Week 13 — How Many Bakers, and What Moves the Number? — Traditional alternative (no AI)

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

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 week you learned how a firm behaves as a buyer of labor: it wants workers because buyers want its product, so labor demand is a derived demand; it turns each worker's extra output into dollars, the value of the marginal product of labor; it hires while that value is at least the wage, reading the rule where marginal product is falling; a change in the wage moves it along its labor demand curve, while a change in the price of its product shifts that curve. In Week 9 you built the bakery's production schedule, and in Weeks 3 and 4 you learned to tell a movement along a curve from a shift of it. In this assignment you work four short problems, interpret each one, and explain the hiring rule 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 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.

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

Deliverables

Submit a single bakery report containing:

• the four answers, each with the arithmetic shown and a brief interpretation as the task describes;
• your message to your friend, explaining the hiring rule in everyday words, saying why a worker who adds less can still be worth hiring, and naming one limit; and
• a one-line restatement of the values 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 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. 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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