Asymmetric Information ECON 370 Microeconomic Theory Summer 2004

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

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 370 - Asymmetric Information 2

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 Value to Consumer Good $14 Bad $8 Econ 370 - Asymmetric Information Cost to Produce $11. 50 $11 3

Example: Full Information Value to Consumer Good $14 Bad $8 Cost to Produce $11. 50 $11 • Under full information, only good umbrellas would be sold • Since the cost to make a bad umbrella exceeds the benefit it provides Econ 370 - Asymmetric Information 4

Example: Asymmetric Information Value to Consumer Good $14 Bad $8 Cost to Produce $11. 50 $11 • 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 Econ 370 - Asymmetric Information 5

Example: Asymmetric Information Value to Consumer Good $14 Bad $8 Cost to Produce $11. 50 $11 • 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 Econ 370 - Asymmetric Information 6

Example: Observations • Under full information we have the efficient result – Total Surplus = $14 – 11. 50 = $2. 50 per umbrella • Under Asymmetric information the market collapses – Total surplus = 0 Econ 370 - Asymmetric Information 7

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 370 - Asymmetric Information 8

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 370 - Asymmetric Information 9

Adverse Selection Type % of Risk of Willingness Cost to Population Illness to Pay Insure Healthy 90% 1/1000 $200 $100 Sick 10% 1/100 $1, 500 $1, 000 • 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 Econ 370 - Asymmetric Information 10

Pooling Equilibrium Type % of Risk of Willingness Cost to Population Illness to Pay Insure Healthy 90% 1/1000 $200 $100 Sick 10% 1/100 $1, 500 $1, 000 • If the insurance company pools everybody, it would charge: – 0. 9 × 100 + 0. 1 × 1000 = $190 • Which everyone is willing to pay • So a Pooling Equilibrium exists Econ 370 - Asymmetric Information 11

Example 2 Type % of Risk of Willingness Cost to Population Illness to Pay Insure Healthy 80% 1/1000 $200 $100 Sick 20% 1/100 $1, 500 $1, 000 • If the insurance company pools everybody, it would charge: 0. 8 × 100 + 0. 2 × 1000 = $280 • Which only the sick are willing to pay • So there is NO Pooling Equilibrium exists • The insurance company must charge $1, 000 Econ 370 - Asymmetric Information 12

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 370 - Asymmetric Information 13

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 370 - Asymmetric Information 14

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 370 - Asymmetric Information 15

Screening Example Type % of Risk of Willingness Cost to Cost of Population Illness to Pay Insure Physical Healthy 50% 1/1000 $140 $100 $40 Sick 50% 1/500 $250 $200 $150 • Average cost to insure everybody: – 0. 5 × 100 + 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 Econ 370 - Asymmetric Information 16

Screening Policies Type % of Risk of Willingness Cost to Cost of Population Illness to Pay Insure Physical Healthy 50% 1/1000 $140 $100 $40 Sick 50% 1/500 $250 $200 $150 • 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 Econ 370 - Asymmetric Information 17

Equilibrium Type % of Risk of Willingness Cost to Cost of Population Illness to Pay Insure Physical Healthy 50% 1/1000 $140 $100 $40 Sick 50% 1/500 $250 $200 $150 • 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 Econ 370 - Asymmetric Information 18

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 370 - Asymmetric Information 19

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 370 - Asymmetric Information 20

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 Value to Population Buyer Seller Good Cars 50% $2, 000 $1, 500 Lemons 50% $1, 000 $500 Econ 370 - Asymmetric Information 21

Pooling Type % of Value to Population Buyer Seller Good Cars 50% $2, 000 $1, 500 Lemons 50% $1, 000 $500 • Since buyers can’t distinguish the cars in advance – They are willing to pay only – 0. 5 × $2000 + 0. 5 × $1000 = $1, 500 • All sellers are willing to participate at that price • So this is a pooling equilibrium Econ 370 - Asymmetric Information 22

