Week 14 — Who Pays for the Smoke?

Assignment 13 of the term — find the efficient quantity when a market's costs spill onto bystanders, measure the deadweight loss, show how a corrective tax fixes it, value a public good, and explain to a non-expert why free riders can sink a project worth doing.

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 surplus as triangles, and in Week 7 you put a 2-dollar tax on the running market and found a deadweight loss of 10; this week the same market gains a cost that lands on its neighbors. 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 the running market with smoke from this week's chapter, Dataset P, and the fireworks show from Dataset Q, with illustrative numbers built for this course (not real data):

• Demand is Qd = 90 − 10P, or P = 9 − Q ⁄ 10, and supply is Qs = 10P − 30, or P = 3 + Q ⁄ 10, with P in dollars per unit and Q in units per day.
• Each unit does 2 dollars of harm to neighbors who neither buy nor sell the good, so marginal social cost is P = 5 + Q ⁄ 10.
• Ignoring the harm, the market trades 30 units a day at 6 dollars.
• In the neighborhood, 100 residents each value a fireworks show at 10 dollars, the show costs 600 dollars, and no one can be kept from watching it.

Work these four problems, showing your arithmetic:

1. In the course's illustrative running market, demand is P = 9 − Q ⁄ 10 and each unit does 2 dollars of harm to neighbors, so marginal social cost is P = 5 + Q ⁄ 10. Setting marginal social benefit 9 − Q ⁄ 10 equal to marginal social cost 5 + Q ⁄ 10, what is the efficient quantity, in units per day?
2. The illustrative market trades 30 units a day, the efficient quantity is 20, and at the 30th unit marginal social cost is 8 dollars while buyers value it at 6. Using the triangle one half times the gap times the extra units, what is the deadweight loss of the externality, in dollars per day?
3. A 2-dollar corrective tax per unit on sellers shifts supply in the illustrative market to Qs = 10P − 50, while demand stays Qd = 90 − 10P. Setting Qd = Qs, what price do buyers pay, in dollars per unit?
4. In the course's illustrative neighborhood, 100 residents each value a fireworks show at 10 dollars, and the show costs 600 dollars. Using total value minus cost, what is the net gain from putting on the show, in dollars?

Beside each answer, add one brief interpretation. For problem 1, say what the efficient quantity means, compare it with the market's 30 units at 6 dollars, and explain why the market makes too much. For problem 2, explain what the deadweight loss is and why it is not the 60 dollars of total harm on all 30 units. For problem 3, say what sellers keep and how many units trade, and explain why the same 2-dollar tax that caused a deadweight loss of 10 in Week 7 removes one of 10 here. For problem 4, explain why the show is a public good and why it may not happen even though it is worth more than it costs.

Explain it to a non-expert

The treasurer of the neighborhood association says: "If the show is really worth 1,000 dollars to us, people will chip in the 600 on their own." Write a 3–5 sentence message to the treasurer that explains in everyday words why voluntary gifts can fall short even for a show worth more than it costs, and one limit, such as that the numbers are a classroom model or that neighbors who know each other may give out of goodwill. Explain any technical term in everyday words. More than one accurate wording can be defensible, and the message does not need to say how the association should raise the money.

For a different, ungraded example, imagine a friend who says: "Everyone on our street loves the new speed bumps, so the residents will gladly split the cost." Model answer: "Everyone on the street gets the quieter, safer road whether or not they pay, so each person is tempted to let the neighbors cover it. When enough people think that way, the collection comes up short even though the street as a whole would gladly pay the full price. That is why shared things like this are often paid for through dues or a city budget instead of a hat passed around. One limit: on a small street where everyone knows each other, people may chip in anyway, so I would want to see how the collection actually goes."

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

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the treasurer 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 externalities: private versus social cost, marginal social cost and the efficient quantity, the deadweight loss of a spillover, the corrective tax, and public goods and the free-rider problem. 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): demand is Qd = 90 − 10P, or P = 9 − Q ⁄ 10, and supply is Qs = 10P − 30, or P = 3 + Q ⁄ 10, with P in dollars per unit and Q in units per day; each unit does 2 dollars of harm to neighbors, so marginal social cost is P = 5 + Q ⁄ 10; ignoring the harm, the market trades 30 units at 6 dollars; 100 residents each value a fireworks show at 10 dollars, it costs 600 dollars, and no one can be kept from watching.
PROBLEM P1: In the course's illustrative running market, demand is P = 9 − Q ⁄ 10 and each unit does 2 dollars of harm to neighbors, so marginal social cost is P = 5 + Q ⁄ 10. Setting marginal social benefit 9 − Q ⁄ 10 equal to marginal social cost 5 + Q ⁄ 10, what is the efficient quantity, in units per day?
PROBLEM P2: The illustrative market trades 30 units a day, the efficient quantity is 20, and at the 30th unit marginal social cost is 8 dollars while buyers value it at 6. Using the triangle one half times the gap times the extra units, what is the deadweight loss of the externality, in dollars per day?
PROBLEM P3: A 2-dollar corrective tax per unit on sellers shifts supply in the illustrative market to Qs = 10P − 50, while demand stays Qd = 90 − 10P. Setting Qd = Qs, what price do buyers pay, in dollars per unit?
PROBLEM P4: In the course's illustrative neighborhood, 100 residents each value a fireworks show at 10 dollars, and the show costs 600 dollars. Using total value minus cost, what is the net gain from putting on the show, in dollars?
After the four answers, I must briefly interpret each one: for P1, what the efficient quantity means, a comparison with the market's 30 units at 6 dollars, and why the market makes too much; for P2, what the deadweight loss is and why it is not the 60 dollars of total harm; for P3, what sellers keep and how many units trade, and why the same 2-dollar tax that caused a deadweight loss of 10 in Week 7 removes one of 10 here; for P4, why the show is a public good and why it may not happen even though it is worth more than it costs. I must then write a 3-5 sentence message to a neighborhood association treasurer who says "If the show is really worth 1,000 dollars to us, people will chip in the 600 on their own," explaining in everyday words why voluntary gifts can fall short and naming one limit. I must explain technical terms in everyday words. The message does not need to say how the association should raise the money, and you must not take a side on that. This week stays with externalities and public goods: do not bring in asymmetric information or behavioral economics, never cite a real pollution, climate, or carbon figure, and never invent data for me.

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 efficient quantity, deadweight loss, buyer price with the tax, or net gain from the fireworks = 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 harm makes the market produce too little does not count. For P2, counting all 60 dollars of harm as the loss does not count. For P3, setting the tax equal to the total harm, or saying the tax wastes surplus here as it did in Week 7, does not count. For P4, BOTH an explanation that the show is neither rival nor excludable and that each resident is tempted to free ride, AND a final message that explains why voluntary gifts can fall short and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. Calling the show a public good only because a group pays for it does not count. 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, pollution level, 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 treasurer 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, and your message to the treasurer — written, or recorded as audio or video with a transcript, or as a labelled sketch that describes the demand line, the supply line, and the marginal-social-cost line 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 14 skills — finding the efficient quantity when costs spill onto bystanders, measuring the deadweight loss of a spillover, showing how a corrective tax moves the market to the efficient quantity, valuing a public good, and explaining the free-rider problem 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 treasurer. 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.

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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