Week 14 · Model Workshop

Week 14 Model Workshop: How Much Smoke Should the Kilns Make?

Principles of Microeconomics Free sample edition

Part 1 — The Big Picture

This week you learned what happens when part of a market's cost lands on people outside the trade: sellers pay only their private cost, so the market makes more than the efficient quantity; the extra units are a deadweight loss; and a corrective tax equal to the harm per unit, or a cap on the total, moves the market back. In this workshop you build a small town's tile kilns' cost table in a spreadsheet, add the harm their smoke does to a school playground, find the market and efficient quantities, measure the deadweight loss, test a corrective tax and a cap, and then catch a chatbot's slips on the same kilns. The habit you build, counting everyone at the table before you call an outcome efficient, carries into the next week's markets where one side knows more than the other.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: How many batches should the town's tile kilns fire each week once the smoke over the playground is counted, and what tax or cap would get the market there?

Workshop data: the illustrative tile kilns

Source: An illustrative tile-making district constructed for this workshop, not real data: many small kilns in one town sell batches of tiles to builders, and the smoke from each batch drifts over a school playground. Demand for tiles is P = 40 − Q and the kilns' supply is P = 4 + Q, where P is dollars a batch and Q is batches a week, and each batch does 4 dollars of harm to people outside the trade.

Rows: 5 quantity levels, 12 to 20 batches a week in steps of 2, in the cost table (the outcome table has 2 rows, one for the market and one for the market with a corrective tax)
Columns: batches a week, the buyers' value of the last batch, and the kilns' cost of the last batch, from which the harm and the full cost are built
Harm per batch: a constant 4 dollars to people outside the trade

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 Batches, Buyers' value, Kilns' cost, Harm, Full cost, and Gap in columns A to F. Type 12, 14, 16, 18, and 20 in A2 to A6. In B2 type =40-A2 for the buyers' value of the last batch and in C2 type =4+A2 for the kilns' cost of it. Copy B2 and C2 down to row 6. Tool: Desmos (free) or Google Sheets (free). Check: Five rows, with the buyers' value falling and the kilns' cost rising by 2 dollars for each step of 2 batches.
In D2 type 4 for the harm per batch, in E2 type =C2+D2 for the full cost to society, and in F2 type =E2-B2 for the gap between the full cost and the buyers' value. Copy D2 to F2 down to row 6. Tool: Desmos (free) or Google Sheets (free). Check: The gap column changes sign once: negative at the low quantities and positive at the high ones.
Find the market quantity, the row where the buyers' value equals the kilns' cost, and the efficient quantity, the row where the gap is zero. Read each price from column B. Check: The efficient quantity is smaller than the market quantity, and its price is higher.
Compute the deadweight loss as one half times the gap at the market quantity times the extra batches. Then add a corrective tax equal to the harm per batch: raise the kilns' cost by the tax, find the new crossing, and record the price builders pay, the price kilns keep, the quantity, and the tax revenue, each on its own line. Check: With the tax, the crossing moves to the efficient row, and the revenue is the tax times the new quantity.
Optional picture: open Desmos and type y = 40 - x for demand, y = 4 + x for the kilns' supply, and y = 8 + x for the full cost to society, with batches a week on the x-axis and dollars a batch on the y-axis. Tap each crossing to read it. Tool: Desmos (free) or Google Sheets (free). Check: The full-cost line runs parallel to supply and 4 dollars above it, and it crosses demand to the left of where supply does.
Fill in the Part 4 tables from your sheet, 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 both Part 4 tables by hand with any calculator, writing each addition, subtraction, or multiplication beside its result. Describe the picture in words instead of drawing it: what is on each axis, where demand, supply, and the full-cost line start and which way each moves, and where the lines cross. 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 kilns' cost table first; every decision in this workshop compares the full cost of a batch with what builders value it at.

