Week 12 · Model Workshop

Week 12 Model Workshop: The Yoga Studio's Price, Before and After Rivals Arrive

Principles of Microeconomics Free sample edition

Part 1 — The Big Picture

This week you learned what happens between the price taker and the monopolist. A monopolistic competitor sells something a little different from its rivals, so its own demand curve slopes down: it sells where MR = MC and reads a price above marginal cost from its demand curve, and entry by new rivals pushes its economic profit to zero. A few rivals who watch each other are an oligopoly, and a payoff matrix shows why each one's best move can leave both worse off. In this workshop you build a yoga studio's revenue and cost tables before and after new studios open, choose its sessions and price each time, check its profit, and then solve a pricing game between two studios and catch a chatbot's slips on the same numbers.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: How many sessions should the yoga studio sell, at what price, and with what profit, before and after rival studios open, and where does a pricing game between two studios settle?

Workshop data: the illustrative yoga studio and its rival

Source: An illustrative studio constructed for this workshop, not real data: a neighborhood yoga studio that sells private sessions a little different from its rivals'. Its fixed cost is 30 dollars a day and each session adds 18 dollars to its cost; Part 4 lists the prices it can charge for 1 to 5 sessions a day before and after new studios open, and the weekly payoffs, in hundreds of dollars, when it and one rival studio each set a high or a low price.

Rows: 5 session levels, 1 to 5 sessions a day, in each of the two revenue tables (the pricing-game table has 2 rows, one per price the first studio can set)
Columns: sessions a day, price, total revenue, marginal revenue, total cost, and profit, in dollars a day
Cost figures: fixed cost 30 dollars a day; 18 dollars more for each session

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 Sessions, Price before entry, Revenue before entry, Marginal revenue before entry, Total cost, and Profit before entry in columns A to F. Type the sessions 1 to 5 in A2 to A6 and the prices 40, 36, 32, 28, and 24 in B2 to B6. Tool: Desmos (free) or Google Sheets (free). Check: Five rows of sessions and prices, with the price falling 4 dollars for each extra session.
In C2 type =A2*B2 for total revenue and copy it down to C6. In D2 type =C2 and in D3 type =C3-C2, then copy D3 down to D6 for marginal revenue. In E2 type =30+18*A2 for total cost and in F2 type =C2-E2 for profit, and copy both down to row 6. Tool: Desmos (free) or Google Sheets (free). Check: Marginal revenue falls faster than the price, and the profit column peaks at one row.
Find the last row whose marginal revenue is at least the 18-dollar marginal cost. That is the studio's output before entry; read its price from column B and its profit from column F. Tool: Desmos (free) or Google Sheets (free). Check: The chosen row's marginal revenue is at least 18 and the next row's is below 18.
Copy columns A to F to a second block starting at the top of column H for the market after new studios open, and replace the prices with 36, 32, 28, 24, and 20. Repeat steps 2 and 3 on the new block, and add a column that divides total cost by sessions for average total cost. Tool: Desmos (free) or Google Sheets (free). Check: Every price is 4 dollars lower than before, and at the chosen row the price equals average total cost.
For the pricing game, type the first studio's payoffs in a small block: 12 and 5 in the High row, 15 and 7 in the Low row, with columns for the second studio pricing high and low. In each column, subtract the High payoff from the Low payoff. Tool: Desmos (free) or Google Sheets (free). Check: Both differences are positive, so the Low row beats the High row in every column.
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 all three Part 4 tables by hand with any calculator, writing each multiplication, subtraction, or division beside its result. Describe the picture in words instead of drawing it: what is on each axis, where the studio's demand line sits before and after entry, where marginal revenue meets the 18-dollar marginal cost, and where the demand line touches average total cost. 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 studio's revenue and cost table before rival studios open; the output rule compares each marginal revenue with the 18-dollar marginal cost.

Student scaffold table 1
Sessions a day	Price before entry (dollars)	Total cost (dollars)
1	40	48
2	36
3	32
4	28
5	24

Rebuild the table after new studios open, when every price is 4 dollars lower, and add average total cost to check the long-run profit.

