Week 3 — Graph & Model Workshop · "The CPI & the Unemployment Rate from Raw Data"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 3 — measuring the price level and the labor market · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 3
Format: build the CPI from a fixed market basket and the unemployment rate & LFPR from raw labor-market counts, in a spreadsheet (free, no account needed), complete a short scaffold, interpret the results in words, then catch the AI's mistakes.

This is the course's signature weekly component. Every instructional week has one workshop: you set up a model, solve it, and explain what it means. All tools are links to free external sites — nothing to buy or download.

Part 1 — The Big Picture

This week you learned two of macro's most-quoted measuring instruments: the Consumer Price Index (CPI), built from a fixed basket of goods priced across time, and the unemployment rate, built from a headcount of who's working, who's searching, and who's neither. Both numbers look simple once computed — but both hide a precise definition that news coverage routinely blurs (a CPI level is not an inflation rate; "unemployed" requires active searching). Today you'll build both from raw data, table by table, and read off exactly what each number does and doesn't tell you.

The tool: 🛠️ any free spreadsheet (Google Sheets, or your OS's built-in spreadsheet app) — no special software required. A calculator works too if you prefer to do it by hand.

Part 2 — The Guiding Question

Starting from raw prices and raw headcounts — not a headline number someone else already computed — exactly how do economists build "the CPI" and "the unemployment rate," and what do these two numbers leave out?

The scenario. A fictional economy tracks its cost of living with a fixed CPI basket: 10 pizzas, 20 cups of coffee, and 4 textbooks. In the base year, pizza costs $8, coffee costs $3, and books cost $15. In Year 2, pizza rises to $9, coffee to $3.30, and books stay at $15. Separately, this same economy's adult (16+) population is 200 million; of these, 114 million are employed and 6 million are unemployed (no job, actively searching).

Part 3 — Set Up the Model (in a spreadsheet)

1. Open a blank spreadsheet. Build Table A — the CPI basket, with one row per item and columns for Item, Quantity, Base-year price, Base-year cost (Qty × Price), Year-2 price, and Year-2 cost (Qty × Price).
2. Fill in the three items (pizza, coffee, books) with their quantities and both years' prices, then let the spreadsheet multiply quantity × price for each cost column and sum both cost columns at the bottom.
3. Build Table B — the labor market, with rows for Employed, Unemployed, Labor force (= Employed + Unemployed), and Adult population. Fill in the two given numbers and let the spreadsheet compute the labor force by addition.

Part 4 — Solve (complete this scaffold)

Fill in the blanks from your two spreadsheet tables and a little arithmetic. Show the steps.

Part 5 — Interpret in Words (this is the SLO-A skill)

In 2–3 sentences, explain what your CPI number (part c) and your unemployment-rate number (part f) each mean for someone who has never taken economics — and be precise about the difference between a CPI level and an inflation rate, and about who exactly counts as "unemployed" versus who is simply outside the labor force altogether.

(Hint: avoid saying "the CPI is 8%" — that sentence mixes up two different numbers. And avoid saying "unemployed" for anyone without a job — say what specifically makes someone count.)

Part 6 — Analysis Questions

1. Suppose 3 million of the 6 million currently-unemployed workers in this economy give up searching for work and become discouraged workers (they still don't have jobs, but they're no longer actively looking). Recompute the unemployment rate with the new (smaller) unemployed count and labor force. Did the unemployment rate go up, down, or stay the same — and does that change reflect a genuinely better job market? Explain.
2. The CPI basket in this workshop is fixed — it always contains 10 pizzas, 20 coffees, and 4 books, no matter how prices change. In one sentence, explain one real-world way this could make the CPI slightly overstate true inflation (think about what a shopper would actually do if pizza got a lot more expensive relative to coffee).
3. Connect to your life: think of a raise, allowance, scholarship, or wage you've received (or one you've heard about). Using this week's real-wage idea, explain in 2–3 sentences why knowing the inflation rate that same year is essential to knowing whether that raise actually made you better off — without declaring whether inflation or wage growth "should" get more attention (that's a values question, not a computation).

Part 7 — AI-Critique Moment (required — the BYOAI step)

Bring in your approved chatbot (Gemini, Claude, or ChatGPT) and be the economist who checks its work.

