Week 13 — How Many Bakers, and What Moves the Number?

Assignment 12 of the term — turn a worker's extra loaves into dollars, apply the hiring rule, tell a movement along labor demand from a shift of it, read what a shift does to a market wage, and explain the hiring rule to someone outside economics.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, evidence-based report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 9 you built the bakery's production schedule and met diminishing marginal returns; in Weeks 3 and 4 you learned to tell a movement along a curve from a shift of it. This week the bakery becomes a buyer of labor, and both ideas come together. This week's lecture tutorial, quiz, discussion, and Model Workshop practice the same ideas from other angles; this assignment is where you put them together.

The task

You will use the bakery from this week's chapter, Dataset K, with illustrative numbers built for this course (not real data):

• With 0 to 6 workers in a fixed kitchen, the bakery bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day.
• The marginal product of the 1st to 6th worker is 10, 15, 20, 15, 10, and 5 loaves a day.
• The bakery takes both the price of bread and the daily wage as given.
• In this assignment, "revenue minus the wage bill" means bread revenue minus the wages paid, leaving the bakery's other costs aside.

Work these four problems, showing your arithmetic:

1. In the course's illustrative bakery, bread sells for 4 dollars a loaf, and the bakery bakes 25 loaves with 2 workers and 45 loaves with 3 workers. What is the value of the marginal product of the 3rd worker, in dollars a day?
2. In the same illustrative bakery, bread sells for 4 dollars a loaf and the daily wage is 50 dollars; the bakery bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day with 0 to 6 workers. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it hires?
3. In the same illustrative bakery, bread still sells for 4 dollars a loaf, but the daily wage falls to 30 dollars. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it now hires?
4. In the same illustrative bakery, the daily wage is 50 dollars, but the price of bread rises to 6 dollars a loaf. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it now hires?

Beside each answer, add one brief interpretation. For problem 1, say in words what the value means for the bakery and why the 3rd worker's extra loaves must be turned into dollars before they can be compared with a wage. For problem 2, name how many workers the bakery hires, use the hiring rule to explain why it stops there, and explain why the 1st worker's low value does not mean the bakery should hire no one. For problem 3, name how many workers it now hires and say whether the change is a movement along the bakery's labor demand curve or a shift of it, and why. For problem 4, name how many workers it now hires, say which way the labor demand curve shifts and why a higher price of bread causes that, and then say in words what would happen to the market wage and employment for bakers in a town where many bakeries saw the same rise in bread prices.

Explain it to a non-expert

A friend manages a smoothie bar and says: "Our newest hire makes fewer smoothies an hour than anyone else, so hiring her was a mistake." Write a 3–5 sentence message to your friend that explains the hiring rule in everyday words, says why a new worker who adds less than the others can still be worth hiring, and names one limit, such as that you would need to know what the smoothies sell for and what she is paid. Explain any technical term in everyday words. More than one accurate wording can be defensible, and the message does not need to decide whether your friend should keep her.

For a different, ungraded example, imagine a print-shop owner who says: "Our big press costs us 300 dollars a week no matter what, so we should hire another operator to spread that cost over more prints." Model answer: "The press costs the same whether you hire anyone or not, so it should not drive this choice. What matters is what one more operator adds: the extra prints that person makes, times what each print sells for, compared with that person's pay. If the extra prints bring in more than the pay, the hire helps; if not, it hurts, however you spread the press cost. One limit: I do not know how many extra prints a new operator would really make with the presses you have, so that is the number to find first."

