Week 6 — Measuring the Gains: Surplus, Efficiency, and Who Benefits

Assignment 6 of the term — measure the gains from trade on this week's illustrative ladder and market, show why the efficient quantity gives the biggest total, and explain to someone outside economics why an efficient market is not automatically a fair one.

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 4 you found where the running market's demand and supply cross; this week you measure the gains on either side of that crossing, and in Week 1 you learned the line between positive and normative statements that the last part of this assignment uses. 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 these materials, all illustrative numbers built for this course (not real data) and all from this week's chapter:

• The used-bicycle ladder: five buyers would pay at most 100, 80, 70, 50, and 30 dollars for one bicycle, and five sellers would accept no less than 20, 30, 50, 70, and 90 dollars. At a price of 60 dollars, three bicycles sell.
• The course's running market, read as prices: demand P = 9 − Q ⁄ 10 and supply P = 3 + Q ⁄ 10, with P in dollars and Q in units per day. The two lines cross at 6 dollars and 30 units a day.

Work these four problems, showing your arithmetic:

1. On the illustrative used-bicycle ladder, bicycles sell for 60 dollars and the three sellers who sell have costs of 20, 30, and 50 dollars. What is the producer surplus?
2. On the same illustrative ladder, pair the buyers who value a bicycle at 100, 80, and 70 dollars with the sellers whose costs are 20, 30, and 50 dollars, highest value with lowest cost. What is the total surplus from these three efficient trades?
3. In the course's illustrative market, demand read as prices is P = 9 − Q ⁄ 10, and the equilibrium is 30 units a day at 6 dollars. What is the consumer surplus at the equilibrium, in dollars per day?
4. In the same illustrative market, supply read as prices is P = 3 + Q ⁄ 10, so at 20 units buyers value the last unit at 7 dollars and it costs sellers 5 dollars. If trading stopped at 20 units a day, what total surplus would those 20 units create, in dollars per day?

Beside each answer, add one brief interpretation. For problem 1, say in words what the producer surplus means for the sellers and tie it to what producer surplus measures. For problem 2, explain why three trades is the efficient number, using the fourth pair on the ladder. For problem 3, describe in words where the consumer-surplus triangle sits on the diagram and why it is a triangle rather than a rectangle. For problem 4, explain what is lost by stopping at 20 units and why 30 units is efficient in the model.

Explain it to a non-expert

A city council member has never studied economics. After hearing about the bicycle market, the council member says: "That market is efficient, so everyone got a fair deal, including the buyer who went home without a bicycle." Write a 3–5 sentence message to the council member that explains in everyday words what "efficient" means here, says which part of the claim the model can check and which part is a question of values, and names one limit, such as that a buyer's willingness to pay also reflects how much money the buyer has. Explain any technical term in everyday words. More than one accurate wording can be defensible, and the message does not need to decide whether the outcome is fair.

For a different, ungraded example, imagine a bake-sale organizer who says: "We sold every cupcake at 3 dollars, so the people who bought them must have wanted them more than anyone who missed out." Model answer: "Selling out tells us each buyer valued a cupcake at 3 dollars or more, so each sale left that buyer ahead. It does not tell us that the people who missed out wanted one less, because someone who arrived late might have valued a cupcake highly and found none left. Whether first come, first served is a fair way to share is a separate question about values, not something the sales numbers can settle. One limit: we never saw anyone's top price, only who paid 3 dollars."

Use that pattern for your message to the council member, with your own explanation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the council member 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 surplus and efficiency: willingness to pay and willingness to sell, consumer, producer, and total surplus on a ladder and as triangles, the efficient number of trades, allocative efficiency, and efficiency versus equity. 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): on the used-bicycle ladder, five buyers would pay at most 100, 80, 70, 50, and 30 dollars and five sellers would accept no less than 20, 30, 50, 70, and 90 dollars, and at 60 dollars three bicycles sell; in the running market, demand read as prices is P = 9 − Q ⁄ 10 and supply is P = 3 + Q ⁄ 10, crossing at 6 dollars and 30 units a day.
PROBLEM P1: On the illustrative used-bicycle ladder, bicycles sell for 60 dollars and the three sellers who sell have costs of 20, 30, and 50 dollars. What is the producer surplus?
PROBLEM P2: On the same illustrative ladder, pair the buyers who value a bicycle at 100, 80, and 70 dollars with the sellers whose costs are 20, 30, and 50 dollars, highest value with lowest cost. What is the total surplus from these three efficient trades?
PROBLEM P3: In the course's illustrative market, demand read as prices is P = 9 − Q ⁄ 10, and the equilibrium is 30 units a day at 6 dollars. What is the consumer surplus at the equilibrium, in dollars per day?
PROBLEM P4: In the same illustrative market, supply read as prices is P = 3 + Q ⁄ 10, so at 20 units buyers value the last unit at 7 dollars and it costs sellers 5 dollars. If trading stopped at 20 units a day, what total surplus would those 20 units create, in dollars per day?
After the four answers, I must briefly interpret each one: for P1, what the producer surplus means for the sellers and what producer surplus measures; for P2, why three trades is the efficient number, using the fourth pair; for P3, where the consumer-surplus triangle sits and why it is a triangle rather than a rectangle; for P4, what is lost by stopping at 20 units and why 30 units is efficient in the model. I must then write a 3-5 sentence message to a city council member who is new to economics and says "That market is efficient, so everyone got a fair deal, including the buyer who went home without a bicycle," explaining in everyday words what efficient means, saying which part of the claim the model can check and which part is a question of values, and naming one limit. I must explain technical terms in everyday words. The message does not need to decide whether the outcome is fair, and you must not take a side on that. This week stays with the free market: do not bring in price ceilings, price floors, taxes, or subsidies.

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 final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct producer surplus, total surplus, consumer surplus, or total surplus at 20 units = 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, producer surplus read as price minus value, or as the buyers' gain, does not count. For P2, "more trades is always better" does not count. For P3, the full rectangle does not count as the triangle. For P4, BOTH an explanation that the units between 20 and 30 are worth more to buyers than they cost sellers, so 30 is efficient in the model, AND a final message that explains efficiency in everyday words, labels fairness as a separate normative question, and names a limit = 2. 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 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, sales figure, 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 message to the council member 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 surplus report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised surplus report with all four answers, their brief interpretations, and your message to the council member — written, or recorded as audio or video with a transcript, or as a labelled diagram that describes the ladder and the two surplus triangles 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 6 skills — summing producer and total surplus on a ladder, finding the efficient number of trades, computing a surplus triangle on the diagram, explaining why the equilibrium quantity is efficient in the model, and explaining the difference between efficiency and fairness 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, and the message to the council member. 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 surplus 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.

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.

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