Customer‘s safety is the future trend of the foodservice and hospitality industry

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Asymmetric Information

Part 1. Private information

Economics 313

Asymmetric Information

 So far the uncertainty we have been talking about it “symmetric”: which means everyone is equally informed and in fact we have assumed they agree on all the relevant probabilities.

 In fact, most people have private information: relevant knowledge about the probability of events that others don’t have.

 More formally private information is information people know about themselves or products that is unobservable to people for transactions take place ex ante (before a transaction)

 This private information may only become known (possibility imperfectly) only after the transaction takes place (ex post)

Examples of Asymmetric Information

 Financial markets  Buyers of risky might not know as well as sellers how risky is a

financial asset. Why are they choosing to sell?  Insurance companies  Risks differ across people, and are sometimes affected by

actions that might be unobservable.  Banks and Loans  Don’t know the type of person you are loaning too (likely to

pay you back or not)  Firms and Workers  Employers do not have perfect knowledge about job

candidates. Employees may know more about their actions than owners.

Consequences of Asymmetric Information

 Earlier we argued that uncertainty itself need not lead to inefficiency.

 When everyone shares the same information, beliefs might differ (or not) but as long as the uncertainty was “priced,” trades would occur to capture surplus.

 When some agents have better information, this may not happen. In extreme cases, markets might collapse entirely, even when everyone knows that trades generally create surplus.

Asymmetric Information

 We will look at two types of phenomena that give rise to market failures in the presence of asymmetric information

1. Adverse Selection 1. Occurs because one party is unable to recognize certain

characteristics of the other party before the trade. “Types” of things or people are fixed

2. Moral Hazard 1. Occurs because one party is unable to recognize certain

characteristics of the other party after the trade. “Type” is a choice variable and actual risk or quality will be a function of an individual’s environment.

Adverse Selection

 Adverse Selection  Our inability to distinguish one type from another type can

result in market outcomes in which - in some sense - the “wrong types” ends up trading.

 That is, the market “adversely selects” for type.

 We often see examples in which adverse selection leads to missing markets for high quality goods.

 Textbook example is the used car market. a.k.a., “the market for lemons.”

Moral Hazard

 Moral Hazard  When “types” are endogenous, our inability to monitor

peoples behavior can result in the “wrong types” of behavior

 Moral hazard problems are present in all situations of insurance (whether formal insurance or informal insurance) including health insurance.

 Example: Insured drivers may be more risky than uninsured drivers because they can “afford” to take risker actions because they will be compensated in case of a bad outcome

-- end of part 1 --

Asymmetric Information

Part 2. Adverse Selection

Economics 313

The Market For Lemons  Suppose that there are 2 types of used cars: good quality cars

and bad quality cars

 There are 50 sellers of good quality cars  Each is willing to sell at a price of $2000 or more

 There are 50 sellers of bad quality cars  Each is willing to sell at a price of $1000 or more

 There are 100 (potential) buyers of cars  Each buyer values good quality cars at $2400 and bad quality

The Market For Lemons

Slide 11

 If there was perfect information about the quality of cars  Bad cars would sell in the price range of $1000 to $1200.  Good cars would sell in the price range of $2000 to $2400.

 All cars would be sold, because buyers value the two types of cars more than the sellers.

 Now suppose the both the buyers and sellers do not know about the quality of cars

 Assume both are risk neutral

The Market For Lemons

Slide 12

 Calculate the expected value to the buyer 0.5 × 1200 + 0.5 × 2400 = 1800

 Calculate the expected value to the seller: 0.5 × 1000 + 0.5 × 2000 = 1500

 Any offer above $1500 would be acceptable; any offer below $1800 would make buyers better off.

 All the cars would sell. The efficient outcome.

The Market For Lemons  But what if sellers know the type of the car they are

selling and buyers don’t (there is asymmetric information)

 Buyers still in the same situation. A randomly chosen car is worth $1800.

 Sellers, however, either have a car worth $1000 or a car worth $2000 to them…. Who would sell?

