Week 12 · Model Workshop

Week 12 Model Workshop: Expectations, Money, and the Island's Prices

Principles of Macroeconomics Free sample edition

Part 1 — The Big Picture

This week you learned that lower unemployment can come with higher inflation along one short-run Phillips curve, that the curve shifts up when people come to expect more inflation, and that the long-run curve stands vertical at the natural rate. You also met the quantity equation, M × V = P × Q, and saw that with velocity and real output fixed, more money means proportionally higher prices. In this Model Workshop you read four years of an illustrative island's record, draw its two short-run curves and its long-run curve in Desmos, decide which moves are slides along a curve and which are shifts, build the island's money supply and price level, separate real growth from rising prices, sort positive claims from normative ones, and then check a chatbot's account of the same island.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: On this illustrative island, which year-to-year moves slide along one short-run Phillips curve and which shift it, why does unemployment end back at 5 percent with inflation higher than it started, and when the monetary base rises from 40 to 48 dollars, what happens to the money supply, the price level, and real output?

Workshop data: Four-year island record and money table (illustrative)

Source: A workshop-only record constructed for this course, not real data: an illustrative island economy's unemployment and inflation over four years, its natural rate, and its monetary base, reserve ratio, velocity, and real output before and after a rise in the base, all printed in full in the scaffold tables.

Rows: 4 years of unemployment and inflation in the first scaffold table, 3 lines in the second table, 2 years in the money table, and 4 quantities in the comparison table
Columns: year, unemployment rate u in percent, inflation rate π in percent, and a blank column for naming each change as a movement along the curve or a shift
Natural rate: 5 percent unemployment
Money table: monetary base 40 dollars in Year A and 48 dollars in Year B, required reserve ratio 0.10, velocity 5 in both years, real output 800 units in both years
Growth record: over the next decade, money grows 9 percent a year and real output grows 2 percent a year

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

Open Desmos at desmos.com/calculator or a blank Google Sheets spreadsheet. Enter the island's four years from the first scaffold table: in Desmos, click the plus sign, add a table, and type the unemployment rates in the x column and the inflation rates in the y column; in Google Sheets, put them in columns A and B starting in row 2. Compute the slope from Year 1 to Year 2 with (6-4)/(4-5) in Desmos or =(B3-B2)/(A3-A2) in Google Sheets. Tool: Desmos (free) or Google Sheets (free). Check: Four plotted points, and a negative slope between Year 1 and Year 2.
In Desmos, type y=14-2x and y=16-2x for the two short-run curves and x=5 for the long-run curve; in Google Sheets, add a column C with =14-2*A2 and a column D with =16-2*A2, filled down. Note which years sit on which line, and record it in the second scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: Two parallel downward-sloping lines, the second higher than the first, and a vertical line through the years when unemployment was 5 percent.
Fill the last column of the first scaffold table: for each change from one year to the next, write whether the island moved along one short-run curve or the curve itself shifted, using the lines from step 2. Tool: Desmos (free) or Google Sheets (free). Check: One slide along the lower curve, one shift up, and one slide along the higher curve back to the vertical line.
Build the money table: in Google Sheets type =40/0.10 and =48/0.10 for the money supply, then =400*5/800 and =480*5/800 for the price level; in Desmos type the same expressions without the equals sign. Record the money supply, M × V, and the price level for both years in the third scaffold table. Tool: Desmos (free) or Google Sheets (free). Check: A money supply ten times the base in each year, and a price level that rises in the same proportion as the money supply.
Fill the comparison table with the percentage change in the money supply, the price level, real output, and nominal output, using (new-old)/old*100 in Desmos or =(C3-C2)/C2*100 in Google Sheets. Then estimate inflation from the growth record with 9-2. Tool: Desmos (free) or Google Sheets (free). Check: Equal percentage changes for money and prices, no change in real output, and an estimate of inflation from money growth minus output growth.
Answer the five analysis questions, then paste the prompt from the critique step into one approved chatbot, or complete the equivalent route below, and write your critique, keeping your Desmos graph or spreadsheet open to check each claim. Tool: Desmos (free) or Google Sheets (free). Check: Written answers and a critique that quotes the text it checks 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 plot the four years, the two short-run lines, and the vertical line on graph paper, labelling each point by its year. Complete all five 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

The island's record: name each change from the year before as a movement along one short-run curve or a shift of the curve.

Student scaffold table 1
Year	Unemployment u (percent)	Inflation π (percent)	Change from the year before: along the curve or a shift?
Year 1	5	4	Starting year
Year 2	4	6
Year 3	4	8
Year 4	5	6

The three lines: record which years each line passes through.

Student scaffold table 2
Line	Equation	Years on this line
Lower short-run curve	y = 14 − 2x
Higher short-run curve	y = 16 − 2x
Long-run curve	x = 5

The money table: build the money supply from the base, then the price level from the quantity equation.

Student scaffold table 3
Year	Monetary base (dollars)	Money supply M (dollars)	M × V	Price level P
Year A	40
Year B	48

The comparison: compute each percentage change from Year A to Year B to see what more money changed and what it left alone.

Student scaffold table 4
Quantity	Year A	Year B
Money supply M
Price level P
Real output Q	800	800
Nominal output P × Q

The growth record: estimate inflation from money growth and output growth, and note the condition the estimate needs.

