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Trace selection or incentive problems from the information structure rather than assuming all information gaps have the same effect.
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You will trace selection or incentive problems from the information structure rather than assuming all information gaps have the same effect, showing the calculation and stating the assumptions that make the conclusion valid.
Use the supplied definitions and units. Separate an accounting identity, a behavioral assumption, and a normative criterion before drawing conclusions.
| Term | What it means |
|---|---|
| Adverse selection | Contract terms change participating types when relevant attributes are hidden. |
| Moral hazard | A contract affects actions that another party cannot fully observe or verify. |
| Participation constraint | The offered arrangement must be at least as attractive as the outside option. |
| Incentive compatibility | The intended action or truthful choice must be privately optimal under the offered terms. |
| Conditional pool average | Expected cost averaged over actual enrollees rather than the original population. |
Asymmetric information means that relevant information is distributed unevenly between parties to an interaction. The phrase alone does not identify a particular failure or its size. An analysis needs to specify the informed party, the hidden fact or action, when it becomes known, and whether it can be verified by someone enforcing an agreement. Knowing a fact privately is different from being able to prove it to another party.
A seller may know the quality of an item before sale, while a buyer cannot distinguish quality until after purchase. Alternatively, a borrower may choose an effort level after receiving funds, and the lender may be unable to observe that effort directly. The first example concerns a hidden characteristic affecting which items or people participate. The second concerns an action and the incentives created by the agreement.
These situations motivate the distinction between adverse selection and moral hazard. Selection concerns how contract terms affect the composition of participating types when some relevant attributes are hidden. Moral hazard concerns how a contract changes an action that is costly to observe or verify. Neither term is a moral diagnosis of a person's character. The problem is a relationship between information, incentives and feasible agreements.
Not every uncertainty is asymmetric information. If neither buyer nor seller knows whether a storm will occur, that is common uncertainty. If both observe product quality but disagree about its value, their preferences differ rather than their information. Keeping these cases separate matters because a policy aimed at disclosure will not necessarily solve a disagreement about preferences or a risk that no participant can predict.
Another way: A pooled price depends on who actually joins
Consider two types of potential participants in a fictional repair warranty. Type one has expected covered repair cost L and type two expected cost H, with H larger. If the fraction of type-two participants is s, expected cost per enrolled contract is (1-s)L+sH. With no administrative cost, profit loading or reserve requirement, that is the break-even pooled premium for that enrolled composition.
The word enrolled is crucial. The fraction of high-cost types in the overall population need not equal the fraction among buyers of the warranty. If a proposed premium leads some low-cost types to opt out, the remaining pool can have a higher expected cost. Recomputing the premium using the original population weights would then conceal the very selection effect the exercise is designed to study.
Suppose half the population has expected cost twenty and half eighty. A proposed all-participant break-even premium is fifty. Suppose low-cost participants are willing to pay at most thirty-five and high-cost participants at most ninety for the specified contract. At fifty, the low-cost group does not join under the stated rule, while the high-cost group does. The expected cost among actual enrollees is eighty, not fifty.
Charging fifty to that selected pool loses thirty per enrolled contract in expectation. A revised premium of eighty covers its expected claims if high-cost participants still join at that price. The final pool excludes the low-cost group, even though a contract priced for that group's own expected cost could have been attractive if types were verifiable and separate terms feasible. The example illustrates a mechanism, not a claim that every insurance market completely disappears.
Another way: Participation and break-even are separate conditions
A participation condition says that an individual weakly prefers the offered contract to the available outside option. A break-even condition says expected receipts cover the modeled costs for the actual participants. One does not imply the other. A premium can cover average costs for a proposed pool while inducing some members of that pool to leave. It can also attract buyers while generating losses for the provider.
In the numerical exercises, willingness to pay is supplied directly and a type joins when its maximum willingness to pay is at least the posted premium. Equality therefore means participation by the stated convention. This convention avoids an unresolved indifference case; a different tie rule could change a pool at exactly that boundary. Always state the tie treatment when the composition depends on it.
For each posted premium, first compare that premium with each type's willingness to pay. Then average expected claims over only the types that join, using their relative numbers. Finally subtract the expected claims from the premium to find the provider's expected margin per enrolled contract. Reversing this order can accidentally average over people who have already opted out.
If nobody joins, expected cost per enrolled contract is not defined because there is no enrolled denominator. Do not enter zero as though it were a measured per-contract cost. There may be zero total claims and zero total premium revenue, but those totals answer a different question. The supplied practice cases keep at least one group enrolled so that the requested conditional average is well defined.
