Week 11 Model Workshop: How Many Lift Tickets, and at What Price?

Part 1 — The Big Picture

This week you learned how a seller with no rivals behaves: to sell more it must cut its price for every buyer, so its marginal revenue falls below its price; it chooses its quantity where marginal revenue equals marginal cost and then reads its price from the demand curve; and, compared with a competitive market, it sells less at a higher price and leaves a deadweight loss. In this workshop you build a small mountain's only ski lift's revenue table in a spreadsheet, find its marginal revenue, choose its quantity and price, compute its profit, compare it with what competing lifts would do, measure the surplus riders lose, and then catch a chatbot's slips on the same lift. The habit you build, quantity from MR = MC and price from demand, carries into every market with fewer sellers that the course studies next.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: How many lift tickets should the mountain's only lift sell, what price should it charge, and what does its market power cost skiers compared with a competitive mountain?

Workshop data: the illustrative ski lift

Source: An illustrative ski lift constructed for this workshop, not real data: the only lift on a small mountain, so it faces the whole market's demand. Demand for lift tickets is P = 30 − 2Q, where P is the price in dollars a ticket and Q is hundreds of tickets a day, and carrying one more skier costs the lift a constant 10 dollars a ticket.

• Rows: 9 quantity levels, 0 to 8 hundred tickets a day, in the revenue table (the comparison table has 2 rows, one for the lift and one for a competitive mountain)
• Columns: hundreds of tickets a day and the price in dollars a ticket, from which total revenue and marginal revenue are built
• Marginal cost: a constant 10 dollars a ticket

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. Label row 1 as Tickets (hundreds), Price, Total revenue, and Marginal revenue in columns A to D. Type 0 to 8 in A2 to A10, and in B2 type =30-2*A2 for the price from demand. Copy B2 down to B10. Tool: Desmos (free) or Google Sheets (free). Check: Nine rows, with the price falling by 2 dollars for each extra hundred tickets, starting from 30 dollars at zero tickets.
2. In C2 type =A2*B2 for total revenue and copy it down to C10. In D3 type =C3-C2 for marginal revenue and copy it down to D10. Tool: Desmos (free) or Google Sheets (free). Check: Total revenue rises and then levels off, and marginal revenue falls by 4 each row, below the price after the first row.
3. Type the marginal cost, 10, in G1. In E3 type =IF(D3>=$G$1,"sell","stop") and copy it down to E10. The last row that says sell is the lift's quantity; read its price from column B. Tool: Desmos (free) or Google Sheets (free). Check: The early rows say sell and the later rows say stop, and the switch happens at one row.
4. Compute profit as the price minus marginal cost, times the quantity. Then find the competitive outcome by setting the price from demand equal to marginal cost, and compute consumer surplus at both outcomes and the deadweight loss as triangles, each on its own line. Check: The competitive quantity is larger and its price lower, and the pieces of surplus add back up to the competitive consumer surplus.
5. Optional picture: open Desmos and type y = 30 - 2x for demand, y = 30 - 4x for marginal revenue, and y = 10 for marginal cost, with hundreds of tickets on the x-axis and dollars a ticket on the y-axis. Tool: Desmos (free) or Google Sheets (free). Check: Demand and marginal revenue start at the same point and spread apart; marginal revenue crosses the flat cost line before demand does.
6. 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 multiplication or subtraction beside its result. Describe the picture in words instead of drawing it: what is on each axis, where demand and the marginal-revenue line start and how steeply each falls, where the flat cost line sits, 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 lift's revenue table first; every decision in this workshop compares a step's marginal revenue with the 10-dollar cost.

Student scaffold table 1

Tickets (hundreds a day)	Price (dollars a ticket)	Total revenue (hundreds of dollars a day)	Marginal revenue (dollars a ticket)
0	30	0	none
1	28
2	26
3	24
4	22
5	20
6	18
7	16
8	14

Compare the lift's choice with what competing lifts would do, and split the surplus.

Student scaffold table 2

Outcome	Tickets (hundreds a day)	Price (dollars a ticket)	Consumer surplus	Lift's profit	Deadweight loss
The only lift
Competing lifts

Part 5 — Analysis Questions

1. Complete the revenue table. Pick one row after the first and explain in a plain sentence why its marginal revenue is below its price.
2. Use MR = MC to choose how many tickets the lift sells, confirm it with the marginal-revenue line MR = 30 − 4Q, read its price from demand, and compute its profit. Say in words what each result means for the lift.
3. Find the competitive outcome with P = MC, then complete the comparison table: consumer surplus at both outcomes, the lift's profit, and the deadweight loss, each on its own line. Explain which piece is a transfer from skiers to the owner and which piece goes to no one, and check that the pieces add up.
4. Compute the lift's Lerner index, the markup of price over marginal cost as a share of the price, and say it in words as a fraction. Then describe how the lift might charge local residents and visitors different prices, and name the three conditions price discrimination would need.
5. Name one way this classroom model differs from a real ski lift, such as costs that are not constant or skiers who could drive to another mountain, and say how it could change one of your answers.
6. Choose one reflection option and answer it: (a) describe a product or service you buy from a seller with no close rival, in words, and say what keeps rivals out; or (b) describe a discount you have used, in words, and say how the seller sorted you and stopped resale.

