealth. Individual initially has a level of wealth of $1,000.

· Medical expenses in the event of illness. If individual becomes sick, he or she will face medical expenses of $100. This financial loss can be broken down into (1) a unit cost component and (2) a component representing the number of units consumed.

· Likelihood of illness. Say .1 probability individual will be ill.

· Price of insurance. Individual can shift risk of loss onto an insurer but will have to pay a premium to do so.

· Behavioral assumption. Individual wants to maximize his/her utility. Table 10-1, p. 230.

Without insurance, has 90% chance of having $1,000 in wealth and a 10% chance of having only $900 because of the medical expense.

E(wealth) = .9(1000) + .1(900) = $990

Suppose that if wealth = $1000, U = 100 units

= $900, U = 89 units

E(U) = .9(100) + .1(89) = 98.9

Suppose that this is the same utility that 100% certainty of having wealth of $970 would yield. (= 98.8)

If he could buy insurance coverage against the $100 loss for, say, $20, he would have $980 left. Suppose $980 gives him 99.4 units of utility, which is more than 98.9 (when he buys no insurance). In fact, he could pay up to $30 to avoid risk of losing wealth due to illness.

Now assume that the unit cost = $150 → Medical expense = $150 if he gets sick.

E(wealth) = .9(1000) + .1(850) = $985

Again suppose U(W = 1000) = 100 and U(850) = 76

E(U) = .9(100) + .1(76) = 97.6

If individual is certain of having $960, she would be certain of getting 98 units of utility → she would be willing to pay up to $40 for insurance.

10.2.2 Limitations of the Theory

10.2.3 The Market Demand for Insurance

10.2.4 Moral Hazard

Assume individual has same utility function as in model discussed earlier. Other basic assumptions are:

· Prob(sick) = .2

· If insured gets sick, he or she will pay $5 for each unit of health care demanded

· Individual’s initial wealth is $1,000.

3 situations: 1. No insurance, individual pays $5.

2. Fully insured and pays zero price for health care

3. 10% copayment →faces price of $.50/unit.

Assume when P = $5, 10 units demanded

“ P = $0, 30 units demanded

P = .50, 12 units demanded

First compare situations 1 and 2

Sit. 1: -20% of getting sick, pay $50, and have $950 left over.

U($950) = 97

-80% of not sick, wealth stays at $1000, and U(1000) = 100 →E(U) = .2(97) + .8(100) = 99.4

Sit. 2. Assume premium = $30 →U(970) = 98.8

E(U) = 98.8 less than E(U) in sit. 1 → No insurance demanded

Sit. 3 Because of 10% copayment, insurance company pays $4.50/unit and since individual demands 12 units if sick, insurance company pays $54.00 total ($4.50 times 12)

Assume premium = $10.80

Individual pays $6.00 if becomes sick (.5 times 12)

Cost to individual = $10.80 + 6.00 if sick

U(1000-10.8-6) = U(983.2) ≈ 99.6

If not sick U(1000 – 10.8) = U(989.2) ≈ 99.8 →E(U) = .2(99.6) + .8(99.8) = 99.76 more than sit. 1 →Individual will buy insurance.

10.3SUPPLY OF HEALTH INSURANCE

10.3.1 Insurer Costs

The calculation of expected costs involves two components: claims paid out and the insurer’s administrative expenses. The administrative expenses are incurred in the selling of insurance policies and the administration of claims. Claims paid out are determined by the price of medical care and the quantity of medical care used by the consumers.

10.3.2 Insurer Revenues or Premiums: 2 basic ways in which premiums can be set: through experience rating or through community rating. Experience rating involves the setting of premiums for individuals or groups according to their risk or loss. Healthy, low-risk individuals will be charged lower premiums. In community rating, a single rate is set for the entire insured population based on the average experience of that population. High and low-risk individuals all pay same rate regardless of their expected loss.

