Information, distribution and policy audits

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1. What you will learn

Analyze information, distribution and policy audits using explicit assumptions, calculated results and a stated limit of the model.

2. Starting point

A market's efficiency depends on its information, incentives and relevant social costs. Total surplus and its distribution are different questions. A percentage share divides a group's amount by the appropriate total, and cumulative shares add groups in order.

3. Terms and units

4. Missing information can change which trades occur

A competitive diagram often assumes that buyers and sellers know the relevant characteristics of what is traded. When one party knows more than another, the price can reflect uncertainty rather than a fully observed quality. Asymmetric information is not simply the absence of perfect knowledge everywhere. It concerns an uneven distribution of information relevant to the agreement and its incentives.

In a used-equipment market, sellers may know their machines' condition while buyers cannot distinguish reliable from unreliable machines before purchase. A buyer's offer based on average expected quality can be too low for owners of reliable machines to accept. If those sellers withdraw, the average quality of remaining offers falls, potentially reducing buyers' willingness to pay further. This adverse-selection mechanism can prevent beneficial trades. It depends on the supplied quality, valuation and information conditions; it is not a claim that every used-goods market collapses.

The hidden characteristic matters before the agreement. In insurance examples, people with different risks may know more about their risk than the insurer. A common premium can attract a different mix of purchasers than the insurer initially expects. The resulting selection changes average cost. The precise outcome requires a model of risks, preferences and contract rules, so one cannot infer it from the word insurance alone.

Signaling and screening can reduce information gaps. An informed seller may offer a credible warranty or disclose verifiable maintenance records. An uninformed buyer may inspect the product or offer contract alternatives that different types select differently. Credibility matters: a costless claim that every type can make equally easily may reveal little. Verification and warranties also cost resources. An institutional remedy should therefore be evaluated for what it actually reveals, how incentives support it and what it costs.

Term	What it means
Asymmetric information	A setting in which relevant information differs between the parties to an exchange.
Adverse selection	A selection problem arising from hidden characteristics before an agreement, potentially changing who trades.
Moral hazard	A hidden-action or incentive problem arising when a party's behavior after an agreement affects outcomes.
Signaling	An informed party taking an action intended to convey information.
Screening	An uninformed party using information gathering or contract choices to distinguish types.
Income	A flow of resources received over a stated period.
Wealth	A stock of assets minus liabilities at a stated point in time.
Lorenz curve	Cumulative income share plotted against cumulative population share, with people ordered from lowest to highest income.
Gini coefficient	A summary of inequality based on the area between the Lorenz curve and the equality line, under a stated definition and data convention.

Another way: Behavior after an agreement raises a different problem

Moral hazard concerns actions or effort that affect outcomes after an agreement and are not fully observed or reflected in the actor's incentives. If someone is fully protected from a loss, the private incentive to take costly precautions may weaken. The technical term does not assert that the person is morally bad. It identifies a change in behavior induced by the arrangement, which must be demonstrated or stipulated rather than assumed from a label.

For example, a maintenance contract might reimburse every repair while the owner's precautionary effort is unobservable. If effort reduces the probability of damage but takes time, full reimbursement can reduce the owner's private return to that effort. A deductible, monitoring rule or incentive payment may restore part of the incentive, but can also reduce risk protection or impose administrative costs. The remedy therefore creates a trade-off rather than a free improvement in every dimension.

Adverse selection and moral hazard can coexist, but they should not be confused. Hidden pre-agreement quality or risk affects which parties enter the contract. Hidden post-agreement behavior affects what they do after entering it. Ask whether the relevant unobserved feature is a type or an action, and when it matters. A question about a poorly maintained machine offered for sale differs from a question about reduced maintenance after a comprehensive repair guarantee is purchased.

Principal-agent problems generalize the incentive issue. An owner may hire a manager whose effort or decisions are difficult to observe and whose objectives differ from the owner's. Contracts, monitoring and performance measures can help align incentives, but measures can be incomplete or encourage gaming. A higher measured output is not always the same as better overall performance if quality or unmeasured tasks deteriorate. The lesson's audit asks which behavior the rule rewards and what remains outside the measure.

