eco question

Health Economics Econ 5860 Prof. Kurt Lavetti

YPY − AL

Y BLY

B

D

A

C

2Benefits and Costs of Insurance

Utility

Wealth ($)

Benefit comes from risk protection

Costs of Insurance:

• In nearly all insurance markets, there are two major factors that cause deadweight loss 1. Moral Hazard 2. Adverse Selection

• The deadweight losses from these two factors imply that providing insurance is costly to society

3

Moral Hazard

• Moral hazard is when people change their behavior or purchase decisions because they have insurance, or are protected from risk

• Driving your car more recklessly because you have insurance that will pay you if you cause an accident

• Order more expensive food at a restaurant if you know you will split the check evenly

• Not facing the full price results in overconsumption

• What if we had “food insurance” that would pay for the cost of any food or any restaurant we wanted to eat at?

• Why does the market for food insurance not exist?

4

Moral Hazard Effect of Insurance on Welfare

5

P

Q

D

Supply

Coinsurance*P

Market Price (P)

Q* QInsured

Deadweight loss

Moral Hazard and Insurance Deductibles

• A potential way to reduce moral hazard is to include a deductible in the insurance contract

• If an insurance contract has a deductible of $X, the consumer must pay 100% of the first $X spent during the year, and after that point the insurance benefits begin

• What is the effect of a deductible on the deadweight loss from moral hazard…?

6

Can Deductibles Reduce Moral Hazard?

7• Step 1: Graph the supply function • Example: Suppose market price per unit of medical care is $100, and

an insurance plan has a $1000 deductible, and a 20% coinsurance rate. What does the supply function look like?

Price

Quantity

Can Deductibles Reduce Moral Hazard?

100

8

S

• Step 1: Graph the supply function • Example: Suppose market price per unit of medical care is $100, and

an insurance plan has a $1000 deductible, and a 20% coinsurance rate. What does the supply function look like?

Price

Quantity

• At what quantity will the deductible be met?

• What happens to the price after the deductible is met?

Can Deductibles Reduce Moral Hazard?

20%*$100

9

S

10

• Step 1: Graph the supply function • Example: Suppose market price per unit of medical care is $100, and

an insurance plan has a $1000 deductible, and a 20% coinsurance rate. What does the supply function look like?

Price

Quantity

100

• At what quantity will the deductible be met?

Ans: 10 ($1000 deducible/$100 per unit)

• What happens to the price after the deductible is met?

Ans: It decreases to $100*coinsurance rate

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

10

S

Deductible/P

• Step 2: Introduce demand function

Price

Quantity

P

D

If the demand function is D, what is the equilibrium?

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

11

S

Deductible/P

• Step 2: Introduce demand function

Price

Quantity

P

D

If the demand function is D, what is the equilibrium?

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

12

S

Deductible/P

• Step 2: Introduce demand function

Price

Quantity

P

D

If demand intersects supply at only one point, this intersection is the equilibrium

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

13

S

Deductible/P

• Step 2: Introduce demand function

Price

Quantity

P

D

• However, a deductible may cause D and S to intersect multiple times

• Which intersection is the equilibrium in this case?

1

3

2

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

14

S

Q2

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point A, how much consumer surplus do they get?

1

3

2

Q3Q1

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

15

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point 1, how much consumer surplus do they get?

• Ans: Triangle A

1

3

2

A

Q2 Q3Q1

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

16

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point 2, how much consumer surplus do they get?

1

3

2

A

Q2 Q3Q1

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

17

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point 2, how much consumer surplus do they get?

• Ans: A minus B • Why? For each unit between

Q1 and Q2, the price (P) is greater than willingness to pay, so B is negative consumer surplus

1

3

2

A

B

Q2 Q3Q1

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

18

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point 3, how much consumer surplus do they get?

1

3

2

A

B

Q2 Q3Q1

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

19

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• If consumer chooses point 3, how much consumer surplus do they get?

• Ans: A-B+C

1

3

2

A

B

Q2 Q3Q1

C

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

20

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

1

3

2

A

B

Q2 Q3Q1

C

• Which intersection gives the most consumer surplus?

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

21

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• Which intersection gives the most consumer surplus?