Another way: Hidden action changes behavior after terms are offered
Now consider a different problem. A project operator can take costly care after receiving a contract. High care costs the operator four credits and raises the success probability from one half to three quarters. Suppose the operator receives a bonus B only on success, with all other payoffs unchanged. The extra expected bonus from care is one quarter of B, so high care is privately worthwhile when that amount covers the four-credit effort cost.
The incentive condition is B at least sixteen, with indifference at exactly sixteen under this simplified specification. A fixed payment added equally to both effort choices affects the operator's participation but not the difference between the two effort payoffs. This makes participation and incentive compatibility distinct requirements. A contract that attracts an operator may still fail to induce the action anticipated by the principal.
The principal's preferred action also depends on the output value and the total resource cost of care. If success is worth thirty credits, the extra expected output from high care is seven and a half credits, which exceeds the four-credit effort cost. High care raises total expected surplus in this example. Whether a feasible contract can implement it also depends on risk preferences, limited liability, outside options and what outcomes can be verified.
The bonus illustration assumes risk neutrality and observable success. If the operator is risk averse, tying compensation to a noisy outcome can impose a risk cost. More powerful incentives may then come with less insurance. This is a trade-off generated by the information structure; simply maximizing the bonus does not necessarily maximize the parties' attainable joint welfare.
Another way: Signals and screening must survive incentive checks
A signal is an observable action taken by an informed party that can affect others' beliefs about a hidden type. Screening is the design of terms by a less-informed party to encourage different types to reveal themselves through different choices. Both ideas require an incentive argument. Attaching a label to a contract or accepting a seller's claim does not establish that types will sort as intended.
Suppose a warranty seller claims high product quality and offers a costly replacement promise. The promise can provide information only if the costs and benefits make it attractive for the claimed type and less attractive for the type it is meant to distinguish. If both types can make the promise cheaply and never honor it, the words do not create a separating signal. Verification and enforcement therefore belong to the analysis.
A screening menu similarly needs self-selection constraints. Each type must prefer its intended contract over mimicking the other type, as well as over declining all contracts. A designer who checks only that each intended contract yields nonnegative profit has not checked whether participants choose those contracts. Information rents can arise because satisfying the informed party's incentive constraints may require leaving it a payoff above its outside option.
Information can also have privacy, administrative and distributional consequences. More detailed classification may reduce a pooling problem while exposing vulnerable people to higher prices or excluding them. A complete policy judgment requires a criterion for those effects rather than equating more information with a universally better outcome. The model identifies a constraint; it does not supply every value needed to choose among institutions.
Another way: Diagnose before choosing a remedy
Disclosure, third-party inspection, reputation, monitoring, deductibles, guarantees and public pooling address different parts of these problems. An inspection can improve information about a fixed quality attribute; it may not reveal a future action. A deductible can preserve some incentive to avoid a loss; it also leaves the insured party bearing more risk. Repeated relationships can create reputational incentives, but their strength depends on future opportunities and whether performance is observed.
Empirical evidence should distinguish selection from changes in behavior. If people with more coverage have more claims, they may have been higher-risk before choosing coverage, or coverage may have altered preventive behavior, or both. The correlation alone cannot separate these explanations. A credible design needs variation or additional information that identifies the channel of interest. This is why an information model begins with timing and observability, not merely a list of differences between groups.
A cooperative considers a one-year warranty for identical tools. The exercise supplies two equally numerous user types. Type one has expected covered repairs of thirty credits and maximum willingness to pay forty-five; type two has expected repairs ninety and maximum willingness to pay one hundred five. Types are privately known, the warranty is identical for everyone, and joining is voluntary. Administrative costs and changes in care are excluded from this first comparison.
If everyone enrolled, expected claims would average sixty. But a premium of sixty exceeds type one's willingness to pay. Only type two joins, so actual expected claims per contract are ninety and the provider's expected margin is negative thirty. The proposed premium is not a self-consistent break-even arrangement for the actual pool. A premium of ninety retains type two under the supplied participation rule and yields zero expected margin for that pool.
The cooperative then considers a separate concern: users may take less care when every repair is reimbursed. That is a hidden-action question, not the selection calculation already completed. The earlier numbers explicitly held care fixed, so they cannot quantify this additional mechanism without new assumptions about behavior and incentives.
A useful report keeps the two mechanisms separate, shows the enrollment comparisons before averaging costs, and identifies which institutional changes address which constraint. Verification might support separate prices, while a deductible might alter care incentives. Each option also changes risk exposure, access or administrative costs. The numerical result does not determine the cooperative's distributional objectives or establish that one remedy is best under every set of values.
Do not average claims over people who decline the contract. Distinguish hidden type from hidden action and check participation separately from incentives. More claims among insured people do not alone distinguish selection from behavioral change.
State equal population shares and costs.
Half have cost 20; half have cost 80
These are expected claims before enrollment decisions.