Student scaffold table 5
Money growth (percent a year)	Output growth (percent a year)	Approximate inflation (percent a year)	Condition
9	2

Part 5 — Analysis Questions

Show the slope from Year 1 to Year 2, the money supply and price level in both money-table years, and every percentage change in the comparison table, each step on its own line. Then say each figure in a plain sentence, including why the money multiplier, and not the spending multiplier, turns the base into the money supply.
Explain why the move from Year 2 to Year 3 is a shift of the short-run Phillips curve and not a movement along it, what change in expected inflation shifted it, and why Year 4 lands on the vertical long-run curve. Then name the curve that the same rise in expected inflation shifts on the AD–AS diagram, and its direction.
Use your comparison table to explain long-run neutrality of money: which quantities changed by 20 percent, which did not change, and why a 20 percent rise in nominal output is not 20 percent growth. Then use the growth record to estimate inflation and state the condition the estimate needs.
Positive or normative? Sort these four claims about the island, and for each positive claim name the number in your tables that tests it or the evidence that would: (1) Holding unemployment at 4 percent raised inflation from 6 to 8 percent once expectations caught up. (2) The central bank ought to have kept unemployment at 4 percent, because jobs matter more than prices. (3) With velocity at 5, raising the base from 40 to 48 dollars raised the price level 20 percent. (4) The island should accept a recession to bring inflation back to 4 percent.
Choose one and answer it in 3–4 sentences. (a) Velocity stays at 5 in the money table. Explain how your price level for Year B and your neutrality conclusion would change if velocity fell instead, and why unpredictable velocity is a hazard for a central bank. (b) The island's natural rate is given as 5 percent. Explain how a central bank that believed the natural rate was 4 percent would read Years 2 and 3 differently, and why the real natural rate is hard to pin down.

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 island economy. Its natural rate of unemployment is 5 percent. Over four years, unemployment and inflation were: Year 1, 5 percent and 4 percent; Year 2, 4 percent and 6 percent; Year 3, 4 percent and 8 percent; Year 4, 5 percent and 6 percent. Separately, its monetary base rose from 40 to 48 dollars, the required reserve ratio is 0.10, the marginal propensity to consume is 0.8, velocity stayed at 5, and real output stayed at 800 units. What is the slope of the short-run Phillips curve between Year 1 and Year 2? Is the move from Year 2 to Year 3 a movement along the short-run curve or a shift of it? What were the money supply and the price level before and after the base rose, and by what percent did the economy grow? Finally, should the island's central bank have kept unemployment at 4 percent?

Test the response for these likely failures:

Chatbots often call the move from Year 2 to Year 3 a movement along the short-run Phillips curve, because unemployment stayed at 4 percent while inflation rose, instead of seeing that the whole curve moved.
Chatbots often grab the spending multiplier because the prompt mentions a marginal propensity to consume, computing 1 ÷ (1 − 0.8) = 5 and a money supply of 5 × 48 = 240 dollars.
Chatbots often report that the economy grew 20 percent because nominal output, the price level times real output, rose from 2.5 × 800 = 2,000 to 3 × 800 = 2,400.
Chatbots often answer whether the central bank should have kept unemployment at 4 percent as if the data settled it, presenting a judgment about jobs and inflation as a model result.

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: "From Year 1 to Year 2 the slope is (6 − 4) ÷ (4 − 5) = −2. From Year 2 to Year 3 the island moved along the same curve, since unemployment stayed at 4 percent. With a marginal propensity to consume of 0.8 the multiplier is 5, so the money supply rose from 200 to 240 dollars. Nominal output rose from 2,000 to 2,400, so the economy grew 20 percent. The data prove the central bank should have kept unemployment at 4 percent." Mark it up: quote each flawed sentence, name what is wrong (a shift of the short-run curve called a movement along it, the spending multiplier used where the money multiplier belongs, nominal output read as real growth, 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 3 and Objective 8) 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 five completed scaffold tables
A screenshot of your Desmos graph with the four years, both short-run lines, and the vertical line, or a labelled hand sketch of them
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 island: five completed tables (the four-year record, the three lines, the money table, the comparison, and the growth record), a screenshot or sketch of the four years with both short-run lines and the vertical line, written answers to five analysis questions including the positive-or-normative sort, and a critique of a chatbot's account of the same island, 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
Reading and computing from the island data	The slope, both money supplies, both price levels, and every percentage change are computed from the printed tables with the money multiplier on the base and every step shown.	Most figures are right, but one uses the spending multiplier on the base, divides the quantity equation the wrong way, or skips its steps.	No figures are computed, or the numbers are not drawn from the printed tables.
Building and shifting the Phillips curves	Both short-run lines and the vertical line are drawn, each year is placed on the right line, the Year 2 to Year 3 change is named as a shift caused by higher expected inflation, and the matching shift of short-run aggregate supply is named with its direction.	The lines are drawn, but a year is misplaced, the shift is called a movement along the curve, or the AD–AS link is missing.	No Phillips-curve graph or reading is submitted.
Money, prices, and long-run neutrality	The comparison shows money and prices rising by the same percentage with real output unchanged, nominal output is read as higher prices rather than growth, and the growth-form estimate is labelled with its stable-velocity condition.	The comparison is filled, but nominal output is read as growth or the estimate's condition is missing.	No neutrality 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 slope, money supply, price level, and percentage change comes from your own calculation on the printed tables, never from memory or a chatbot.
Each year-to-year change is named as a movement along one short-run curve or a shift of the curve, and the shift is tied to a change in expected inflation.
The money multiplier, not the spending multiplier, turns the base into the money supply.
Real output is kept apart from nominal output, and the 20 percent rise in nominal output is read as higher prices.
The growth-form estimate is labelled an approximation that needs stable velocity.
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.

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