Ans: If area C > area B then point 1 maximizes surplus If area C < area B then point 3 maximizes surplus

1

3

2

A

B

Q2 Q3Q1

C

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

22

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• Does point 2 ever maximize consumer surplus?

1

3

2

A

B

Q2 Q3Q1

C

Can Deductibles Reduce Moral Hazard?

Coinsurance*P

23

S

• Step 3: Calculate consumer surplus at each intersection point

Price

Quantity

P

D

• Does point 2 ever maximize consumer surplus?

Ans: No, because point 1 always gives more consumer surplus than point 2

1

3

2

A

B

Q2 Q3Q1

C

Moral Hazard and Insurance Deductibles

• Can deductibles reduce the deadweight loss from moral hazard?

• Yes, if area C > area B, then the insurance plan can still provide some risk protection against large medical expenses without causing any deadweight loss from moral hazard

• This can potentially increase welfare relative to an insurance plan with the same coinsurance rate and $0 deductible

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Tradeoff Between Benefit and (Social) Cost of Insurance

 We discussed why full insurance is optimal if premiums are actuarially fair

 However we also know that insurance can cause deadweight loss to society due to moral hazard

 What is the optimal tradeoff?  How much insurance should people have?

 Given that everyone doesn’t have perfect health insurance, can moral hazard explain why?

25

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‘Excess’ Health Insurance • The level of coinsurance directly impacts the size of the deadweight loss

due to moral hazard

• Increasing coinsurance reduces moral hazard costs, but also increases risk faced by consumers

• What is the optimal level of coinsurance given this tradeoff?

• Question studied by Feldstein (1973) • Consider a change in coinsurance rates from 33% to 66%

• Estimates that moral hazard costs fall much faster than the welfare losses from reducing risk protection

• Net welfare gain (gains from reducing moral hazard minus losses from reducing risk protection) would be $27.8 billion per year in 1984 dollars (about $62.3 billion in 2013)

• More recent numbers (Feldman and Dowd 1991) suggest net welfare gains between $74 - $244 billion per year (2013 dollars)

• Implication: Health Insurance plans in the US are too generous, on average

Asymmetric Information and Adverse Selection

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Intro

 A man walks into the office of a life insurance company.  He wants to buy a $1 million life insurance policy

for a term of one day. Your company will have to pay $1 million to his heirs if and only if he dies tomorrow.

 You know nothing else about this man.

 How much do you charge?

Asymmetric information

 Definition: a situation in which agents in a potential economic transaction do not have the same information about the quality of the good being transacted

 Asymmetric information is the key source of many problems in health insurance markets

The “Lemons” Problem

 Akerlof (1970)  Demonstrates that asymmetric information (as

opposed to imperfect information) leads undersupply  Welfare enhancing transactions do not occur

 Difficult because markets may not exist (as opposed to observably performing poorly)

30

Akerlof Model of the Used Car Market

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First: Symmetric Information

 Imagine a well-functioning used car market

 Sellers advertise cars, and buyers can accurately assess the condition of each car for sale

 Some buyers will be willing to pay more for cars in good condition; others are happy to get a low-priced deal

 Symmetric information: buyers and sellers have symmetric info about car quality. This is crucial.

 Outcome: each car sells for a different price, depending on its quality

Symmetric Information

 Pareto-improving transaction: a transaction that leaves all parties at least as well-off

 In any perfectly competitive market with full information, any Pareto-improving transaction will always occur  All the cars will end up with the people who

value them the most

Next: Asymmetric Information

 New assumption: sellers can determine car quality, but buyers cannot

 All cars look identically good to the buyers

 This market will look different from the previous one in several ways:  Any cars that sell, sell for the same price

 The best cars will not be offered on the market

 It is possible that the cars will not end up with the people who value them most (buyers)

Why is there only one price?

 Imagine that two cars are offered for different prices in this market: P and P’ > P

 No buyer will want to buy the expensive car, because both cars will seem the same

 All sellers will have to lower their prices to match the lowest price on the market

Why are some cars not offered?  We know the market has one price P  Consider the seller who owns the nicest car on

the market – it is probably worth way more than P  That seller has no reason to remain in the market  Why doesn’t he advertise the high quality of his

vehicle and charge a higher price?  Remember, buyers can’t “see” quality

 Outcome: only the lower-quality cars stay on the market. This is our first example of adverse selection.

