Week 7 Model Workshop: How Far Does a Stimulus Move the Economy?

Part 1 — The Big Picture

This week you learned that fiscal policy is the legislature's spending and taxes, that the marginal propensity to consume sets how far each round of re-spending travels, that the spending multiplier 1 ÷ (1 − MPC) scales new spending into output while the tax multiplier −MPC ÷ (1 − MPC) does a little less, and that a deficit is a yearly flow that adds to the debt, a stock. In this Model Workshop you measure an MPC yourself from five illustrative households, use it to size two stimulus choices, shift aggregate demand in Desmos and read where the price level and real output land, trace each choice through the budget, sort positive claims from normative ones, and then check a chatbot's account of the same economy.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: A government in this illustrative economy can spend 40 billion dollars more on a bridge or cut taxes by 40 billion dollars: how much does each choice raise output in the simple model, where do the price level and real output land after the bridge shifts aggregate demand, what does each choice do to the deficit and the debt, and which claims about the choice are positive rather than normative?

Workshop data: Five-household spending survey and bridge-or-tax-cut budget (illustrative)

Source: A workshop-only table constructed for this course, not real data: the extra income and extra spending of five illustrative households, plus an illustrative economy's linear AD–AS pair and starting budget, printed in full in the scaffold tables.

• Rows: 5 households, each with one extra-income figure and one extra-spending figure; the first scaffold table shows those 5 rows plus a totals row, 6 rows
• Columns: household, extra income (dollars), extra spending (dollars), and a blank share-spent cell
• AD–AS pair: aggregate demand P = 18 − Y⁄125 and short-run aggregate supply P = 2 + Y⁄125, with Y in billions of dollars and P an index
• Starting budget: revenue 600, spending 620, and a debt of 1,500 at the start of the year, in billions of dollars

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 Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. If you use Google Sheets, type the five households from the first scaffold table into columns A to C: the household letter in column A, extra income in column B, and extra spending in column C, starting in row 2. Tool: Desmos (free) or Google Sheets (free). Check: Five rows of data, with extra income in column B and extra spending in column C.
2. Compute the economy's marginal propensity to consume as total extra spending divided by total extra income. In Google Sheets, type =SUM(C2:C6)/SUM(B2:B6) in cell B8; in Desmos, type (360+480+450+560+250)/(400+600+500+700+300) on its own line. Fill in the share spent for each household too, and copy the totals into the first scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: One MPC for the whole group, a decimal between 0 and 1, plus five household shares.
3. Compute the spending multiplier and the tax multiplier from that MPC. In Google Sheets, type =1/(1-B8) in B9 and =-B8/(1-B8) in B10; in Desmos, type each formula with your MPC in place of B8. Then multiply each multiplier by the size of its policy, remembering that a tax cut is a negative change in taxes, and record both changes in output in the second scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: A spending multiplier larger than the tax multiplier in size, and a larger change in output for the bridge than for the tax cut.
4. In Desmos, type y=18-x/125 for aggregate demand and y=2+x/125 for short-run aggregate supply, letting x stand for real output Y and y for the price level P. Click the crossing and record it. Then type y=a-x/125 on a new line, accept the slider for a, set it to 18, and drag it to 20 to show the bridge shifting aggregate demand right. Record the new crossing in the third scaffold table. In Google Sheets, solve each crossing by setting the two lines equal instead. Tool: Desmos (free) or Google Sheets (free). Check: Two crossings, the second up and to the right of the first along the unchanged supply line.
5. Trace each choice through the budget in the fourth scaffold table: add the bridge to spending, or subtract the tax cut from revenue, then compute the year's deficit as spending minus revenue and the end-of-year debt as the starting debt plus the deficit. Tool: Desmos (free) or Google Sheets (free). Check: A deficit and an end-of-year debt for each choice, labelled flow and stock.
6. Sort the four claims in analysis question 4 into positive and normative, and for each positive claim note the number in your tables that tests it, or say what evidence would test it. Tool: Desmos (free) or Google Sheets (free). Check: Two claims labelled positive with a number or a test beside each, and two labelled normative.
7. Paste the Part 6 prompt into one approved chatbot, or use the equivalent route instead, and compare its answers with your tables on all four checks. Tool: Desmos (free) or Google Sheets (free). Check: A short critique that quotes the chatbot or the printed analysis and corrects at least two errors.

