Week 6 · Model Workshop

Week 6 Model Workshop: The Skate Swap and the Wheel Market

Principles of Microeconomics Free sample edition

Part 1 — The Big Picture

This week you learned to measure the gains from trade: consumer surplus is what buyers would have paid minus what they pay, producer surplus is the price minus what selling costs, and total surplus adds the two. You also saw why, in the model, the competitive equilibrium makes total surplus as large as it can be, and why that is a claim about size, not fairness. In this workshop you build a surplus ladder for a weekend skate swap in a spreadsheet, draw a town's wheel-set market in Desmos and measure its two triangles, and then catch a chatbot's slips on the same two markets. The habit you build here, say whose gain it is and keep size apart from split, carries into every policy question the course asks next.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: At the skate swap and in the wheel market, who gains from trading, by how much, and does the market reach the quantity that makes the total gain as large as it can be?

Workshop data: the illustrative skate swap and the town's wheel-set market

Source: Two small illustrative markets constructed for this workshop, not real data: a weekend skate swap where six people want to buy a used skateboard and six want to sell one at a going price of 72 dollars, and a town's weekly market for skateboard wheel sets described by one demand line and one supply line. Every value is printed in Part 4.

Rows: 6 buyer-and-seller pairs at the swap and 3 checked quantities in the wheel market (the scaffold tables have 6, 3, and 4 rows)
Columns: buyer's value, seller's cost, and price in dollars at the swap; quantity in sets a week, value, and cost in dollars in the wheel market
Rules: wheel-set demand P = 16 − Q ⁄ 5 and supply P = 4 + Q ⁄ 10, with P in dollars and Q in sets a week

Part 3 — Materials & Procedure

Tools and materials

Desmos (free) or Google Sheets (free)

Ways of working

build-the-supply-and-demand-schedule
shift-vs-move-along-the-curve
compute-elasticity-by-the-midpoint-formula

Procedure

Open a blank Google Sheets file. Label row 1 as Buyer's value, Seller's cost, Pair gain, Buyer's gain at 72, and Seller's gain at 72 in columns A to E. Type the buyers' values 120, 105, 90, 75, 60, and 45 in A2 to A7 and the sellers' costs 30, 40, 55, 70, 85, and 100 in B2 to B7. Tool: Desmos (free) or Google Sheets (free). Check: Six rows hold one buyer and one seller each, values falling down column A and costs rising down column B.
In C2 type =A2-B2 and copy it down to C7. Tool: Desmos (free) or Google Sheets (free). Check: Column C falls from row to row and turns negative partway down; the rows above the turn are the trades worth making.
In D2 type =MAX(0,A2-72) and in E2 type =MAX(0,72-B2), then copy both down to row 7. In D8 type =SUM(D2:D7) and in E8 type =SUM(E2:E7). Tool: Desmos (free) or Google Sheets (free). Check: Buyers whose value is below 72 and sellers whose cost is above 72 show 0, because they sit out; row 8 holds the two totals.
Open Desmos. Quantity goes on the x-axis and price on the y-axis, so type y = 16 - x/5 for demand and y = 4 + x/10 for supply, and click the point where the two lines cross. Tool: Desmos (free) or Google Sheets (free). Check: Demand falls from the price axis at 16 dollars, supply rises from it at 4 dollars, and Desmos labels the crossing point.
In Desmos, use the polygon command to shade each surplus: give it three corners, the point where the curve meets the price axis, the crossing price on the price axis, and the crossing point itself. Then click each line at x = 30 and x = 50 and record both heights in Part 4. Tool: Desmos (free) or Google Sheets (free). Check: Two shaded triangles sit on either side of the crossing price, and at each checked quantity you have one height on demand and one on supply.
Fill in the Part 4 tables from your sheet and graph, answer the analysis questions in Part 5, then do the AI-critique step in Part 6 or its equivalent route.

Fallback route

When to use it: Use this route if you cannot open Google Sheets or Desmos, or your device cannot run them.

Complete all three Part 4 tables by hand with any calculator, writing each subtraction or area formula in words beside its result. Describe the wheel market's graph in words instead of drawing it in Desmos: what is on each axis, where each line meets the price axis, where they cross, and which triangle sits where. Answer all six analysis questions, do the critique step, and submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Build the skate swap's surplus ladder one pair at a time; this table shows who trades at 72 dollars and how much each person gains.

Student scaffold table 1
Pair	Buyer's value (dollars)	Seller's cost (dollars)
1	120	30
2	105	40
3	90	55
4	75	70
5	60	85
6	45	100

Read the wheel market's two lines at three quantities to see which units are worth trading.

Student scaffold table 2
Quantity (sets a week)	Value to the buyer: 16 − Q ⁄ 5	Cost to the seller: 4 + Q ⁄ 10	Gain or loss on that unit
30
40
50

Measure the wheel market's surplus areas with one half times base times height, or a trapezoid where the shape has two parallel sides.

Student scaffold table 3
Area	Base (sets a week)	Height or sides (dollars)	Area (dollars a week)
Consumer surplus at the crossing
Producer surplus at the crossing
Total surplus at the crossing
Total surplus if trading stopped at 30 sets

Part 5 — Analysis Questions

Complete the ladder table. How many boards sell at 72 dollars, and what are consumer surplus, producer surplus, and total surplus at the swap? Say in one plain sentence what each figure means for buyers or sellers.
Using the pair gains, find the efficient number of trades at the swap, and compare it with the number that sells at 72 dollars. What would one more trade do to total surplus, and why?
In the wheel market, find the crossing point and compute consumer surplus, producer surplus, and total surplus as triangles. Describe in words where each triangle sits on your Desmos graph.
Use the 30th and 50th wheel sets to explain why the crossing quantity makes total surplus as large as it can be, and compare total surplus at the crossing with total surplus if trading stopped at 30 sets. Label your claim as positive or normative.
Name one limitation of these models, such as the straight lines, the single going price at the swap, or the fact that willingness to pay reflects how much money a buyer has as well as how much the buyer wants a board, and explain how it could change what you conclude about the market.
Choose one reflection option, (a) or (b), and answer it in 3–4 sentences.

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 consumer and producer surplus in an introductory microeconomics course. In an illustrative example, not real data, a weekend skate swap has six buyers who would pay at most 120, 105, 90, 75, 60, and 45 dollars for a used skateboard and six sellers who would accept no less than 30, 40, 55, 70, 85, and 100 dollars, and boards sell for 72 dollars. Separately, the town's market for skateboard wheel sets has demand P = 16 − Q ⁄ 5 and supply P = 4 + Q ⁄ 10, with P in dollars and Q in sets a week. Compute consumer surplus, producer surplus, and total surplus at the swap and in the wheel market, tell me how many trades at the swap are efficient, and tell me whether each outcome is efficient and fair. Then answer: if the price of wheel sets rises, what happens to demand for wheel sets? How price-sensitive are wheel buyers? Should the town cap the wheel price or tax each set sold, and who would pay that tax? What price should a wheel shop charge to maximize profit, and how much profit do wheel sellers earn? Should the town make its own wheels because its factory is the best at making them? And do the sellers' costs already include the noise skateboarders make for the neighbors?

Test the response for these likely failures:

Chatbots often write that the swap and the wheel market are efficient and therefore fair, passing a value judgment off as a model result.
Chatbots often draw a rise in the price of wheel sets as the whole demand curve shifting left.
Chatbots often say a higher wheel price makes demand fall.
Chatbots often read the demand line's steady drop of 5 sets per dollar as the buyers' price elasticity.
Chatbots often call wheel buyers elastic or inelastic with no calculation at all.
Chatbots sometimes say the town should make its own wheels because its factory is the best at it.
Chatbots sometimes call a cap on the wheel price a price floor, or analyze it in detail.
Chatbots often say a tax on each wheel set falls entirely on whoever pays it to the town.
Chatbots sometimes invent an average cost per wheel set and treat it as the cost of one more set.
Chatbots often say a wheel shop should set its price equal to marginal cost to maximize profit.
Chatbots often call producer surplus the sellers' profit.
Chatbots sometimes claim the sellers' costs already include the noise for the neighbors.

Write 3–5 sentences naming what the chatbot got right and at least two places where it slipped into one of the failures above, or computed a surplus as a full rectangle, or swapped consumer and producer surplus, quoting its words and correcting each by hand against your own completed tables and Chapter 6. For any claim about later material, say that it is out of scope this week and why.

Equivalent route (no AI required)

No AI account is required for this workshop. This route assesses the same objectives, Objective 4 (measure consumer surplus, producer surplus, and market efficiency, and analyze price ceilings, price floors, taxes, and subsidies, including who bears a tax and the deadweight loss) and Objective 2 (explain how demand and supply determine a market's equilibrium price and quantity, and predict how a shift in demand or supply changes them), takes comparable effort of about the same 90 minutes, uses the same rubric, and earns the same credit. Instead of the chatbot, critique this flawed analysis of the skate swap and the wheel market, printed here in full: "At the skate swap, consumer surplus is the sellers' gain: (72 − 30) + (72 − 40) + (72 − 55) + (72 − 70). Five trades would be better than four, because more trades always add gains. In the wheel market, consumer surplus is the full rectangle, the quantity times the gap between 16 dollars and the price. Both markets are efficient, so their outcomes are fair to everyone. If the wheel price rises, demand for wheels shifts left, and because buyers lose 5 sets per dollar their elasticity is 5, so demand is elastic. The town should cap the wheel price, which is a price floor, and a tax paid by sellers would fall entirely on sellers. A wheel shop should charge a price equal to its average cost, and the producer surplus is the sellers' economic profit. The town should make its own wheels because its factory is the best at it, and the sellers' costs already include the noise for the neighbors." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 6, and flag each claim about later material as out of scope this week. Submit the marked-up analysis with your corrections in place of the chatbot report and share link.

Part 7 — What to Submit

The three completed scaffold tables, from a spreadsheet, Desmos, or by hand
Written answers to all six analysis questions
The chatbot critique report with its share link, or the equivalent route's marked-up correction of the printed flawed analysis

Deliverable:

A short Model Workshop report on the skate swap and the wheel market: three completed tables (the swap's surplus ladder, the wheel market's values and costs at three quantities, and its surplus areas), written answers to six analysis questions, and a critique of a chatbot's answers about the same two markets, 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 how you show it: written answers, a recorded explanation with a transcript, or a labelled diagram that describes the triangles in words with a short note; every form is graded by the same 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
Surplus ladder built and summed	Every pair gain is value minus cost, the trades at 72 dollars are identified, each buyer's and seller's gain is shown by formula or by hand, and the three totals are each read in a plain sentence.	The ladder is mostly complete, but one or two gains are wrong or missing, or the plain sentences are missing.	No ladder, or gains computed as price minus value for buyers throughout.
Triangles computed and described	The crossing point is found, consumer and producer surplus are each computed as one half times base times height with the right heights, total surplus is their sum, and each triangle's place on the graph is described in words.	The triangles are set up, but one area uses the full rectangle, a wrong height, or a swapped label.	No areas, or both surpluses computed as rectangles.
Efficiency explained with units on both sides	The efficient number of swap trades is tied to the sign of the pair gains, the 30th and 50th wheel sets are read off both lines, total surplus at 30 sets is compared with the crossing, and the efficiency claim is labeled positive.	Efficiency is asserted with only one side checked, or the claim is not labeled positive.	No explanation of why the market's quantity is efficient.
Plain-sentence analysis, limitation, and reflection	All six analysis questions are answered from the two markets' own numbers, the limitation is named with its effect on a conclusion, and the chosen reflection option is answered with a specific example.	Most questions are answered, but the limitation is missing or vague, or the reflection is missing.	No analysis answers.
AI critique or equivalent correction	The chatbot's reply, or the printed flawed analysis on the equivalent route, is quoted, at least two slips are named with the failure each shows, each is corrected by hand, and out-of-scope claims are flagged; either route earns this band equally.	One slip is named and corrected on either route, or slips are named without a correction.	No critique on either route, or the chatbot's reply is pasted without any check.

Quality Gate

Every buyer's gain is value minus price and every seller's gain is price minus cost, shown by formula or by hand, never from memory or a chatbot.
Every surplus area is a triangle or trapezoid computed as one half times base times height or the trapezoid rule, never the full rectangle.
Consumer surplus is placed below demand and above the price, and producer surplus above supply and below the price.
Every efficiency claim is labeled as positive, and every fairness claim as normative.
Every computed result ends with one plain sentence about what it means for buyers, sellers, or the market.
No real-world price, sales figure, statistic, or study is invented anywhere in the submission.
The critique quotes the chatbot, or the printed flawed analysis, and corrects each slip by hand.

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