Adverse selection Abhinash adhikari Astha gyawali Bijay chalise Salim l. awale Sweta bhattarai

Adverse selection It refers to that market condition where sellers have information that buyers do not, or vice-versa, about some aspect of product quality. The asymmetry of information often leads to making bad decisions. Focus on how and when mangers use their informational advantage to increase performance.

The market for lemon Ackerlof’s model: used car market Used cars are either gems(which is good) or lemons ( which is bad)

The market for lemon Sellers have more information than buyer does about the quality of the car Buyers assume car must be of average quality so they don’t want to pay more than average (Break even point) Buyers Sellers

The market for lemon Ackerlof’s model: used car market Sellers will sell car if the quality of car is average or low then average, “Lemon”. Average price of a used car finally equal to the value of a lemon. This is a case of adverse selection where only lemons being offered for sale on the used car market.

Adverse selection in automobile insurance Insurers distinguish the drivers bases on various characteristics Good drivers pay low premiums Bad drivers pay high premiums

Asymmetry of information Buyers have more information Sellers Buyers

example Wealth=125 In the case of loss, Loss=100 High-risk drivers Low risk drivers Wealth=125 In the case of loss, Loss=100 Wealth is reduced to 25 Probability of loss= 75% Thus, Expected loss=(0.75*100)=75 Wealth=125 In the case of loss, Loss=100 Wealth is reduced to 25 Probability of loss= 25% Thus, Expected loss=(0.25*100)=25

graph Utility=(Wealth)0.5

Perfect information Premium=Expected loss=75 High risk drivers Low risk drivers Premium=Expected loss=75 Utility with insurance = (125-75)0.5 =7.071 Utility with no insurance =(0.25)(125)0.5+(0.75)(25)0.5 =6.545 Premium=Expected loss=25 Utility with insurance = (125-25)0.5 =10 Utility with no insurance =(0.75)(125)0.5+(0.25)(25)0.5 =9.635

Asymmetric information Average premium=0.5(25+75)=50 High risk drivers Low risk drivers Utility with insurance = (125-50)0.5 =8.660 Utility with no insurance =(0.25)(125)0.5+(0.75)(25)0.5 =6.545 Utility with insurance = (125-50)0.5 =8.660 Utility with no insurance =(0.75)(125)0.5+(0.25)(25)0.5 =9.635

Result!! Market failure!! Only the people who most likely need insurance will actually end up paying for it.

Restoring the market Competition between insurers Strategic designs

It is a form of insurance or investment entitling the investor to a series of annual payment. Annuity helps solve problem of income guarantee after retirement.

Insurance Company

Insurance Company

What are the incentives of the managers at the annuity firm ? For this let us consider 1000 65-year-old women who pay $300,000 for the annuity plan. There are two possible scenario: The health status of each individual is known to both manager and that person. i.e. Annuity with full information. There is asymmetric information, the person knows her health status the manager does not. i.e. Annuity with asymmetric information.

MARKET WITH FULL INFORMATION A quarter of our population lives for 5 years Half are in good health and live for 15 Years A quarter is in excellent health and live for 25 Years

MARKET WITH FULL INFORMATION 250 65-yr-old women are paid =$300,000/5 =$60,000/yr 500 65-yr-old women are paid =$300,000/15 =$20,000/yr 250 65-yr-old women are paid =$300,000/25 =$12,000/yr

MARKET WITH ASYMMETRIC INFORMATION: ADVERSE SELECTION Because Managers do not know health status, they estimate the firm can break even if it receives $300,000. who should be offered annuity of $20,000 Here Receipt: =1000 times $300,000 =300,000,000 Payments: =250*$20,000*5 =$25,000,000 or $100,000/person =500*$20,000*15 =$150,000,000 or $300,000/person =250*$20,000*25 =$125,000,000 or $500,000/person Total Payments = $300,000,000

WHO BUYS THE ANNUITY ? Of course managers can anticipate that only those in average or better than average health will buy the policy.

