Week 5 Model Workshop: Pricing the Neighborhood Pool's Day Passes

Part 1 — The Big Picture

This week you learned to measure how strongly buyers respond to a price change with the midpoint formula, to read an elasticity's sign and magnitude, to see why elasticity is not the slope, and to use the total-revenue test. In this workshop you build a real schedule for a neighborhood pool's summer day passes in a spreadsheet or Desmos, compute the elasticity of every 2-dollar segment, and use the revenue column to answer a question every pool manager faces: will a higher price bring in more money? Then you catch a chatbot's slips on the same pool. The habit you build here, compute the percentages before you trust a steep or flat line, carries into the weeks on surplus and taxes.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Should the neighborhood pool raise its day-pass price to bring in more money, and on which part of its demand curve would a price rise help or hurt?

Workshop data: the illustrative neighborhood pool's day-pass demand

Source: A small illustrative schedule constructed for this workshop, not real data: daily demand for summer day passes at a neighborhood pool, given by the rule Qd = 240 − 20P. Every value is printed in Part 4.

• Rows: 5 prices from 1 to 9 dollars in 2-dollar steps, each with its quantity of day passes (the scaffold tables have 5 and 4 rows)
• Columns: price in dollars, day passes demanded per day, total revenue in dollars, and the elasticity of each segment
• Rule: Qd = 240 − 20P day passes a day

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

1. Open a blank Google Sheets file. In column A, type the prices 1, 3, 5, 7, and 9 in cells A2 to A6, and label row 1 as Price, Passes, Revenue, and Elasticity. Tool: Desmos (free) or Google Sheets (free). Check: Five prices sit in A2 to A6 under the label Price.
2. In B2 type =240-20*A2 and copy it down to B6. In C2 type =A2*B2 and copy it down to C6. Tool: Desmos (free) or Google Sheets (free). Check: Column B reads 220, 180, 140, 100, and 60, and each row's revenue in column C is its price times its passes.
3. In D3 type =((B3-B2)/((B2+B3)/2))/((A3-A2)/((A2+A3)/2)) and copy it down to D6, so each cell holds the midpoint elasticity of the segment that ends in that row. Tool: Desmos (free) or Google Sheets (free). Check: Every value in column D is negative, and the values grow in size as you move down the column toward higher prices.
4. Open Desmos. Quantity goes on the x-axis and price on the y-axis, so type y = 12 - x/20 to draw the demand curve, and click the line at x = 140 to read its price. Tool: Desmos (free) or Google Sheets (free). Check: The line falls steadily from the upper left to the lower right and passes through (140, 5); its steepness is the same everywhere.
5. Fill in the two Part 4 tables from your sheet, writing each segment's percentage changes, its elasticity, its label, and the change in revenue across it. Check: Each segment row has a quantity percentage, a price percentage, an elasticity, a label, and a revenue change.
6. 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 midpoint and each product on its own line. Describe the demand curve in words instead of drawing it in Desmos: what is on each axis, where the line starts and ends, and where it is elastic and inelastic. 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 pool's schedule and its revenue column; every elasticity and every revenue judgment in this workshop comes from these five rows.

Student scaffold table 1

Price (dollars)	Day passes demanded: 240 − 20P	Total revenue (dollars)
1	220
3	180
5	140
7	100
9	60

Measure each 2-dollar segment with the midpoint formula, label it, and check the label against what happens to revenue across that segment.

Student scaffold table 2

Segment (dollars)	Percent change in passes	Percent change in price	Elasticity and label	Change in revenue (dollars)
1 to 3
3 to 5
5 to 7
7 to 9

Part 5 — Analysis Questions

1. Complete both tables: the revenue at each price and, for each segment, the two midpoint percentages, the elasticity with its sign, and its label. Say in one plain sentence what the elasticity column shows about swimmers.
2. Compare the slope of the pool's demand line on each segment with that segment's elasticity. Describe what stays the same and what changes as the price rises, and explain why.
3. Use the total-revenue test to say whether the pool takes in more or less money if it raises the price from 3 to 5 dollars, from 5 to 7 dollars, and from 7 to 9 dollars. Tie each answer to that segment's elasticity.
4. Name two determinants of price elasticity that could make swimmers more responsive than this schedule shows, such as a free public beach nearby or a whole summer to plan ahead, and say which way each would push the elasticity.
5. Name one limitation of this model, such as the straight-line rule, a single summer day's schedule, or the fact that revenue is not profit, and explain how it could change a decision the pool's manager makes.
6. 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 elasticity in an introductory microeconomics course. A neighborhood pool sells summer day passes, in an illustrative example, not real data. Its daily demand is Qd = 240 − 20P, where P is the price of a day pass in dollars, so it sells 220 passes at 1 dollar, 180 at 3, 140 at 5, 100 at 7, and 60 at 9. Using the midpoint formula, compute the price elasticity of demand on each 2-dollar segment, say whether demand is elastic, inelastic, or unit-elastic on each, and compute total revenue at each price. Then answer: should the pool raise its price from 7 to 9 dollars to bring in more money? Is the steady loss of 20 passes per dollar the swimmers' elasticity? Should the city cap the day-pass price, and who would pay a 1-dollar tax on each pass? What price maximizes the pool's profit, and how much profit does it make? Should the pool specialize in day passes because it is the best pool in town, and do its costs already include the crowding on the street outside?