Fallback route

When to use it: Use this route if neither Desmos nor Google Sheets is available, or if you cannot get online.

Do every calculation by hand or with any calculator, writing each step on its own line, and sketch the two aggregate demand lines and the short-run aggregate supply line on graph paper, marking both crossings. Complete all four scaffold tables, every analysis question, and the critique step from your hand work; submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Your household data: fill in each share spent as extra spending divided by extra income, then the totals row, which gives the economy's MPC.

Student scaffold table 1

Household	Extra income (dollars)	Extra spending (dollars)	Share spent
Household A	400	360
Household B	600	480
Household C	500	450
Household D	700	560
Household E	300	250
All five households

Sizing the two choices: use the spending multiplier for the bridge and the tax multiplier for the tax cut.

Student scaffold table 2

Policy choice	Multiplier used	Multiplier value	Change in output (billions of dollars)
Bridge: 40 billion dollars of new spending
Tax cut of 40 billion dollars

Shifting aggregate demand: record each crossing as real output and the price level, before and after the bridge.

Student scaffold table 3

Situation	Aggregate demand line	Real output Y (billions of dollars)	Price level P
Before the bridge	P = 18 − Y⁄125
After the bridge	P = 20 − Y⁄125

The budget: start from revenue of 600, spending of 620, and a debt of 1,500, all in billions of dollars, and label the deficit a flow and the debt a stock.

Student scaffold table 4

Policy choice	Revenue	Spending	Deficit for the year (flow)	Debt at the end of the year (stock)
Bridge
Tax cut

Part 5 — Analysis Questions

1. Show the MPC calculation, both multipliers, and both changes in output, every step on its own line. Then say each figure in a plain sentence, including why the bridge adds more output than a tax cut of the same size.
2. Name the curve the bridge shifts and its direction, give the crossing before and after, and explain why the price level and real output move together. Then compute real output growth from your third table and explain why the change in nominal spending, the price level times real output, is not the same as the change in output.
3. Use your fourth table to compare the two choices' deficits and end-of-year debts. Explain which figure is a flow and which is a stock, and why choices with the same deficit can still raise output by different amounts.
4. Positive or normative? Sort these four claims about the illustrative economy, and for each positive claim name the number in your tables that tests it or the evidence that would: (1) In the simple model, the bridge raises output by more than the tax cut. (2) The government ought to build the bridge, because jobs now matter more than debt later. (3) Borrowing 60 billion dollars this year will push up interest rates enough to cancel the bridge's effect on output. (4) A balanced budget is the fair choice for future taxpayers.
5. Choose one and answer it in 3–4 sentences. (a) The simple multiplier holds the price level still. Explain why the crossing in your Desmos graph moved less than the multiplier's change in output, and what that suggests about using 6.25 as a real-world forecast. (b) Your MPC comes from five households. Explain why a real economy's MPC could differ, and what leaks, such as taxes and imports, would make the real multiplier smaller.

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:

I am studying an illustrative economy. Five households were each given extra income and reported how much of it they spent: 400 and 360, 600 and 480, 500 and 450, 700 and 560, and 300 and 250 dollars. Its aggregate demand is P = 18 − Y⁄125 and its short-run aggregate supply is P = 2 + Y⁄125, with Y in billions of dollars. The government is choosing between spending 40 billion dollars more on a bridge and cutting taxes by 40 billion dollars, and its budget starts with revenue of 600, spending of 620, and a debt of 1,500, all in billions. What is the marginal propensity to consume, and which multiplier should I use for each choice? By how much does each choice raise output in the simple multiplier model? If the bridge shifts aggregate demand to P = 20 − Y⁄125, what are the new price level and real output, and how much did output grow? What is the deficit and the end-of-year debt for each choice? Finally, should the government build the bridge?

Test the response for these likely failures:

• Chatbots often reach for the money multiplier, 1 ÷ RR, or divide 1 by the MPC itself, 1 ÷ 0.84 ≈ 1.19, instead of using the spending multiplier on a spending question.
• Chatbots sometimes say the higher price level shifts aggregate demand back to the left, or call the rise in the price level a shift of short-run aggregate supply.
• Chatbots often report the gain in nominal spending, from 10 × 1,000 = 10,000 to 11 × 1,125 = 12,375, as if it were the gain in output, which mixes the higher price level with more production.
• Chatbots often answer whether the government should build the bridge as if the multiplier arithmetic settled it, presenting a value judgment as a fact.

