Asymmetric Information ECON 370: Microeconomic Theory Summer 2004 – Rice University Stanley Gilbert

Econ Asymmetric Information2 Asymmetric Information Up to now, we have assumed –Everyone is fully informed –Or equally uninformed In many cases one party has economically relevant information that another party does not have We term this “Asymmetric Information” It can produce economic inefficiency

Econ Asymmetric Information3 Example Suppose there are two types of umbrellas –Good and Bad They cannot be distinguished until after they have been used –Bad umbrellas disintegrate after a little use Umbrellas are valued as follows Good Bad Value to Consumer Cost to Produce $11.50$14 $11$8

Econ Asymmetric Information4 Example: Full Information Under full information, only good umbrellas would be sold Since the cost to make a bad umbrella exceeds the benefit it provides Good Bad Value to Consumer Cost to Produce $11.50$14 $11$8

Econ Asymmetric Information5 Example: Asymmetric Information If ⅔ umbrellas are good –People are willing to pay: –⅔(14) + ⅓(8) = $12 per umbrella –Which is greater than the cost to produce them Good Bad Value to Consumer Cost to Produce $11.50$14 $11$8

Econ Asymmetric Information6 Example: Asymmetric Information But firms make more money selling bad umbrellas If all firms are small, they have incentive to switch to making bad umbrellas Once ⅔ of firms make bad umbrellas: –People are willing to pay ⅓(14) + ⅔(8) = $10 –Which is less than it costs to make any umbrella Good Bad Value to Consumer Cost to Produce $11.50$14 $11$8

Econ Asymmetric Information7 Example: Observations Under full information we have the efficient result –Total Surplus = $14 – = $2.50 per umbrella Under Asymmetric information the market collapses –Total surplus = 0

Econ Asymmetric Information8 Problems Adverse Selection –People with a poor hidden characteristic… –take advantage of other’s ignorance –Example: Sick people buying life insurance Moral Hazard –People who can take hidden actions… – take advantage of other’s ignorance –Example: Making poor umbrellas –Example: Employees shirking

Econ Asymmetric Information9 Adverse Selection Example A company offers Health insurance Each illness costs $100,000 Two types of people: –“Healthy” –“Sick” –Insurance company cannot distinguish them Types of people differ in probability of getting sick and in willingness to pay for insurance

Econ Asymmetric Information10 Adverse Selection Actuarially Fair insurance charges rates exactly equal to the cost to insure A Pooling Equilibrium is one in which everyone is charged the same rates, regardless of type Type % of Population Risk of Illness Willingness to Pay Healthy90%1/1000$200 Sick10%1/100$1,500 Cost to Insure $100 $1,000

Econ Asymmetric Information11 Pooling Equilibrium If the insurance company pools everybody, it would charge: –0.9 × × 1000 = $190 Which everyone is willing to pay So a Pooling Equilibrium exists Type % of Population Risk of Illness Willingness to Pay Healthy90%1/1000$200 Sick10%1/100$1,500 Cost to Insure $100 $1,000

Econ Asymmetric Information12 Example 2 If the insurance company pools everybody, it would charge: 0.8 × × 1000 = $280 Which only the sick are willing to pay So there is NO Pooling Equilibrium exists The insurance company must charge $1,000 Type % of Population Risk of Illness Willingness to Pay Healthy80%1/1000$200 Sick20%1/100$1,500 Cost to Insure $100 $1,000

Econ Asymmetric Information13 Observations Since the company cannot tell “sick” people from “healthy” people It can only charge a single average rate Although it would happily insure everyone at fair rates –And people would willing pay those rates It cannot because it cannot tell people apart Therefore a majority are uninsured

Econ Asymmetric Information14 Responses Some market players lose as a result of asymmetric information So they have developed strategies to (partially) overcome the problem Two main strategies –Signalling –Screening

Econ Asymmetric Information15 Screening Screening: –is an action taken by the ignorant party –to determine types of people In general, –It is a cost imposed on the “low-value” party –That the “high-value” parties are unwilling to endure

Econ Asymmetric Information16 Screening Example Average cost to insure everybody: –0.5 × × 200 = $150 Which only the sick are willing to pay Since there is no pooling equilibrium, –the insurance company must charge at least $200 Type % of Population Risk of Illness Willingness to Pay Cost to Insure Cost of Physical Healthy50%1/1000$140$100$40 Sick50%1/500$250$200$150

Econ Asymmetric Information17 Screening Policies Suppose the insurance company offers two policies –One for $240 with no restrictions –One for $100 but you must pass a physical to get it Anyone can “pass” the physical –But “sick” people have to bribe the doctor to do it Type % of Population Risk of Illness Willingness to Pay Cost to Insure Cost of Physical Healthy50%1/1000$140$100$40 Sick50%1/500$250$200$150

