Week 14 — Graph & Model Workshop · "Exchange Rates & Net Exports"

Course: Principles of Macroeconomics (ECON 2) · Silver Oak University (fictional sample) · Prof. Ashford
Objective 8 — the inflation–unemployment tradeoff & the quantity theory; open-economy tools · SLO A
Worth 50 points · Model Workshops group = 15% of the grade · Workshop 14
Format: convert two goods, both directions of trade, at both exchange rates in a spreadsheet or by hand, complete a short scaffold, interpret the NX 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 why countries trade at all — comparative advantage. This week you learn the price that makes trade actually happen: the exchange rate. Today you'll take the SAME currency move — the dollar going from $1 = ¥100 to $1 = ¥120 — and run it through two goods, in both directions of trade (a U.S. export and a Japanese import), at both exchange rates, so you can watch the two prices move in opposite directions from one single event. Then you'll combine both effects into one net-exports (NX) conclusion — the same combine-two-effects-into-one-verdict habit you'll use for the rest of your economic life whenever a currency moves.

The tool: 🔗 Desmos Graphing Calculator — https://www.desmos.com/calculator (free, instant, no login) — or any spreadsheet. Either works for the arithmetic below; Desmos is handy if you want to enter the multiplication/division as expressions and let it compute for you.

Part 2 — The Guiding Question

When a currency's exchange rate moves, exactly how much does a foreign buyer's price for a U.S. export change, exactly how much does a U.S. buyer's price for a foreign import change, and what does combining both changes tell you about net exports?

The scenario. Last year, $1 = ¥100. This year, $1 = ¥120. Two goods cross the border in opposite directions:

• Export: a $25,000 American-made car, sold to a buyer in Japan.
• Import: a ¥1,200,000 Japanese-made machine, sold to a buyer in the U.S.

Part 3 — Set Up the Model (in Desmos or a spreadsheet)

1. Write down the two exchange rates as two rows: Rate 1: $1 = ¥100 and Rate 2: $1 = ¥120.
2. For the export (car), the conversion is: price in yen = price in dollars × (yen per dollar). Enter 25000 * 100 and 25000 * 120 (or the spreadsheet equivalent) to get both yen prices.
3. For the import (machine), the conversion runs the other way: price in dollars = price in yen ÷ (yen per dollar). Enter 1200000 / 100 and 1200000 / 120 to get both dollar prices.
4. Notice which operation you used for each direction — multiply to convert a dollar price into yen (export), divide to convert a yen price into dollars (import). Mixing these up is the single most common error on this workshop.

Part 4 — Solve (complete this scaffold)

Fill in the blanks. Show the arithmetic, not just the final number.

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

In 2–3 sentences, explain what happened to the car's price and the machine's price in plain English (not just the numbers), and state clearly why one price went up while the other went down from the exact same currency move. (Hint: think about which currency each price is being converted INTO, and whether that currency now buys more or less of the other.)

Part 6 — Analysis Questions

1. Suppose instead the exchange rate had moved from $1=¥100 to $1=¥80 (a depreciation, not the appreciation you just solved). Without recomputing every step, predict in one sentence: would the car get cheaper or pricier abroad this time, and would the machine get cheaper or pricier at home? (You do not need to show the arithmetic — just state the reversed direction and why.)
2. A classmate says, "Since the machine got cheaper for U.S. buyers, that's just good news — nothing bad happened here." Use your Part 4 results to explain what this classmate is missing about the car's side of the story. (You are not being asked whether the OVERALL move is good or bad — just to point out the piece the classmate skipped.)
3. Connect to policy: a country's manufacturing-export industry and a country's import-heavy retail sector would likely react very differently to news that their currency just appreciated. In 2–3 sentences, explain why — without declaring which industry's reaction should matter more to policymakers.

