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Asymmetric Information
1.
Asymmetric Information, Uncertainty,
and, Auctions Prepared by CĆ©sar R. Sobrino Universidad del Turabo August 16, 2018 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
2.
Outline 1 Asymmetric Information Moral
Hazard Adverse Selection 2 Uncertainty Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
3.
Asymmetric Information In purely
competitive markets all agents are fully informed about traded commodities and other aspects of the market. Markets with one side or the other imperfectly informed are markets with imperfect information. Imperfectly informed markets with one side better informed than the other are markets with asymmetric information. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
4.
Asymmetric Information: Some
examples A worker knows more than his employer about how much eļ¬ort he puts into his job. (example of a hidden action) A seller of a used car knows more than the buyer about the carās condition. (example of a hidden characteristic). a customer knows her taste for a good or a service better than the ļ¬rm that supplies and prices it. (example of a hidden characteristic). a person knows more about his driving habits than the company that provides his auto insurance (example of a hidden characteristic) Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
5.
Asymmetric Information Hidden actions
are actions taken by one side of an economic relationship (agent) that the other side of the relationship (principal) cannot observe. Agent: a person who is performing an act for another person, called the Principal. Hidden characteristics are things that one side of a transaction knows about itself that the other side would like to know but does not. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
6.
Asymmetric Information Moral Hazard Problems
after a contract is written. The tendency of an imperfectly monitored agent to engage in dishonest or otherwise undesirable behavior. Adverse Selection Problems before a contract is written. Refers to the tendency for the mix of unobserved attributes to become undesirable from the standpoint of an uniformed party. Imperfect information inļ¬uences resource allocation and the price system. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
7.
Moral Hazard Classic example:
employment. The employer is the principal and the worker is the agent. Moral Hazard is the temptation of imperfectly monitored workers to shirk their responsibilities. Employerās possible responses to Moral Hazard: better monitoring. higher wages ā employer pays above Value Marginal Product of Labor (VMPL). Then, the worker getting this wage is less likely to shirk because if caught he will not be able to ļ¬nd another high-paying job. delayed payment ā the employer can delay part of workerās compensation so that, if caught shirking and ļ¬red, the worker incurs a higher loss. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
8.
Moral Hazard A homeowner
buys ļ¬re insurance and then is likely to buy too few ļ¬re extinguishers because the homeowners bears the cost of each extinguisher while the insurance company receives much of the beneļ¬t. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
9.
Adverse Selection Market for
used cars. The lack of complete information when purchasing a used car increases the risk of the purchase and lowers the value of the car. Automobile Insurance: A ļ¬rm selling car insurances cannot identify owners living in high crime areas. If average cost is charged, it can lead to insurance ļ¬rm losing out. The Market for Credit: Asymmetric information creates the potential that only high risk borrowers will seek loans. How can credit histories help make this market more eļ¬cient and reduce the cost of credit? Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
10.
Adverse Selection Medical Insurance:
Buyers of health insurance know more about their health problems than do insurance companies. Because people with greater hidden health problems are more likely to buy health insurance than are other people, the price of health insurance reļ¬ects the cost of a sicker-than-average person. Is it possible for insurance companies to separate high and low risk policy holders? If not, only high risk people will purchase insurance. Adverse selection would make medical insurance unproļ¬table. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
11.
Adverse Selection When markets
suļ¬er from adverse selection, there are some problems: Owners of good cars may choose to keep them rather than sell them at the low price that skeptical buyers are willing to pay. In insurance markets, buyers with low risk may choose to remain uninsured, because the policies they are oļ¬ered are too expensive, given their true characteristics. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
12.
