Week 3 Model Workshop: A Family Budget and a County Job Report

Part 1 — The Big Picture

This week you learned to price a fixed basket, turn the price index into an inflation rate, test a raise against inflation, and count a labor market. In this workshop you do all four with a family's own budget and a county's job report, in a spreadsheet or a graphing calculator, so every number comes from a formula you can check. Then you use the same numbers to separate what the data show from what someone thinks ought to happen, and you catch a chatbot's slips on a similar example. The habit you build here, compute first, then say it in words, carries into every model this course builds next.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Did the family's paycheck keep up with the prices of the things it buys, and is the county's job market really improving when its unemployment rate falls?

Workshop data: the illustrative family budget and county job report

Source: Two small illustrative tables constructed for this workshop, not real data: a family's monthly basket of rent, grocery trips, and bus passes priced over three years, and a county's counts of adults, employed people, and unemployed people. Both are printed in Part 4.

• Rows: 3 basket items priced in 3 years, plus 3 labor-market counts (the scaffold tables have 3, 4, 3, and 4 rows)
• Columns: item, quantity, and price in the base year, year 2, and year 3; then group and count of people
• Categories: rent, grocery trips, bus passes; adults 16 and over, employed, unemployed

Part 3 — Materials & Procedure

Tools and materials

• Desmos (free) or Google Sheets (free)

Ways of working

• read-and-compute-from-macro-data
• build-and-shift-the-ad-as-model
• separate-positive-from-normative-claims

Procedure

1. Open a new Google Sheet (or a Desmos graphing calculator if you prefer to type each expression on its own line). In cells A2 to A4 type the three items: rent, grocery trips, bus passes. In B2 to B4 type the monthly quantities 1, 4, and 2. In C2 to C4 type the base-year prices 1000, 100, and 50; in D2 to D4 the year-2 prices 1040, 105, and 50; in E2 to E4 the year-3 prices 1140, 115, and 58. Tool: Desmos (free) or Google Sheets (free). Check: A three-row table whose entries match the family basket table in Part 4 cell for cell.
2. In C6 type =SUMPRODUCT(B2:B4,C2:C4) to get the base-year cost of the basket. Copy the formula to D6 and E6 so each column's prices are multiplied by the same quantities. In Desmos, type the same sum as 1*1000+4*100+2*50 and the matching lines for years 2 and 3. Tool: Desmos (free) or Google Sheets (free). Check: Three basket costs that rise from left to right; the base-year cost equals the three item costs you can add by hand.
3. In C7 type =C6/C6*100, in D7 type =D6/C6*100, and in E7 type =E6/C6*100 to build the price index for each year, always dividing by the base-year cost. Tool: Desmos (free) or Google Sheets (free). Check: The base-year cell shows exactly 100, and the two later cells show levels above 100 with no percent sign.
4. In D8 type =(D7-C7)/C7*100 for the inflation rate into year 2, and in E8 type =(E7-D7)/D7*100 for the inflation rate into year 3. Then, in a spare cell, type =E7-D7 to see the gap in index points. Tool: Desmos (free) or Google Sheets (free). Check: Two percentages, where the year-3 formula divides by the year-2 index, and an index-point gap that differs from the year-3 rate.
5. A family member's hourly wage rises from 25.00 dollars in year 2 to 26.75 dollars in year 3. In a spare cell type =(26.75-25)/25*100 for the nominal raise, and in the next cell subtract the year-3 inflation rate from it to estimate the real wage change. Tool: Desmos (free) or Google Sheets (free). Check: A positive nominal raise and a real wage change with the opposite sign or a smaller size, said in words as about how much buying power changed.
6. Start a second block. In cells K2 to K4 type the county's counts: 125000 adults aged 16 and over, 89300 employed, and 5700 unemployed. In K5 type =K3+K4 for the labor force, in K6 type =K4/K5*100 for the unemployment rate, and in K7 type =K5/K2*100 for the participation rate. Tool: Desmos (free) or Google Sheets (free). Check: A labor force smaller than the adult population, an unemployment rate well under 10, and a participation rate between 50 and 100.
7. Now suppose 1,000 of the unemployed stop looking for work. In cells L3 to L5 rebuild the counts with the employed unchanged, the unemployed 1,000 lower, and the labor force 1,000 lower, then copy the two rate formulas into L6 and L7. Tool: Desmos (free) or Google Sheets (free). Check: A lower unemployment rate and a lower participation rate, with the employed count unchanged.

