Week 7 — Who Pays and What Is Lost: Price Controls and a Tax

Assignment 7 of the term — measure what a price ceiling and a per-unit tax do to this week's illustrative market, find who really bears a tax, and explain to a small-business owner why writing the check is not the same as paying the tax.

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, in Week 5 you measured how strongly quantity responds to price, and in Week 6 you measured the gains from trade as triangles; this assignment puts all three to work on a government rule. 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 course's running market: demand Qd = 90 − 10P and supply Qs = 10P − 30, with P in dollars and Q in units per day. Read as values and costs, demand is P = 9 − Q ⁄ 10 and supply is P = 3 + Q ⁄ 10. With no intervention the market clears at 6 dollars and 30 units a day.
• The who-bears-it market: demand Qd = 60 − 5P and supply Qs = 15P − 40, meeting at 5 dollars and 35 units a day.

Work these four problems, showing your arithmetic:

1. In the course's illustrative running market, demand is Qd = 90 − 10P and supply is Qs = 10P − 30, and the government sets a price ceiling of 4 dollars. What is the shortage, in units per day?
2. In the same illustrative market under the 4-dollar ceiling, only 10 units trade instead of the equilibrium 30, and at 10 units buyers value the last unit at 8 dollars while it costs sellers 4. What is the deadweight loss, in dollars per day?
3. In the same illustrative market, a tax of 2 dollars per unit collected from sellers cuts the quantity traded from 30 to 20 units a day. What is the deadweight loss of the tax, in dollars per day?
4. In the course's illustrative who-bears-it market, demand is Qd = 60 − 5P and supply is Qs = 15P − 40, which meet at 5 dollars, and a tax of 4 dollars per unit is collected from sellers. How many dollars of the tax do buyers bear?

Beside each answer, add one brief interpretation. For problem 1, say in words what the shortage means for buyers and why a ceiling at 4 dollars binds while one at 7 would not. For problem 2, explain what the deadweight loss measures and why it is a triangle rather than a rectangle. For problem 3, explain why the tax revenue is not part of the deadweight loss. For problem 4, explain why buyers bear more of the tax than sellers even though sellers write the check, using how many units each side changes per dollar.

Explain it to a non-expert

A food-cart owner has never studied economics. After hearing that the city will add a per-unit tax on each meal sold, collected from vendors, the owner says: "I write the check to the city, so the whole tax comes out of my pocket." Write a 3–5 sentence message to the owner that explains in everyday words the difference between who writes the check and who bears the tax, says what decides how the burden is split, and names one limit, such as that the model's straight lines are a classroom simplification and the real split depends on how strongly the owner's customers respond. Explain any technical term in everyday words. The message does not need to say whether the tax is a good idea, and it should not.

For a different, ungraded example, imagine a commuter who says: "The parking garage pays the city's fee on every space, so the fee never touches my wallet." Model answer: "The garage hands the fee to the city, but that only tells us who writes the check. If drivers keep parking there even when the price goes up, the garage can raise its price and pass most of the fee along to drivers like you. If drivers would switch to the bus at the first price increase, the garage has to absorb more of the fee itself. One limit: we cannot know the split without knowing how strongly drivers and the garage respond to price."

Use that pattern for your message to the food-cart owner, with your own explanation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the food-cart owner 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 price controls and taxes: price ceilings and price floors and when they bind, shortages and surpluses, deadweight loss, a per-unit tax's wedge and revenue, and who bears a tax versus who writes the check. 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): in the running market, demand is Qd = 90 - 10P and supply is Qs = 10P - 30, read as values and costs P = 9 - Q/10 and P = 3 + Q/10, clearing at 6 dollars and 30 units a day; in the who-bears-it market, demand is Qd = 60 - 5P and supply is Qs = 15P - 40, meeting at 5 dollars and 35 units a day.
PROBLEM P1: In the course's illustrative running market, demand is Qd = 90 − 10P and supply is Qs = 10P − 30, and the government sets a price ceiling of 4 dollars. What is the shortage, in units per day?
PROBLEM P2: In the same illustrative market under the 4-dollar ceiling, only 10 units trade instead of the equilibrium 30, and at 10 units buyers value the last unit at 8 dollars while it costs sellers 4. What is the deadweight loss, in dollars per day?
PROBLEM P3: In the same illustrative market, a tax of 2 dollars per unit collected from sellers cuts the quantity traded from 30 to 20 units a day. What is the deadweight loss of the tax, in dollars per day?
PROBLEM P4: In the course's illustrative who-bears-it market, demand is Qd = 60 − 5P and supply is Qs = 15P − 40, which meet at 5 dollars, and a tax of 4 dollars per unit is collected from sellers. How many dollars of the tax do buyers bear?
After the four answers, I must briefly interpret each one: for P1, what the shortage means for buyers and why a ceiling at 4 dollars binds while one at 7 would not; for P2, what the deadweight loss measures and why it is a triangle rather than a rectangle; for P3, why the tax revenue is not part of the deadweight loss; for P4, why buyers bear more of the tax than sellers even though sellers write the check, using how many units each side changes per dollar. I must then write a 3-5 sentence message to a food-cart owner who is new to economics and says "I write the check to the city, so the whole tax comes out of my pocket," explaining in everyday words the difference between who writes the check and who bears the tax, what decides the split, and one limit. I must explain technical terms in everyday words. The message does not need to say whether the tax is a good idea, and you must not take a side on that. Do not name any politician, party, news outlet, or advocacy group, and do not treat this week's tax as fixing a market failure.

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 shortage, deadweight loss of the ceiling, deadweight loss of the tax, or buyers' share of the tax = 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, calling the gap a surplus does not count. For P2, the full rectangle does not count as the triangle. For P3, treating tax times quantity as the loss does not count. For P4, BOTH an explanation that buyers bear more because quantity demanded changes by only 5 units per dollar while quantity supplied changes by 15, AND a final message that separates who writes the check from who bears the tax in everyday words 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, tax rate, 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 food-cart owner 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 intervention report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised intervention report with all four answers, their brief interpretations, and your message to the food-cart owner — written, or recorded as audio or video with a transcript, or as a labelled diagram that describes the ceiling, the tax wedge, and the two loss 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 7 skills — computing a binding ceiling's shortage, measuring the deadweight loss of a ceiling and of a tax, keeping tax revenue apart from the loss, finding who bears a tax from how strongly each side responds, and explaining the difference between writing the check and bearing the tax 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 food-cart owner. 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 intervention 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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