Market for used
cars:āPeachesā and āLemonsā Akerlof, George A. (1970). āThe Market for āLemonsā: Quality Uncertainty and the Market Mechanismā. Quarterly Journal of Economics. The MIT Press. 84 (3): 488ā500. Sellers of cars know their vehiclesā defects while buyers often do not. Because owners of the worst cars are more likely to sell them than are the owners of the best cars, buyers fear they would get a ālemonā. Low quality goods drive high quality goods out of the market. The market has failed to produce mutually beneļ¬cial trade. Adverse selection occurs; the only cars on the market will be low quality cars. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
13.
Market for used
cars:āPeachesā and āLemonsā Two types of cars: ālemonsā and āpeachesā. Each lemon seller will accept $1,000; a buyer will pay at most $1,200. Each peach seller will accept $2,000; a buyer will pay at most $2,400. If every buyer can tell a peach from a lemon, then lemons sell for between $1,000 and $1,200, and peaches sell for between $2,000 and $2,400. Gains-to-trade are generated when buyers are well informed. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
14.
Market for used
cars:āPeachesā and āLemonsā Suppose no buyer can tell a peach from a lemon before buying. What is the most a buyer will pay for any car? Let Ī» be the fraction of peaches. For all, Ī» ā ]0, 1[ (1 ā Ī») is the fraction of lemons. Expected value (EV) to a buyer of any car is at most Suppose EV > $2000. Every seller can negotiate a price between $2000 and $EV (no matter if the car is a lemon or a peach). All sellers gain from being in the market. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
15.
Market for used
cars:āPeachesā and āLemonsā Suppose EV < $2000. A āpeachā seller cannot negotiate a price below $2000 and will exit the market. So all buyers know that remaining sellers own lemons only. Buyers will pay at most $1200 and only lemons are sold. Hence ātoo manyā lemons ācrowd outā the peaches from the market. Gains-to-trade are reduced since no peaches are traded. The presence of the lemons inļ¬icts an external cost on buyers and peach owners. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
16.
Market for used
cars:āPeachesā and āLemonsā How many lemons can be in the market without crowding out the peaches? Buyers will pay $2000 for a car only if EV = $1200(1 ā Ī») + $2400Ī» ā„ $2000 Ī» ā„ 2 3 So if over one-third of all cars are lemons, then only lemons are traded. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
17.
Market for used
cars:āPeachesā and āLemonsā A market equilibrium in which both types of cars are traded and cannot be distinguished by the buyers is a pooling equilibrium. A market equilibrium in which only one of the two types of cars is traded, or both are traded but can be distinguished by the buyers, is a separating equilibrium. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
18.
Quality Choice Now each
seller can choose the quality, or value, of her product. Two umbrellas; high-quality and low-quality. Which will be manufactured and sold? Buyers value a high-quality umbrella at $14 and a low-quality umbrella at $8. Before buying, no buyer can tell quality. Marginal production cost of a high-quality umbrella is $11. Marginal production cost of a low-quality umbrella is $10. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
19.
Quality Choice Suppose every
seller makes only high-quality umbrellas. Every buyer pays $14 and sellersā proļ¬t per umbrella is $14 - $11 = $3. But then a seller can make low-quality umbrellas for which buyers still pay $14, so increasing proļ¬t to $14 - $10 = $4. There is no market equilibrium in which only high-quality umbrellas are traded. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
20.
Quality Choice Is there
a market equilibrium in which only low-quality umbrellas are traded? All sellers make only low-quality umbrellas. Buyers pay at most $8 for an umbrella, while marginal production cost is $10. There is no market equilibrium in which only low-quality umbrellas are traded. Now we know there is no market equilibrium in which only one type of umbrella is manufactured. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
21.
Quality Choice Is there
an equilibrium in which both types of umbrella are manufactured? A fraction Ī» of sellers make high-quality umbrellas; 0 < Ī» < 1 Buyersā expected value of an umbrella is EV = 14Ī» + 8(1 ā Ī») = 8 + 6Ī» High-quality manufacturers must recover the manufacturing cost EV = 8 + 6Ī» ā„ 11 ā Ī» ā„ 1 2 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
22.