EVIDENCE OF ADVERSE SELECTION IN ANNUITY Managers can use simple test to see whether annuity markets are subject to adverse selection. In early example life expectancy calculated as: = (250*5+500*15+250*25)/1000 = 15 years If $20,000 was annuity only 750 people will buy annuity so = (500*15+250*25)/750 = 18.33 years

MORTALITY DISTRIBUTIONS FOR US POPULATION AND ANNUITANTS

The Absence of Adverse Selection in Life Insurance Whereas annuities insure against “living too long "life insurance protects the survivors of people who “die too soon”.

Managers at life insurance firms have been very effective in establishing the health status of their policy holders. There seems to be no traceable adverse selection here.

Resolving adverse selection through self selection While Ackerlof described the adverse selection Problem, Michael Rothschild and Joseph Stiglitz laid out a solution to adverse selection. i.e. managers should design policies that separate behavior between good and bad drivers.

Resolving adverse selection through self selection Example 1: Policy A:high premium and full insurance Policy B:low premium high deductible Example 2: Policy C:high premium that is constant from year to year Policy D:higher(than C) premium at first that declines from year to year

Separating equilibrium This solution to adverse selection induces policy holders to select their relative risk types High risk drivers Low risk drivers

Separating equilibrium This solution to adverse selection induces policy holders to select their relative risk types High risk drivers Low risk drivers

High risk drivers No insurance:0.25(125)^0.5+0.75(125-100)^5 = 6.545 Policy 1: (125-75)^0.5 = 7.071 Policy 2: 0.25(125-2.5)^0.5+0.75(125-100-2.5+10)^5 =7.043

Low risk drivers No insurance:0.75(125)^0.5+0.25(125-100)^0.5 =6.545 Policy 1: (125-75)^0.5 =7.071 Policy 2:0.75(125-2.5)^0.5+0.25(125-100-2.5=10)^0.5 =9.726

USING EDUCATION AS A SIGNAL: ADVERSE SELECTION IN THE JOB MARKET How can managers predict which job applicant will have good work skills??? Applicants have some self-awareness about their job market skills, Information asymmetry, Simply asking applicants to reveal their private information does not work. Relationship between job skills and academic performance,

Example: Average direct and indirect cost per course are, High-quality job skills = $2000 per course Low-quality job skills = $3450 per course ( they take longer to finish) Now assume that if employers knew the skill levels of applicants, they would pay the following wages: High-quality job skills = $50000 per year for 5 years Low-quality job skills = $30000 per year for 5 years

The benefit and cost of achieving x courses: High skill: Benefit of achieving x courses = $100000 Cost of achieving x courses = $2000 times x The benefit exceeds the costs if x is less than 50. Low skill: Cost of achieving x courses = $3450 times x The benefit exceeds the costs of x is less than 29.

Contd. So the employers choose a level of x between 29 and 50, Another way of thinking about this is provided by our MBA students, Must set its standards sufficiently high to discourage low- skilled people, Other functions in addition to sorting people according to job skills, Ideally people learn something as well.

USING EDUCATION AS A SIGNAL: ADVERSE SELECTION IN THE PRODUCT MARKET Experience goods, Unable to determine the true quality of the goods, Separating equilibrium so consumer can accurately determine product quality, Common method use to create this separation: Product Warranty Credible signal of product quality, Product that carry a credible warranty is most desirable in market.

How Managers Can Construct Warranties To Mitigate Adverse Selection Competitive market: too many competitive products with same functions, Products of different qualities (high and low quality), Price and production cost of the product differs according to their qualities, Separate market for high quality product and low quality product, Firms producing high-quality product want to construct a separating mechanism,

Here is how they can do so using a product warranty: Two possible scenarios: First scenario: Consumers perceive any good with a warranty (X years) to be a high- quality good. Second scenario: Consumers perceive the good with the longer warranty (X years) to be the high-quality good.

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Contd. But now, think strategically… If the high-quality producer issued a warranty of YH, The low-quality producer can’t afford to offer more than YL, High-quality producer out-warranty the low-quality producer, A warranty of YH = YL + 1 ** Notice the similarity to auctions..