Another way: Measure distribution without confusing stocks and flows

Income is a flow over a period, such as annual earnings and transfers under a defined accounting convention. Wealth is a stock at a date: assets minus liabilities. A household can have modest current income but substantial wealth, or high current income and large debts. An income table cannot be relabeled as a wealth distribution. Comparisons also need consistent units, household definitions, population coverage and periods.

A Lorenz curve orders people or equal-sized groups from lowest to highest income and plots cumulative population share horizontally against cumulative income share vertically. If four equal-sized groups receive ten, twenty, thirty and forty percent of total income, the points are (0,0), (25,10), (50,30), (75,60) and (100,100). The middle ordinate is thirty because the lower two groups' income shares add, not because the second group alone receives thirty.

The equality line joins (0,0) to (100,100). Along it, every cumulative population share receives the same cumulative income share. A Lorenz curve farther below this line indicates greater concentration in the usual nonnegative-income setting. Curves can cross, in which case a simple statement that one distribution is unambiguously more equal under every criterion is not justified by dominance. A summary index may rank them, but its aggregation choice should be acknowledged.

The Gini coefficient summarizes the area between the equality line and the Lorenz curve relative to the area below the equality line. With shares measured from zero to one, it equals one minus twice the area under the Lorenz curve. Connecting the four-group example's points linearly gives trapezoid areas totaling 0.375, so the corresponding grouped-data Gini is 0.25. This value assumes the represented within-group equality and linear segments. Coarse group totals generally conceal within-group inequality, so they do not identify every feature of an underlying individual distribution.

Inequality and poverty are also different concepts. A distribution can be relatively equal while everyone has low resources, or relatively unequal while fewer people fall below a specified poverty threshold. Poverty measures require a defined threshold and resource concept; inequality measures compare dispersion or shares. Neither alone describes opportunity, mobility, nonmonetary well-being or the fairness of how outcomes arose. State what the chosen statistic measures before using it in a policy claim.

Another way: Combine efficiency, incentives and distribution in an audit

Suppose four equal-sized household groups receive ten, twenty, thirty and forty dollars of income. A transfer of five dollars from the highest group to the lowest changes incomes to fifteen, twenty, thirty and thirty-five. Total income stays one hundred under this purely accounting exercise, and the bottom half's share rises from thirty to thirty-five percent. The arithmetic establishes that change in shares; it does not establish how production, work effort or reporting would respond in a real policy.

Budget neutrality means the transfer's inflow and outflow balance in the specified account. It does not automatically imply zero administrative cost, unchanged behavior or no effect on future income. Those are separate assumptions. Likewise, a policy that raises total surplus may still leave particular groups worse off. An audit should retain the aggregate calculation and the distributional entries rather than allowing one to erase the other.

A structured policy comparison begins with an explicit objective. Is the proposal intended to correct an external cost, improve information, finance a public good, reduce poverty or change income distribution? Next identify the mechanism: a price wedge, a disclosure rule, a contract incentive, a quantity limit or a transfer. Then state the behavioral and information assumptions that connect the mechanism to the predicted outcome. A recommendation unsupported by that chain is not made rigorous by attaching a familiar economic term.

Compare with a feasible counterfactual. Doing nothing can have costs when a market failure exists, while intervention can have measurement, enforcement and incentive costs. A flawless policy compared with an imperfect market is as misleading as a flawless market compared with an imperfect policy. Use the supplied assumptions consistently on both sides, and identify uncertainties that could reverse the ranking.

Finally, distinguish positive and normative conclusions. A model can calculate that a transfer changes the bottom-half share by five percentage points, that a warranty changes selection under stated types, or that a tax aligns a private and social margin. Choosing the preferred distribution or balancing competing objectives involves values as well as evidence. Our final constructed audit assesses the transparent calculations and the limits of inference, not whether the learner endorses a political position or offers financial advice to a real household.

5. An invented grant report with two separate claims

A fictional city council receives a report on four equal-sized household groups with incomes of ten, twenty, thirty and forty dollars for a specified period. The report proposes moving five dollars from the highest group to the lowest. The initial total is one hundred, the lowest group's share is ten percent and the bottom half's share is thirty percent. After the transfer, incomes are fifteen, twenty, thirty and thirty-five. The total remains one hundred and the bottom half receives thirty-five percent.

