Week 12 — Graph & Model Workshop · "MV = PQ & the Phillips Curve"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 8 — the Phillips curve & the quantity theory of money · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 12
Format: build a quantity-theory (MV = PQ) table in a spreadsheet or Desmos, then plot the two short-run Phillips-curve (SRPC) points and the vertical long-run Phillips curve (LRPC) in Desmos, 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 met two of macro's most consequential ideas: the short-run Phillips curve, a real (but temporary) trade-off between inflation and unemployment, and the quantity theory of money (MV = PQ), which explains why sustained inflation is, in the long run, fundamentally about money growth. Today you'll compute the quantity theory numerically and then plot the Phillips-curve picture — both the short-run downward-sloping curve AND the long-run vertical line — so you can see, side by side, why THE CLASSIC ERROR (treating the short-run trade-off as permanent) is a mistake. (Next week you'll open the economy up to trade — comparative advantage, and why a "trade deficit" isn't automatically a country "losing.")

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login). A spreadsheet works equally well for Part 3's table.

Part 2 — The Guiding Question

If a central bank grows the money supply faster than the economy grows, exactly how much of that shows up as higher prices rather than more real output — and does a lower unemployment rate bought with a bit more inflation actually last?

The scenario. The fictional economy of Meadowland currently has money supply M = 600, velocity of money V = 5, and real output Q = 1,500. Meadowland's central bank is considering growing the money supply by 10%. Separately, Meadowland's short-run Phillips curve currently runs through two well-documented points: (unemployment = 4%, inflation = 6%) and (unemployment = 6%, inflation = 2%) — and economists agree its natural rate of unemployment is 5%.

Part 3 — Set Up the Model (spreadsheet + Desmos)

Quantity theory (spreadsheet-friendly):
1. Build a small table with columns M, V, Q, M×V, P = (M×V)/Q — one row for Meadowland's current numbers, one row for after the 10% money-supply increase.
2. Fill in the current row first: M = 600, V = 5, Q = 1,500.
3. Compute the after row: new M = current M × 1.10 (V and Q unchanged).

Phillips curve (in Desmos):
4. Open Desmos. Plot the two SRPC points: (4, 6) and (6, 2) — treat the x-axis as the unemployment rate (%) and the y-axis as the inflation rate (%). Desmos will draw a line through them if you type both points and connect them, or you can simply plot the two points and sketch the line by eye.
5. On the same axes, plot a vertical line at x = 5 (type x = 5 into Desmos) — this is the LRPC, at Meadowland's natural rate of unemployment.

Part 4 — Solve (complete this scaffold)

Fill in the blanks from your table and Desmos graph. Show the steps.

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

In 2–3 sentences, explain what your answer to (f)/(g) demonstrates about the long-run relationship between money growth and inflation (this is long-run monetary neutrality — name it), and then, in a separate 2–3 sentences, explain what the SRPC and LRPC together tell you about whether Meadowland's central bank could permanently hold unemployment below 5% by tolerating a bit more inflation. (Hint: your answer to the second part should explicitly name THE CLASSIC ERROR and explain why it's a mistake — not just describe the two curves.)

Part 6 — Analysis Questions

1. Meadowland's central bank grows the money supply 10% and, for a while, sees unemployment dip below 5% while inflation ticks up — matching a move along the SRPC. Using this week's material, explain why that lower unemployment rate probably won't last, even though the SRPC clearly shows the two moving together in the short run.
2. Someone claims: "MV = PQ proves that growing the money supply always helps the economy, since M×V has to go up." Using your table from Part 4, explain what's wrong with this claim — specifically, which variable actually absorbs the change in the long run, and which one doesn't move.
3. Connect to policy: Meadowland's policymakers are debating how aggressively to respond if inflation expectations start rising. In 2–3 sentences, explain the trade-off involved — what does acting quickly (to keep expectations anchored) risk in the short run, and what does waiting risk instead? (You are not being asked which choice is "right" — just to explain the trade-off fairly, the same evenhanded habit as this week's discussion.)

