Week 15 — Graph & Model Workshop · "The Lemons Market & the Quintile Table"

Course: Principles of Microeconomics (ECON 1) · Silver Oak University (fictional sample) · Prof. Kessler
Objective 8 — asymmetric information & inequality · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 15
Format: model the lemons market in a spreadsheet; read and analyze an illustrative quintile income-share table; then catch the AI's mistakes on both models.

This is the course's signature weekly component — the economics analog of a lab. This week you work TWO related models: the adverse-selection calculation that shows why a used-car market can unravel, and the quintile-share arithmetic that economists use to describe income distribution. Both involve precise computation; both require interpretation in words; both give the chatbot a chance to slip up.

---

Part 1 — The Big Picture

This week gave you two tools that work together: asymmetric information (when one side knows more, markets can fail) and distribution measurement (how economists describe who gets what). The lemons model shows how information asymmetry destroys mutually beneficial trade. The quintile table shows how income is distributed — and forces the positive-vs-normative distinction into sharp relief.

The tools:
- 🔗 Spreadsheet (Google Sheets, Excel, or Numbers — free): https://sheets.google.com / https://office.com
- 🔗 FRED — Federal Reserve Economic Data (for real distributional data, as a contrast): https://fred.stlouisfed.org/

---

Part 2 — The Guiding Questions

MODEL 1: If buyers don't know whether a used car is good or bad, is the buyer's best offer ever high enough to keep good sellers in the market — and what happens when it isn't?

MODEL 2: What does the income distribution look like when the top quintile holds 50% and the bottom holds 4% — and is that a positive or a normative question?

---

Part 3 — Model A: The Lemons Market

The scenario (USE THESE NUMBERS EXACTLY — verified):
- Good used car: worth $4,000 to both buyer and good-car seller.
- Bad used car ("lemon"): worth $2,000 to both buyer and bad-car seller.
- 50/50 probability of each type; buyers cannot distinguish them before purchase.

Set Up the Spreadsheet

Build a small table with these columns:

Car type	Probability	Value to buyer
Good	0.5	$4,000
Bad	0.5	$2,000
Expected value	—	=0.5·$4,000 + 0.5·$2,000

---

Part 4A — Solve the Lemons Model (complete this scaffold)

Fill in the blanks. Show every step.

Question	Your answer
(a) Buyer EV = ½ · $4,000 + ½ · $2,000 = ?	$______
(b) Will a good-car seller accept this EV? (Is EV ≥ $4,000?)	Yes / No
(c) If good sellers exit, who remains in the market?	______
(d) Once buyers know only lemons remain, what is the most they will pay?	$______
(e) What is the name of this market failure?	______

---

Part 5A — Interpret the Lemons Model in Words

In 2–3 sentences, explain in plain English why the lemons problem is a market failure — not just a bad deal for buyers, but a situation where mutually beneficial trades (a good-car owner and a good-car buyer who both want to trade at a fair price) are destroyed by information asymmetry. What does this imply about the social value of things like warranties, inspections, and reputation systems?

---

Part 6A — Analysis Questions (Lemons)

1. If a mechanic offered buyers a verified inspection report for $50, would this help? Why — which information gap does it close, and how?
2. A dealer offers a 12-month warranty on all used cars. How does this act as a signal? What would make the signal credible and not just cheap talk?
3. Connect to class: is the lemons problem an example of adverse selection or moral hazard? State the timing (before or after the purchase decision) to justify your answer.

---

Part 3B — Model B: The Quintile Table

The scenario (ILLUSTRATIVE NUMBERS — engineered, not real-country data):

Build a simple spreadsheet table:

Quintile	Income Share
Bottom 20%	4%
Second 20%	9%
Middle 20%	15%
Fourth 20%	22%
Top 20%	50%
Sum	=SUM above

---

Part 4B — Solve the Quintile Table (complete this scaffold)

Question	Your answer
(a) Sum of all five shares = ?	______%
(b) Top-quintile share ÷ bottom-quintile share = 50 ÷ 4 = ?	______×
(c) The top quintile holds how many times more income share than the bottom?	______×
(d) Is "the ratio of 12.5× shows the income distribution is unfair" positive or normative?	______

---

Part 5B — Interpret the Quintile Table in Words

In 2–3 sentences, explain (a) what the quintile shares describe (this is the positive part) and (b) why the question of whether the distribution is "too unequal" is normative — what would a person need to believe or value to say 12.5× is acceptable vs. not? Note explicitly that these numbers are illustrative and engineered, not data from any real country.

---

Part 6B — Analysis Questions (Inequality)

1. The Lorenz curve plots cumulative income share against cumulative population share. In this table, what fraction of total income does the bottom 40% receive combined? Show the calculation. (Hint: add the bottom two quintile shares.)
2. If the distribution shifted so the top quintile held 35% and the bottom held 8%, would the Gini coefficient rise or fall? Explain the direction.
3. Positive vs. normative: write one positive claim and one normative claim about the quintile data in this table, and label each clearly.

---

Part 7 — AI-Critique Moment (required — the BYOAI step)

Bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the economist who checks its work.