Calculate the proposed pooled premium.
0.520+0.580=50
The average assumes both types participate.
Compare type one's reservation amount.
Maximum 35<50, so type 1 declines
Voluntary participation depends on the actual offer.
Compare type two's reservation amount.
Maximum 90>=50, so type 2 joins
Only this type remains in the pool.
Recompute claims and provider margin.
Conditional cost 80; margin 50-80=-30
The original population average no longer describes enrollees.
State the two expected costs.
Equal groups:cost 20 and 60
The provider cannot observe individual type.
Compute the proposed average premium.
(20+60)/2=40
No loading or administrative cost is included.
Check the low-cost willingness to pay.
Maximum 45>=40
The lower-risk group still values coverage enough to join.
Check the high-cost willingness to pay.
Maximum 75>=40
The second group joins as well.
Verify conditional break-even.
Both join; claims 40; margin 40-40=0
Asymmetric information does not force exclusion in every parameter configuration.
State success probabilities and effort cost.
Low care p0.5; high care p0.75; effort cost 4
Care is chosen after the contract and is not directly verifiable.
Describe the observable payment rule.
Bonus B on success; no bonus on failure
Success rather than effort can be contracted on.
Compute the extra success probability.
0.75-0.5=0.25
This is the incentive-relevant probability difference.
Compute the incremental expected reward.
0.25B
A fixed payment common to both choices cancels.
Compare reward with private effort cost.
0.25B>=4, so B>=16
High care is weakly optimal at the boundary.
Separate incentives from participation.
The outside option must still be checked independently
Inducing effort does not alone ensure that the operator accepts the contract.
Equal groups have costs 30,90 and willingness 45,105; premium 60.
Type 1 declines; type 2 joins
Joining requires willingness at least as large as the premium.
Condition claims on participation.
Expected cost=90
The excluded group receives no weight among enrollees.
Calculate the provider's margin.
Two equally numerous types have expected claims 20,80 and maximum willingness 35,90 respectively. Premium 50; a type joins iff willingness>=premium, including equality. Encode joins 1, declines 0. Produce both participation indicators, conditional expected claims and premium-minus-claims margin.
| Your result | |
|---|---|
| Type 1 joins:1 or 0 | |
| Type 2 joins:1 or 0 | |
| Expected cost per enrollee | |
| Expected margin per enrollee |
Equally numerous types have expected claims 16,64 and willingness 30,80. Premium 40; willingness at least premium means participation. Only the second type joins. Complete the original all-type average, selected-pool claims and actual provider margin.
Average the population costs before selection.
population
This is not automatically the enrolled pool.
Use the expected claims of the participating type.
conditional
The low-cost group is excluded by its participation decision.
Subtract enrolled expected claims from premium.
margin
Retain the sign of any expected loss.
Equal groups have claims 20,60 and willingness 45,75. Premium 40; willingness>=premium means joins 1, otherwise 0. Produce both indicators, expected claims among enrollees and expected margin.
Type 1 joins:1 or 0: v0. Type 2 joins:1 or 0: v1. Expected cost per enrollee: v2. Expected margin per enrollee: v3.
Equal groups have claims 10,50 and willingness 30,70. Premium 30; equality joins. Use 1 for joins and 0 for declines, then calculate conditional claims and provider margin.
Type 1 joins:1 or 0: v0. Type 2 joins:1 or 0: v1. Expected cost per enrollee: v2. Expected margin per enrollee: v3.
A risk-neutral operator chooses hidden effort. High effort raises success probability from 0.4 to 0.6 and costs 6. A success-only bonus B is the sole payment difference across effort choices. Produce the probability increase and minimum B making high effort weakly optimal.
Probability increase: v0. Minimum bonus: v1.
A fictional warranty cooperative has equally numerous types with claims 30,90 and willingness 45,105. At premium 60, use 1 for joins if willingness>=premium and 0 otherwise. Calculate participation, conditional claims and expected margin; care behavior is held fixed, so this isolates selection.
Type 1 joins:1 or 0: v0. Type 2 joins:1 or 0: v1. Expected cost per enrollee: v2. Expected margin per enrollee: v3.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Fresh equal-size types have expected claims 24,72 and maximum willingness 42,84. The premium is 48 and joining occurs iff willingness>=premium. Construct both 1/0 participation indicators, expected claims per actual enrollee and the signed premium-minus-claims margin.
Type 1 joins:1 or 0: v0. Type 2 joins:1 or 0: v1. Expected cost per enrollee: v2. Expected margin per enrollee: v3.
Reconstruct a fresh case without the worked solution. Explain which assumption would change its conclusion and which result is only an accounting or model condition.
10. Complete the selected-pool account, step 3
60-90=-30
The offer attracts buyers without covering their expected claims.