Quality Choice So at
least half of the sellers must make high-quality umbrellas for there to be a pooling market equilibrium. But then a high-quality seller can switch to making low-quality and increase proļ¬t by $1 on each umbrella sold. Since all sellers reason this way, the fraction of high-quality sellers will shrink towards zero ā but then buyers will pay only $8. So there is no equilibrium in which both umbrella types are traded. The market has no equilibrium with just one umbrella type traded with both umbrella types traded so the market has no equilibrium at all. Adverse selection has destroyed the entire market! Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
23.
Mechanisms that reduce
adverse selection There is a number of mechanisms that may reduce adverse selection, and, increase the volume of trade and the total welfare. These mechanisms include: Regulation: for instance, the government regulates the markets for food and drugs, so you can be sure that even at a very low price you will not buy a ālemonā that will poison you. Reputation: well-established businesses, such as big car dealerships, cannot aļ¬ord to sell ālemonsā because it hurts their reputation and future proļ¬ts. Assurance: the less-informed party can pay for an expert opinion, e.g. ,it is common to hire a mechanic to inspect a used car, and to check the history of the car. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
24.
Mechanisms that reduce
adverse selection Warranty: The seller of a used car who claims it to have a top quality may commit to pay a compensation to the buyer if the car needs a repair within a certain time period. In order for warranty to work, it must incur diļ¬erent costs for owners of cars of diļ¬erent qualities. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
25.
Signalling and Screening Signalling.
The better-informed party takes the lead Often the better informed party would beneļ¬t from communicating this information. High-quality seller must do something costly and veriļ¬able to signal quality convincingly. E.g. reputation, warranty, job market, etc. Informed individuals may ļ¬nd ways to signal information about their unobservable knowledge through observable actions. Screening The less-informed party takes the lead. Uninformed parties may develop mechanism to distinguish , or screen , informed individuals who have diļ¬erent information. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
26.
Signalling: Examples Looking Busy:
Ever known someone whose desk was always a mess of papers and who always looked frazzled? You could argue that looking busy is a way of signaling that your role is important ā and keeping the boss oļ¬ your back. Seller of a used car could oļ¬er to allow a prospective buyer to take the car to a mechanic. Firms may spend money on advertising to signal to potential buyers. Students earning college and postgraduate degrees signal to potential employers that they are high-ability individuals. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
27.
Signalling: Labor Market Michael
Spence (1973). āJob Market Signallingā. Quarterly Journal of Economics. 87 (3): 355ā374. Two types of workers; high-ability and low-ability. A high-ability workerās marginal product is aH = 80 A low-ability workerās marginal product is aL = 40 The workersā eļ¬ort is ļ¬xed (say 40 Hrs. a week) and plays no role in signalling. The employers are perfectly competitive (rather than being a monopoly). 50% (= Ī») of all workers are high-ability, and, 50% (=(1 ā Ī»)) is the fraction of low-ability workers. Each worker is paid his expected marginal product. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
28.
Signalling: Labor Market If
ļ¬rms knew each workerās type they would pay each high-ability worker wH = aH. pay each low-ability worker wL = aL. In the perfect information case when the productivity of each worker is known to the employers, the able workers will receive the wage 80 and the unable the wage 40. Pooling equilibrium: if ļ¬rms cannot tell workersā types then every worker is paid the wage rate; i.e. the expected marginal product wP = (1 ā Ī»)aL + Ī»aH wP = 1/2 Ć 40 + 1/2 Ć 80 = 60 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
29.
Signalling: Labor Market Separating
equilibrium wP = (1 ā Ī»)aL + Ī»aH < aH, the wage rate paid when the ļ¬rm knows a worker really is high-ability. High-ability workers have an incentive to ļ¬nd a credible signal. Workers can acquire āeducationā. Education costs: For a high-ability worker cH per unit. cH = 10 For a low-ability worker cL per unit. cL = 20 Crucial assumption: Signaling costs are negatively correlated with productive ability. It could simply be eļ¬ort (Hrs. of study necessary to learn a particular thing). Or the more able students usually receive more ļ¬nancial support. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
30.
