The role of insurance in health care, part 2

Today: More on moral hazard

Other issues in insurance

Problems with insurance

Health care

Suppose that Angela has been admitted to the hospital after being in a car accident

She has a substantial MB for the first night in the hospital, due to the care that she needs

Health care

As Angela’s condition improves, her MB declines

When the demand hits the horizontal axis, she is completely better

Think of demand like MB

Think of supply like MC

20 percent co-insurance

Assume that Angela pays 20% of her costs This is also known as coinsurance

Angela will then decide to stay in the hospital as long as MB for each night exceeds its MC She will want to stay in the hospital as long as her

benefit is at least 20% of the hospital’s cost

What about a percentage co-payment? What if Angela had to

pay 20% of her costs while in the hospital Her PRIVATE MC is

two-tenths of MC curve (See dashed line)

Equilibrium is at the yellow circle

0.2 MC

Only a co-payment

Suppose that Angela’s insurance only mandates that she makes a co-payment

Angela’s PRIVATE MC is zero after being admitted

If hospital lets Angela stay in the hospital as long as she wants, equilibrium occurs at Q2 MB and private MC are

both zero here

What is optimal?

Angela’s optimal length of hospital stay occurs when the PUBLIC MC equals MB This occurs at point A

Deadweight loss due to 20% coinsurance

Flat-of-the-curve medicine

Flat-of-the-curve Spending that occurs with low MB

Is the US practicing this type of medicine? Likely in some cases, due to insurance

Analysis across countries is more complicated Countries with nationalized medicine may not provide some

services with MB > MC Malpractice costs Health care costs for selected countries: See Figure 9.5, p.

200

Some final issues

Externalities Graying of the population

Longer life expectancy Retiring baby boomers

Improved technology Reimbursement policies

Externalities

Externalities of health care exist in limited cases

Examples Vaccination (positive) Overuse of antibiotics (negative) Staying home when sick (positive)

Graying of the population

The average age of the population is increasing for two reasons Longer life expectancy Retiring baby boomers

Older people generally have higher health care costs per person This can increase premiums for everyone working for the

same firm More on this topic in later lectures

Government-provided health care Social Security

Improved technology

Old methods of health care are often not expensive Aspirin first marketed over 100 years ago

Modern drugs can have monthly price tags over $1,000 Should someone that is unable to afford a new

drug be left out of using it? Commodity egalitarian arguments have led to price

discrimination by pharmaceutical companies Prices slightly above MC are charged to poor people

Reimbursement policies

Reimbursement policies for medical services to try to keep costs down Review boards Discharge criteria from hospitals

New directions for health insurance? As health care costs continue to increase,

consumers must pay for it one way or another

New methods to keep premiums down Explicit reductions in benefits More drug tiers

See readings on class website for more on this Restructuring of benefits

Restructuring benefits

As we saw with Angela… Over consumption of health care Extra consumption passed on to others’ premium

fees How can we avoid this?

Provide accounts that carry over from year to year Lower premiums but increase deductibles

Example that decreases moral hazard problem: Lower premiums by $2000 per year, but increase deductible by $2000 per year

What are the other issues of insurance? Do some individuals have a discount rate that

is too high? Government insurance

Reimbursement rates Talk about this more next week

Emergency rooms Increased costs for all How can costs be further controlled in the

future?

Problems

1. Hospital demand given insurance (or lack thereof)

2. Deadweight loss due to insurance

3. Insurance problem

Problem 1

If a day in the hospital costs $15,000 per day, and you demand hospital care based on the demand P = $30,000 – 1,000 Q, how many days will you stay in the hospital under each of the following situations Full insurance with no co-payment A co-insurance of 20% of your bill No insurance

Problem 1

Full insurance with no co-payment With full insurance, the patient will stay in the

hospital until MB = 0 To find the number of days in the hospital under

these conditions, set 0 = 30,000 – 1,000Q Q = 30

Problem 1

A co-insurance of 20% of your bill With a 20% co-insurance payment, the patient will

stay in the hospital until MB is 20% of the daily cost, or $3,000

Set 3,000 = 30,000 – 1,000Q Q = 27

Problem 1

No insurance With no insurance, set MC = MB Set 15,000 = 30,000 – 1,000Q

Q = 15

Problem 2

Using the information in the previous problem, what is the deadweight loss (DWL) due to insurance? Note that there is no DWL when there is no

insurance

Problem 2

Note that above 15 days of care, MB is less than MC

With full insurance, the DWL triangle has base of 30 – 15, or 15

The height of the triangle is the MC, or 15,000

Area: ½ of 15 *15,000, or 112,500

Problem 2

With a 20% co-insurance payment, the DWL triangle has base of 27 – 15, or 12

The height of the triangle is the MC minus the 20%, which is 15,000 – 3,000, or 12,000

Area: ½ of 12 *12,000, or 72,000

Problem 3

Cautious George is so cautious In fact, he is so cautious that he has the

following risk-averse utility function U(n) = n⅓

Problem 3

Suppose that George could receive one of two possible payouts in the following gamble $125 with 40% probability $1,000,000 with 60% probability

What is the expected payout? What is the expected utility? How much is George willing to pay to be fully

insured?

Problem 3

Expected payout (Y) $125 * 0.4 +

$1,000,000 * 0.6 =$600,050

Expected utility U(125) = 5 U(1,000,000) = 100 Expected utility is

5 * 0.4 + 100 * 0.6 =62

Income

Util

ity

Y Z

UA

UC

UD

UBD

C

B

A

X

Willingness to pay (WTP) for insurance is Z – X, which is more than Z – Y

Problem 3

We need to find some y such that U(X) = 62 X⅓ = 62 X = $238,328

George is indifferent between taking $238,328 with certainty versus the previously-mentioned gamble

Income

Util

ity

Y Z

UA

UC

UD

UBD

C

B

A

X

Willingness to pay (WTP) for insurance is Z – X, which is more than Z – Y

Problem 3

George is willing to pay Z – X to be fully insured Z = $1,000,000 (the

higher of the two payouts)

X = $238,328 George is willing to

pay up to $761,672 to be fully insured

Income

Util

ity

Y Z

UA

UC

UD

UBD

C

B

A

X

Willingness to pay (WTP) for insurance is Z – X, which is more than Z – Y

Problem 3

Expected value of gamble (Y) $600,050

Certainty equivalent of the gamble (X) $238,328

George is willing to pay up to $761,672 to be fully insured

Income

Util

ity

Y Z

UA

UC

UD

UBD

C

B

A

X

Willingness to pay (WTP) for insurance is Z – X, which is more than Z – Y

Next week

Monday: The role of government in health care Read Chapter 10

Wednesday: Social Security Read pages 228, 232-236, and 240-251