Week 5 — How Strongly Buyers Respond: Elasticity, Revenue, and Related Goods

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 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 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. 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 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:

1. 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?
2. 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?
3. 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?
4. 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.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to the café owner 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 elasticity: the price elasticity of demand by the midpoint formula, its sign and magnitude, elastic, inelastic, and unit-elastic demand, the total-revenue test, and the income and cross-price elasticities of demand. 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 elasticity schedule Qd = 200 - 20P gives 160 units at 2 dollars, 120 at 4, 80 at 6, and 40 at 8; a household's income rises from 40,000 to 60,000 dollars a year while its restaurant meals rise from 6 to 10 a month; at a café the price of coffee rises from 2 to 3 dollars a cup while muffin sales fall from 50 to 30 a day. The course computes every elasticity by the midpoint formula: each change divided by the average of its two values.
PROBLEM P1: 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?
PROBLEM P2: 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?
PROBLEM P3: 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?
PROBLEM P4: 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?
After the four answers, I must briefly interpret each one: for P1, the sign, the label, and why the midpoint gives the same result as the rise from 4 to 6 dollars; for P2, whether revenue rises or falls and how that follows from the elasticity of the segment through the total-revenue test; for P3, what the sign and the size say about the kind of good; for P4, the sign and the relationship between muffins and coffee. I must then write a 3-5 sentence message to a café owner who is new to economics and says "Raising the price can only help: we make more on every cup, and muffin sales have nothing to do with it," recommending a more accurate way to think about the decision, explaining in everyday words why whether revenue rises depends on how strongly customers respond, saying what the café's numbers suggest about muffin sales, and naming one limit. I must explain technical terms in everyday words. The message does not need to decide whether the owner should raise the price, and you must not take a side on that. This week is elasticity only: do not ask me to compute a consumer surplus, a tax burden, or a point elasticity with calculus.

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 price elasticity, revenue change, income elasticity, or cross-price elasticity = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation, such as dividing by the starting value instead of the midpoint = 0. Do not penalize an alternative valid method, equivalent notation, or an equivalent rounding of the same exact value.
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, the sign and the unit-elastic label must be read correctly and the direction-free midpoint result explained; dropping the sign and calling the result inelastic does not count. For P2, the revenue change must be tied to the elastic segment through the total-revenue test. For P3, the sign must sort the good as normal and the magnitude as income-elastic. For P4, BOTH a complements reading of the negative sign AND a final message that recommends a more accurate way to think about the decision, explains how responsiveness decides revenue, names the effect on muffin sales, and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. 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 midpoints, percentages, or revenues = 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, sales figure, real elasticity, 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 café owner 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 elasticity report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised elasticity report with all four answers, their brief interpretations, and your message to the café owner — written, or recorded as audio or video 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;
• 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 5 skills — computing price, income, and cross-price elasticities by the midpoint formula, reading each sign and magnitude, tying a price change to total revenue, and explaining to someone new to economics why a higher price does not always bring in more money — 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 café owner. 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 elasticity 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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