Signalling: Labor Market For
simplicity, assume that the education does not aļ¬ect productivity at all and serves only the signalling purpose. High-ability workers will acquire eH education units if wH ā wL = aH ā aL > cHeH, and wH ā wL = aH ā aL < cLeH Acquiring eH units of education beneļ¬ts high-ability workers. Acquiring eH education units hurts low-ability workers. if cHeH < aH ā aL < cLeH, so Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
31.
Signalling: Labor Market aH
ā aL cL < eH < aH ā aL cH 80 ā 40 20 < eH < 80 ā 40 10 2 < eH < 4 Note: if 4 < eH the able will not want to get the education eH because it is not worth it: the cost of such education is above 40, and hence is greater than the wage diļ¬erential. if 2 > eH then both able and unable will choose eH units of education because the cost is below 40 hence, is less than the wage diļ¬erential. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
32.
Signalling: Labor Market Acquiring
such an education level credibly signals high-ability, allowing high-ability workers to separate themselves from low-ability workers. Given that high-ability workers acquire eH units of education, how much education should low-ability workers acquire? Zero. Low-ability workers will be paid wL = aL. so long as they do not have eH units of education and they are still worse oļ¬ if they do. Signalling can improve information in the market. But, total output did not change and education was costly so signalling worsened the marketās eļ¬ciency. So improved information need not improve gains-to-trade. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
33.
Screening: Examples Insurance Insuree knows
her risk, insurer does not Insurer oļ¬ers several packages with diļ¬erent premiums and deductibles. Search for historical Records, demographic characteristics, etc Finance Borrower knows the risk of project, lender does not Lender oļ¬ers several packages with diļ¬erent interest rates and collateral requirements Hiring Applicants know their ability, employer does not Employers give aptitude tests, check letters of recommendation, school aļ¬liations, GPA. Give bonuses, etc. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
34.
Screening: Examples Pricing Buyer knows
her valuation of the product, seller does not Seller oļ¬ers diļ¬erent qualities at diļ¬erent prices, or quantity discounts Selling used cars Sellers of cars know their vehiclesā defects while buyers often do not. Buyer may ask that car may be checked by a mechanic before the sale. If seller refuses, he reveals his private information that the car is a lemon. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
35.
Screening: Insurance A ļ¬rm
sells car insurance. Desirable: charge a low premium to safe drivers and a high premium to risky drivers. How can the ļ¬rm separate the drivers?. Firm separates drivers by oļ¬ering diļ¬erent insurance policies. Policy 1: high premium and covers all costs (no deductible). Policy 2: lower premium but the driver is responsible for the ļ¬rst $1000 of damage ($1000 deductible). Policy 2 is more of a burden for risky drivers because they are more likely to have an accident. With a large enough deductible, risky drivers will choose Policy 1 while safe drivers choose Policy 2. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
36.
Screening: Credit Market J.
E. Stiglitz and A. Weiss (1981) āCredit Rationing in Markets with Imperfect Informationā The American Economic Review, 71 (3): 393-410. If markets worked perfectly, supply and demand for credit would ļ¬x the interest rate at which lendersā d assume the risk, and borrowersād accept it in order to fund their projects. If the project succeeds, the loan is repaid to the bank; if it fails, the investor declares bankruptcy and the bank gets nothing. The possibilities are: acquiring the loan in good will but despite your best eļ¬orts youāll probably default anyway simply do not care about the interest rate because you have no intention of paying the loan back in the ļ¬rst place. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
37.
Screening: Credit Market Banks
do not know diļ¬erent kinds of investors. Each of several potential liquidity constrained investors has access to a project. The projectās proļ¬tability is private information. The bank might be reluctant to raise the interest rates to a level that clears the loan market. Thus, credit might be rationed and investment curtailed. Credit rationing implies that credit is not available for all those who want it, at any interest rate. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
38.