Signaling Type % of Value to Population Buyer Seller Good Cars 50% $2, 000 $1, 500 Lemons 50% $1, 000 $500 • 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 Econ 370 - Asymmetric Information 23

Inspecting Lemons Type % of Value to Cost to pass Population Buyer Seller inspection Good Cars 50% $2, 000 $1, 500 $200 Lemons 50% $1, 000 $500 $1, 100 • 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 Econ 370 - Asymmetric Information 24

Separating Lemons Type % of Value to Cost to pass Population Buyer Seller inspection Good Cars 50% $2, 000 $1, 500 $200 Lemons 50% $1, 000 $500 $1, 100 • 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 Econ 370 - Asymmetric Information 25

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 370 - Asymmetric Information 26

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 370 - Asymmetric Information 27

Moral Hazard • 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 370 - Asymmetric Information 28

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 – f(e) – And can get work elsewhere with utility u. A Econ 370 - Asymmetric Information 29

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 370 - Asymmetric Information 30

Full-Information CEO • The CEO must provide the optimal effort willingly • Thus we have a Participation Constraint – w* – f(e*) ≥ u. A • We have no reason to want to pay more, so set – w* – f(e*) = u. A • Profit maximization means: • Which implies that the optimal e* satisfies: Econ 370 - Asymmetric Information 31

Full-Information Observations • An optimal contract would consist of – w* = u. A + f(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 370 - Asymmetric Information 32

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))] – f(e*) ≥ u. A • Set E[w(Π(e*, ε))] = u. A + f(e*) • Profits become Econ 370 - Asymmetric Information 33

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))] – f(e*) ≥ E[w(Π(e, ε))] – f(e) Econ 370 - Asymmetric Information 34

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 370 - Asymmetric Information 35

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) – f(e) – We let f(e 2) = 0, and f(e 1) = α, and u(0) = 0 – Reservation wage is zero – Wage becomes w 1 if profits are 1, w 0 otherwise Econ 370 - Asymmetric Information 36

Risk-Averse CEO Analysis Assume: e 1 is optimal e 2 is optimal Participation Constraint: E[u(w(Π(e 1, ε)))] – f(e 1) ≥ u. A or pu(w 1) + (1 – p)u(w 0) – α ≥ 0 Participation Constraint: E[u(w(Π(e 2, ε)))] – f(e 2) ≥ u. A or u(w 0) – 0 ≥ 0 or w 0 = 0 Incentive Compatibility: Is satisfied by w 1 = w 0 = 0 E[u(w(Π(e 1, ε)))] – f(e 1) ≥ E[u(w(Π(e 2, ε)))] – f(e 2) pu(w 1) + (1 – p)u(w 0) – α ≥ u(w 0) or p(u(w 1) + u(w 0)) ≥ α Econ 370 - Asymmetric Information 37

Risk-Averse CEO Solution if: e 1 is optimal e 2 is optimal Participation Constraint: pu(w 1) + (1 – p)u(w 0) = α w 1 = w 0 = 0 Incentive Compatibility: p[u(w 1) – u(w 0)] = α Substituting the latter into the former u(w 0) = 0 or w 0 = 0 So Econ 370 - Asymmetric Information 38

Risk-Averse Expected Profits if: e 1 is optimal w 0 = 0 w 1 = u-1(α / p) Expected Profits: E[Π(e 2, ε) – w(Π(e 2, ε))] p(1 – u-1(α / p)) + (1 – p)(0 – 0) e 2 is optimal w 1 = w 0 = 0 Expected Profits: 0– 0=0 Expected Profits = p(1 – u-1(α / p)) Expected Profits = 0 So, e 1 is optimal if 1 ≥ u-1(α / p) Econ 370 - Asymmetric Information 39

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 370 - Asymmetric Information 40

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 Econ 370 - Asymmetric Information 41