Adverse selection

 Definition: the oversupply of low- quality goods, products, or contracts that results when there is asymmetric information.

 This is (arguably) the single most important concept in understanding the economics of private health insurance markets.

A Formal Model

 We will introduce a formal model of the market we discussed in the previous slides.

 We will present explicit utility functions and a specific distribution of car quality to make the argument more concrete.

 But remember – the logic of the argument is the same as what we just saw.

Seller and buyer utility functions

 Sellers and buyers derive utility from the cars they own and other goods

 Buyers value cars 50% more than sellers (that’s why it is Pareto efficient for them to buy)

 Xj = quality of the jth car owned

 M = utility from other goods

Distribution of car quality  Car quality X is uniformly distributed between 0 and 100

 Cars are equally likely to have any quality level between 0 and 100

 You are equally likely to have a car of quality level 50 as you are to have a car of quality 96, 17.5, 42, or any other real number between 0 and 100

 We use the term Xi to denote the quality of car i

Information assumptions

 Buyers do not know the true quality of a particular car

 Buyers know the utility function of the sellers and know the distribution of cars available for sale

 They also understand that sellers will withdraw highest-quality cars if the price does not justify selling.

Which cars will sellers offer?

 A seller will put a car on the market if selling it will increase their utility.

 If a seller sells their car of quality X for P dollars, they lose X units of utility but gain P dollars

 Hence, they will only put car j on the market if P > Xj

When will buyers buy?

 Figuring out when buyers buy is trickier due to uncertainty.

 Like sellers, buyers are trying to maximize utility. But think about a buyer who is considering buying a car of uncertain quality. How do they know what will happen to utility?

 Buyers have to think in terms of expected utility.

When will buyers buy?

 Suppose a buyer buys a car in this market.  They pay P dollars and thus lose P units of utility.  They gain a car with expected value E[X|P], so

gain 3/2 E[X|P] units of utility.  Remember, E[X|P] means “expectation of X

conditional on P.” We need to think about P because it affects sellers’ decisions, and hence affects the distribution of quality X.

 Hence, buyers will buy if they expect buying to increase their utility:

When will buyers buy?

 We need to find E[X|P] to decide if buyers will buy  Remember the distribution of cars now:

 The formula for expectation for a uniform distribution is simply the average of the endpoints. So E[X|P] = ½ P

When will buyers buy?

 We found E[X|P] = ½ P  We plug that into our condition for buying:

3/2 E[X|P] > P 3/2 * ½ P > P ¾ P > P

 This is impossible; hence buyers will not buy for any P!

 No cars sell, no Pareto-improving trades take place, the cars stay with sellers (who do not want them as much as the buyers do). The market unravels.

What just happened?

 To review:  A single price P is somehow established in the market

 Sellers remove all cars of quality greater than P

 Of the cars that remain, the average quality (E[X|P]) is only ½ P

 Buyers do not like cars enough to buy a car of quality ½ P for a price of P

 No cars sell, even though buyers like cars better than sellers and all the cars “should” end up with buyers.

 This result is called an ADVERSE SELECTION DEATH SPIRAL, and it can cause an entire market to fail to exist.

What does this used car market have to do with health insurance?  Analogy between these two markets

 The “cars” are customers’ bodies  The “sellers” are customers  The “buyers” are insurance companies  The sellers try to convince the buyers that the

“cars” are healthy; just as a high-quality car is worth a lot to buyers, a healthy customer is worth a lot to insurers

 Just like high-quality cars leave the market when a universal price is set, high-quality bodies will leave the market when a universal premium is set.

Health insurance market

 Suppose the insurer offers a contract with premium $10,000 for the year.

 What happens? Who stays in the market?

Health insurance market

 Only the least healthy people buy insurance; their average health expenditures are $15,000.

 The insurer raises premiums to $15,000 the next year.

Adverse selection death spiral

 There is nothing to stop this cycle, which is called an adverse selection death spiral.

 Definition: successive rounds of adverse selection that destroy an insurance market.

 The heart of the problem is adverse selection: only the worst customers stay in the market when the insurer sets the premium.

 No way for the insurer to turn a profit in this very simple model.

When is it possible to avoid a death spiral?

