1、Chapter Thirty-SixAsymmetric InformationInformation in Competitive MarketsuIn purely competitive markets all agents are fully informed about traded commodities and other aspects of the market.uWhat about markets for medical services,or insurance,or used cars?Asymmetric Information in MarketsuA docto
2、r knows more about medical services than does the buyer.uAn insurance buyer knows more about his riskiness than does the seller.uA used cars owner knows more about it than does a potential buyer.Asymmetric Information in MarketsuMarkets with one side or the other imperfectly informed are markets wit
3、h imperfect information.uImperfectly informed markets with one side better informed than the other are markets with asymmetric information.Asymmetric Information in MarketsuIn what ways can asymmetric information affect the functioning of a market?uFour applications will be considered:0adverse selec
4、tion 0signaling 0moral hazard0incentives contracting.Adverse SelectionuConsider a used car market.uTwo types of cars;“lemons”and“peaches”.uEach lemon seller will accept$1,000;a buyer will pay at most$1,200.uEach peach seller will accept$2,000;a buyer will pay at most$2,400.Adverse SelectionuIf every
5、 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.uGains-to-trade are generated when buyers are well informed.Adverse SelectionuSuppose no buyer can tell a peach from a lemon before buying.uWhat is the most a buyer will pay
6、 for any car?Adverse SelectionuLet q be the fraction of peaches.u1-q is the fraction of lemons.uExpected value to a buyer of any car is at mostEVqq$1200()$2400.1Adverse SelectionuSuppose EV$2000.uEvery seller can negotiate a price between$2000 and$EV(no matter if the car is a lemon or a peach).uAll
7、sellers gain from being in the market.Adverse SelectionuSuppose EV$2000.uA peach seller cannot negotiate a price above$2000 and will exit the market.uSo all buyers know that remaining sellers own lemons only.uBuyers will pay at most$1200 and only lemons are sold.Adverse SelectionuHence“too many”lemo
8、ns“crowd out”the peaches from the market.uGains-to-trade are reduced since no peaches are traded.uThe presence of the lemons inflicts an external cost on buyers and peach owners.Adverse SelectionuHow many lemons can be in the market without crowding out the peaches?uBuyers will pay$2000 for a car on
9、ly if2000$2400$)1(1200$qqEVAdverse SelectionuHow many lemons can be in the market without crowding out the peaches?uBuyers will pay$2000 for a car only ifuSo if over one-third of all cars are lemons,then only lemons are traded.322000$2400$)1(1200$qqqEVAdverse SelectionuA market equilibrium in which
10、both types of cars are traded and cannot be distinguished by the buyers is a pooling equilibrium.uA 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.Adverse SelectionuWhat if there is more th
11、an two types of cars?uSuppose that0 car quality is Uniformly distributed between$1000 and$20000any car that a seller values at$x is valued by a buyer at$(x+300).uWhich cars will be traded?Adverse SelectionSeller values10002000Adverse Selection100020001500Seller valuesAdverse Selection100020001500The
12、 expected value of anycar to a buyer is$1500+$300=$1800.Seller valuesAdverse Selection100020001500The expected value of anycar to a buyer is$1500+$300=$1800.So sellers who value their cars atmore than$1800 exit the market.Seller valuesAdverse Selection10001800The distribution of valuesof cars remain
13、ing on offerSeller valuesAdverse Selection100018001400Seller valuesAdverse Selection100018001400The expected value of anyremaining car to a buyer is$1400+$300=$1700.Seller valuesAdverse Selection100018001400The expected value of anyremaining car to a buyer is$1400+$300=$1700.So now sellers who value
14、 their carsbetween$1700 and$1800 exit the market.Seller valuesAdverse SelectionuWhere does this unraveling of the market end?uLet vH be the highest seller value of any car remaining in the market.uThe expected seller value of a car is12100012 vH.Adverse SelectionuSo a buyer will pay at most121000123
15、00 vH.Adverse SelectionuSo a buyer will pay at mostuThis must be the price which the seller of the highest value car remaining in the market will just accept;i.e.12100012300 vH.12100012300 vvHH.Adverse Selection12100012300 vvHH vH$1600.Adverse selection drives out all carsvalued by sellers at more t
16、han$1600.Adverse Selection with Quality ChoiceuNow each seller can choose the quality,or value,of her product.uTwo umbrellas;high-quality and low-quality.uWhich will be manufactured and sold?Adverse Selection with Quality ChoiceuBuyers value a high-quality umbrella at$14 and a low-quality umbrella a