10.3.3 Predictions about Supply

A simple supply model would show a typical positive relationship between price and quantity supplied. We can also draw conclusions about the effect of changes in other variables on the supply schedule of the insurer. Increases in the supply schedule (more risks accepted at a given premium rate) will be induced by the following: a less risk averse utility function on the part of the insurer, a greater initial level of reserves, a reduction in administrative costs, and a drop in the losses that may be experienced by the consumers. Several additional aspects of supply behavior are worth y of emphasis.

First, if all consumers do not have the same risk function and the insurer can choose between experience rating and community rating, the analysis becomes more complex. Suppose there are two groups, one high risk and the other low risk. With experience rating, a premium would be set that reflected each group’s loss experience. Under community rating, there would be a single premium rate, which would fall somewhere between those of the high-risk and low-risk groups.

Second, insurers can lower their costs (and increase their profits) by reducing the consumers’ utilization of insured health care services and by lowering the amounts they reimburse the providers of care.

Third, whereas previously insurers had played a passive role in the setting of prices, they have become increasingly active in contracting with providers and pushing for favorable terms. They have sought to gain a market advantage over providers so they can either pass the lower prices on to consumers or else can capture the gains for themselves.

10.4ADVERSE SELECTION IN HEALTH INSURANCE MARKETS

In this insurance model, assume there are 3 separate groups of 100 individuals. Assumptions about their demand conditions are as follows:

· Group 1: (healthiest) each person has 10% prob. of becoming ill and requiring care. Group 2: (intermediate) prob = 40%, group 3, prob is 80%.

· Cost of treatment for a person in any group is $100.

· Individuals have utility function as in Table 4-1

If insured, E(U) for group 1 will be

E(U) = .1[U(900)] + .9[U(1000)] = .1(89) + .9(100) = 98.9

For group 2

E(U) = .4[U(900)] + .6[U(1000)] = .4(89) + .6(100) = 95.6

For group 3

E(U) = .8[U(900)] + .2[U(1000)] = .8(89) + .2(100) = 91.2

Each member of group 1 would pay a premium up to $30 to get insurance.

For group 2, premium would be up to $60.

For group 3, premium would be up to $90.

Now turn to supply side.

Assumptions:

· Administrative expenses = $2000.

· Total cost = Administrative expenses + Reimbursements

· Insurance company just wants to break even, i.e., TR = TC.

Insurance company could choose experience rating, which involves dividing total pool into subgroups and setting rates according to each subgroup’s expected loss.

Or it could choose community rating, i.e., all individual pay same rate.

Assume, community rating is used.

Expected reimbursements = 10 (for group 1)(.1 times 100). $100 = $1,000.

+ 40 (.4 times 100). $100 = 4,000.

+ 80 (.8 times 100). 100 = 8,000.

$13,000

Add to it administrative expenses 2,000

Total cost $15,000

Over 300 people, rate =

Since $50 > $30 group 1 will not insure.

Since 50 < 60 and <90 Groups 2 and 3 will insure.

As group 1 drops out of market, expected reimbursements + admin. Costs = $14000

Over 200 people, new rate =

Since $70 > $60 Group 2 will drop out →TC = $10,000

Over 100 people, new rate =

Since $100 > 90 group 3 will drop out, too. →Market collapses.

This phenomenon is joint result of adverse selection (those with highest risks remain in market) and community rating (chosen because information asymmetry prevents insurer from being able to distinguish between individuals in the 3 groups).

If experience rating was possible:

Group 1 members would be charged:

E(cost) = 10($100) + 1/3 [assume that administrative expenses are split 3 way] (2,000) = 1000 + 666 = 1666.

Over 100 people, group 1’s rate =

Since $16.66 < $30 group 1 will choose insurance.

For group 2:

E(cost) = 40($100) + 1/3 [assume that administrative expenses are split 3 way] (2,000) = 4000 + 666 = 4666.

Group 2’s rate =

Since $46.66 < $60: group 2 will choose to be insured.

Finally: group 3

E(cost) = 80($100) + 1/3 [assume that administrative expenses are split 3 way] (2,000) = 8000 + 666 = 8666.

Group 3’s rate = so group 3 will also get insurance.

So it is community rating that caused the market to disappear.