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 monopoly in an introductory microeconomics course. In an illustrative example, not real data, a small mountain has only one ski lift. Demand for lift tickets is P = 30 − 2Q, where P is dollars a ticket and Q is hundreds of tickets a day, and each extra skier costs the lift a constant 10 dollars. How many tickets should the lift sell, what price should it charge, and what is its profit? What would competing lifts with the same cost do, and what is the deadweight loss of the monopoly? Then answer: when the lift raises its price, does demand for lift tickets fall? Does a higher price shift the demand curve? The demand line falls 2 dollars for each hundred tickets; is that slope its elasticity, and is demand elastic or inelastic at the lift's price? Should the government cap the lift's price? Should the mountain run only the lift because it runs lifts better than anyone else? Is a 15-dollar legal maximum on tickets a price ceiling or a price floor? Who really pays if the town taxes each ticket sold? Should the lift sell tickets until the price equals its average cost? Is the lift's profit accounting profit? Does the traffic skiers add on the mountain road impose a cost the lift's price misses?

Test the response for these likely failures:

• Chatbots often apply P = MC to the single lift and answer 10 hundred tickets at 10 dollars, or read the price at the 10 dollars where marginal revenue meets marginal cost.
• Chatbots sometimes tell the lift to sell until the price equals its average cost.
• Chatbots often add that the government should cap the lift's price, presenting a value judgment as a model result.
• Chatbots sometimes call the lift's profit of 50 an accounting profit.
• Chatbots sometimes say a higher lift price shifts the demand curve left.
• Chatbots often say demand for lift tickets falls when the price rises.
• Chatbots sometimes call the slope of 2 dollars per hundred tickets the elasticity of demand.
• Chatbots sometimes label the lift's demand inelastic because skiers have no rival lift.
• Chatbots sometimes say the mountain should run only the lift because it runs lifts better than anyone else.
• Chatbots sometimes call a 15-dollar legal maximum a price floor.
• Chatbots often say the lift bears a per-ticket tax in full because it hands the tax to the town.
• Chatbots sometimes add the cost of road traffic to the lift'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 11. 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 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) 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 ski lift, printed here in full: "The lift should follow P = MC, so it sells 10 hundred tickets at 10 dollars. Its marginal revenue equals its price, as for any firm. The price is the 10 dollars where marginal revenue meets marginal cost. The lift can charge whatever it likes, since it has no rival. Its profit of 50 is the deadweight loss. When the lift raises its price, demand for tickets falls and the demand curve shifts left. The slope of 2 is the elasticity, and demand is inelastic because skiers have no other lift. The government should cap the price. The mountain should run only the lift because it runs lifts best. A 15-dollar legal maximum is a price floor, a ticket tax is paid entirely by the lift, the lift should sell until price equals average cost, its profit is accounting profit, and road traffic belongs in its marginal cost." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 11, 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 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 ski lift: two completed tables (the revenue table and the lift-versus-competition table), written answers to six analysis questions, and a critique of a chatbot's answers about the same lift, 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, and the marginal-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
Revenue table built	Price, total revenue, and marginal revenue are computed for every row with each step shown, and one row's marginal revenue is explained as below its price because the price cut reaches every skier.	The table is mostly complete, but one or two values are wrong, or marginal revenue is computed without explaining why it is below the price.	No revenue table, or marginal revenue set equal to the price throughout.
Quantity, price, and profit	The quantity is chosen where marginal revenue last stays at least the marginal cost and confirmed on the marginal-revenue line, the price is read from demand at that quantity, and profit is computed as the markup times the tickets, with each result read in a plain sentence.	Two of the three are right, or the price is read where marginal revenue meets marginal cost once, or the plain sentences are missing.	No quantity or price, or the lift's price set where price equals marginal cost.
Competitive benchmark and deadweight loss	The competitive outcome is found with P = MC, consumer surplus at both outcomes and the deadweight loss are computed as triangles on their own lines, the profit is named as a transfer and the deadweight loss as surplus no one gets, and the pieces are shown to add up.	The competitive outcome and one of the areas are right, or the areas are right but the transfer and the loss are not told apart.	No comparison, or the profit called the deadweight loss.
Lerner index and price discrimination	The Lerner index is computed and said in words as a fraction, and a resident-and-visitor price plan is described with all three conditions named.	The index or the three conditions are given, but not both, or the index is left as a decimal with no words.	No Lerner index and no conditions named.
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 a price times a quantity and every marginal revenue is a difference of two total revenues, shown by formula or by hand, never from memory or a chatbot.
• The quantity follows MR = MC and the price is read from the demand curve, never P = MC and never the point where marginal revenue meets marginal cost.
• Profit is the markup per ticket times the tickets sold, and the deadweight loss is a triangle kept apart from the profit.
• Consumer surplus, profit, and deadweight loss are checked to add up to the competitive consumer surplus.
• The Lerner index is said in words as a fraction, not keyed as a decimal.
• Every judgment about what the lift or a regulator ought to do is labelled normative.
• No real-world price, cost, 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.