Week 4 — Growth Report: Rates, Doubling, and Living Standards — Traditional alternative (no AI)

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

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 week you learned to read long-run growth as an outward shift of the frontier, to compute a growth rate by dividing the change by the starting value, to estimate doubling times with the rule of 70, to compute per-capita growth, and to measure productivity and name its three sources. 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. In this assignment you work four short problems, interpret each one, and explain to a neighbor what a growth headline does and does not say. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles.

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.

How to work

1. Draft all four figures, the four brief interpretations, and your message for the neighbor.
2. Check your draft against the attached scoring criteria, criterion by criterion: is every growth rate divided by the starting value, is every doubling time written with "about", and is every figure explained in plain words?
3. Revise at least one calculation or explanation, and write two or three sentences on what you changed and why.

Deliverables

Submit your growth report with all four figures, their brief interpretations, your message for the neighbor, and your two or three sentences on the revision. You may submit it written, 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.

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

The calculations, reasoning, and explanations must be your own work. This version is built to be completed without any AI tool, and no part of it requires one. Use the chapter, your notes, and a calculator or spreadsheet, and show every step so your work can be checked. Do not copy another student's figures or wording.

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