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Week 11 · Assignment: Traditional alternative (no AI)

Week 11 — Why Does the Ferry Sell Only 8? — Traditional alternative (no AI)

Principles of Microeconomics Free sample edition
Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI. An instructor who prefers it publishes it and unpublishes or deletes the adaptive one, as the note at its top says.

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

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 week you learned how a single seller behaves: barriers to entry keep rivals out; to sell more it must cut its price for every buyer, so its marginal revenue is below its price; it chooses its quantity with MR = MC and reads its price from the demand curve; and, compared with a competitive market, it sells less at a higher price and leaves a deadweight loss. In Week 6 you measured consumer surplus as a triangle, and in Week 10 you met marginal revenue and the rule MR = MC. In this assignment you work four short problems, interpret each one, and explain what a monopoly costs riders to someone who has never studied economics. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles.

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.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

Deliverables

Submit a single ferry report containing:

  • the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
  • your message to the council member, explaining why demand still limits the fare, what riders lose that no one gains, and one limit; and
  • a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes 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. 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.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without any AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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