eco question

DEMAND FOR INSURANCE

Comparing insurance contracts

 For anyone risk-averse, actuarially fair & full insurance contract offers the most utility

Comparing fair insurance contracts

 AF -- Actuarially fair & full  AP -- Actuarially fair & partial  A -- Uninsurance

 U(AF) > U(AP) > U(A)

Comparing unfair contracts

 AF – Full but actuarially unfair contract  AP – Partial but actuarially fair contract

Comparing unfair contracts

 In the previous graph, U(AF) > U(AP)

 Even though AF is actuarially unfair, its relative fullness (i.e. higher payout) makes it more desirable

 But notice if contract AF became more unfair, then expected income E[I] falls

 If too unfair, AF may generate less utility than AP

 Similarly, AP may become more full by increasing its payout

 Uncertainty falls, so point AP moves

 At some point, this consumer will be indifferent between the two contracts

 Where is that point?

Comparing unfair contracts

 AF’ – Full but actuarially unfair contract

 AP – Partial but actuarially fair contract

 In this case, both contracts give same expected utility

 In addition to the expected loss, how much extra money would this consumer be willing to pay for insurance?

 This amount is called the “risk premium,” and it describes the willingness to pay, or individual demand, for insurancedoc,docx,pdf,txt,odt

Risk Premium

 Before buying any insurance, expect to be at point A. Risk premium at point A is equal to the distance

 After buying partial insurance, expect to be at point AP. Risk premium at point AP is equal to the distance  This is the additional amount of money the consumer is willing to pay, beyond their

expected loss, in order to eliminate all remaining uncertainty

 Risk premium is positive because consumer is risk averse

 is less than because there is less remaining uncertainty once a consumer has already purchased partial insurance

B

D

A

C

• Total willingness to pay for insurance (demand) is equal to the expected loss that will be paid by the insurer plus the risk premium

• Risk premium is greater when: • There is larger variance in the potential outcomes

• Eg Variance(Y1,Y2) < Variance (Y1,Y3) causes CD<AB • There is less information about which value of Y will occur

• Eg A 50/50 chance of high/low wealth is the largest amount of uncertainty. • If the probability of losing money is 99% the risk premium is LOWER (all else equal)

because the outcome is nearly certain • Important lesson: if a consumer knows for sure (100%) that a loss will occur, there is zero benefit to buying insurance (assuming the consumer and insurer both have complete information)

Utility

Wealth ($) Y3 Y2 E[Y] Y1

Willingness to Pay (Demand) for Insurance

Supply of Insurance: Why are firms willing to sell insurance?

 Example: A Very Simple Insurance Pool:  Imagine 10 people each facing a risk of losing $100 with a

probability of 0.1  E(loss) = 0.1($100) + 0.9($0) = $10

 Each individual agrees to pay $10 and the ‘loser’ will get the $100  Actuarially fair premium is $10 (expected loss)

 Each individual ends up paying $10, and there is no remaining risk of losing money

 An insurance company is a firm that creates and manages an (or multiple) insurance pool(s)

Supply of Insurance: Why are firms willing to sell insurance?

 Insurance works by pooling risks across many people  Relies on the statistical Law of Large numbers

 As the number of pool members gets very large the average loss converges to the expected loss

 In this case, the insurance company’s revenue per customer (r) will equal is costs per customer (pq)

 This simple pooling of risk works if: 1. The probability of a loss can be predicted accurately 2. Losses are uncorrelated across people

 These two conditions do not always hold!!  Example: what would an insurance pool look like in the case of earthquake risk?  You should not be surprised to learn that in general a private, competitive

market for earthquake insurance will not function well (ie prices will likely be very actuarially unfair, and the market may not exist at all without regulation)

YPY − AL

Y BLY

B

D

A

C

Benefits 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

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?

Moral Hazard Effect of Insurance on Welfare

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…?

Can Deductibles Reduce Moral Hazard? • 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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

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?

‘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

Intro

 Suppose you own a life insurance company  A customer walks into the office an asks to buy a $1 million life insurance policy that expires in one day  Your company will have to pay $1 million if the customer dies

by tomorrow

 You know nothing else about this customer  What price will you charge for this insurance contract?

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)

Akerlof Model of the Used Car Market

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 they are buyers in the first place)

 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 proposed

 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.