 In this world, only the owners of lemons would be willing to sell their cars.

The Market For Lemons

Slide 14

 Knowing this buyers would update their beliefs and know that only lemons (bad cars) would be sold

 Thus buyers willing are only willing to pay $1200 for a car.

 Not all mutually beneficial trades are made

 This is a market failure due to the adverse selection of cars into the market

The Market For Lemons

Slide 15

 When an individual tries to sell a bad car, he or she affects the purchaser’s perceptions of the expected quality of the average car on the market.

 This lowers the price that they are willing to pay for the average car, and thus hurts the people who are trying to sell good cars.

 If too many low-quality cars are offered for sale it makes it difficult for the owners of high-quality cars to sell their products.

-- end of part 2 --

Asymmetric Information

Part 3. Responses to Adverse Selection

Economics 313

The Market For Lemons: A Solution?

Slide 18

 The sellers of the good used cars have the incentive to convey the quality of their car to the buyers

 But talk is cheap and just by telling potential buyers that they have a good car isn’t convincing as anyone could say that.

Warranty as a Signal

Slide 19

 One sensible signal would be for the owner of a good used car to offer warranty  This is a promise to pay the purchaser some agreed upon

amount if the car turned out to be a lemon.

 Suppose sellers can make a take-it or leave it offer

 Also assume lemons are 100% detected after the car is sold.

 How high would the warranty have to be to will function as a signal of a good quality car?

Warranty as a Signal

Slide 20

 Since sellers make the offers, they will extract the maximum price for the cars from the buyers.  For good cars: $2400, and bad ones $1200.  Remember sellers value good cars at $2000 and bad ones at $1000

 Let’s say I am the seller and I offer you the car for $2400 dollars and say I will give you back $500 if the car breaks down. Will you take my offer?

 It makes sense to say no because a seller of a bad car would also make that offer: 2400 − 500 > 1000. The bad car seller is still up $900 from selling the car with this warranty. Not informative.

Warranty as a Signal  All cars will be bought if buyers are indifferent

between buying a good one or a bad one

 Everybody offering a car at $2400, would have to offer a warranty of at least $1400 to convince the buyer the car was a good one

 Sellers of lemons will not offer a warranty and sell their cars for $1200, while sellers of “cherries” sell their cars at $2400 and offer a warranty of $1400

Warranty Achieves Pareto Efficiency

Slide 22

 In this case warranty only imposes a cost on the sellers of bad cars, but not the seller of good cars

 The outcome with warranty is Pareto-optimal: All trades are made and in equilibrium, nobody ever pays the warranty

 In the case of the lemon market, we have a Pareto improvement over the situation in which only lemons are sold. By introducing the warranty nobody is made worse off and sellers of good cars are made better off.

Signalling  Warranty acts as signal that perfectly separates the

sellers of good and bad cars

 A separating equilibrium exists when a signal is sent that perfectly distinguishes types (the sellers of good cars and bad cars) and no one has an incentive to change their actions

 If the types are not separated and no credible signal is sent, then a pooling equilibrium may exist.

Other Ways to Solve Adverse Selection  Reducing asymmetric information directly  Example: having a mechanic investigate the vehicle before

purchase

 Repeated Interactions between buyer and seller  Reputation

 Increasing the average “good quality” in the market  This increases buyers willingness to pay and encourages more

“good quality” sellers to sell

What I Expect You to Know  Identify when adverse selection may be problem

 Explain why markets may fail with adverse selection

 Propose solutions to this market failure

-- end of part 3 --

Asymmetric Information

Part 4. Moral Hazard

Economics 313

Moral Hazard-Hidden Action

Slide 28

 So far we have assumed looked at asymmetries at the time of signing a contract, when “types” are unobservable.

 Now we consider asymmetries after the contract is signed, and the case where payoffs depend on “actions” taken by individuals

 If these actions cannot be monitored we have a problem of “hidden action” or Moral Hazard

Moral Hazard-Hidden Action

Slide 29

 Applications where people can prevent bad things from happening to them by taking precaution.

 Examples: health, theft, fire etc.