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 exchange rate moves from $1 = ¥100 to $1 = ¥120. Did the dollar appreciate or depreciate? What happens to the price, in yen, of a $25,000 American car sold in Japan? What happens to the price, in dollars, of a ¥1,200,000 Japanese machine sold in the U.S.? What happens to net exports overall?"
2. Audit every claim against your own work:
   - Did it correctly say the dollar appreciated (¥120 > ¥100 — more yen per dollar), or did it flip the label and call this a "weaker" dollar because 120 is a bigger number?
   - Did it get the car's yen price rising (¥2,500,000 → ¥3,000,000), or did it accidentally divide instead of multiply and report a falling price?
   - Did it get the machine's dollar price falling ($12,000 → $10,000), or did it accidentally multiply instead of divide and report a rising price?
   - Did it correctly conclude NX falls (exports down, imports up), or did it jump straight to a policy verdict ("so this is bad for America") without finishing the economics?
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 flip an appreciation/depreciation label, use the wrong conversion operation for one direction, or leap to a policy verdict without doing the arithmetic — 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 or spreadsheet work is welcome but optional. Due Sun, Dec 6, 11:59 p.m. (50 points).

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

Every number pre-computed and independently verified (see the Week-14 verified-numbers check).

• (a) $1=¥100 → $1=¥120: ¥120 is MORE yen than ¥100, so one dollar buys more than before → the dollar APPRECIATED. ✓
• (b) $25,000 × 100 = ¥2,500,000. ✓
• (c) $25,000 × 120 = ¥3,000,000. ✓
• (d) ¥3,000,000 > ¥2,500,000 → the car got PRICIER for the Japanese buyer. ✓
• (e) ¥1,200,000 ÷ 100 = $12,000. ✓
• (f) ¥1,200,000 ÷ 120 = $10,000. ✓
• (g) $10,000 < $12,000 → the machine got CHEAPER for the U.S. buyer. ✓
• (h) Car pricier abroad → fewer sales → U.S. exports FALL. Machine cheaper at home → more purchases → U.S. imports RISE. Exports down and imports up together mean NET EXPORTS (NX) FALL. ✓
• Part 5: the car's price ROSE once converted into yen because the dollar (what the car is priced in) now buys MORE yen — the same dollar amount converts to a bigger yen number. The machine's price FELL once converted into dollars because that SAME strengthened dollar can now buy the SAME yen amount using FEWER dollars. One currency move, two goods priced in two different currencies, two opposite-direction results — that is exactly why "the dollar got stronger" cannot be summarized as simply "prices went up" or "prices went down."
• Part 6: (1) A depreciation ($1=¥100→$1=¥80) reverses both directions: the car would get CHEAPER abroad (fewer yen buy the same dollar amount... more precisely, the dollar buys FEWER yen, so the SAME $25,000 converts to fewer yen: 25,000×80=¥2,000,000 < ¥2,500,000) and the machine would get PRICIER at home (1,200,000÷80=$15,000 > $12,000) — every arrow flips. (2) The classmate is only looking at the IMPORT side (the machine, which got cheaper — good for the U.S. buyer) and skipping the EXPORT side (the car, which got pricier abroad — bad for the Japanese buyer, and bad for the U.S. company trying to sell it, since sales likely fall). A complete answer needs BOTH sides. (3) A manufacturing-export industry sells its output abroad, so a stronger dollar making its goods pricier abroad tends to hurt its sales and the jobs tied to it; an import-heavy retail sector buys goods from abroad, so a stronger dollar making those goods cheaper tends to help its margins and its customers' purchasing power. Full credit for any answer that explains BOTH reactions fairly without ranking one industry's interest above the other (evenhandedness).
• Part 7: full credit for a specific catch — most commonly the AI flipping the appreciation/depreciation label (calling ¥120-per-dollar a weaker dollar), using the wrong conversion operation for one of the two goods (multiplying when it should divide, or vice versa), or jumping to an unearned policy verdict ("so this is bad for America") before finishing the NX arithmetic.

Grading rubric — 50 points

Quality gate (self-checked): quantitative gate — car (¥2,500,000; ¥3,000,000), machine ($12,000; $10,000), and the depreciation-reversal figures (¥2,000,000; $15,000) all Python-re-verified ✓. Graph-logic check — appreciation = pricier exports/cheaper imports/NX↓ (never flipped), depreciation reverses every arrow, all correct ✓. Quantitative gate: PASS. Graph-logic check: PASS.