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Week 12 · Assignment: Traditional alternative (no AI)

Week 12 — Why Do Both Coffee Shops End Up Pricing Low? — Traditional alternative (no AI)

Principles of Microeconomics Free sample edition
Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI. An instructor who prefers it publishes it and unpublishes or deletes the adaptive one, as the note at its top says.

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 11 of the term — find a dominant strategy in a payoff matrix, test the Nash equilibrium, measure the prisoner's dilemma, explain why a price-fixing deal is unstable, and explain the dilemma to someone outside economics.

This week you learned how firms behave when they are neither price takers nor lone sellers: a monopolistic competitor produces where MR = MC and loses its economic profit to entry, while a few interdependent rivals in an oligopoly must think about each other's choices. A payoff matrix shows each rival's best reply, its dominant strategy, and the Nash equilibrium, and the prisoner's dilemma explains why a price-fixing deal breaks down. In Week 10 the chair workshop took its price and in Week 11 the ferry chose its own; this week you work four short problems on the coffee shops' game, interpret each one, and explain the dilemma to someone who has never studied economics. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles.

The task

You will use the two coffee shops' pricing game from this week's chapter, Dataset O, with illustrative numbers built for this course (not real data):

  • Each shop picks a high price or a low price for the month.
  • Payoffs are monthly profit in thousands of dollars, written (first shop, second shop).
  • Both price high: (10, 10). First shop high, second shop low: (4, 14). First shop low, second shop high: (14, 4). Both price low: (6, 6).
  • The shops are a classroom model, not real companies.

Work these four problems, showing your arithmetic:

  1. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. If the second shop prices high, how many thousand dollars a month more does the first shop earn by pricing low than by pricing high?
  2. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Each shop plays its dominant strategy. What is the two shops' joint monthly profit at the Nash equilibrium, in thousands of dollars?
  3. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. How many thousand dollars a month more would the two shops earn together at (high, high) than at the Nash equilibrium, (low, low)?
  4. In the course's illustrative pricing game, two coffee shops each price high or low, with monthly profit in thousands of dollars written (first shop, second shop): (10, 10) if both price high, (4, 14) if the first prices high and the second low, (14, 4) if the first prices low and the second high, and (6, 6) if both price low. Suppose the shops secretly agree that both will price high, and the first shop cheats by pricing low while the second keeps the deal. How many thousand dollars a month does the second shop lose compared with both keeping the deal?

Beside each answer, add one brief interpretation. For problem 1, say in words what the gain means and explain why low is the first shop's dominant strategy, comparing its payoffs within each of the second shop's choices. For problem 2, name the Nash equilibrium and test it: would either shop gain by switching its own price alone? For problem 3, explain why the gap is a prisoner's dilemma, and label whether the low prices are good for customers as a positive claim or a normative judgment. For problem 4, explain why the price-fixing deal is unstable as well as illegal under U.S. antitrust law, and why a deal that held would have the two shops act like the Week 11 monopolist, charging a price above marginal cost.

Explain it to a non-expert

Your relative runs a hair salon across the street from a rival salon, and asks you: "We both keep cutting prices to win customers, and we both make less than we used to. Why can't we stop?" Write a 3–5 sentence message to your relative that explains the prisoner's dilemma in everyday words, ties it to the salons' price cuts, and names one limit, such as that the course's model is a single round while the two salons meet month after month, or that you do not know their real profits. Explain any technical term in everyday words. More than one accurate wording can be defensible. The message must not suggest that the salons agree on their prices, because price-fixing agreements are illegal.

For a different, ungraded example, imagine two roommates who share a kitchen and each decide every evening whether to wash their own dishes. One asks: "Why is our sink always full when we both hate a messy kitchen?" Model answer: "Each of you saves a little time by skipping your dishes, whatever the other one does, so skipping feels like the smart move every single night. When you both skip, you both end up with the messy kitchen neither of you wants. That is a trap economists call a prisoner's dilemma: each person's own best move leaves both worse off. One limit: I am guessing at how much each of you minds the mess, so the trap might not hold if one of you minds it much more."

Use that pattern for your message to your relative, with your own explanation and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the payoffs above without guessing which cells or steps you used.

Deliverables

Submit a single game report containing:

  • the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
  • your message to your relative, explaining the prisoner's dilemma in everyday words, tying it to the salons' price cuts, and naming one limit; and
  • a one-line restatement of the payoffs you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled payoff table described cell by cell in words with a short note. Every form is graded by the same scoring criteria. 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.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without any AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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