The report's first claim is therefore a valid accounting statement under the supplied no-behavioral-change assumption. Its second claim, that the proposal must increase future total income because the distribution is more equal, does not follow from those entries. A future-income prediction needs a model of incentives, resources and responses. The table also concerns income rather than assets and liabilities, so it cannot establish the wealth distribution.

The city council also considers a repair warranty intended to improve confidence in used equipment. To evaluate it, the analyst asks whether it credibly reveals pre-existing quality, addressing adverse selection, or changes owners' maintenance behavior after purchase, creating a moral-hazard concern. Both mechanisms can be present. The warranty's mere existence does not prove that information is perfect or that every behavioral effect is beneficial.

A complete audit keeps those questions separate: the income-share arithmetic, the behavioral assumptions behind transfers, the information revealed by a warranty and the incentives it creates. It can then compare the proposal with a clearly described alternative and identify who pays, who benefits and which conclusions remain uncertain. The exercise ends with a bounded, reviewable analysis rather than an unqualified endorsement of a policy.

6. Check the tempting shortcut

Adverse selection concerns hidden characteristics before agreement; moral hazard concerns behavior and incentives after it. Income is a flow and wealth a stock. A budget-neutral transfer preserves a total only within its accounting assumptions, and a Lorenz share does not by itself settle fairness or predict future production.

7. In the fictional Alder model, four equal-sized household groups have total incomes [10, 20, 30, 40] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 5 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

8. In the fictional Birch model, four equal-sized household groups have total incomes [20, 40, 60, 80] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 10 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

9. In the fictional Cedar model, four equal-sized household groups have total incomes [30, 60, 90, 120] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 15 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

10. In the fictional Dune model, four equal-sized household groups have total incomes [40, 80, 120, 160] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 20 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

11. Guided practice

In the fictional Elm model, four equal-sized household groups have total incomes [50, 100, 150, 200] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 25 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

12. Guided practice

In the fictional Dune model, four equal-sized household groups have total incomes [40, 80, 120, 160] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 20 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

13. Guided practice

In the fictional Fern model, four equal-sized household groups have total incomes [60, 120, 180, 240] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 30 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

14. Practice

In the fictional Grove model, four equal-sized household groups have total incomes [70, 140, 210, 280] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 35 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

15. Practice

Classify three supplied information mechanisms with codes: 1=hidden characteristic before agreement (adverse selection); 2=hidden action after agreement (moral hazard); 3=both. A: sellers know pre-existing machine quality, buyers cannot inspect, and quality affects which sellers accept an offer; maintenance after sale is fully observable. B: all initial risk types are known, but a repair guarantee changes unobserved precaution after purchase. C: buyers cannot observe pre-existing quality and a guarantee also changes unobserved precautions afterward. Enter each case's code; do not judge anyone's character.

16. Somewhere new

A city council's grant report claims a transfer changes both the distribution and the total size of income. Audit only the supplied accounting experiment, which assumes no production response. Preserve the difference between a cumulative income share and a prediction about future wealth. In the fictional Island model, four equal-sized household groups have total incomes [90, 180, 270, 360] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 45 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

In the fictional Juniper model, four equal-sized household groups have total incomes [100, 200, 300, 400] dollars respectively, already ordered from lowest to highest. Within each group households receive equal income. A budget-neutral transfer moves 50 dollars from the highest-income group to the lowest, without changing any production or behavior in this stipulated accounting exercise. Calculate total income, the lowest group's initial percentage share, and the bottom two groups' percentage share after the transfer. These shares do not measure wealth or establish which distribution is fair.

19. What you can do now

Reconstruct the model without the worked example. Explain each requested measure's units and identify an assumption that the conclusion depends on.

Working for the steps left to you

	Calculated value
Total income
Initial lowest share (percent)
New bottom-half share (percent)

	Constructed result
Case A
Case B
Case C

	Calculated value
Total income
Initial lowest share (percent)
New bottom-half share (percent)

	Calculated value
Total income
Initial lowest share (percent)
New bottom-half share (percent)