 E.g. once insurance is bought, people might become careless and the probability of theft changes.

 An insurance company not taking into account the change in probability of thefts might end up loosing money instead of making a profit.

Example: Insurance Against Burglary

Slide 30

 Imagine you own that $100 million dollar home. Now there is a chance that your house gets burglarized

 In this case you will only have the value of your house without the furniture, entertainment centre and art objects, which is 25 million

Example: Insurance Against Burglary

Slide 31

 Suppose you also like to sleep with the window open at night. Closed windows lower your utility.

 Assume your utility function over wealth is 𝑈𝑈 = 𝑤𝑤 1 2, and

that the utility from sleeping with the window open would be equivalent to an additional 1 million in wealth.

 This action (sleeping with the window open) would increase the chance of attracting burglars from 20% to 25%

Insurance Against Burglary Example

Slide 32

 Without insurance, would you choose to sleep with your window open or closed?

 Your expected utility with windows closed:

𝐸𝐸𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0.2(25) 1 2 + 0.8(100)

1 2 = 9

 Your expected utility with windows open:

𝐸𝐸𝑈𝑈 𝑐𝑐𝑜𝑜𝑐𝑐𝑜𝑜 = 0.25(25 + 1) 1 2+0.75(100 + 1)

1 2= 8.8122

 You will choose to sleep with your windows closed.

Insurance Against Burglary Example

Slide 33

 Your insurance company is risk neutral

 Suppose your insurance firm does not know about your desire to sleep with the window open and cannot observe your choice, and charges you the “fair” premium, assuming the chance of burglary is 20%

 What is your premium? Recall this gives zero profit:

𝑃𝑃𝑃𝑃𝑐𝑐𝑃𝑃𝑃𝑃𝑃𝑃 = 0 = 0.8 𝑃𝑃 − 0 + 0.2(𝑃𝑃 − 75) 𝑃𝑃 = 0.2 × 75 = 15

Insurance Against Burglary Example

Slide 34

 What’s your expected utility if you buy insurance and you continue to sleep with the windows closed?

𝐸𝐸𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐, 𝑃𝑃𝑜𝑜𝑐𝑐𝑖𝑖𝑃𝑃𝑐𝑐𝑐𝑐 = 0.2(100 − 15) 1 2+0.8(100 − 15)

1 2

= 9.2195

 What’s your expected utility if you now leave the windows open after buying insurance?

𝐸𝐸𝑈𝑈 𝑐𝑐𝑜𝑜𝑐𝑐𝑜𝑜, 𝑃𝑃𝑜𝑜𝑐𝑐𝑖𝑖𝑃𝑃𝑐𝑐𝑐𝑐

= 0.25(101 − 15) 1 2+0.75(101 − 15)

1 2= 9.2736

Insurance Against Burglary Example

Slide 35

 Will you change your behavior after being fully insured? A. Yes B. No

 Yes, utility is higher if you get insurance and sleep with your window open.

Insurance Against Burglary Example

Slide 36

 What happens to the insurance’s expected profit if you changes your behavior? A. It goes up B. It goes down C. It goes down and they make a loss D. It goes up and they break even

Insurance Against Burglary Example

Slide 37

 What happens to the insurance’s expected profit if you changes your behavior? A. It goes up B. It goes down C. It goes down and they make a loss D. It goes up and they break even

𝑃𝑃𝑃𝑃𝑐𝑐𝑃𝑃𝑃𝑃𝑃𝑃 = 0.75 15 − 0 + 0.25 15 − 75 = −3.75

 The insurance company loses money in expectation.

Insurance Against Burglary Example

Slide 38

 If the insurance company knows about your desire to leave the window open, what would be the premium that guarantees that the insurance will break even?