Test the response for these likely failures:

• Chatbots often call the steady loss of 20 passes per dollar the swimmers' price elasticity, or say a straight line has one elasticity everywhere.
• Chatbots often swap the labels, calling the high-price segment from 7 to 9 dollars inelastic because quantity is small there, or call −0.5 elastic.
• Chatbots sometimes describe the pool's own price rise as shifting the demand curve left.
• Chatbots often write that raising the price from 7 to 9 dollars lowers demand by 40 passes.
• Chatbots often fold a value judgment, such as that a public pool should be cheap for everyone, into the revenue result.
• Chatbots sometimes say the pool should specialize in day passes because it is the best pool in town.
• Chatbots sometimes call a city cap on the day-pass price a price floor.
• Chatbots often say a 1-dollar tax paid by the pool is borne entirely by the pool, or entirely by swimmers.
• Chatbots sometimes invent a cost per swimmer and treat that average cost as the cost of one more swimmer.
• Chatbots often say the pool should set its price equal to marginal cost to maximize profit.
• Chatbots sometimes call the 700 dollars of revenue at 5 or 7 dollars the pool's profit.
• Chatbots sometimes claim the pool's costs already include the crowding and parking on the street outside.

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 5. 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 3 (compute and interpret price, income, and cross-price elasticities of demand by the midpoint formula, and relate price elasticity to total revenue) 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 neighborhood pool, printed here in full: "The pool loses 20 passes for every dollar, so its elasticity is −20 on every segment, and because the line is straight, demand is equally elastic everywhere. From 7 to 9 dollars only 60 to 100 swimmers are left, so demand there is inelastic, and raising the price to 9 dollars will raise revenue. The price rise from 7 to 9 dollars lowers demand by 40 passes and shifts the demand curve left. A public pool should always be cheap, so the model shows the price must stay at 1 dollar. The city should cap the price at 3 dollars, which is a price floor, and a 1-dollar tax paid by the pool falls entirely on the pool. The pool should price at marginal cost, its average cost of 2 dollars a swimmer, and its 700 dollars at 5 dollars is its economic profit. It should specialize in day passes because it is the best pool in town, and its costs already include the crowding on the street outside." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 5, 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 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 neighborhood pool: two completed tables (the schedule with its revenue column, and four segments measured with the midpoint formula), written answers to six analysis questions, and a critique of a chatbot's answers about the same pool, 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 curve's elastic and inelastic stretches 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
Schedule and revenue built	All five quantities and all five revenues are shown by formula or by hand, each revenue as price times quantity, with a plain sentence on what the revenue column shows.	The schedule is mostly complete, but one or two revenues are wrong or missing, or the plain sentence is missing.	No schedule or revenue column, or revenue computed as something other than price times quantity.
Elasticities computed and labeled	All four segment elasticities are computed with the midpoint formula, both percentages shown, each sign kept, and each segment correctly labeled elastic, inelastic, or unit-elastic.	Two or three segments are computed and labeled correctly, or all four are computed but a sign is dropped or a label is swapped.	No elasticities, or every percentage is taken on the starting value instead of the midpoint.
Revenue test and slope reasoning	The revenue answers for all three price rises follow from each segment's elasticity by the total-revenue test, the slope is shown to stay the same while elasticity changes, two determinants are named with directions, and the limitation and the chosen reflection option are answered with specifics.	Most questions are answered, but the revenue answers are not tied to elasticity, or the slope comparison, the limitation, or the reflection is missing or vague.	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.
Model built in the tools, or by hand	The spreadsheet formulas or the Desmos line are shown or described, including the midpoint elasticity formula, or the fallback's hand work and written curve description are complete.	The model is partly shown, such as the schedule without the elasticity column.	No evidence of how the numbers or the curve were produced.

Quality Gate

• Every elasticity is computed by the midpoint formula, with both percentages shown, never from memory or a chatbot.
• Every elasticity keeps its sign and carries the right label: elastic, inelastic, or unit-elastic.
• Every revenue judgment comes from the revenue column and is tied to the segment's elasticity by the total-revenue test.
• Every computed result ends with one plain sentence about what it means for the pool or its swimmers.
• No real-world price, attendance figure, elasticity, or study is invented anywhere in the submission.
• The critique quotes the chatbot, or the printed flawed analysis, and corrects each slip by hand.