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

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to your friend before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Respond in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about factor and labor markets: derived demand, the value of the marginal product of labor, the hiring rule read on the falling part of the schedule, a wage change as a movement along labor demand, a change in the output price as a shift of labor demand, and what a shift does to a market wage. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The data, all illustrative numbers built for the course (not real data): with 0 to 6 workers in a fixed kitchen the bakery bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day, so the marginal product of the 1st to 6th worker is 10, 15, 20, 15, 10, and 5 loaves. It takes the price of bread and the wage as given. "Revenue minus the wage bill" means bread revenue minus the wages paid, leaving other costs aside.
PROBLEM P1: In the course's illustrative bakery, bread sells for 4 dollars a loaf, and the bakery bakes 25 loaves with 2 workers and 45 loaves with 3 workers. What is the value of the marginal product of the 3rd worker, in dollars a day?
PROBLEM P2: In the same illustrative bakery, bread sells for 4 dollars a loaf and the daily wage is 50 dollars; the bakery bakes 0, 10, 25, 45, 60, 70, and 75 loaves a day with 0 to 6 workers. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it hires?
PROBLEM P3: In the same illustrative bakery, bread still sells for 4 dollars a loaf, but the daily wage falls to 30 dollars. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it now hires?
PROBLEM P4: In the same illustrative bakery, the daily wage is 50 dollars, but the price of bread rises to 6 dollars a loaf. Using the hiring rule, what is bread revenue minus the wage bill, in dollars a day, at the number of workers it now hires?
After the four answers, I must briefly interpret each one: for P1, what the value means and why loaves must be turned into dollars before comparing them with a wage; for P2, how many workers the bakery hires, why the hiring rule stops there, and why the 1st worker's low value does not mean hiring no one; for P3, how many workers it now hires and whether the change is a movement along labor demand or a shift of it; for P4, how many workers it now hires, which way labor demand shifts and why, and what happens to the market wage and employment for bakers in a town where many bakeries see the same rise in bread prices. I must then write a 3-5 sentence message to a friend who manages a smoothie bar and says "Our newest hire makes fewer smoothies an hour than anyone else, so hiring her was a mistake," explaining the hiring rule in everyday words, saying why a worker who adds less can still be worth hiring, and naming one limit. I must explain technical terms in everyday words. The message does not need to decide whether my friend should keep her, and you must not take a side on that. This week stays with an employer that takes the wage as given: do not bring in employers that set wages, and never invent a real wage, a market wage, or a number employed for a whole market.

SCORING CRITERIA: Score only evidence I supply: correct computations from the data (40 points), economic reasoning and interpretation (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct value of the 3rd worker's marginal product, revenue minus the wage bill at a 50-dollar wage, revenue minus the wage bill at a 30-dollar wage, or revenue minus the wage bill at 6 dollars a loaf = 2; the right values and operation with only an arithmetic slip = 1; a missing result or the wrong values or operation = 0. Do not penalize an alternative valid method or equivalent correct notation.
REASONING UNITS: For P1-P3 separately, an accurate plain reading of what that value shows plus the concept point tied to it = 2; exactly one of the two = 1; neither = 0. For P1, comparing loaves with the wage does not count. For P2, stopping at zero workers because the 1st worker adds less than the wage does not count. For P3, calling the wage change a shift of labor demand does not count. For P4, BOTH an explanation that the higher price of bread raises every worker's value so labor demand shifts right, with the market wage and employment rising in a town where many bakeries are affected, AND a final message that explains the hiring rule in everyday words, says why a worker who adds less can still be worth hiring, and names a limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to economics, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my reply. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word reply is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early. Never state a real price, wage, or other real-world statistic, and never invent data for me.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to my friend AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised bakery report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised bakery report with all four answers, their brief interpretations, and your message to your friend — written, or recorded as audio or video with a transcript, or as a labelled sketch that describes the two value-of-the-marginal-product lines and the wage lines in words with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

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.

Equivalent route (no AI required)

This route assesses the same Week 13 skills — turning a worker's extra output into dollars, applying the hiring rule on the falling part of the schedule, telling a movement along labor demand from a shift of it, reading what a shift does to a market wage, and explaining the hiring rule to someone new to economics — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to your friend. Then audit your own first draft against the attached scoring criteria, criterion by criterion, and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised bakery report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

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

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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