Week 4 — Growth Report: Rates, Doubling, and Living Standards

Assignment 4 of the term — work four short growth problems, explain what each figure means, and tell a neighbor whether a city's growth headline means people there are better off.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, checkable 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 1 you read the production possibilities frontier, in Week 2 you measured output with real GDP, and in Week 3 you computed a rate of change as the change divided by the starting level; this week you put all three together to measure growth. 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 and explain them.

The task

This report uses the week's illustrative numbers, constructed for this course and not real data: an economy whose real GDP rises from 800 billion dollars to 840 billion dollars, the rule of 70, a city whose output grows 3 percent while its population grows 1 percent, and a print shop whose output per worker rises from 200 to 250 posters a day after it buys a faster press.

Work these four problems, showing every step on its own line:

1. An illustrative economy's real GDP rises from 800 billion dollars last year to 840 billion dollars this year. What is its growth rate, in percent?
2. Using the rule of 70, about how many years does an economy growing 5 percent a year take to double its real output?
3. An illustrative city's real output grows 3 percent in a year while its population grows 1 percent. About what is its per-capita growth rate, in percent?
4. At an illustrative print shop, output per worker rises from 200 posters a day to 250 posters a day after the shop buys a faster press. By what percent did productivity grow?

Beside each figure, add one brief interpretation in plain words. For problem 1, say what the growth rate means for the economy's output, and what this kind of growth looks like on a production possibilities frontier. For problem 2, say what the doubling time means and why it is written with "about". For problem 3, say what per-capita growth means for the average resident. For problem 4, say what the productivity growth means for each worker, and which of the three sources of growth (physical capital, human capital, or technology) the faster press belongs to.

Explain it to a non-expert

A neighbor who runs a small food business reads a headline that says the city's economy grew 3 percent last year, and asks whether that means people in the city are better off. Write a 3–5 sentence message your neighbor could follow: what per-capita growth is in everyday words, how the city's population growth changes the picture, and one honest limit of the per-person figure, such as what an average leaves out. Explain any technical term in everyday words. More than one good limit can be defended.

For a different, ungraded example, imagine a coastal town whose fishing fleet doubles its catch while the number of boats also doubles. Model message: "The town is catching twice as many fish, which sounds like great news. But there are twice as many boats doing the catching, so each boat brings in about the same as before. If you want to know whether the crews are better off, look at the catch per boat, not the town's total. Even that is an average, so it cannot tell you whether a few boats did very well while others struggled."

Use that pattern for the city, with your own explanation.

Here is one honest note about scope: every number in this assignment is illustrative, so do not add a real growth figure from the news. Over a lifetime, though, the same arithmetic is what separates places that pull ahead from places that stall.

Part 1 — Student instructions

1. Draft all four figures, the four brief interpretations, and your message for the neighbor 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. Answer 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 right.
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 long-run economic growth: growth rates divided by the starting value, the rule of 70 as an approximation, per-capita growth, productivity, and the three sources of growth. 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. Every number is illustrative, constructed for my course, not real data. The data: an economy's real GDP rises from 800 billion dollars to 840 billion dollars; the rule of 70 says doubling time is about 70 divided by the growth rate in percent; a city's output grows 3 percent while its population grows 1 percent; a print shop's output per worker rises from 200 to 250 posters a day after a faster press.
PROBLEM P1: An illustrative economy's real GDP rises from 800 billion dollars last year to 840 billion dollars this year. What is its growth rate, in percent?
PROBLEM P2: Using the rule of 70, about how many years does an economy growing 5 percent a year take to double its real output?
PROBLEM P3: An illustrative city's real output grows 3 percent in a year while its population grows 1 percent. About what is its per-capita growth rate, in percent?
PROBLEM P4: At an illustrative print shop, output per worker rises from 200 posters a day to 250 posters a day after the shop buys a faster press. By what percent did productivity grow?
After the four figures, I must briefly interpret each one: for P1, what the growth rate means for the economy's output and what this growth looks like on a production possibilities frontier; for P2, what the doubling time means and why it is written with about; for P3, what per-capita growth means for the average resident; for P4, what the productivity growth means for each worker and which source of growth the faster press belongs to. I must then write a 3-5 sentence message for a neighbor who runs a small food business, explaining per-capita growth in everyday words, how population growth changes the picture, and one honest limit of the per-person figure.

SCORING CRITERIA: Score only evidence I supply: correct growth computations (40 points), reasoning about growth, doubling, and living standards (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 message for the neighbor only with P3.
COMPUTATION UNITS: A correct growth rate, doubling time, per-capita growth rate, or productivity growth rate = 2; the right values and operation with only an arithmetic slip = 1; a missing figure or the wrong values or operation, such as dividing by the new value or multiplying by 70, = 0. Do not penalize an alternative valid method or equivalent notation.
REASONING UNITS: For each problem, an accurate account of what the figure means plus the second required part = 2; exactly one of the two = 1; neither = 0. The second parts: P1, what the growth looks like on a production possibilities frontier; P2, why the doubling time is an approximation; P3, a message for the neighbor explaining per-capita growth with one honest limit; P4, the source of growth the faster press belongs to. 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 message for the neighbor with P3. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a figure 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. Never bring in a real-world growth figure.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer 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.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four figures and their brief interpretations AND written my message for the neighbor 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 growth report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised growth report with all four figures, their brief interpretations, and your message for the neighbor — written, or recorded as audio or video with a transcript, or as a labelled sketch of the frontier shift 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 4 skills — computing a growth rate by dividing the change by the starting value, estimating a doubling time with the rule of 70 and treating it as an approximation, computing per-capita growth as total growth minus population growth, computing productivity growth and naming its source, and reading growth as an outward shift of the frontier — 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 for the neighbor. 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 growth 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, and do not let it supply a real-world growth figure. 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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