microlower.jpg © 2010 W. W. Norton & Company, Inc. microtitle.jpg microedition.jpg varianname.jpg 37 Asymmetric Information microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Information in Competitive Markets uIn 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? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Asymmetric Information in Markets uA doctor knows more about medical services than does the buyer. uAn insurance buyer knows more about his riskiness than does the seller. uA used car’s owner knows more about it than does a potential buyer. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Asymmetric Information in Markets uMarkets with one side or the other imperfectly informed are markets with imperfect information. uImperfectly informed markets with one side better informed than the other are markets with asymmetric information. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Asymmetric Information in Markets uIn what ways can asymmetric information affect the functioning of a market? uFour applications will be considered: 0adverse selection 0signaling 0moral hazard 0incentives contracting. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uConsider 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uIf 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. uGains-to-trade are generated when buyers are well informed. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uSuppose no buyer can tell a peach from a lemon before buying. uWhat is the most a buyer will pay for any car? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uLet q be the fraction of peaches. u1 - q is the fraction of lemons. uExpected value to a buyer of any car is at most microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uSuppose EV > $2000. uEvery seller can negotiate a price between $2000 and $EV (no matter if the car is a lemon or a peach). uAll sellers gain from being in the market. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uSuppose 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uHence “too many” lemons “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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uHow many lemons can be in the market without crowding out the peaches? uBuyers will pay $2000 for a car only if microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uHow many lemons can be in the market without crowding out the peaches? uBuyers will pay $2000 for a car only if uSo if over one-third of all cars are lemons, then only lemons are traded. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uA market equilibrium in which 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uWhat if there is more than two types of cars? uSuppose that 0 car quality is Uniformly distributed between $1000 and $2000 0any car that a seller values at $x is valued by a buyer at $(x+300). uWhich cars will be traded? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection Seller values 1000 2000 microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 2000 1500 Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 2000 1500 The expected value of any car to a buyer is $1500 + $300 = $1800. Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 2000 1500 The expected value of any car to a buyer is $1500 + $300 = $1800. So sellers who value their cars at more than $1800 exit the market. Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 1800 The distribution of values of cars remaining on offer Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 1800 1400 Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 1800 1400 The expected value of any remaining car to a buyer is $1400 + $300 = $1700. Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection 1000 1800 1400 The expected value of any remaining car to a buyer is $1400 + $300 = $1700. So now sellers who value their cars between $1700 and $1800 exit the market. Seller values microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uWhere 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 is microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uSo a buyer will pay at most microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection uSo a buyer will pay at most uThis must be the price which the seller of the highest value car remaining in the market will just accept; i.e. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection Adverse selection drives out all cars valued by sellers at more than $1600. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uNow each seller can choose the quality, or value, of her product. uTwo umbrellas; high-quality and low-quality. uWhich will be manufactured and sold? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uBuyers value a high-quality umbrella at $14 and a low-quality umbrella at $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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uSuppose every seller makes only high-quality umbrellas. uEvery buyer pays $14 and sellers’ profit per umbrella 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uThere is no market equilibrium in which only high-quality umbrellas are traded. uIs there a market equilibrium in which only low-quality umbrellas are traded? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uAll 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uNow 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? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uA fraction q of sellers make high-quality umbrellas; 0 < q < 1. uBuyers’ expected value of an umbrella is EV = 14q + 8(1 - q) = 8 + 6q. uHigh-quality manufacturers must recover the manufacturing cost, EV = 8 + 6q ³ 11 Þ q ³ 1/2. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uSo 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 to making low-quality and increase profit by $1 on each umbrella sold. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uSince 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 traded. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uThe market has no equilibrium 0with just one umbrella type traded 0with both umbrella types traded microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uThe market has no equilibrium 0with just one umbrella type traded 0with both umbrella types traded uso the market has no equilibrium at all. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Adverse Selection with Quality Choice uThe market has no equilibrium 0with just one umbrella type traded 0with both umbrella types traded uso the market has no equilibrium at all. uAdverse selection has destroyed the entire market! microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uAdverse selection is an outcome of an informational 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uA labor market has two types of workers; high-ability and low-ability. uA high-ability worker’s marginal product is aH. uA low-ability worker’s marginal product is aL. uaL < aH. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uA fraction h of all workers are high-ability. u1 - h is the fraction of low-ability workers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uEach worker is paid his expected marginal product. uIf firms knew each worker’s type they would 0pay each high-ability worker wH = aH 0pay each low-ability worker wL = aL. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uIf 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uwP = (1 - h)aL + haH < aH, the wage rate paid when the firm knows a worker really is high-ability. uSo high-ability workers have an incentive to find a credible signal. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uWorkers can acquire “education”. uEducation costs a high-ability worker cH per unit uand costs a low-ability worker cL per unit. ucL > cH. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uSuppose that education has no effect on workers’ productivities; i.e., the cost of education is a deadweight loss. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uHigh-ability workers will acquire eH education units if (i) wH - wL = aH - aL > cHeH, and (ii) wH - wL = aH - aL < cLeH. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uHigh-ability workers will acquire eH education units if (i) wH - wL = aH - aL > cHeH, and (ii) wH - wL = aH - aL < cLeH. u(i) says acquiring eH units of education benefits high-ability workers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uHigh-ability workers will acquire eH education units if (i) 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 units hurts low-ability workers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling and together require Acquiring such an education level credibly signals high-ability, allowing high-ability workers to separate themselves from low-ability workers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uQ: Given that high-ability workers acquire eH units of education, how much education should low-ability workers acquire? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uQ: 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 still worse off if they do. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Signaling uSignaling can improve information in the market. uBut, total output did not change and education was costly so signaling worsened the market’s efficiency. uSo improved information need not improve gains-to-trade. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Moral Hazard uIf you have full car insurance are you more likely to leave your car unlocked? uMoral hazard is a reaction to incentives to increase the risk of a loss uand is a consequence of asymmetric information. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Moral Hazard uIf an insurer knows the exact risk from insuring an individual, then a contract specific to that person can be written. uIf all people 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Moral Hazard uExamples of efforts to avoid moral hazard by using signals are: 0 higher life and medical insurance premiums for smokers or heavy drinkers of alcohol 0 lower car insurance premiums for contracts with higher deductibles or for drivers with histories of safe driving. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting uA worker is hired by a principal to do a task. uOnly the worker knows the effort she exerts (asymmetric information). uThe effort exerted affects the principal’s payoff. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting uThe principal’s problem: design an incentives contract that induces the worker to exert the amount of effort that maximizes the principal’s payoff. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting ue is the agent’s effort. uPrincipal’s reward is uAn incentive contract is a function s(y) specifying the worker’s payment when the principal’s reward is y. The principal’s profit is thus microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting uLet be the worker’s (reservation) utility of not working. uTo get the worker’s participation, the contract must offer the worker a utility of at least uThe worker’s utility cost of an effort level e is c(e). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting So the principal’s problem is choose e to subject to (participation constraint) To maximize his profit the principal designs the contract to provide the worker with her reservation utility level. That is, ... microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting the principal’s problem is to subject to (participation constraint) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting the principal’s problem is to subject to (participation constraint) Substitute for and solve microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting the principal’s problem is to subject to (participation constraint) The principal’s profit is maximized when Substitute for and solve microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting The contract that maximizes the principal’s profit insists upon the worker effort level e* that equalizes the worker’s marginal effort cost to the principal’s marginal payoff from worker effort. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting How can the principal induce the worker to choose e = e*? The contract that maximizes the principal’s profit insists upon the worker effort level e* that equalizes the worker’s marginal effort cost to the principal’s marginal payoff from worker effort. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting ue = e* must be most preferred by the worker. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracting ue = e* must be most preferred by the worker. uSo the contract s(y) must satisfy the incentive-compatibility constraint; microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Rental Contracting uExamples 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 principal’s profit? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Rental Contracting uGiven the contract the worker’s payoff is and to maximize this the worker should choose the effort level for which microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Rental Contracting uHow large should be the principal’s rental fee R? uThe principal should extract as much rent as possible without causing the worker not to participate, so R should satisfy i.e. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Other Incentives Contracts u(ii) Wages contracts: In a wages contract the payment to the worker is w 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Other Incentives Contracts u(iii) Take-it-or-leave-it: Choose e = e* and be paid a lump-sum L, or choose e ¹ e* and be paid zero. uThe worker’s utility from choosing e ¹ e* is - c(e), so the worker will choose e = e*. uL is chosen to make the worker indifferent between participating and not participating. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Incentives Contracts in General uThe 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.