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: "An economy has money supply M = 600, velocity V = 5, and real output Q = 1,500. What is the price level? If the money supply rises 10% (V and Q unchanged), what is the new price level, and what happens to real output in the long run? Also, if a short-run Phillips curve passes through (unemployment = 4%, inflation = 6%) and (unemployment = 6%, inflation = 2%), can a central bank use this curve to permanently keep unemployment below 5%?"
2. Audit every claim against your own work:
   - Did it get the price level right — P = 2, rising to P = 2.2 after the 10% money-supply increase (not some other number, and not a P that "conveniently" matches a percentage other than 10%)?
   - Did it correctly say real output is unchanged in the long run (long-run monetary neutrality), or did it mistakenly claim real output also rises 10% — a common chatbot mix-up between the short-run transmission-mechanism story (Weeks 10–11, where money DOES move real output) and this week's long-run neutrality story (where it doesn't)?
   - Did it correctly say NO — the central bank cannot permanently hold unemployment below 5% using this one SRPC, because expectations will adjust and the curve will shift (THE CLASSIC ERROR) — or did it wave through the idea of a permanent trade-off without that caveat?
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 blur the short-run/long-run line on money and output, or wave through the "permanent trade-off" claim — catching it is the point.

Part 8 — What to Submit

One document (or text entry) 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 of your Desmos Phillips-curve plot is welcome but optional. Due Sun, Nov 22, 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-12-numbers.txt). Anchors: M=600, V=5, Q=1,500; SRPC points (4,6) and (6,2); LRPC vertical at u*=5.

• (a) 600 × 5 = 3,000. ✓
• (b) P = 3,000 ÷ 1,500 = 2. ✓
• (c) 600 × 1.10 = 660. ✓
• (d) 660 × 5 = 3,300. ✓
• (e) P = 3,300 ÷ 1,500 = 2.2. ✓
• (f) (2.2 − 2) ÷ 2 = 0.2 ÷ 2 = 10%. ✓
• (g) Yes — the 10% rise in the price level exactly matches the 10% rise in the money supply. This confirms long-run monetary neutrality: with V and Q fixed, a money-supply change produces a proportional price-level change and no real-output change. ✓
• (h) Unemployment rises (4% → 6%); inflation falls (6% → 2%) — confirming the SRPC slopes down. ✓
• (i) The LRPC at u = 5 is a vertical straight line. In plain words: at any inflation rate, unemployment returns to 5% in the long run — the curve has no leftward or rightward movement as inflation changes. ✓
• Part 5: the (f)/(g) result demonstrates long-run monetary neutrality — a 10% money-supply increase produces a 10% price-level increase and no change in real output, when velocity and real output are held fixed. Read together, the SRPC and LRPC show that Meadowland's central bank cannot permanently hold unemployment below 5% by tolerating more inflation: the SRPC describes a real short-run trade-off, but if the bank keeps trying to exploit it, people come to expect the resulting inflation, the SRPC shifts up and to the right, and unemployment drifts back to the natural rate (5%) anyway — just with permanently higher inflation. Treating the short-run trade-off as a permanent menu is THE CLASSIC ERROR.
• Part 6: (1) the lower unemployment rate won't last because, once the resulting inflation becomes expected, it gets built into wages and prices, the SRPC shifts up/right, and unemployment rises back toward 5% — the LRPC's vertical shape is this outcome. (2) The claim is wrong because MV = PQ is an identity, not a policy prescription: M×V does rise, but in the long run (with V and Q roughly fixed), all of that rise shows up in P, not in real output (Q) — nothing "extra" gets produced; prices simply rise. (3) Acting quickly to anchor expectations risks a sharper, more disruptive short-run slowdown (higher unemployment sooner); waiting risks letting inflation expectations become entrenched, which can require an even larger and more painful correction later. Both are legitimate positions — full credit for any answer that states the trade-off fairly without declaring one option objectively "right" (evenhandedness).
• Part 7: full credit for a specific catch — most commonly the AI claiming real output also rises with the money supply in the long run (conflating this week's long-run neutrality story with the short-run transmission mechanism from Weeks 10–11), or failing to flag that a central bank cannot permanently exploit the SRPC (missing THE CLASSIC ERROR caveat).

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — P before/after (2, 2.2; +10%=+10%) Python-re-verified ✓ (see _build/logs/week-12-numbers.txt). Graph-logic check — SRPC slopes down through (4,6) and (6,2); LRPC vertical at u=5; expected-inflation shift is up/right; THE CLASSIC ERROR correctly stated as a mistake, never endorsed ✓. Quantitative gate: PASS. Graph-logic check: PASS.*