1. Paste this to the chatbot: "A CPI basket cost $200 in the base year and $216 this year. What is the CPI, and what is the inflation rate? Separately, a country has 114 million employed and 6 million unemployed (actively searching) out of a 200 million adult population — what is the unemployment rate, and what is the labor-force participation rate?"
2. Audit every claim against your own work:
   - Did it correctly compute CPI = 108 and inflation rate = 8% as two separate numbers — or did it call 108 itself "the inflation rate"?
   - Did it divide the unemployed by the labor force (120 million) to get the unemployment rate — 5% — or did it mistakenly divide by the total population (200 million), which would wrongly give 3%?
   - Did it correctly compute the LFPR (120 ÷ 200 × 100 = 60%) using the population as the denominator — the opposite denominator from the unemployment rate?
3. Write 2–3 sentences naming what the AI got right and at least one thing you had to correct or watch. (If it got everything right, explain how you verified each claim — that's the skill.)

The habit all term: the tool drafts, you judge. A chatbot will confidently call a CPI level "the inflation rate," or divide by the wrong denominator when computing the unemployment rate — catching it is the point.

Part 8 — What to Submit

One document (or text entry, or a shared spreadsheet link) with: your Part 4 scaffold (with the arithmetic), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot or link to your spreadsheet is welcome but optional. Due Sun, Sep 20, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see _build/logs/week-03-numbers.txt).

• (a) (10×$8) + (20×$3) + (4×$15) = $80 + $60 + $60 = $200. ✓
• (b) (10×$9) + (20×$3.30) + (4×$15) = $90 + $66 + $60 = $216. ✓
• (c) CPI = (216 ÷ 200) × 100 = 108. ✓
• (d) Inflation rate = 108 − 100 = 8%. ✓ (Valid shortcut specifically because this compares to the base year.)
• (e) Labor force = 114 + 6 = 120 million. ✓
• (f) Unemployment rate = 6 ÷ 120 × 100 = 5%. ✓
• (g) LFPR = 120 ÷ 200 × 100 = 60%. ✓
• (h) Real wage change ≈ 4% − 5% = ≈ −1%. ✓ (a real pay cut despite a nominal raise)
• Part 5: the CPI (108) is a level showing prices are 8% above the base year — the inflation rate (8%) is the percent change, a separate number from the level itself. "Unemployed" specifically means no job and actively searching (the 6 million); people not working and not searching (retirees, students not seeking work, discouraged workers) sit outside the labor force entirely — they are counted in neither the "employed" nor "unemployed" totals.
• Part 6: (1) New unemployed = 6 − 3 = 3 million (the 3 million who stopped searching are no longer counted as unemployed); new labor force = employed + new unemployed = 114 + 3 = 117 million; new unemployment rate = 3 ÷ 117 × 100 ≈ 2.56% — the measured rate FALLS noticeably (from 5% to about 2.6%), even though not one new job was created — the 3 million people are just as jobless as before, they've simply stopped being counted. This is the textbook illustration of why a falling unemployment rate doesn't automatically mean the job market improved: it can fall because discouraged workers exit the labor force (shrinking BOTH the numerator and the denominator), not because of genuine hiring. (2) A fixed basket can't reflect that shoppers would buy less pizza and more coffee if pizza got relatively pricier — a fixed basket assumes the same quantities every year, so it can overstate the true cost-of-living increase (the "substitution" issue, a well-documented, factual limitation of a fixed-basket index). (3) Full credit for any answer connecting a personal raise/wage to the real-wage formula (nominal change minus inflation) and explaining that the nominal number alone can't tell you whether you're actually better off — full credit whether the student concludes their own real change was positive, negative, or unclear, as long as the reasoning is sound and no side is declared objectively more important (evenhandedness on the values question).
• Part 7 (AI-critique): full credit for a specific catch — most commonly the AI conflating CPI=108 with "8% inflation" as the same number, or computing the unemployment rate by dividing 6 by 200 (population) instead of 120 (labor force), which would incorrectly yield 3% instead of the correct 5%.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — basket sums ($200, $216), CPI (108), inflation rate (8%), labor force (120M), unemployment rate (5%), LFPR (60%), real wage (≈−1%) all Python-re-verified ✓. Graph-logic check (measurement-logic analog) — CPI level vs. inflation rate never conflated; unemployment-rate and LFPR denominators correctly assigned and never swapped; discouraged-worker exclusion mechanism correctly reasoned through ✓. Quantitative gate: PASS. Graph-logic check: PASS.