Audit task 1 — Lemons:
Paste this to the chatbot: "In a used-car market, good cars are worth $4,000 and bad cars worth $2,000; 50/50 chance; sellers know which they have but buyers don't. What is the buyer's expected value, and what happens to the market?"
Audit each claim:
- Did it compute EV correctly as $3,000 (½·$4,000 + ½·$2,000)?
- Did it correctly say good sellers EXIT (because $3,000 < $4,000)?
- Did it label this adverse selection (not moral hazard)?
- Did it explain that this is a PRE-contract information problem?

Audit task 2 — Adverse selection vs. moral hazard:
Paste this: "Is it adverse selection or moral hazard when a person drives more recklessly after getting full-coverage car insurance?"
Audit: the correct answer is moral hazard (behavior changes AFTER the contract). If the chatbot says adverse selection, it has swapped the timing — note it and correct it.

Write 2–3 sentences naming what the AI got right and at least one thing you had to correct or watch (most commonly: the EV arithmetic, the adverse/moral timing label, or the "who exits" step). If it got everything right, explain how you verified each claim against the verified numbers.

The habit all term: the tool drafts, you judge. The adverse-selection/moral-hazard distinction is one of the most commonly mis-stated items in chatbot economics — catching it is the point.

---

Part 8 — What to Submit

One document (or text entry) with: Part 4A scaffold (with arithmetic); Part 5A interpretation; Part 6A answers; Part 4B scaffold; Part 5B interpretation; Part 6B answers; and the Part 7 AI-critique paragraph. A screenshot of your spreadsheet is welcome but optional. Due Sun, Dec 13, 11:59 p.m. (50 points).

---

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified. The lemons numbers: good = $4,000; bad = $2,000; EV = $3,000. Quintile shares: 4/9/15/22/50; ratio = 12.5×.

Model A — Lemons

• (a) ½ · $4,000 + ½ · $2,000 = $2,000 + $1,000 = $3,000 ✓
• (b) No — $3,000 < $4,000; a good seller will not accept it. ✓
• (c) Only bad-car sellers remain (lemons). ✓
• (d) $2,000 — the value of a bad car. ✓
• (e) Adverse selection (or "the lemons problem"). ✓
• Part 5A: the market failure is that good-car sellers who WOULD have traded at $4,000 cannot because buyers, unable to verify quality, won't pay $4,000 under uncertainty. The result: a class of mutually beneficial trades never occurs — an allocative failure. Warranties, inspections, and reputation systems mitigate this by closing the information gap.
• Part 6A: (1) An inspection report resolves the information asymmetry BEFORE the purchase — turning an asymmetric-information market into an informed one; good sellers can now credibly charge $4,000. (2) A warranty signals quality because a bad-car dealer who offers one faces high expected repair costs — the signal is costly enough that only good sellers can afford to send it. (3) Adverse selection — the information problem exists BEFORE the purchase decision (pre-contract).

Model B — Quintile Table

• (a) 4+9+15+22+50 = 100% ✓
• (b) 50 ÷ 4 = 12.5× ✓
• (c) 12.5× ✓
• (d) Normative — "unfair" is a value judgment. ✓
• Part 5B: the quintile shares describe (positive) how income is distributed across the population; measuring 12.5× is an empirical calculation, not a judgment. Whether 12.5× is "too much" is normative and depends on what you value: equality of outcome, equality of opportunity, total growth, or mobility — these are genuine disagreements among thoughtful people, not questions data alone resolves. These numbers are illustrative/engineered — not real-country statistics.
• Part 6B: (1) Bottom 40% share = 4% + 9% = 13% of total income. (2) The Gini coefficient would fall (toward more equality) — a lower top share and higher bottom share means the Lorenz curve bows less. (3) Positive: "the top quintile holds 12.5 times the income share of the bottom quintile in this table." Normative: "this distribution gives too little to the bottom 20%." (Any reasonable positive/normative pair earns credit.)

Grading rubric — 50 points

Criterion	Full	Partial	None
Lemons scaffold (Part 4A) — EV = $3,000, good sellers exit, only lemons remain, $2,000, adverse selection — all with arithmetic (15)	15	7–12	0–6
Lemons interpretation + analysis (Parts 5A & 6A) — market-failure mechanism; inspection/warranty logic; adverse-selection label with timing (10)	10	5–8	0–4
Quintile scaffold (Part 4B) — sum = 100%, ratio = 12.5×, normative label (10)	10	5–8	0–4
Quintile interpretation + analysis (Parts 5B & 6B) — positive/normative distinction; bottom-40% sum = 13%; Gini direction; one P + one N claim (8)	8	4–6	0–3
AI-critique (Part 7) — names a specific thing checked or corrected in BOTH audits (7)	7	3–5	0–2

Quality gate (self-checked): quantitative gate — EV ½·4000+½·2000=3000 ✓; 50÷4=12.5 ✓; 4+9+15+22+50=100 ✓; 4+9=13 (bottom 40%) ✓ — all Python-re-verified. Graph/logic check — good sellers exit because 3000<4000 ✓; adverse selection = PRE-contract ✓; moral hazard = POST-contract ✓; Gini falls as top share drops ✓; normative/positive distinction correctly applied ✓. Quintile table labeled illustrative/engineered ✓.