Week 7 — Who Pays and What Is Lost: Price Controls and a Tax — Traditional alternative (no AI)

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

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 week you learned what a price ceiling and a price floor do when they bind, how to measure the deadweight loss of a control or a tax, and how to find who really bears a per-unit tax. 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 uses all three. You work four short problems, interpret each one, and explain a claim 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 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.

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 intervention report containing:

• the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
• your message to the food-cart owner, separating who writes the check from who bears the tax in everyday words, saying what decides the split, 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 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. 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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