What if buyers value cars very highly?

 Let’s assume new utility functions:

 Now buyers value cars much more than sellers. Will this fix the market?

What if buyers value cars very highly?

 Nothing on the seller side has changed, so just as before:  E[X|P] = ½ P

 We plug that into our condition for buying: 5/2 E[X|P] > P 5/2 * ½ P > P 1.25* P > P

 This is always true!  All cars will sell, and each sale is Pareto-

improving

What if there is a minimum guaranteed car quality?  The condition for buyers is as it was before, but now

E[X|P] will be different because a different subset of cars is on the market.

 This is promising: the worst cars were forced off the market, so the remaining cars are better.

What if there is a minimum guaranteed car quality?  When do buyers buy?

 If 3/2 E[X|P] > P

 What is E[X|P]  Based on the formula for the expectation of a

uniform distribution, E[X|P] = ½ * (P + 10)

 Buyers buy if: 3/2 E[X|P] > P

3/2 * ½ * (P + 10) > P 3/4 P + 15/2 > P

 Buyers will buy if the price is below $30.

Policy Tools that could help Counter Adverse Selection

1. Price subsidization  If the government helped subsidize insurance purchases, that

will increase willingness to pay (for example, from 3/2 to 5/2), potentially preventing a market death spiral

2. High-Risk pools  Remove the sickest people from the private market, and put

them in a different public insurance plan

 This will remove the worst “lemons” from the market, creating a similar effect as the guaranteed minimum quality example

 The ACA, and some state policies create “high-risk pools” that do exactly this, in order to help keep the private insurance market from experiencing a death spiral

 Many other policy tools, to be discussed soon…

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Conclusion  Asymmetric information causes parties to

misrepresent themselves  Adverse selection removes high-quality goods

from the market, leaving only low-quality  Generally, the market will unravel unless:

 Someone values a product highly enough to have a positive change in utility

 Government regulation through a price floor promotes a minimum standard of quality

 One major concept has been missing in this whole analysis: risk aversion.

 The Rothschild-Stiglitz model combines asymmetric information and risk aversion.

Generalizing Adverse Selection to Insurance Markets

 Expected costs are correlated with willingness to pay

 Marginal consumer differs from the average consumer

 Consumer expectations about costs are not observable to insurance company, so insurers can’t tell who will be high cost or low cost

 As a result insurers set prices based on the average cost of everyone who buys insurance

 Welfare loss due to the inability to discriminate between the two

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Welfare Loss from Adverse Selection

 Equity Loss: Should people who are born sick, or get sick because of something beyond their control have to pay more?

 Efficiency Loss: Generally causes an equilibrium involving less than full insurance  This is true even markets with adverse selection that

are otherwise perfectly competitive

60

Implications for Insurance Markets

 More competition is not necessarily better  Offering lots of insurance plan options does not fix the

problem of adverse selection

 Health insurance companies prefer not to offer goods that sick people prefer  Prefer not to offer tools that improve health for chronically ill

 Instead offer gym memberships to attract fit people

61

Adverse Selection in Health Insurance Markets: Graphical Representation of Akerlof Model 62

• Consider the market for a specific insurance contract

• Consumers make a single choice: buy the insurance or not

• Consumers have private information about their expected healthcare costs

• Insurers cannot observe expected healthcare costs, and view all consumers as identical

Adverse Selection in Health Insurance Markets: Graphical Representation of Akerlof Model 63

• Demand curve represents willingness to pay for insurance

• MC (marginal cost) curve represents the medical costs the insurer will have to pay if they sell one more unit of insurance

• Why does the demand curve lie above the MC curve?

• Why is the MC curve downward sloping?

• What is different about the relationship between MC and demand here?

Adverse Selection in Health Insurance Markets: Graphical Representation of Akerlof Model 64

• Because the MC curve is downward sloping, the next consumer to buy insurance is always cheaper than the average of those who previously purchased insurance

• Therefore, the AC (average cost) curve is also downward sloping

Adverse Selection in Health Insurance Markets: Graphical Representation of Akerlof Model 65

• Since insurers cannot observe any differences between consumers, they can only charge one single price

• What is the equilibrium market price of insurance?

• Who will buy insurance at this price?

• What the effect of adverse selection on social welfare?