Week 10 — Graph & Model Workshop · "The Money Market"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 7 — money, banking & monetary policy; the money market · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 10
Format: build and read the money market in Desmos (free, no account), shift money supply both directions, complete a short scaffold, 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

Last week you learned how a single deposit multiplies through the banking system. This week you meet the graph where that whole money supply actually meets demand — the money market. It looks like a cousin of the AD–AS model from Week 5: one curve slopes, one curve is a straight vertical line the Fed can slide left or right. Once you can shift that vertical line confidently in both directions and read the resulting interest rate, next week's full transmission mechanism (money market → investment → Aggregate Demand) will click almost immediately.

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login).

Part 2 — The Guiding Question

When the Federal Reserve buys or sells bonds, exactly how far does the interest rate move — and which direction — and why does only ONE of the two curves in this market ever shift?

The scenario. In a simplified macro economy, money demand is given by r = 12 − M/100, where M is the quantity of money (in billions of dollars) and r is the interest rate (in percent). The money supply is set directly by the Federal Reserve and is a vertical line at whatever quantity the Fed has chosen. Right now, the Fed has set the money supply at M = 600.

Part 3 — Set Up the Model (in Desmos)

1. Open Desmos. Type the money-demand line: r = 12 - M/100 (Desmos will plot it — it slopes down as M rises).
2. Type the money-supply line as a vertical line at the base quantity: M = 600.
3. Find where the two lines cross — that intersection is the equilibrium interest rate.
4. Now change the vertical line to M = 700 (the Fed buys bonds) and find the new intersection. Then change it to M = 500 (the Fed sells bonds) and find that intersection too.

Part 4 — Solve (complete this scaffold)

Fill in the blanks from your Desmos graph and a little arithmetic. Show the steps.

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

In 2–3 sentences, explain why money supply is drawn as a vertical line in this model (what does that shape represent about how the Fed sets policy?), and explain why an interest-rate change on its own never shifts money demand — it only moves you along the curve you already have. (Hint: think about what's different about how the Fed sets the quantity of money compared to how an ordinary seller responds to price.)

Part 6 — Analysis Questions

1. Besides buying or selling bonds, name one other Fed tool (the discount rate, reserve requirements, or interest on reserves) and state the direction that tool would need to move for the interest rate to fall from the 6% base case.
2. A classmate says, "The Fed lowering interest on reserves (IOR) should make the interest rate rise, since IOR is a kind of interest rate itself, and lowering any rate should push other rates up to match." Use the model to explain what's actually wrong with that reasoning.
3. Connect to policy: if the economy were sliding into a recession, would the Fed be more likely to buy bonds or sell bonds, based purely on the direction that lowers interest rates? Explain the mechanical logic in 2–3 sentences. (You are not being asked whether the Fed should intervene at all in any specific real situation — just to trace which direction lowers r, mechanically.)

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: "Money demand is r = 12 − M/100, where M is in billions of dollars and r is a percent. Money supply is vertical at M = 600. If the Federal Reserve buys bonds and money supply rises to M = 700, what happens to the equilibrium interest rate? Does buying bonds shift money demand or money supply?"
2. Audit every claim against your own work:
   - Did it correctly say the rate falls from 6% to 5%? Chatbots sometimes reason that "buying" sounds like spending or tightening and get the direction backwards.
   - Did it correctly say it is money SUPPLY that shifts (the vertical line moves right), and that money demand does NOT shift? Chatbots sometimes claim the interest-rate change itself shifts money demand — that's backwards; it's a movement along Md, not a shift of it.
   - Did it keep straight which curve is vertical (Ms) and which one slopes down (Md)?
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 reverse a buy/sell direction or claim the wrong curve shifted — 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 graph is welcome but optional. Due Sun, Nov 8, 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-10-numbers.txt). Money demand: r = 12 - M/100.

• (a) M = 600 → r = 12 − 600/100 = 12 − 6 = 6%. ✓
• (b) Buy bonds → Ms line moves RIGHT (M = 600 → M = 700, since buying bonds injects reserves and MS rises) → r = 12 − 700/100 = 12 − 7 = 5%. ✓
• (c) 5% vs. 6% → the interest rate FELL. ✓
• (d) Sell bonds → Ms line moves LEFT (M = 600 → M = 500, since selling bonds drains reserves and MS falls) → r = 12 − 500/100 = 12 − 5 = 7%. ✓
• (e) 7% vs. 6% → the interest rate ROSE. ✓
• (f) Money supply (the vertical line) moved in both cases; money demand never shifted — the interest-rate changes we found are read as points ALONG the fixed Md curve. ✓
• Part 5: Money supply is vertical because the Fed sets the quantity of money directly through its policy tools, rather than that quantity responding to a price the way an ordinary supplier's output responds to the price it can charge — the vertical line IS the graph's way of showing "the Fed chose this amount." An interest-rate change never shifts money demand on its own because Md's position only changes when something other than the rate itself changes (such as income); within this week's story, the ONLY thing that moves is the Fed's chosen quantity (Ms), so every interest-rate change here is a movement along the fixed Md curve, never a shift of it.
• Part 6: (1) Any of: lower the discount rate (cheaper to borrow reserves → MS↑ → r↓), lower reserve requirements (banks lend more of each deposit → MS↑ → r↓), or lower interest on reserves (less reason to hold reserves at the Fed → MS↑ → r↓) — full credit for naming one tool with the correct direction. (2) The classmate's reasoning is wrong because IOR is a rate the Fed pays banks, not a market rate that "leads" other rates up or down by imitation; lowering IOR makes holding reserves at the Fed less attractive, so banks lend more, MS rises, and the equilibrium interest rate (from the money-market graph) falls — the opposite of the classmate's claim; the error is treating IOR like a signal other rates must "follow" rather than tracing its actual effect on bank lending and MS. (3) Buy bonds — buying raises MS, which (per the graph) lowers r, the mechanically expansionary direction; full credit for the mechanical trace (no verdict required on whether the Fed should act in any real situation — evenhandedness).

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — base r=6% (12−6), buy-bonds r=5% (12−7), sell-bonds r=7% (12−5), all Python-re-verified ✓ (see _build/logs/week-10-numbers.txt). Graph-logic check — buy bonds shifts Ms RIGHT (r↓), sell bonds shifts Ms LEFT (r↑), an interest-rate change moves ALONG Md and never shifts it, all correct ✓. Quantitative gate: PASS. Graph-logic check: PASS.