Econ Asymmetric Information18 Equilibrium Healthy people –Are unwilling to buy the $240 policy –But will pay the $100 + $40 to get the other policy Sick –Are willing to buy the $240 policy –Would pay the $100 + $150 for the other policy, –But, it is more expensive than the original policy Type % of Population Risk of Illness Willingness to Pay Cost to Insure Cost of Physical Healthy50%1/1000$140$100$40 Sick50%1/500$250$200$150

Econ Asymmetric Information19 Screening Observations The insurance company imposes a requirement –That is more costly for “sick” people to meet And so is able to separate out “healthy” from “sick” people –And insure everyone Since no one has an incentive to change –This qualifies as a separating equilibrium Notice that –Compared to the full-information situation –This is inefficient, due to the cost of the physical

Econ Asymmetric Information20 Signaling In several of the example above, –The “low-cost” people stood to gain by being identifiable While Screening is a cost imposed by the ignorant party to identify types Signaling is a cost voluntarily adopted by knowledgeable parties to signal their types Example: Lemon Model

Econ Asymmetric Information21 Lemon Model On the used car market Two types of cars –Good Cars –Lemons The types are indistinguishable to the buyers The market has the following characteristics Type % of Population Value to Buyer Value to Seller Good Cars50%$2,000$1,500 Lemons50%$1,000$500

Econ Asymmetric Information22 Pooling Since buyers can’t distinguish the cars in advance –They are willing to pay only –0.5 × $ × $1000 = $1,500 All sellers are willing to participate at that price So this is a pooling equilibrium Type % of Population Value to Buyer Value to Seller Good Cars50%$2,000$1,500 Lemons50%$1,000$500

Econ Asymmetric Information23 Signaling Sellers of good cars would like to signal the quality of their cars Since doing so would enable them to charge $2,000 But, it has to be in a way that sellers of lemons are unwilling to emulate Type % of Population Value to Buyer Value to Seller Good Cars50%$2,000$1,500 Lemons50%$1,000$500

Econ Asymmetric Information24 Inspecting Lemons Sellers can submit their cars for inspection and certification Profits for owners of good cars with inspection: –2000 – 200 – 1500 > 1500 – 1500 So profits from deviating exceed pooling profits So there is no longer a pooling equilibrium Type % of Population Value to Buyer Value to Seller Cost to pass inspection Good Cars50%$2,000$1,500$200 Lemons50%$1,000$500$1,100

Econ Asymmetric Information25 Separating Lemons Evaluate the separating equilibrium Obviously, owners of good cars have no incentive to deviate Lemon Owners profits from deviating –2000 – 1100 – 500 < 1000 – 500 So Lemon owners will not deviate either Type % of Population Value to Buyer Value to Seller Cost to pass inspection Good Cars50%$2,000$1,500$200 Lemons50%$1,000$500$1,100

Econ Asymmetric Information26 Observations on Signaling In our example, owners of good cars have an incentive to deviate from the pooling case –So, the pooling case is not stable –There is no pooling equilibrium when the inspection regime is available On the other hand, no one has an incentive to deviate from the separating case The only stable equilibrium here is the separating equilibrium

Econ Asymmetric Information27 General Comments Different models of this sort may have different outcomes All the following are possible –Pooling equilibrium but no separating equilibrium –Separating equilibrium but no pooling equilibrium –Both pooling and separating equilibria –Neither pooling nor separating equilibria

Econ Asymmetric Information28 Moral Hazard –The knowledgeable party acts differently… –than when everyone possesses full information Minimizing Moral hazard requires providing incentives to act efficiently Example –If I didn’t insure my car, I would install an alarm –But since it is insured, I do not –Insurance company’s solution: –Provide a discount for installing a car alarm

Econ Asymmetric Information29 Example: Hiring a CEO Our company, YZA Corporation, is hiring a CEO Our objective is to maximize profits The CEO’s objective is to maximize utility Profits depend on the ‘effort’ the CEO exerts Effort is costly to the CEO Let profits be: Π(e) – w –Where ‘e’ represents ‘effort’ The CEO’s utility is: U = w –  (e) –And can get work elsewhere with utility u A

Econ Asymmetric Information30 CEO Roadmap We will evaluate the following cases: Full-information equilibrium Asymmetric information equilibrium –When the CEO is risk-neutral –When the CEO is risk-averse We seek to identify –The optimal amount of effort the CEO should exert –And an optimal contract to induce that effort