Student scaffold table 2
Sessions a day	Price after entry (dollars)	Total revenue (dollars)	Marginal revenue (dollars)	Total cost (dollars)	Average total cost (dollars)	Profit (dollars)
1	36
2	32
3	28
4	24
5	20

Solve the two studios' pricing game: weekly profit in hundreds of dollars, written (first studio, second studio); fill in each studio's best reply.

Student scaffold table 3
First studio's price	Second studio prices high	Second studio prices low	First studio's best reply
High	(12, 12)	(5, 15)
Low	(15, 5)	(7, 7)

Part 5 — Analysis Questions

Complete the before-entry table. Which session is the last one whose marginal revenue is at least 18 dollars? Read the price from demand at that quantity, give the profit, and say in one plain sentence how far the price sits above marginal cost.
Complete the after-entry table. Choose the sessions with MR = MC again, read the price, and compute the profit and the average total cost at that quantity. Say in words what happened to the studio's profit when rivals opened, and which curve shifted which way.
After entry, the studio's price equals its average total cost but not its marginal cost. Explain why both are true, why zero economic profit is a normal return for the owner, and how this long run differs from a price taker's.
Complete the pricing-game table. Find each studio's dominant strategy by comparing within each column, name the Nash equilibrium, and compare the two studios' joint profit there with their joint profit if both priced high. Say in one sentence why this is a prisoner's dilemma.
Name one way this classroom model differs from a real yoga studio, such as sessions that cannot be split, prices that change by day of the week, or rivals that differ in size, and say how it could change one of your answers.
Choose one reflection option and answer it: (a) describe a kind of business near you where new shops keep opening, in words, and say what that seems to do to each shop's customers and prices; or (b) describe two businesses you know that seem to watch each other's prices, in words, and say what happens when one of them changes its price.

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 monopolistic competition and game theory in an introductory microeconomics course. In an illustrative example, not real data, a neighborhood yoga studio sells private sessions, and its sessions differ a little from its rivals'. Its fixed cost is 30 dollars a day and each session adds 18 dollars to its cost. Before new studios open, it can sell 1, 2, 3, 4, or 5 sessions a day at prices of 40, 36, 32, 28, or 24 dollars. After new studios open, it can sell the same numbers of sessions at 36, 32, 28, 24, or 20 dollars. How many sessions should it sell, and at what price, before and after the new studios open, and what is its profit each time? Is its long-run price equal to its marginal cost? Separately, two studios each set a high or a low weekly price, with weekly profit in hundreds of dollars written (first studio, second studio): (12, 12) if both price high, (5, 15) if the first prices high and the second low, (15, 5) if the first prices low and the second high, and (7, 7) if both price low. What is each studio's dominant strategy, and what is the Nash equilibrium? Then answer: when the studio lowers its own price, does its demand curve shift? Does the price cut mean demand for sessions changed? What is the price elasticity of demand the studio faces, and is it elastic or inelastic? Should the city limit the number of yoga studios? Should the studio teach only yoga because it teaches yoga better than a gym does? Is the zero profit after entry a sign the owner earns nothing? Who really pays if the city taxes each session? Is a 25-dollar legal maximum on sessions a price ceiling or a price floor? Does noise from classes impose a cost on neighbors that the studio's costs miss?

Test the response for these likely failures:

Chatbots often have the studio set its price equal to its 18-dollar marginal cost, as if it were a price taker, or say its long-run price equals marginal cost.
Chatbots sometimes choose the number of sessions where price equals average total cost, or treat the 28-dollar average total cost as the cost of one more session.
Chatbots often read the zero profit after entry as the owner earning nothing.
Chatbots sometimes say the studio's own price cut shifts its demand curve, or that new studios opening is a movement along it.
Chatbots sometimes say that cutting the price from 32 to 28 dollars increased demand for sessions.
Chatbots sometimes give the studio's demand a slope of 4 dollars per session and call that its elasticity.
Chatbots sometimes label the studio's demand elastic or inelastic without a calculation.
Chatbots often say the city should limit the number of studios, or call (high, high) the equilibrium because it is the best outcome, mixing a value judgment with the model's prediction.
Chatbots sometimes say the studio should teach only yoga because it teaches yoga better than a gym does.
Chatbots often say the studio bears a per-session tax in full because it pays the city.
Chatbots sometimes call a 25-dollar legal maximum a price floor.
Chatbots sometimes add a cost for class noise on neighbors to the studio's marginal cost.