Screening: Credit Market An
increase in the bankās interest rate. Its proļ¬ts increase in the event that the project is successful. Signal 1: if we have a good credit rating and are not desperately in need of funds, we probably wonāt accept excessively high interest rates, we will simply put oļ¬ our projects or purchases. Signal 2: When interest rates rise above a certain level, ļ¬nancial agents can assume that you are a ālemonā, and that the risk of you defaulting on your credit is too high. It attracts riskier investors at the margin because the greater amount that needs to be repaid can only be generated through riskier projects. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
39.
Screening: Credit Market Suppose
two types of borrowers, As and Bs. Both want to invest in similar projects with a diļ¬erent level of risk. Suppose As invest in āsaferā projects than Bs although the mean return is the same, 110. As ROIs between 90 and 120 for their investment. If they invest 100, then for interest rates over 20% their proļ¬t will be 0 even if their project is successful. Bs ROIs between 70 and 180 for their investment. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
40.
Screening: Credit Market If
Bs are really optimistic (as riskier investors tend to be), they can potentially accept interest rates of up to 80% and still break even. Suppose both As and Bs default on their credit if their ROI is negative (below 100). Suppose that all those willing to accept rates of over 20% are therefore risky investors, Bs. When interest rates approach Bs, credit will simply dry up as all those willing to accept higher rates and still borrow will be singled out as probable defaulters. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
41.
Expected Utility Theory:
Utility Theory Can we even measure satisfaction or happiness? Suppose that everyone likes to eat gourmet food at ļ¬ve-star hotels, drink French wine, vacation in exotic places, and drive luxury cars. All these goods are assumed to provide satisfaction, some more than others. Utility Theory bases its beliefs upon individualsā preferences. rests upon the idea that people behave as if they make decisions by assigning imaginary utility values to the original monetary values Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
42.
Expected Utility Theory:
Utility Theory It explains behavior of individuals based on the premise people can consistently rank order their choices depending upon their preferences. Placing certain restrictions, preferences can be represented using a utility function It is a mathematical formulation that ranks the preferences of the individual in terms of satisfaction diļ¬erent consumption bundles provide. Under the assumptions of utility theory, we can assume that people behaved as if they had a utility function and acted according to it. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
43.
Expected Utility Theory:
Uncertainty While Utility Theory deals with situations in which there is no uncertainty, the Expected Utility Theory deals with choices individuals make when the outcomes they face are uncertain. If individuals maximize utility under certainty, they will also attempt to maximize expected utility under uncertainty. Using Expected Utility Theory, we will ļ¬nd that even if governments did not make purchase of insurance mandatory, the product would still have existed. Risk-averse individuals would always demand insurance for the peace of mind it confers. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
44.
Expected Utility Theory:
Uncertainty What is uncertain in economic systems? tomorrowās prices future wealth future availability of commodities present and future actions of other people. What are rational responses to uncertainty? buying insurance (health, life, auto) a portfolio of contingent consumption goods. States of Nature: āCar accidentā and āno car accidentā. Each one occurs with a certain probability. Contingencies: A contract implemented only when a particular state of nature occurs is state-contingent. E.g. the insurer pays only if there is an accident. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
45.
Expected Utility Theory:
Uncertainty Expected value (EV) computed as a weighted average of the events, and the weights are the probabilities those events will take place with. Expected utility allows people to compare gambles Given two gambles, we assume people prefer the situation that generates the greatest expected utility. People maximize expected utility. Many people are risk averse and prefer certainty to the uncertain gamble. For example Job A: certain income of $50K and Job B: 50% chance of $10K and 50% chance of $90K Expected income is the same ($50K) but Job A implies a certain income. Which one is preferred? Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
46.
