Week 5 · Assignment: Traditional alternative (no AI)

Week 5 — How Strongly Buyers Respond: Elasticity, Revenue, and Related Goods — 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Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI.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 5 of the term — compute and interpret price, income, and cross-price elasticities with the midpoint formula, tie a price change to total revenue, and explain to someone outside economics why a higher price does not always bring in more money.

This week you learned to measure how strongly buyers respond to a price change with the midpoint formula, to read an elasticity's sign and magnitude, to tie a price change to total revenue, and to measure responses to income and to another good's price. In Week 3 you learned that a change in a good's own price is a movement along the demand curve, and you met normal and inferior goods, substitutes and complements; this week puts numbers on all of them. In this assignment you work four short problems on this week's illustrative data, 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 elasticity schedule: Qd = 200 − 20P, so buyers want 160 units at 2 dollars, 120 at 4, 80 at 6, and 40 at 8.
A household whose income rises from 40,000 to 60,000 dollars a year, with its restaurant meals and bus rides.
A café where the price of coffee rises from 2 to 3 dollars a cup, with its tea and muffin sales.

Work these four problems, showing every percentage and every product on its own line:

On the course's illustrative elasticity schedule, Qd = 200 − 20P, with P in dollars and Qd in units, the price falls from 6 dollars, where 80 units are demanded, to 4 dollars, where 120 are demanded. Using the midpoint formula, what is the price elasticity of demand?
On the same illustrative schedule, a seller charging 6 dollars sells 80 units and is considering 8 dollars, where 40 units would sell. By how many dollars does total revenue change if the seller raises the price from 6 to 8 dollars?
In an illustrative household, income rises from 40,000 to 60,000 dollars a year and restaurant meals rise from 6 to 10 a month. Using the midpoint formula, what is the income elasticity of demand for restaurant meals?
At an illustrative café, the price of coffee rises from 2 to 3 dollars a cup and muffin sales fall from 50 to 30 a day. Using the midpoint formula, what is the cross-price elasticity of demand for muffins with respect to the price of coffee?

Beside each answer, add one brief interpretation. For problem 1, state the sign, name the label (elastic, inelastic, or unit-elastic), and explain why the midpoint formula gives the same result as a price rise from 4 to 6 dollars. For problem 2, say whether revenue rises or falls and tie that to the elasticity of the segment from 6 to 8 dollars with the total-revenue test. For problem 3, keep the sign and say what it and the size of the result tell you about the kind of good. For problem 4, keep the sign and name the relationship between muffins and coffee.

Explain it to a non-expert

A café owner who has never studied economics plans to raise the price of coffee and says: "Raising the price can only help: we make more on every cup, and muffin sales have nothing to do with it." Write a 3–5 sentence message to the owner that recommends a more accurate way to think about the decision, explains in everyday words why whether revenue rises depends on how strongly customers respond, says what the illustrative café's numbers suggest about muffin sales when coffee costs more, and names one limit, such as that these are illustrative numbers and real customers may respond differently over a week than over a year. Explain any technical term in everyday words. The message does not need to decide whether the owner should raise the price; that is the owner's judgment.

For a different, ungraded example, imagine a gym manager who says: "Our members love us, so we can raise the class fee as much as we like and only gain." Model answer: "A higher fee brings in more money only if members barely react to it. If many members can switch to another gym or to running outside, they will drop classes faster than the fee rises, and total takings fall. Before raising the fee, it is worth asking how many good substitutes members have. One limit: members who stay this month may still leave over the next few months, once they have had time to look around."

Use that pattern for your message to the café owner, with your own recommendation 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 elasticity report containing:

the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
your message to the café owner, recommending a more accurate way to think about the decision, explaining why revenue depends on how strongly customers respond, saying what the café's numbers suggest about muffin sales, 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 elasticity schedule's elastic, unit-elastic, and inelastic stretches 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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