Week 15 — When One Side Knows More, and Who Gets What

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 adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 6 you measured the surplus a market creates, and in Week 14 you saw how a market fails when costs spill onto bystanders; this week a market fails because one side cannot see what it is buying, and you measure how evenly income is shared. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles; this assignment is where you put them together.

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.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, the choose-the-tool paragraph, and your message to your friend before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Respond in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about asymmetric information, the lemons market, signaling and screening, the Lorenz curve, the Gini coefficient, and the line between positive and normative claims. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data, all illustrative numbers built for the course (not real data): half the used cars of one model are good and half are lemons; a good car is worth 10,000 dollars to a buyer and 9,000 to its owner, and a lemon is worth 4,000 to a buyer and 3,000 to its owner. Households from the poorest fifth to the richest receive 5, 10, 15, 25, and 45 percent of income, with cumulative shares of 5, 15, 30, 55, and 100 percent.
PROBLEM P1: 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?
PROBLEM P2: 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?
PROBLEM P3: 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?
PROBLEM P4: 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?
After the four answers, I must briefly interpret each one: for P1, which owners accept the offer and why, named as adverse selection; for P2, what buyers learn, why good cars stay off the market, that this does not mean all used cars are bad, and one signal or screen with the side that acts; for P3, a word description of the Lorenz curve built from cumulative shares and where it sags below the line of perfect equality; for P4, a reading of the Gini coefficient on its 0-to-1 scale, with any claim that it is too high labeled normative. With P4 I must also choose the one course tool I would use first to analyze a town rule that every used-car dealer must offer a short warranty (the timing test, signaling and screening, consumer and producer surplus, the Lorenz curve and Gini coefficient, or the positive and normative labels), say why it fits best, and say why one plausible alternative fits less well. I must then write a 3-5 sentence message to a friend who volunteers at a community food bank and asks "What does that number mean, and does it prove the region is unfair?", explaining the Gini coefficient in everyday words with 0.38 as the example, answering whether it proves unfairness, and naming one limit. I must explain technical terms in everyday words. Never supply a real Gini figure or income figure for any place, never take a side on redistribution for me, and never name a politician, party, company, advocacy group, or news outlet.

SCORING CRITERIA: Score only evidence I supply: correct computations from the data (40 points), economic reasoning and interpretation (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my choose-the-tool paragraph and final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct uninformed offer, overpayment for a lemon, area under the Lorenz curve, or Gini coefficient = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate plain reading of what that value shows plus the concept point tied to it = 2; exactly one of the two = 1; neither = 0. For P1, saying the good-car owners accept the offer does not count as the concept point. For P2, reading the lemons result as "all used cars are bad", or mixing up which side signals and which screens, does not count. For P3, plotting each fifth's own share instead of the cumulative share does not count. For P4, BOTH a reading of the Gini on its 0-to-1 scale with any too-high claim labeled normative and a choose-the-tool paragraph that gives a reason and one alternative that fits less well, AND a final message that explains the Gini in everyday words, answers whether it proves unfairness, and names a limit = 2. Reading a Gini of 0 as perfect inequality, or presenting "0.38 is too high" as a model result, does not count. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to economics, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the choose-the-tool paragraph and the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my reply. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word reply is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early. Never state a real price, income, or other real-world statistic, and never invent data for me.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my choose-the-tool paragraph AND written my message to my friend AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised report with all four answers, their brief interpretations, your choose-the-tool paragraph, and your message to your friend — written, or recorded as audio or video 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;
• the coach's five-line report; and
• the conversation share link.

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.

Equivalent route (no AI required)

This route assesses the same Week 15 skills — working the lemons market, explaining adverse selection with a signal or a screen, building a Lorenz curve and computing a Gini coefficient, choosing the right course tool for a policy question, keeping positive and normative claims apart, and explaining the Gini coefficient to someone new to economics — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, the choose-the-tool paragraph, and the message to your friend. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

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

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

Built with The Course Maker · samples.thecoursemaker.com