Week 11 — Graph & Model Workshop · "Trace the Transmission Mechanism"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 7 — money, banking, the Fed & monetary policy; the transmission mechanism · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 11
Format: complete a chain table, link by link, for expansionary monetary policy in a spreadsheet or Desmos note, then reverse every link for contractionary policy, interpret the result 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

Weeks 9 and 10 built two separate pieces — how banks create money, and how the money market sets the interest rate. This week you connect the LAST piece: how a new interest rate actually changes real output and the price level. That connecting path is the monetary-transmission mechanism — five links in a row, each one causing the next. Today you'll fill in every link for an expansionary policy move, then do the harder skill: run the exact same chain backward for a contractionary move, without skipping or half-flipping a step. (Next week, you'll use this same "trace it link by link" habit for the quantity theory of money.)

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login) — or a spreadsheet; either works for building the chain table below.

Part 2 — The Guiding Question

When the Fed changes the money supply, exactly how many separate links does that change have to travel through before it shows up as a change in real output and the price level — and what does each link do to the next?

The scenario. The money market starts where Week 10 left it: money supply MS = $600 billion, equilibrium interest rate r = 6%. This course's engineered rules: investment (I) changes $20 billion for every 1-percentage-point change in the interest rate (opposite direction — a rate drop raises I, a rate rise lowers I), and the spending multiplier is 5 (MPC = 0.8, so 1/(1−0.8) = 5).

Part 3 — Set Up the Model (chain table)

1. Open a spreadsheet (or a Desmos note) and build a table with these six columns: Fed action | MS | interest rate (r) | ΔI | ΔY (= ΔI × multiplier) | AD direction & P/Y outcome.
2. Row 1 = the expansionary case: the Fed buys bonds, MS rises from $600B to $700B.
3. Row 2 = the contractionary case: the Fed sells bonds, MS falls from $600B to $500B.
4. Fill in every cell using the rules above — show every intermediate number, not just the final answer.

Part 4 — Solve (complete this scaffold)

Fill in the blanks. Show the steps for every column — this workshop is graded on the chain, not just the final ΔY.

Row 1 — Expansionary (the Fed BUYS bonds)

Row 2 — Contractionary (the Fed SELLS bonds) — reverse EVERY link

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

In 2–3 sentences, explain why every single link in the chain has to reverse together when you switch from expansionary to contractionary policy — not just the final P/Y outcome. (Hint: what would go wrong if you only flipped the LAST step and left the interest-rate direction from Row 1 unchanged?)

Part 6 — Analysis Questions

1. Which multiplier did you use in column (e)/(l) — the money multiplier (1/RR, from Week 9) or the spending multiplier (1/(1−MPC), from Week 7)? In one sentence, explain why the OTHER multiplier does not belong in this chain.
2. Suppose banks respond to the Fed's bond purchase by holding the new reserves as excess reserves instead of lending them out. In 2–3 sentences, explain which specific link in the chain would weaken, and why the final ΔY would likely come in smaller than $100 billion as a result.
3. Connect to policy: economists disagree about how reliably and how quickly this chain operates in the real world — some favor active Fed "fine-tuning," others are skeptical because of lags and prefer simpler rules. In 2–3 sentences, explain both sides of that disagreement fairly. (You are not being asked which side is right — just to present the strongest version of each case.)

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: "The Fed sells bonds, and the interest rate rises from 6% to 7%. If investment changes $20 billion for every 1-point change in the interest rate, and the spending multiplier is 5, what happens to real GDP, aggregate demand, the price level, and real output? Walk through every link of the chain."
2. Audit every claim against your own work:
   - Did it get investment falling by $20 billion (not rising)? Chatbots sometimes carry over the "rises" direction from a prior expansionary example instead of correctly reversing it for a bond sale.
   - Did it compute ΔY = −$100 billion using the spending multiplier (5) — not the money multiplier (1/RR from Week 9), which does not belong in this chain at all?
   - Did it correctly say AD shifts LEFT, and that BOTH the price level and real output FALL together (not one up and one down)?
   - Did it walk through every link explicitly (MS → r → I → AD → P/Y), or did it skip straight from "the Fed sells bonds" to "output falls" without showing the interest-rate and investment steps in between?
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 grab the wrong multiplier, skip a link, or only half-reverse the chain — catching it is the point.