Student scaffold table 1
Batches a week	Buyers' value of the last batch (dollars)	Kilns' cost of the last batch (dollars)	Harm to the playground (dollars)
12	28	16	4
14	26	18	4
16	24	20	4
18	22	22	4
20	20	24	4

Compare the market with the market under a corrective tax, and count everyone's gains and losses.

Student scaffold table 2
Outcome	Batches a week	Price builders pay	Price kilns keep	Consumer surplus	Producer surplus	Tax revenue	Harm to the playground	Social surplus
Market, no tax						none
Market with the corrective tax

Part 5 — Analysis Questions

Complete the cost table. Find the market quantity and price and the efficient quantity and price, and explain in a plain sentence why the market fires more batches than is efficient.
Compute the deadweight loss of the smoke as a triangle, then check it by computing social surplus at both outcomes in the outcome table, each on its own line. Say in words what the loss means for the town.
With a corrective tax equal to the harm per batch, record what builders pay, what kilns keep, the quantity, and the revenue. Explain why the tax is the harm on each batch rather than the week's total harm, and compare this tax with Week 7's 2-dollar tax, which caused a deadweight loss in a market with no harm.
Suppose the town instead caps the kilns at the efficient number of batches and issues tradable permits for that many. Explain why the cap reaches the same quantity, and use the cost table to say what a permit would be worth to a kiln at that quantity. Label one sentence of your reasoning positive and one normative.
Name one way this classroom model differs from a real town's kilns, such as harm that grows faster as smoke piles up or harm that is hard to measure in dollars, and say how it could change one of your answers.
Choose one reflection option and answer it: (a) describe a spillover from a business near where you live or work, in words, and say which of this week's fixes might fit it; or (b) describe a time two neighbors or roommates settled a spillover between themselves, in words, and say whether bargaining was cheap or costly.

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 externalities in an introductory microeconomics course. In an illustrative example, not real data, a small town's tile kilns sell to many builders. Demand for tiles is P = 40 − Q and the kilns' supply is P = 4 + Q, where P is dollars a batch and Q is batches a week, and each batch sends smoke over a school playground that does 4 dollars of harm. What quantity and price does the market reach, and what are the efficient quantity and price? What is the deadweight loss of the smoke, and what corrective tax per batch fixes it? Then answer: who really pays the tax, the kiln owners or the builders? Should the town tax the kilns? Does the tax shift the demand curve for tiles? Does demand for tiles fall after the tax? The demand line falls 1 dollar per batch; is that slope its elasticity, and is demand elastic or inelastic? Should the town keep making tiles because its kilns are faster than any other town's? Is a 20-dollar legal minimum price for tiles a price ceiling or a price floor? Should the tax equal the average harm, or should the kilns fire until price equals average cost? Should the kilns set marginal revenue equal to marginal cost? Is the kilns' producer surplus their accounting profit?

Test the response for these likely failures:

Chatbots often solve with the kilns' own cost line alone and report 18 batches a week at 22 dollars as the efficient outcome, using private cost where social cost belongs.
Chatbots often say the kiln owners bear the whole 4-dollar tax because they hand it to the town.
Chatbots often add that the town should tax the kilns, presenting a value judgment as a model result.
Chatbots sometimes say the tax shifts the demand curve for tiles to the left.
Chatbots often say demand for tiles falls after the tax.
Chatbots sometimes call the demand line's slope of 1 dollar per batch its elasticity.
Chatbots sometimes label demand for tiles inelastic because builders need tiles.
Chatbots sometimes say the town should keep making tiles because its kilns make them faster than any other town.
Chatbots sometimes call a 20-dollar legal minimum price for tiles a price ceiling.
Chatbots sometimes set the tax equal to the average harm per batch over the whole week or tell the kilns to fire until price equals average cost.
Chatbots sometimes treat the kilns as a monopolist and look for marginal revenue.
Chatbots sometimes call the kilns' producer surplus their accounting profit.