Expected Utility Theory:
Uncertainty Risk-averse individuals: Utility function U(X) = ā X EUa = ā 50000 = $223.61 and EUb = 0.5 ā 10000 + 0.5 ā 90000 = $200 Job (a) is preferred Risk-neutral individuals: Utility function U(X) = X EUa = 50000 = $50000 and EUb = 0.5 Ć 10000 + 0.5 Ć 90000 = $50000 Individuals are indiļ¬erent toward risk Risk-seeking individuals: Utility function U(X) = X2 EUa = 500002 = 25 Ć (10000)2 and EUb = 0.5 Ć (10000)2 + 0.5 Ć (90000)2 = 41 Ć (10000)2 Job (b) is preferred Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
47.
Insurance: Risk Aversion Ty
is a student who gets a monthly allowance of $200 (initial wealth W0) from his parents. He might lose $100 on any given day with a probability 0.5 or not lose any amount with 50% chance. His expected loss (E[L]) is 0.5($0) + 0.5($100) = $50. His expected ļ¬nal wealth is E(FW) = 0.5 ā ($200 ā $0) + 0.5 ā ($200 ā $100) = W0 ā E(L) = $150. How much Ty would be willing to pay to hedge his expected loss of $50? Assume that Tyās utility function is U(W) = ā W , a risk averterās utility function Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
48.
Insurance: Risk Aversion Expected
utility, no insurance He retains all the uncertainty. His expected ļ¬nal wealth of $150 as calculated above. What is his expected utility? The expected utility is calculated as a weighted sum of the utilities in the two states, ālossā and āno lossā. EU = 0.5ā ($200 ā $0)+0.5ā ($200 ā $100) = $12.07 What is the actuarially fair premium (AFP) for Ty? The AFP is the expected loss ($50). Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
49.
Insurance: Risk Aversion Expected
Utility with insurance at AFP(=$50) With āno lossā, his ļ¬nal wealth is $150 (($200)-AFP ($50)). With a ālossā, his ļ¬nal wealth = $200-AFP ($50)-Loss ($100)+Indemnity ($100)= $150. Ty has purchased a certain wealth of $150, by paying an AFP of $50. His expected utility is $12.25 . Ty will always purchase full insurance at AFP. A risk-averse person will always hedge the risk completely at a cost (AFP) that equals the expected loss. A risk-averse person always prefers certainty to uncertainty, if uncertainty can be hedged away at its actuarially fair price. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
50.
Insurance: Risk Aversion Expected
Utility with insurance at a price greater than AFP What is the maximum premium Ty would be willing to pay? We should equate the utility when Ty purchases insurance at P to the expected utility in the no-insurance case ($12.07). Now, Tyās certain utility is ā 200 ā P, and the expected utility is: EU = 0.5ā ($200 ā $P)+0.5ā ($200 ā $P) = 12.07 P = $54.29. The risk premiun is $54.29-$50= $4.29 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
51.
Insurance: Risk Aversion Risk
Premium: The premium above the AFP that a risk-averse person is willing to pay to get rid of the risk. Any insurance company that charges a premium greater than $54.29 will not be able to sell insurance to Ty. Individualsā risk aversion is a key component in insurance pricing. The greater the degree of risk aversion, the higher the risk premium an individual will be willing to pay. The premium has to be less than or equal to the maximum premium the person is willing to pay. Otherwise, the individual will never buy full insurance. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
52.
Risk Aversion Most individuals
with average wealth and good education tend to be risk neutral over small gambles. Over larger gambles individuals tend to be risk averse. (Except when buying lottery tickets.) Large organizations: banks, insurance companies, ļ¬rms tend to be risk neutral.Two reasons: The risks are small relative to the organizationās size. They have so many risky things that they on average tend to cancel each other out ā ādiversiļ¬ed riskā. A risk averse individual will always be better oļ¬ buying actuarially fair insurance. As insurance becomes less fair (administration costs, deductibles, copays etc), risk averse individuals will buy less insurance. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
53.