17、t$8.uBefore buying,no buyer can tell quality.uMarginal production cost of a high-quality umbrella is$11.uMarginal production cost of a low-quality umbrella is$10.Adverse Selection with Quality ChoiceuSuppose every seller makes only high-quality umbrellas.uEvery buyer pays$14 and sellers profit per u
18、mbrella is$14-$11=$3.uBut then a seller can make low-quality umbrellas for which buyers still pay$14,so increasing profit to$14-$10=$4.Adverse Selection with Quality ChoiceuThere is no market equilibrium in which only high-quality umbrellas are traded.uIs there a market equilibrium in which only low
19、-quality umbrellas are traded?Adverse Selection with Quality ChoiceuAll sellers make only low-quality umbrellas.uBuyers pay at most$8 for an umbrella,while marginal production cost is$10.uThere is no market equilibrium in which only low-quality umbrellas are traded.Adverse Selection with Quality Cho
20、iceuNow we know there is no market equilibrium in which only one type of umbrella is manufactured.uIs there an equilibrium in which both types of umbrella are manufactured?Adverse Selection with Quality ChoiceuA fraction q of sellers make high-quality umbrellas;0 q 1.uBuyers expected value of an umb
21、rella is EV=14q+8(1-q)=8+6q.uHigh-quality manufacturers must recover the manufacturing cost,EV=8+6q 11 q 1/2.Adverse Selection with Quality ChoiceuSo at least half of the sellers must make high-quality umbrellas for there to be a pooling market equilibrium.uBut then a high-quality seller can switch
22、to making low-quality and increase profit by$1 on each umbrella sold.Adverse Selection with Quality ChoiceuSince all sellers reason this way,the fraction of high-quality sellers will shrink towards zero-but then buyers will pay only$8.uSo there is no equilibrium in which both umbrella types are trad
23、ed.Adverse Selection with Quality ChoiceuThe market has no equilibrium0with just one umbrella type traded0with both umbrella types tradedAdverse Selection with Quality ChoiceuThe market has no equilibrium0with just one umbrella type traded0with both umbrella types tradeduso the market has no equilib
24、rium at all.Adverse Selection with Quality ChoiceuThe market has no equilibrium0with just one umbrella type traded0with both umbrella types tradeduso the market has no equilibrium at all.uAdverse selection has destroyed the entire market!SignalinguAdverse selection is an outcome of an informational
25、deficiency.uWhat if information can be improved by high-quality sellers signaling credibly that they are high-quality?uE.g.warranties,professional credentials,references from previous clients etc.SignalinguA labor market has two types of workers;high-ability and low-ability.uA high-ability workers m
26、arginal product is aH.uA low-ability workers marginal product is aL.uaL aH.SignalinguA fraction h of all workers are high-ability.u1-h is the fraction of low-ability workers.SignalinguEach worker is paid his expected marginal product.uIf firms knew each workers type they would 0pay each high-ability
27、 worker wH=aH0pay each low-ability worker wL=aL.SignalinguIf firms cannot tell workers types then every worker is paid the(pooling)wage rate;i.e.the expected marginal product wP=(1-h)aL+haH.SignalinguwP=(1-h)aL+haH cH.SignalinguSuppose that education has no effect on workers productivities;i.e.,the
28、cost of education is a deadweight loss.SignalinguHigh-ability workers will acquire eH education units if(i)wH-wL=aH-aL cHeH,and(ii)wH-wL=aH-aL cHeH,and(ii)wH-wL=aH-aL cHeH,and(ii)wH-wL=aH-aL cLeH.u(i)says acquiring eH units of education benefits high-ability workers.u(ii)says acquiring eH education
29、units hurts low-ability workers.SignalingHHLHecaa HLLHecaa andtogether require.HLHHLLHcaaecaa Acquiring such an education level crediblysignals high-ability,allowing high-abilityworkers to separate themselves fromlow-ability workers.SignalinguQ:Given that high-ability workers acquire eH units of edu
30、cation,how much education should low-ability workers acquire?SignalinguQ:Given that high-ability workers acquire eH units of education,how much education should low-ability workers acquire?uA:Zero.Low-ability workers will be paid wL=aL so long as they do not have eH units of education and they are s
31、till worse off if they do.SignalinguSignaling can improve information in the market.uBut,total output did not change and education was costly so signaling worsened the markets efficiency.uSo improved information need not improve gains-to-trade.Moral HazarduIf you have full car insurance are you more