Fallback route

When to use it: Use this route if you cannot open Google Sheets or Desmos, or your device cannot run them.

Complete every table in Part 4 by hand with any calculator, writing each formula in words beside its result (for example, basket cost in year 2 ÷ basket cost in the base year × 100). Answer all six analysis questions, do the critique step, and submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

This is the family's fixed monthly basket; the quantities stay the same every year so that only prices move the total.

Student scaffold table 1

Item	Quantity each month	Base-year price (dollars)	Year-2 price (dollars)	Year-3 price (dollars)	Base-year cost of this item (price × quantity)
Rent	1	1000	1040	1140
Grocery trips	4	100	105	115
Bus passes	2	50	50	58

Fill in the basket cost, the price index, and the inflation rate for each year so the level and the rate sit side by side.

Student scaffold table 2

Year	Basket cost (dollars)	Price index (base year = 100)	Inflation rate from the year before (%)	Formula or steps used
Base year			not applicable
Year 2
Year 3
Index-point gap, year 2 to year 3			not a rate

These are the county's counts of people, in the same three groups the survey uses.

Student scaffold table 3

Group	Count of people	Notes
Adults aged 16 and over	125000	everyone the participation rate divides by
Employed	89300
Unemployed	5700

Fill in both rates before and after 1,000 people stop looking, so you can see what a falling rate does and does not tell you.

Student scaffold table 4

Measure	Before	After 1,000 stop looking	Formula or steps used
Labor force
Unemployment rate (%)
Participation rate (%)
Employed	89300

Part 5 — Analysis Questions

1. Report the three basket costs, the three index levels, and the two inflation rates, each with its formula. Then report the nominal raise and the estimated real wage change for the family member, and say in one sentence whether the paycheck kept up with the basket.
2. Compare the index-point gap from year 2 to year 3 with the year-3 inflation rate. Explain in two sentences why they differ and which one answers the question "how fast did prices rise this year?"
3. Report the county's labor force, unemployment rate, and participation rate before and after 1,000 people stop looking, with the formulas shown. State in one sentence why the unemployment rate divides by the labor force and the participation rate divides by all adults.
4. A local news site plans to run the headline "County jobless rate falls; job market improving." Using your before-and-after table, write 3–4 sentences that separate the positive claim the data support from the normative or interpretive claim the headline adds, and say which extra number a careful reader should check.
5. Choose one reflection and answer it in 3–5 sentences: (a) think of a basket of things you buy every month and explain how you would build your own price index for it, and why it might differ from the family's; or (b) think of a person you know who is out of work, described without names, and explain whether the survey would count that person as unemployed, outside the labor force, or discouraged, and why.
6. Name two limits of these measures as you used them: one about the fixed basket (for example, what happens when the family switches to cheaper goods or quality changes) and one about the unemployment rate (for example, who it leaves out). Say how each limit could make the number mislead a reader.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

For a practice example: an illustrative city's price index was 120 last year and 126 this year, and a bus driver there got a 3% raise. The city has 50,000 adults, 30,400 employed, and 1,600 unemployed. Please do five things. First, give the inflation rate this year. Second, say whether the bus driver's buying power went up or down, and by about how much. Third, give the unemployment rate. Fourth, a council member says, "Prices rose too fast, so the city should cap bus fares." Is that statement positive or normative? Fifth, explain which curve shifted to cause the price rise, and use a multiplier to say how much the price rise will add to the city's output.

Test the response for these likely failures:

• The chatbot says the driver is better off because the paycheck grew 3%, treating a nominal raise as a gain in buying power.
• The chatbot claims aggregate demand or supply shifted and names the direction, as if a measured rise in a price index proved which curve moved.
• The chatbot multiplies the price rise or the jobless count by a multiplier, such as 1 ÷ RR or 1 ÷ (1 − MPC), to predict output.
• The chatbot calls the council member's whole sentence positive because it mentions prices, or calls a plain measured fact normative.

In 3–5 sentences, say what the chatbot got right, quote at least two things it got wrong or flagged too late, and correct each one with the week's formulas, including the inflation rate of 5%, the unemployment rate of 5%, and the participation rate of 64% for the practice city.