 The fair premium where burglary occurs with probability

𝑃𝑃𝑃𝑃𝑐𝑐𝑃𝑃𝑃𝑃𝑃𝑃 = 0 = 0.75 𝑃𝑃 − 0 + 0.25(𝑃𝑃 − 75) 𝑃𝑃 = 0.25 × 75 = 18.75

Insurance Against Burglary Example  Would you buy insurance at this premium? Yes

 Your utility would be

𝐸𝐸𝑈𝑈 𝑐𝑐𝑜𝑜𝑐𝑐𝑜𝑜, 𝑃𝑃𝑜𝑜𝑐𝑐𝑖𝑖𝑃𝑃𝑐𝑐𝑐𝑐 = 0.25(101 − 18.75)

1 2+0.75(101 − 18.75)

1 2= 9.0692

 This utility is higher than in the case where you do not buy insurance (and so close your windows):

𝐸𝐸𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐, 𝑖𝑖𝑜𝑜𝑃𝑃𝑜𝑜𝑐𝑐𝑖𝑖𝑃𝑃𝑐𝑐𝑐𝑐 = 0.2(25) 1 2 + 0.8(100)

1 2 = 9

The Commitment Problem

Slide 40

 However, your utility would be even higher if you could commit to your insurance company that you will keep the windows closed and buy insurance at a premium of 15. (𝐸𝐸𝑈𝑈 = 9.2195 rather than 9.0692.)

 But this is not credible: because they cannot observe whether the windows are open, you have no incentive to keep your word, and will open the windows once you have been fully insured.

Comparison of Payoffs

Windows Open (probability bad state 25%)

Windows Closed (probability bad state 20%)

With Full coverage and premium per dollar = 0.2

(9.2736, -3.75)* (9.2195, 0)

With Full coverage and premium per dollar = 0.25

(9.0692, 0) (9.0139, 3.75)**

No Insurance (8.8122, 0) (9, 0)

(Your Payoff, Insurance Firms Pay off)

*If allowed, would over-insure with 133 of coverage for payoffs: (9.3458,-6.64) **would not fully insure, with 35 of coverage for payoffs: (9.074, 1.75)

exit

entryCompetitive Equilibrium

entryentry

The Commitment Problem

Slide 42

 Your utility would be even higher if you could commit to your insurance company that you will keep the windows closed and buy insurance at a premium of 15. (𝐸𝐸𝑈𝑈 = 9.2195 rather than 9.0692.)

 But this is not credible: because they cannot observe whether the windows are open, you have no incentive to keep your word, and will open the windows once you have been fully insured.

-- end of part 4 --

Asymmetric Information

Part 5. Responses to Moral Hazard

Economics 313

Payoffs again in terms of Wealth

Windows Open (probability bad state 25%)

Windows Closed (probability bad state 20%)

With Full coverage and premium per dollar = 0.2

(82.25, -3.75)* (85, 0)

With Full coverage and premium per dollar = 0.25

(82.25, 0) (81.25, 3.75)**

No Insurance (77.65, 0) (81, 0)

(Your CE Payoff, Insurance Firms Pay off)

*If allowed, would over-insure with 133 of coverage for payoffs: (87.34,-6.64) **would not fully insure, with 35 of coverage for payoffs: (82.33, 1.75)

Competitive Equilibrium

Moral Hazard Leads to Market Failure

Slide 46

 It is clear that the competitive equilibrium is not Pareto efficient

 You could be made better off without making the insurance company worse off, if you could commit to not changing your behavior after you get insurance

 We encountered here a case of market failure due to Moral Hazard: the temptation to cheat undermines the optimal contract

Mitigating Moral Hazard

Slide 47

 Insurance companies could require certain actions and insure the have been taken

 Co-payments and deductibles  Co-payments and deductibles do not provide full coverage, and therefore

the utility in both states of the world would not be the same for the insured individual anymore

 Deductible is a specified amount of money that the insured must pay before an insurance company will pay a claim. Co-payments are typically smaller and paid at the same time (like a doctors visit)

 Neither perfect, but brings us closer to Pareto efficiency

Example: Deductibles

Slide 48

 In the Competitive Equilibrium without deductibles you paid 18.75 for full insurance, which gives you a utility of 9.0692.

 We will see that by adding to the contract a deductible 𝐷𝐷 we can improve on the competitive equilibrium.