32、 likely to leave your car unlocked?uMoral hazard is a reaction to incentives to increase the risk of a lossuand is a consequence of asymmetric information.Moral HazarduIf an insurer knows the exact risk from insuring an individual,then a contract specific to that person can be written.uIf all people
33、 look alike to the insurer,then one contract will be offered to all insurees;high-risk and low-risk types are then pooled,causing low-risks to subsidize high-risks.Moral HazarduExamples of efforts to avoid moral hazard by using signals are:0 higher life and medical insurance premiums for smokers or
34、heavy drinkers of alcohol0 lower car insurance premiums for contracts with higher deductibles or for drivers with histories of safe driving.Incentives ContractinguA worker is hired by a principal to do a task.uOnly the worker knows the effort she exerts(asymmetric information).uThe effort exerted af
35、fects the principals payoff.Incentives ContractinguThe principals problem:design an incentives contract that induces the worker to exert the amount of effort that maximizes the principals payoff.Incentives Contractingue is the agents effort.uPrincipals reward isuAn incentive contract is a function s
36、(y)specifying the workers payment when the principals reward is y.The principals profit is thus).()()(efsefysyp ).(efy Incentives ContractinguLet be the workers(reservation)utility of not working.uTo get the workers participation,the contract must offer the worker a utility of at leastuThe workers u
37、tility cost of an effort level e is c(e).u.uIncentives ContractingSo the principals problem is choose e to)()(maxefsefp subject to.)()(uecefs (participation constraint)To maximize his profit the principaldesigns the contract to provide the worker with her reservation utility level.That is,.Incentive
38、s Contractingthe principals problem is to)()(maxefsefp subject to.)()(uecefs (participation constraint)Incentives Contractingthe principals problem is tosubject to(participation constraint)Substitute for and solve)()(maxefsefp .)()(uecefs .)()(maxuecefp )(efsIncentives Contractingthe principals prob
39、lem is tosubject to(participation constraint)The principals profit is maximized when).()(ecef )()(maxefsefp .)()(uecefs .)()(maxuecefp Substitute for and solve)(efsIncentives Contracting.*)()(eeecef The contract that maximizes theprincipals profit insists upon theworker effort level e*that equalizes
40、the workers marginal effort cost tothe principals marginal payoff fromworker effort.Incentives ContractingHow can the principal induce theworker to choose e=e*?.*)()(eeecef The contract that maximizes theprincipals profit insists upon theworker effort level e*that equalizesthe workers marginal effor
41、t cost tothe principals marginal payoff fromworker effort.Incentives Contractingue=e*must be most preferred by the worker.Incentives Contractingue=e*must be most preferred by the worker.uSo the contract s(y)must satisfy the incentive-compatibility constraint;.0allfor),()(*)(*)(eecefsecefsRental Cont
42、ractinguExamples of incentives contracts:(i)Rental contracts:The principal keeps a lump-sum R for himself and the worker gets all profit above R;i.e.uWhy does this contract maximize the principals profit?.)()(Refefs Rental ContractinguGiven the contractthe workers payoff isand to maximize this the w
43、orker should choose the effort level for which)()()()(ecRefecefs .*,isthat);()(eeecef Refefs )()(Rental ContractinguHow large should be the principals rental fee R?uThe principal should extract as much rent as possible without causing the worker not to participate,so R should satisfyi.e.;*)(*)(uRece
44、fs .*)(*)(uecefsR Other Incentives Contractsu(ii)Wages contracts:In a wages contract the payment to the worker isw is the wage per unit of effort.K is a lump-sum payment.u and K makes the worker just indifferent between participating and not participating.)(Kwees *)(efw Other Incentives Contractsu(i
45、ii)Take-it-or-leave-it:Choose e=e*and be paid a lump-sum L,or choose e e*and be paid zero.uThe workers utility from choosing e e*is-c(e),so the worker will choose e=e*.uL is chosen to make the worker indifferent between participating and not participating.Incentives Contracts in GeneraluThe common feature of all efficient incentive contracts is that they make the worker the full residual claimant on profits.uI.e.the last part of profit earned must accrue entirely to the worker.