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 12. For any claim about earlier or later 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 7 (analyze monopolistic competition and oligopoly, including a two-player game, the prisoner's dilemma, and Nash equilibrium, and analyze labor markets as derived demand with the value-of-the-marginal-product hiring rule) and Objective 6 (analyze perfect competition and monopoly with the profit-maximizing rules (P = MC for a price taker; MR = MC for a monopolist), the shutdown rule, long-run entry and exit, and the deadweight loss of market power), 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 yoga studio, printed here in full: "Before the new studios open, the studio should set its price equal to its 18-dollar marginal cost and sell as many sessions as buyers want. After entry it sells sessions until the price equals average total cost, so it sells 5. When the studio lowers its own price, its demand curve shifts right, and the price cut means demand for sessions rose. The new studios are a movement along the studio's demand curve. Zero profit after entry means the owner earns nothing, and the profit before entry is only accounting profit. The studio's demand has a slope of 4, so its elasticity is 4, which is elastic. In the pricing game, (high, high) is the Nash equilibrium because it pays both studios the most, and the city should limit the number of studios. The studio should teach only yoga because it teaches yoga better than a gym. A tax on each session is paid entirely by the studio, a 25-dollar legal maximum is a price floor, and the studio should add class noise to its marginal cost." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 12, and flag each claim about earlier or later 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 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 yoga studio: three completed tables (before entry, after entry, and the pricing game), written answers to six analysis questions, and a critique of a chatbot's answers about the same studio, 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 marginal-revenue line, the marginal-cost line, and the average-total-cost curve 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
Revenue and cost tables built	Total revenue, marginal revenue, total cost, and profit are computed for 1 to 5 sessions in both tables with each step shown, and average total cost is computed after entry.	The tables are mostly complete, but one or two values are wrong, or average total cost is missing.	No tables, or marginal revenue taken as the price at every row.
Output and price with MR = MC	Before and after entry the sessions are chosen by comparing marginal revenue with the 18-dollar marginal cost, the price is read from demand at that quantity, and the gap between price and marginal cost is stated in a plain sentence.	One of the two choices is right, or the price is read from the marginal-revenue column once, or the plain sentence is missing.	No output choice, or the price set equal to marginal cost throughout.
Entry and zero economic profit	Entry is shown as the studio's demand curve shifting left, the after-entry price is shown equal to average total cost with zero economic profit, and that profit is read as a normal return while price stays above marginal cost.	The shift or the zero profit is right, but the other is missing, or zero economic profit is left unexplained.	No long-run answer, or entry said to raise the studio's profit, or zero economic profit read as earning nothing.
Pricing game solved	Each studio's dominant strategy is found by comparing within both columns, the Nash equilibrium is named and tested by a one-studio switch, joint profit at the equilibrium is compared with joint profit at (high, high), and the prisoner's dilemma is explained in a sentence.	The dominant strategy or the Nash equilibrium is right but not both, or the comparison is made by picking the biggest number, or the dilemma is not explained.	No game answer, or (high, high) named as the Nash equilibrium without a test.
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 or later 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 total revenue is price times sessions and every marginal revenue is the difference of two revenues, shown by formula or by hand, never from memory or a chatbot.
Output before and after entry follows MR = MC with the price read from demand, never P = MC and never price equals average total cost.
Every profit subtracts total cost from revenue, and the after-entry profit is checked as price minus average total cost, times sessions.
Entry is shown as each existing studio's demand curve shifting left, with the long-run price named and economic profit read as a normal return.
Each studio's dominant strategy is found by comparing within each column, and the Nash equilibrium is tested by one studio switching alone.
No number, study, or real-world figure is invented; every value comes from the workshop's own tables.

Built with The Course Maker · samples.thecoursemaker.com