 There are several conditions that need to be satisfied, and in general more than one combination of premiums and deductibles will satisfy these.

Some Conditions on the Contract:

Slide 49

 We assume that the contract is for the whole loss of 75. This is realistic, as in the real world, firms will generally not “over-insure”

 We assume that this firms offering this contract are earning zero profit. This is required for competitive equilibrium in the contracts with deductibles.

Some Conditions on the Contract:

Slide 50

 We assume that you are better off taking the contract than an alternative, which we will assume it the equilibrium contract from a firm that does not use deductibles. This “reservation utility” is 9.0692

 We assume that the deductible and premiums are such that you prefer to sleep with the windows closed. That is that you can “credibly commit” to a probability of loss of 0.20, and the firms can price to this likelihood. It is “incentive compatible”

The Contract:

Slide 51

 We will show that a contract for 75 units of insurance priced at p = 0.148 per unit with a deductible of 𝐷𝐷 = 19.5 will satisfy all of these constraints and be a Pareto improvement on the Competitive Equilibrium without deductibles.

 With a price of 0.148, insuring the full loss of 75 means the premium is 𝑃𝑃 = 11.1

 Let’s check the constraints…

Constraints: The Insurer

Slide 52

 By assumption, the full loss is insured.

 The profits for the insurer are

0.80 𝑃𝑃 + 0.20 𝑃𝑃 − (75 − 𝐷𝐷) = 0

0.80 11.1 + 0.20 11.1 − (75 − 19.5) = 0

 Insurance companies makes zero expected profit, so will participate, but not attract entry.

Constraints: The buyer

Slide 53

 The utility paying the premium and deductible and not leaving the windows open must be higher than with the premium and deductible and leaving your window open:

0.8(100 − 𝑃𝑃)1/2+0.2(100 − 𝑃𝑃 − 𝐷𝐷)1/2 ≥ 0.75(101 − 𝑃𝑃)1/2+0.25(101 − 𝑃𝑃 − 𝐷𝐷)1/2

 If this inequality is satisfied, you prefer to close your windows during the night. Given the deductible, the additional risk isn’t worth it. Compare with the case where you didn’t have any insurance.

The Contract: Incentive Compatibility

Slide 54

 Exp. utility with windows closed: 0.8 (100 − 11.1)1/2 + 0.2 (100 − 11.1 − 19.5)1/2 = 9.2090

 Exp. utility with windows open: 0.75 (100 − 11.1)1/2 + 0.25 (101 − 11.1 − 19.5)1/2 = 9.2088

 With this contract you will prefer to sleep with your windows closed

Incentives: Participation

Slide 55

 It also has to be in your interest to buy insurance at the premium and deductible offered  It needs to be in your best interest to participate

 Your utility from buying insurance and keeping your windows closed must be at least as high as your utility with the next best alternative  In this case, it is buying insurance at a premium of 18.75 and

leaving the windows open

. 0.8 (100 − 11.1)1/2 + 0.2 (100 − 11.1 − 19.5)1/2= 9.2090 ≥ 101 − 18.75

1 2 = 9.0692

A Pareto Improvement

Slide 56

 The insurance schedule with premium of 11.1 and deductible of 19.5 is a Pareto-improvement over the competitive equilibrium without deductibles with the insurance premium of 18.75

 The insurance company is equally well off, and you are better off.

The Optimal Contract

Slide 57

 Generally we can characterize the types of contracts that can emerge. We need:

1. We need both parties’ to participate  their participation constraints are satisfied: having the

insurance contract in place is not making parties worse off as compared to their next best alternative

2. We need to make sure that the buyer of insurance takes the appropriate amount of care

 The buyer’s incentive compatibility constraint is satisfied: having the insurance contract in place makes it in your best interest to behave the way the company wants you to

What I Expect You To Know  How to identify when moral hazard is a problem and how

it differs from adverse selection

 Be able to write down a set of participation constraints and incentive compatibility constraints

 Propose Pareto improvements to moral hazard problem

-- end of part 5 --