Part 8 — What to Submit

One document (or text entry) with: your Part 4 chain table (both rows, all 14 cells, with the arithmetic shown), your Part 5 interpretation, your Part 6 answers, and your Part 7 AI-critique paragraph. A screenshot of your spreadsheet or Desmos note is welcome but optional. Due Sun, Nov 15, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see the Week-11 verified-numbers check).

Row 1 — Expansionary (the Fed BUYS bonds):
- (a) MS: $600B → $700B. ✓
- (b) Interest rate: 6% → 5%. ✓
- (c) The rate FELL by 1 percentage point. ✓
- (d) ΔI = 1 point × $20B/point = +$20 billion (I rises, because r fell). ✓
- (e) ΔY = $20B × 5 = +$100 billion. ✓
- (f) AD shifts RIGHT. ✓
- (g) Walking up the fixed SRAS curve: the price level RISES (P↑) and real output RISES (Y↑) — together. ✓

Row 2 — Contractionary (the Fed SELLS bonds) — every link reversed:
- (h) MS: $600B → $500B. ✓
- (i) Interest rate: 6% → 7%. ✓
- (j) The rate ROSE by 1 percentage point. ✓
- (k) ΔI = 1 point × $20B/point = −$20 billion (I falls, because r rose). ✓
- (l) ΔY = −$20B × 5 = −$100 billion. ✓
- (m) AD shifts LEFT. ✓
- (n) Walking down the fixed SRAS curve: the price level FALLS (P↓) and real output FALLS (Y↓) — together. ✓

• Part 5: every link has to reverse together because each link causes the next — if the Fed sells bonds but you leave the interest rate falling (instead of correctly rising), every downstream number (ΔI, ΔY, AD direction, P/Y) inherits that one wrong link and comes out backward. The chain is only as correct as its weakest link; flipping just the ending while leaving an earlier arrow unchanged produces an internally inconsistent, wrong answer even though the final digits might accidentally look plausible.
• Part 6: (1) the spending multiplier, 1/(1−MPC) = 5, belongs here — the money multiplier (1/RR, Week 9) answers a completely different question (how banks expand the money supply from a new deposit), not how a change in investment spending ripples into a change in GDP. (2) If banks hold new reserves as excess reserves instead of lending them, Link 3 (the investment response) weakens — the money never fully reaches borrowers as new loans, so ΔI (and therefore ΔY) would likely come in smaller than the clean $20B-per-point / $100B totals predict; the chain's later links (AD shift, P/Y direction) still point the same way, just with a smaller magnitude. (3) Fine-tuning case (Keynesian tradition): the Fed has real tools and enough information to lean against recessions and overheating as they emerge, and an imperfect, timely nudge is better than doing nothing while a downturn deepens. Skeptical/rules case (monetarist/classical tradition): because inside and outside lags are "long and variable" (Friedman's critique, named factually), and information is imperfect, discretionary fine-tuning risks acting on yesterday's problem after today's has already changed — a mistimed nudge can add instability rather than remove it, favoring simple, predictable rules instead. Full credit for presenting both fairly, without declaring a winner.
• Part 7: full credit for a specific catch — most commonly the AI carrying the "investment rises" direction over from an expansionary example instead of correctly reversing it, reaching for the money multiplier (1/RR) instead of the spending multiplier, or skipping the interest-rate/investment links and jumping straight from "the Fed sells bonds" to a P/Y conclusion.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — MS $600B→$700B/$500B, r 6%→5%/7%, ΔI ±$20B, multiplier 5, ΔY ±$100B, all Python-re-verified ✓. Graph-logic check — expansionary: AD right, P↑/Y↑ walking up fixed SRAS; contractionary: AD left, P↓/Y↓ walking down fixed SRAS; every one of the five links reversed together (not just the P/Y ending) ✓. Quantitative gate: PASS. Graph-logic check: PASS.