Week 11 — Why Does the Ferry Sell Only 8?

Assignment 10 of the term — compute a single seller's marginal revenue from its revenue table, choose its quantity with MR = MC and read its fare from demand, find its profit, measure the deadweight loss against the competitive outcome, and explain to a non-expert what a monopoly costs riders.

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 consumer surplus as a triangle, and in Week 10 you used marginal revenue and the rule MR = MC for a price taker; this week that rule meets a seller with no rivals. 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 town's only ferry from this week's chapter, Dataset N, with illustrative numbers built for this course (not real data):

• Demand is P = 20 − Q, where P is the fare in dollars a ticket and Q is hundreds of tickets a day.
• Total revenue for 1 to 10 hundred tickets is 19, 36, 51, 64, 75, 84, 91, 96, 99, and 100 hundred dollars a day.
• The marginal-revenue line is MR = 20 − 2Q, and marginal cost is a constant 4 dollars a ticket.
• The ferry is the only seller: to sell more tickets, it must lower the fare for every rider.

Work these four problems, showing your arithmetic:

1. In the course's illustrative ferry, the fare is 13 dollars at 7 hundred tickets a day and 12 dollars at 8 hundred tickets a day. Using total revenue equals fare times quantity, what is the marginal revenue of the 8th hundred tickets, in dollars a ticket?
2. The same illustrative ferry has demand P = 20 − Q and marginal-revenue line MR = 20 − 2Q, with a constant marginal cost of 4 dollars a ticket. Using MR = MC to choose the quantity and the demand curve to set the fare, what fare does the ferry charge, in dollars a ticket?
3. At 8 hundred tickets a day and a fare of 12 dollars, with a constant marginal cost of 4 dollars a ticket, what is the illustrative ferry's profit, in hundreds of dollars a day, using profit equals the fare minus marginal cost, times quantity?
4. A competitive crossing with the same 4-dollar marginal cost would sell 16 hundred tickets a day, while the illustrative ferry sells 8 hundred at a fare of 12 dollars. Using the triangle one half times (16 − 8) times (12 − 4), what is the deadweight loss of the monopoly, in hundreds of dollars a day?

Beside each answer, add one brief interpretation. For problem 1, say in words what the marginal revenue means and why it is below the fare. For problem 2, say how many tickets the ferry sells, why it stops there, and why the fare comes from the demand curve rather than from P = MC. For problem 3, describe the profit rectangle in words, its height and its width, and say what stops the ferry from charging even more. For problem 4, explain what the deadweight loss is, how it differs from the ferry's profit, and check that riders' surplus, profit, and the loss add up to the competitive surplus of 128.

Explain it to a non-expert

A member of the town council says: "The ferry has no competition, so it can charge whatever it likes, and its profit is exactly what riders lose." Write a 3–5 sentence message to the council member that explains in everyday words why demand still limits the fare, what riders lose that no one gains, and one limit, such as that the ferry is a classroom model and a real crossing's costs and demand would have to be measured. Explain any technical term in everyday words. More than one accurate wording can be defensible, and the message does not need to say what the council should do about the ferry.

For a different, ungraded example, imagine a friend who says: "The only parking garage near the stadium could charge a thousand dollars a car if it wanted." Model answer: "It could post that price, but almost no one would pay it, so the garage would sit empty and earn nothing. A seller with no rival still picks a price from what drivers are willing to pay, and it does best at a price where enough cars still come. The cost to drivers is the trips to the stadium that people skip because the price is above what parking really costs the garage. One limit: I am reasoning from a classroom model, so I would need real numbers on what drivers would pay before saying what the garage actually charges."

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 monopoly: barriers to entry, why a single seller's marginal revenue is below its price, the rule MR = MC with the price read from the demand curve, monopoly profit, the competitive benchmark, and the deadweight loss of monopoly. 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): the town's only ferry faces demand P = 20 − Q, where P is the fare in dollars a ticket and Q is hundreds of tickets a day, and its marginal cost is a constant 4 dollars a ticket; its total revenue for 1 to 10 hundred tickets is 19, 36, 51, 64, 75, 84, 91, 96, 99, and 100 hundred dollars a day; its marginal-revenue line is MR = 20 − 2Q. The ferry is not a real company.
PROBLEM P1: In the course's illustrative ferry, the fare is 13 dollars at 7 hundred tickets a day and 12 dollars at 8 hundred tickets a day. Using total revenue equals fare times quantity, what is the marginal revenue of the 8th hundred tickets, in dollars a ticket?
PROBLEM P2: The same illustrative ferry has demand P = 20 − Q and marginal-revenue line MR = 20 − 2Q, with a constant marginal cost of 4 dollars a ticket. Using MR = MC to choose the quantity and the demand curve to set the fare, what fare does the ferry charge, in dollars a ticket?
PROBLEM P3: At 8 hundred tickets a day and a fare of 12 dollars, with a constant marginal cost of 4 dollars a ticket, what is the illustrative ferry's profit, in hundreds of dollars a day, using profit equals the fare minus marginal cost, times quantity?
PROBLEM P4: A competitive crossing with the same 4-dollar marginal cost would sell 16 hundred tickets a day, while the illustrative ferry sells 8 hundred at a fare of 12 dollars. Using the triangle one half times (16 − 8) times (12 − 4), what is the deadweight loss of the monopoly, in hundreds of dollars a day?
After the four answers, I must briefly interpret each one: for P1, what the marginal revenue means and why it is below the fare; for P2, how many tickets the ferry sells, why it stops there, and why the fare comes from demand rather than from P = MC; for P3, the profit rectangle described in words and what stops the ferry from charging more; for P4, what the deadweight loss is, how it differs from the profit, and a check that riders' surplus, profit, and the loss add up to the competitive surplus of 128. I must then write a 3-5 sentence message to a town council member who says "The ferry has no competition, so it can charge whatever it likes, and its profit is exactly what riders lose," explaining in everyday words why demand still limits the fare, what riders lose that no one gains, and one limit. I must explain technical terms in everyday words. The message does not need to say what the council should do, and you must not take a side on that. This week stays with a single seller: do not bring in markets with a few rivals or game theory, never invent prices or fares for groups of riders, and never name a real company as a monopoly.

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 marginal revenue of the 8th hundred tickets, fare, profit, or deadweight loss = 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 marginal revenue equals the fare does not count. For P2, setting the fare where price equals marginal cost, or reading the fare where MR meets MC, does not count. For P3, "the ferry can charge whatever it wants" does not count. For P4, BOTH an explanation that the deadweight loss is the value of trips never taken, kept apart from the profit as a transfer to the owner, AND a final message that explains why demand limits the fare, what riders lose, and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. Calling the profit the deadweight loss 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, market share, 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 ferry report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised ferry 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 sketch that describes the demand line, the marginal-revenue line, and the marginal-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 11 skills — computing a single seller's marginal revenue from its revenue table, choosing its quantity with MR = MC and reading its fare from demand, computing its profit, measuring the deadweight loss against the competitive outcome, and explaining what a monopoly costs riders 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 ferry 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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