Week 15 — When One Side Knows More, and Who Gets What — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 14 of the term — work the lemons market, measure what hidden quality costs, compute a Gini coefficient from a Lorenz curve, choose the right course tool for a policy question, and explain inequality's best-known number to someone outside economics.

This week you learned that a market can fail when one side cannot see what it is buying: an uninformed offer drives good used cars away, and a warranty or an inspection can bring the trade back. You also learned to measure how evenly income is shared, with a Lorenz curve built from cumulative shares and a Gini coefficient that runs from 0 to 1. In Week 6 you measured the surplus a market creates and in Week 14 you saw a market fail through a spillover; this week you work four short problems, choose the right course tool for a policy question, and explain the Gini coefficient to someone who has never studied economics. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles.

The task

You will use two datasets from this week's chapter, both with illustrative numbers built for this course (not real data):

• Dataset R, the used-car market. Half the cars of one model are good and half are lemons. A good car is worth 10,000 dollars to a buyer and 9,000 dollars to its owner; a lemon is worth 4,000 dollars to a buyer and 3,000 dollars to its owner.
• Dataset S, the illustrative income quintiles. Households from the poorest fifth to the richest receive 5, 10, 15, 25, and 45 percent of income, so the cumulative shares are 5, 15, 30, 55, and 100 percent. These are not any country's figures.

Work these four problems, showing your arithmetic:

1. In the course's illustrative used-car market, half the cars of one model are good and half are lemons; a good car is worth 10,000 dollars to a buyer and 9,000 dollars to its owner, and a lemon is worth 4,000 dollars to a buyer and 3,000 dollars to its owner. A buyer who cannot tell the two kinds of car apart offers the average of the two buyer values. How many dollars does the buyer offer?
2. In the course's illustrative used-car market, half the cars of one model are good and half are lemons; a good car is worth 10,000 dollars to a buyer and 9,000 dollars to its owner, and a lemon is worth 4,000 dollars to a buyer and 3,000 dollars to its owner. Only lemons are offered at the uninformed buyer's offer of 7,000 dollars. How many dollars does a buyer overpay by paying that offer for a lemon?
3. In the course's illustrative income quintiles, households from the poorest fifth to the richest receive 5, 10, 15, 25, and 45 percent of income, so the cumulative shares are 5, 15, 30, 55, and 100 percent. Using five trapezoids, each 0.2 wide, what is the area under the Lorenz curve on a chart whose axes both run from 0 to 1?
4. In the course's illustrative income quintiles, households from the poorest fifth to the richest receive 5, 10, 15, 25, and 45 percent of income, so the cumulative shares are 5, 15, 30, 55, and 100 percent. The area under its Lorenz curve is 0.31, and the Gini coefficient equals 1 minus 2 times that area. What is the Gini coefficient?

Beside each answer, add one brief interpretation. For problem 1, say which owners accept the offer and why, and name the problem the offer creates. For problem 2, explain what buyers learn, why good cars stay off the market even though each is worth more to a buyer than to its owner, and name one signal or one screen that could bring the trade back, with the side that acts. For problem 3, describe the Lorenz curve in words: what it plots, and where it sags below the line of perfect equality. For problem 4, read the Gini coefficient on its scale from 0 to 1, and label any claim that it is too high or about right as positive or normative.

Choose the tool (a synthesis of the course)

This is the last assignment of the course, so the fourth interpretation also asks you to choose among methods you have already learned. A town council is debating a rule that every used-car dealer must offer a short warranty on every car. Choose the one course tool you would use first to analyze the rule, from these: the timing test for adverse selection and moral hazard (this week), signaling and screening (this week), consumer and producer surplus (Week 6), the Lorenz curve and Gini coefficient (this week), or the positive and normative labels (Week 1). In 3–4 sentences, say why your tool fits the question best and why one plausible alternative from the list fits less well. More than one choice can be defended; the reason is what counts.

Explain it to a non-expert

A friend who volunteers at a community food bank reads a report saying a region's Gini coefficient went up, and asks you: "What does that number mean, and does it prove the region is unfair?" Write a 3–5 sentence message to your friend that explains the Gini coefficient in everyday words, using Dataset S's 0.38 as the example, answers whether the number by itself proves unfairness, and names one limit, such as that a single number hides who moved where, or that Dataset S is illustrative rather than any real region's data. Explain any technical term in everyday words. More than one accurate wording can be defensible. Do not use a real Gini figure or income figure for any place.

For a different, ungraded example, imagine a neighbor who notices that a phone plan renewed itself and asks: "Why do companies make plans renew unless you cancel?" Model answer: "When a plan renews unless you act, staying in is the default, the choice that happens if you do nothing. Most people stick with a default because changing takes time and attention, and the cost of switching shows up now while the benefit comes later. So more people stay subscribed than would sign up again from scratch. One limit: I do not know how many customers actually forget to cancel, so I cannot say how big the effect is for this plan."

Use that pattern for your message to your friend, with your own explanation and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

Deliverables

Submit a single report containing:

• the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
• your choose-the-tool paragraph, naming the tool you would use first, why, and one alternative that fits less well;
• your message to your friend, explaining the Gini coefficient in everyday words, answering whether it proves unfairness, and naming one limit; and
• a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled Lorenz chart described point by point in words with a short note. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Looking ahead to the final

The cumulative final exam comes in Week 16. Its study guide, practice exam (the Final Practice Exam), and exam-prep tutorial sit in the Week 16 exam bundle. The choose-the-tool move you practice here, matching a question to the model that answers it and saying why another model fits less well, is the same move those materials ask you to make with every unit of the course.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without any AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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