In 3–5 sentences, quote the chatbot's answer on each of the four checks, say what it got right, and correct at least two errors using your own tables and the course rule, labelling which of its statements were positive and which were normative.

Equivalent route (no AI required)

No AI account is required for this Model Workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "The households spent 2,100 of 2,500 extra dollars, so the multiplier is 1 ÷ 0.84, about 1.19, or, using the banking multiplier with a reserve ratio of 0.10, it is 10. Either way, the bridge and the tax cut have the same effect, because both put 40 billion dollars into the economy. After the bridge, the higher price level shifts aggregate demand back to the left. Spending in the economy rose from 10,000 to 12,375, so output grew 23.75 percent. Both choices add 60 to the deficit, so the debt is now 60. The numbers prove the government should build the bridge." Mark it up: quote each flawed sentence, name what is wrong (the wrong multiplier and a multiplier from banking used on a fiscal question, a tax cut treated as equal to spending, a movement along a curve called a shift, nominal spending read as real output, the deficit confused with the debt, and a normative judgment presented as a fact), cite the evidence from your tables or the course rule, and write a corrected sentence beneath it. This route assesses the same objectives (Objective 5 and Objective 6) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its marked-up analysis is the submission artifact that replaces the chatbot report and share link.

Part 7 — What to Submit

• All four completed scaffold tables
• A screenshot of your Desmos graph with aggregate demand before and after the shift, or a labelled hand sketch of the three lines and both crossings
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Model Workshop report on an illustrative stimulus choice: four completed tables (the household MPC, the two multipliers and changes in output, the aggregate demand shift, and the budget), a screenshot or sketch of aggregate demand before and after the shift, written answers to five analysis questions including the positive-or-normative sort, and a critique of a chatbot's account of the same economy, 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 a written, recorded, or visual form for your answers; 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
Computing the MPC and the multipliers from the data	The MPC, both multipliers, and both changes in output are computed from the household table with the right multiplier for each choice and every step shown.	Most figures are right, but one divides 1 by the MPC, uses one multiplier for both choices, or skips its steps.	No MPC or multiplier is computed, or the numbers are not drawn from the printed table.
Shifting aggregate demand in the AD–AS model	Aggregate demand is shifted right, both crossings are read correctly, the price level and real output are shown rising together along the unchanged supply line, and real output growth is kept apart from nominal spending.	The shift is drawn, but a crossing is misread, the direction is reversed, or real and nominal are mixed.	No aggregate demand shift is submitted.
The budget: deficit and debt	Both choices are traced through the budget, each deficit and end-of-year debt is computed, and the deficit is labelled a flow and the debt a stock.	The budget is traced, but the deficit and the debt are confused or one choice is missing.	No budget work appears.
Positive versus normative	All four claims are sorted correctly, and each positive claim is tied to a number in the tables or to the evidence that would test it.	Two or three claims are sorted correctly, or the positive claims are not tied to evidence.	The sort is missing or fewer than two claims are sorted correctly.
Critique of the chatbot or the printed analysis	On either route, the chatbot critique or the equivalent route's marked-up analysis quotes the text it checks, corrects at least two errors with evidence from the tables or the course rule, and labels its positive and normative statements; both routes earn the same credit.	On either route, the critique names an error but does not correct it with evidence, or corrects only one.	On either route, no critique is submitted, or pasted output appears without any checking.

Quality Gate

• Every MPC, multiplier, and change in output comes from your own calculation on the printed household table, never from memory or a chatbot.
• The spending multiplier is used for the bridge and the tax multiplier for the tax cut, and the money multiplier appears nowhere in the calculations.
• The aggregate demand shift is named with its direction, and the price level and real output are read from both crossings.
• Real output growth is kept apart from the change in nominal spending.
• The deficit is labelled a flow and the debt a stock for each choice.
• Each of the four claims is labelled positive or normative, with a number or a test beside each positive claim.
• No number, rule, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence or the course rule.