Insurance: Moral Hazard An
insurance company has to decide whether to sell an auto insurance policy to Luke. Luke is a risk-averse person whose utility function is U(W) = ā W. Luke claims to be a good risk because Lukeās driving record is excellent. Luke can also choose to be either a careful driver or a not-so-careful driver. Luke drives a car carrying a market value of $10,000. The only other asset he owns is the $3,000 in his checking account. His total initial wealth of $13,000 If he drives carefully, he incurs a cost of $3,000. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
54.
Insurance: Moral Hazard Luke
faces the following āloss distributionā Drives with Care without Care Prob. Loss Prob. Loss accident 0.25 $10,000 0.75 $10,000 no accident 0.75 0 0.25 0 When he has an accident, his car is a total loss. The probabilities of ālossā and āno lossā are reversed when he decides to drive without care. EV[loss]= $2,500 and EV[loss]= $7,500. Lukeās problem has 4 parts: whether to drive with or without care, (I) when he has no insurance and (II) when he has insurance. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
55.
Insurance: Moral Hazard Case
I when he carries no insurance. Drives with Care without Care Prob. U(W) Prob. U(W) accident 0.25 0 0.75 $54.77 no accident 0.75 $100 0.25 $114.02 Drives with care and has an accident: W = $13000 ā $3000 ā $10000 = 0 ā U(0) = 0 Drives with care and has not an accident: W = $13000ā$3000ā0 = $10000 ā U($10000) = $100 Drives without care and has an accident: W = $13000 ā 0 ā $10000 = $3000 ā U($3000) = $54.77 Drives without care and has not an accident: W = $13000 ā 0 ā 0 = $13000 ā U($13000) = $114.02 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
56.
Insurance: Moral Hazard The
expected utility of driving with care: EU = 0.25 Ć 0 + 0.75 Ć 100 = $75 The expected utility of driving without care: EU = 0.75 Ć 54.77 + 0.25 Ć 114.02 = $69.58 Luke will drive carefully since his expected utility is higher when he exercises due care. His utility is $75 versus $69.58. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
57.
Insurance: Moral Hazard Case
II when he carries insurance. Insurance premiun= $2750 = $2500 Ć (1 + 0.1) Drives with Care without Care Prob. U(W) Prob. U(W) accident 0.25 $85.15 0.75 $101.24 no accident 0.75 $85.15 0.25 $101.24 With an insurance, Luke has eliminated the uncertainty. If he has an accident, the insurance company indemniļ¬es him with $10,000. Drives with care and has an accident: W = $10250 ā $3000 ā $10000 + $10000 = $7250 ā U(7250) = $85.15 Drives with care and has not an accident: W = $10250 ā $3000 = $7250 ā U(7250) = $85.15 Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
58.
Insurance: Moral Hazard Drives
without care and has an accident: W = $10250 ā 0 ā $10000 + $10000 = $10250 ā U(10250) = $101.24 Drives without care and has not an accident: W = $10250 ā 0 = $10250 ā U(10250) = $101.24 The expected utility of driving with care: EU = 0.25 Ć 85.15 + 0.75 Ć 85.15 = $85.15 The expected utility of driving without care: EU = 0.75 Ć 101.24 + 0.25 Ć 101.242 = $101.24 The net result is he switches to driving with no care Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
59.
Insurance: Moral Hazard Why
do we get this result? The cost of insurance is cheaper than the cost of care. Insurance companies can charge a price greater than the cost of care up to a maximum of what Luke is willing to pay. In the event of asymmetric information, the insurance company will not know the cost of care. Inexpensive insurance distorts the incentives and individuals switch to riskier behavior ex post. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
60.
References Varian, Hal R.
2010. Intermediate microeconomics: a modern approach. New York: W.W. Norton & Co. Prepared by CĆ©sar R. Sobrino Asymmetric Information, Uncertainty, and, Auctions
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