Equivalent route (no AI required)

No AI account is required for this workshop. This route assesses the same objectives, Objective 3 (measure the price level and the labor market — compute and interpret the CPI, the inflation rate, a real wage change, the unemployment rate, and the labor-force participation rate — and classify frictional, structural, and cyclical unemployment) and Objective 2 (measure an economy's output with gross domestic product by the expenditure approach (C + I + G + NX), decide what counts and what does not, distinguish real from nominal GDP, and compute and interpret the GDP deflator), takes comparable effort of about the same 90 minutes, uses the same rubric, and earns the same credit. Instead of the chatbot, critique this flawed analysis of the practice city in Part 6, printed here in full: "The price index went from 120 to 126, so inflation was 6%. The bus driver's 3% raise means the driver is 3% better off. The unemployment rate is 1,600 ÷ 50,000 × 100 = 3.2%. The council member's sentence is positive, because it is about prices. Aggregate demand shifted right, which caused the price rise, and with a money multiplier of 10 the city's output will grow ten times the price rise." Mark every error you can find, quote at least two, and correct each one in 3–5 sentences with the week's formulas, flagging the curve and multiplier claims as topics that come later in the course. Submit the marked-up analysis and your corrections in place of the chatbot report and share link.

Part 7 — What to Submit

• The four completed scaffold tables, from a spreadsheet, a graphing calculator, or by hand
• Written answers to all six analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up correction of the printed flawed analysis

Deliverable:

A short Model Workshop report on the family budget and the county job report: four completed tables (the basket, its costs, index levels, and inflation rates; and the county's counts and rates before and after people stop looking), written answers to six analysis questions, and a critique of a chatbot's answers about a similar example, or, on the equivalent route, a marked-up correction of the printed flawed analysis. 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. Choose how you show it: written answers, a recorded explanation with a transcript, or a labelled diagram that traces the basket to the index and the counts to the rates with short notes; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Building the basket and the price index	All three basket costs come from price times quantity for every item, each index divides by the base-year cost and is written as a level, and the base year reads 100.	Most costs and levels are right, but one item is left out of a cost, an index divides by the wrong year, or a level is labelled as a percent.	No basket costs or index levels are submitted, or they are copied without any formula or steps.
Turning levels into rates and testing the raise	Both inflation rates divide the change by the starting level, the index-point gap is explained as different from the rate, and the real wage change is estimated as the raise minus inflation and said in words.	One rate divides by the wrong level, the index-point gap is called a rate, or the raise is computed but not compared with inflation.	No inflation rate or real wage change is attempted.
Counting the labor market and the discouraged-worker test	The labor force, unemployment rate, and participation rate are correct before and after, each with the right denominator, and the answer explains why the rate fell with no one hired.	Most counts and rates are right, but one rate uses the wrong denominator or the before-and-after change is computed without an explanation.	No labor-market counts or rates are attempted.
Interpreting in words and separating positive from normative	Every result is said in plain words, the headline answer labels the positive and the normative parts and names the participation rate as the extra check, and the limitation answer names one basket limit and one unemployment-rate limit.	Some results are interpreted, but the positive and normative parts are blurred or only one limitation is named.	Results are reported with no interpretation, and no limitation is named.
Critique and correction	The chatbot critique report or the marked-up flawed analysis quotes at least two errors and corrects each with this week's formulas or definitions, and flags the curve-shift and multiplier claims as later topics; both routes earn this band equally.	The chatbot critique report or the marked-up flawed analysis names an error but corrects it without the formula, or corrects only one; both routes earn this band equally.	No chatbot critique report or marked-up flawed analysis is submitted, or the output is pasted without any check; both routes are scored the same way.

Quality Gate

• Every basket cost, index level, and rate comes from a formula or hand calculation shown beside it, never from memory or a chatbot.
• Every index level is written without a percent sign, and every inflation rate divides by the starting level.
• The unemployment rate divides by the labor force and the participation rate divides by all adults aged 16 and over.
• Every computed result ends with one plain sentence about what it means for the family or the county.
• Positive claims and normative claims are labelled as such wherever the answers discuss the headline.
• No real-world inflation rate, unemployment rate, statistic, or study is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence.