Week 10 — How Many Chairs, and Should the Doors Stay Open? — Traditional alternative (no AI)

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

Assignment 9 of the term — choose a price taker's output with P = MC, read its profit two ways, decide whether it should stay open at a loss, find where entry and exit push the price, and explain the shutdown rule to someone outside economics.

This week you learned how a firm in a perfectly competitive market behaves: it takes the market price as given, so its marginal revenue is the price; it chooses output with P = MC on the rising part of marginal cost; it reads its profit or loss as a rectangle; it stays open at a loss while the price covers average variable cost; and, in the long run, entry and exit push the price to the lowest average total cost. In Week 9 you built the chair workshop's cost table, and this week a market price meets it. In this assignment you work four short problems, interpret each one, and explain the shutdown rule 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 chair workshop from this week's chapter, Dataset M, with illustrative numbers built for this course (not real data):

• Fixed cost is 60 dollars a day, and total cost is 60, 90, 110, 126, 148, 180, and 228 dollars a day for 0 to 6 chairs.
• Marginal cost is 30, 20, 16, 22, 32, and 48 dollars for the 1st to 6th chair.
• Average variable cost is lowest at 22 dollars, and average total cost is lowest at 36 dollars, at 5 chairs.
• The workshop is a price taker: it sells every chair at the market price, which it cannot change.

Work these four problems, showing your arithmetic:

1. In the course's illustrative chair workshop, a price taker, the market price is 40 dollars a chair, marginal cost is 30, 20, 16, 22, 32, and 48 dollars for the 1st to 6th chair, and total cost is 60, 90, 110, 126, 148, 180, and 228 dollars for 0 to 6 chairs. Using P = MC, what is its daily profit, in dollars?
2. At a market price of 50 dollars a chair, the same illustrative workshop makes 6 chairs, where its average total cost is 38 dollars a chair. Using profit equals price minus average total cost, times quantity, what is its daily profit, in dollars?
3. At a market price of 30 dollars a chair, the same illustrative workshop makes 4 chairs; its fixed cost is 60 dollars a day and its variable cost at 4 chairs is 88 dollars. What is its daily profit, in dollars (a negative number is a loss)?
4. In the long run, entry and exit push the market price to the illustrative workshop's lowest average total cost, which it reaches at 5 chairs, where total cost is 180 dollars. What is the long-run price, in dollars per chair?

Beside each answer, add one brief interpretation. For problem 1, say in words what the profit means and use P = MC to explain why the workshop makes the number of chairs it does, including why marginal revenue equals the price for a price taker. For problem 2, describe the profit rectangle in words, its height and its width, and say why a higher price raises profit. For problem 3, say what the loss means and use the shutdown rule to explain whether the workshop should operate or close for the day. For problem 4, explain how entry and exit move the market price to that level, which curve shifts and which way, and what zero economic profit means for the owner.

Explain it to a non-expert

A neighbor grows sweet corn and sells it to a wholesale buyer at whatever price the market sets that week. The neighbor says: "Prices are so low this week that I lose money on every truckload, so I should stop picking until prices come back." Write a 3–5 sentence message to your neighbor that explains the shutdown rule in everyday words, says which of the neighbor's costs are paid even when picking stops, and names one limit, such as that you would need to know which costs really stop when the picking stops. Explain any technical term in everyday words. More than one accurate wording can be defensible, and the message does not need to decide whether your neighbor should keep picking.

For a different, ungraded example, imagine a soap maker who sells plain bars at a crafts market at the going price and says: "My bars cost me 4 dollars each on average, and they sell for 6, so I should make as many as I possibly can." Model answer: "The 4 dollars is your whole month's cost shared over every bar, including the booth fee you pay no matter how many bars you make. What matters for the next batch is what that batch adds to your costs. Once your kitchen gets crowded, an extra batch can cost more per bar than the 6 dollars it brings in, and then it lowers your profit even though your average looks fine. One limit: I only know your average, so we would need your costs at two different batch sizes to see what the next batch really adds."

Use that pattern for your message to your neighbor, 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 workshop report containing:

• the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
• your message to your neighbor, explaining the shutdown rule in everyday words, naming the costs paid even when picking stops, and naming 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 price line, the marginal-cost curve, and the average-total-cost curve 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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