Write 3–5 sentences naming what the chatbot got right and at least two places where it slipped into one of the failures above, quoting its words and correcting each by hand against your own completed tables and Chapter 14. For any claim about earlier material that this workshop cannot check, say so and why.

Equivalent route (no AI required)

No AI account is required for this workshop. This route assesses the same objectives, Objective 8 (analyze market failures — externalities, public goods, common resources, and asymmetric information — evaluate responses such as corrective taxes, cap-and-trade, and private bargaining, and survey behavioral economics and the measurement of inequality evenhandedly) and 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), 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 tile kilns, printed here in full: "The kilns' supply line shows the full cost, so 18 batches at 22 dollars is efficient and there is no deadweight loss. The smoke makes the market produce too little. The corrective tax should be the whole week's harm, 4 × 18 = 72 dollars. The kiln owners pay the whole tax because they send the check to the town. The town should tax the kilns. The tax shifts demand for tiles to the left, and demand for tiles falls. The slope of 1 is the elasticity, and demand is inelastic because builders need tiles. The town should keep making tiles because its kilns are fastest. A 20-dollar legal minimum is a price ceiling. The kilns should fire until price equals average cost and set marginal revenue equal to marginal cost, and their producer surplus is their accounting profit." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 14, and flag each claim about earlier material that this workshop cannot check. Submit the marked-up analysis with your corrections in place of the chatbot report and share link.

Part 7 — What to Submit

The two 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 tile kilns: two completed tables (the cost table and the outcome table), written answers to six analysis questions, and a critique of a chatbot's answers about the same kilns, 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 sketch that describes the demand line, the supply line, and the full-cost line 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
Cost table built	The full cost and the gap are computed for every row with each step shown, and the market and efficient quantities and prices are read from the table with a plain sentence on why the market fires more batches.	The table is mostly complete, but one or two values are wrong, or the quantities are found without the plain sentence.	No cost table, or the efficient quantity read from the kilns' cost alone.
Deadweight loss and social surplus	The deadweight loss is computed as a triangle on the batches beyond the efficient quantity, social surplus at both outcomes is computed on its own lines with the harm subtracted, the two are shown to agree, and the loss is read in a plain sentence.	The triangle or the social-surplus check is right but not both, or the plain sentence is missing.	No deadweight loss, or the week's total harm called the deadweight loss.
Corrective tax and the Week 7 contrast	The tax is set to the harm per batch, the builder price, kiln price, quantity, and revenue are each computed, the revenue is kept apart from the loss, and the contrast with Week 7's tax causing a loss where there was no harm is explained.	The tax outcome is right but the contrast is missing, or the contrast is explained with one computed value wrong.	No tax analysis, or the tax set to the week's total harm.
Cap and permit value	The cap is shown to reach the same quantity, the permit's value is read from the table at that quantity, and one sentence each is labelled positive and normative.	The cap or the permit value is explained, but not both, or the labels are missing.	No cap analysis.
Limitation and reflection	A real limitation of the model is named with its effect on an answer, and the chosen reflection option is answered with a specific example described in words.	The limitation is vague or not linked to an answer, or the reflection is missing.	No limitation and no reflection.
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 claims about earlier material 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 full cost is the kilns' cost plus the 4-dollar harm, and every gap is a difference of two table values, shown by formula or by hand, never from memory or a chatbot.
The efficient quantity comes from the full cost to society, never from the kilns' cost alone.
The deadweight loss is a triangle on the batches beyond the efficient quantity, never the week's total harm.
The corrective tax equals the harm per batch, and the tax revenue is kept apart from the deadweight loss.
Social surplus at both outcomes is checked against the deadweight loss.
Every judgment about what the town ought to do is labelled normative.
No real-world price, pollution level, climate figure, statistic, or company is invented or named anywhere in the submission.
The critique quotes the chatbot, or the printed flawed analysis, and corrects each slip by hand.

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