Econ Asymmetric Information31 Full-Information CEO The CEO must provide the optimal effort willingly Thus we have a Participation Constraint –w * –  (e * ) ≥ u A We have no reason to want to pay more, so set –w * –  (e * ) = u A Profit maximization means: Which implies that the optimal e * satisfies:

Econ Asymmetric Information32 Full-Information Observations An optimal contract would consist of –w * = u A +  (e * ) if she works e * –Zero otherwise This is exactly what she would work if she owned the company herself –To see this, write an expression for her utility under those circumstances Effort does not need to be directly observable –Since profit is a function only of effort, –We can determine how much effort was exerted simply be observing profits

Econ Asymmetric Information33 Risk-Neutral CEO Here let profits be Π(e, ε) – w –Where ε is a random variable Since we cannot observe effort –Pay must take the form: w(Π) Our Participation Constraint is –E[w(Π(e *, ε))] –  (e * ) ≥ u A Set E[w(Π(e *, ε))] = u A +  (e * ) Profits become

Econ Asymmetric Information34 Risk-Neutral Contract Requirements An optimal contract would satisfy the Incentive Compatibility Constraint That is, the Utility maximizing CEO will exert exactly the Profit maximizing effort That is, mathematically: –E[w(Π(e *, ε))] –  (e * ) ≥ E[w(Π(e, ε))] –  (e)

Econ Asymmetric Information35 Risk-Neutral Contracts As before, optimal effort is exactly what she would work if she owned the company One optimal contract (then) is to sell her the company Another is to allow her to keep any amount above expected profits Both have the effect of placing all risk on her –(Since she is risk-neutral, that doesn’t bother her) And ensure she makes the optimal decision

Econ Asymmetric Information36 Risk-Averse CEO We greatly simplify our model for this case Two possible states of the world, ε 1, ε 2 –The states occur with probability p, 1 – p Two possible effort levels, e 1, e 2 Profits are Π(e 1, ε 1 ) = 1 –Otherwise, profits are zero CEO utility is U = u(w) –  (e) –We let  (e 2 ) = 0, and  (e 1 ) = α, and u(0) = 0 –Reservation wage is zero –Wage becomes w 1 if profits are 1, w 0 otherwise

Econ Asymmetric Information37 Risk-Averse CEO Analysis Assume: e 1 is optimale 2 is optimal E[u(w(Π(e 2, ε)))] –  (e 2 ) ≥ u A or u(w 0 ) –  ≥ 0 or w 0 = 0 Is satisfied by w 1 = w 0 = 0 Participation Constraint: or E[u(w(Π(e 1, ε)))] –  (e 1 ) ≥ u A pu(w 1 ) + (1 – p)u(w 0 ) – α ≥ 0 Incentive Compatibility: E[u(w(Π(e 1, ε)))] –  (e 1 ) ≥ E[u(w(Π(e 2, ε)))] –  (e 2 ) pu(w 1 ) + (1 – p)u(w 0 ) – α ≥ u(w 0 ) p(u(w 1 ) + u(w 0 )) ≥ α or

Econ Asymmetric Information38 Risk-Averse CEO Solution if: e 1 is optimale 2 is optimal w 1 = w 0 = 0 Participation Constraint: pu(w 1 ) + (1 – p)u(w 0 ) = α Incentive Compatibility: p[u(w 1 ) – u(w 0 )] = α Substituting the latter into the former u(w 0 ) = 0 So w 0 = 0or

Econ Asymmetric Information39 Risk-Averse Expected Profits 0 – 0 = 0 w 1 = w 0 = 0w 1 = u -1 (α / p)w 0 = 0 Expected Profits: E[Π(e 2, ε) – w(Π(e 2, ε))] p(1 – u -1 (α / p)) + (1 – p)(0 – 0) Expected Profits = p(1 – u -1 (α / p))Expected Profits = 0 if: e 1 is optimale 2 is optimal So, e 1 is optimal if 1 ≥ u -1 (α / p)

Econ Asymmetric Information40 Risk-Averse Observations Since w 1 > α / p –Profits are reduced from the Risk-Neutral case –The firm must reimburse the risk-averse CEO for taking on part of the risk –This amounts to sharing part of the profits with the CEO –Much like Stock Options If u -1 (α / p) > 1 > α / p –Then with a risk-Neutral CEO, the optimal amount of effort is e 1 –While with a risk-averse CEO, the optimal amount of effort is e 2 –In such a case, an inefficient amount of effort is supplied

Econ Asymmetric Information41 In General Where both principal (the firm) –And agent (the CEO) are risk-neutral –Then the optimal contract is essentially to sell the firm to the agent Where the principal is risk-neutral –And agent is risk-averse –Then the optimal contract is to pay a portion of profits as an incentive to the agent –Even still, the result will usually be inefficient