Week 13 · Model Workshop

Week 13 Model Workshop: How Many Workers Should the Greenhouse Hire?

Principles of Microeconomics Free sample edition

Part 1 — The Big Picture

This week you learned how a firm behaves as a buyer of labor: it wants workers because buyers want what they make; 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 lower wage moves it along its labor demand curve, and a higher price for its product shifts the curve. In this workshop you build a small greenhouse's hiring table in a spreadsheet, test three cases, decide how many workers it hires in each, label each change as a movement or a shift, say what a shift would do to a market wage, and then catch a chatbot's slips on the same greenhouse. The habit you build, putting workers in dollars before comparing them with a wage, carries into every factor market the course studies.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: In each case, how many workers should the greenhouse hire, and is the change from one case to the next a movement along its labor demand curve or a shift of it?

Workshop data: the illustrative greenhouse

Source: An illustrative greenhouse constructed for this workshop, not real data: a small greenhouse that sells trays of seedlings to garden centers at a price it takes as given and hires workers at a daily wage it also takes as given. With 0 to 6 workers it fills 0, 8, 24, 36, 44, 50, and 54 trays a day; the three cases to test are 5 dollars a tray with a 45-dollar wage, 5 dollars a tray with a 25-dollar wage, and 8 dollars a tray with a 45-dollar wage.

Rows: 7 staffing levels, 0 to 6 workers, in the hiring table (the decision table has 3 rows, one per case)
Columns: workers and trays filled a day, from which marginal product and the value of the marginal product at each tray price are built
Cases to test: 5 dollars a tray with a 45-dollar wage, 5 dollars a tray with a 25-dollar wage, and 8 dollars a tray with a 45-dollar wage

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 Workers, Trays, Marginal product, Value of the marginal product, and Revenue minus wages in columns A to E. Type the workers 0 to 6 in A2 to A8 and the trays 0, 8, 24, 36, 44, 50, and 54 in B2 to B8. Tool: Desmos (free) or Google Sheets (free). Check: Seven rows of workers and trays, starting from 0 trays with no workers.
Type the tray price, 5, in J1 and the wage, 45, in J2. In C3 type =B3-B2 for marginal product, in D3 type =$J$1*C3 for the value of the marginal product, and in E2 type =$J$1*B2-$J$2*A2 for revenue minus wages. Copy C3 and D3 down to row 8 and E2 down to row 8. Tool: Desmos (free) or Google Sheets (free). Check: Marginal product rises and then falls, the value column has the same shape, and the revenue-minus-wages column peaks at one row.
Read down column D, starting where marginal product begins to fall, and find the last worker whose value is at least the wage in J2. Check that the same row has the largest number in column E. Tool: Desmos (free) or Google Sheets (free). Check: The hiring rule and the largest revenue minus wages point to the same number of workers.
Change J2 to 25 and repeat step 3. Then set J2 back to 45, change J1 to 8, and repeat step 3 again. Note the number of workers each time and which cell you changed. Tool: Desmos (free) or Google Sheets (free). Check: The number of workers changes in both cases, once because the wage changed and once because the tray price changed.
Optional picture: open Desmos and enter the value of the marginal product at 5 dollars and at 8 dollars as two tables of points, with workers on the x-axis and dollars a day on the y-axis, and add flat lines such as y = 45 and y = 25 for the wages. Tool: Desmos (free) or Google Sheets (free). Check: Each set of value points rises and then falls, and each flat wage line crosses the falling side between two worker counts.
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 subtraction or multiplication beside its result. Describe the picture in words instead of drawing it: what is on each axis, where each set of value points rises and falls, and where each flat wage line crosses the falling side. 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 greenhouse's hiring table first; every decision in this workshop compares a wage with one of these value columns.

Student scaffold table 1
Workers	Trays a day	Marginal product (trays)	Value of the marginal product at 5 dollars (dollars a day)	Value of the marginal product at 8 dollars (dollars a day)
0	0	none	none	none
1	8
2	24
3	36
4	44
5	50
6	54

Test each case: choose the workers with the hiring rule, compute revenue minus wages, and label the change from the first case as a movement or a shift.

Student scaffold table 2
Case	Workers hired	Tray revenue (dollars)	Wage bill (dollars)	Revenue minus wages (dollars)	Movement or shift from case 1
5 dollars a tray, 45-dollar wage					not applicable
5 dollars a tray, 25-dollar wage
8 dollars a tray, 45-dollar wage

Part 5 — Analysis Questions

Complete the hiring table. With which worker do diminishing marginal returns set in? Say in one plain sentence what the value of the marginal product of the 3rd worker means for the greenhouse at 5 dollars a tray.
Complete the decision table. For each case, show the comparison of each worker's value with the wage that picks the number of workers, then compute tray revenue, the wage bill, and revenue minus wages. Say in words what each result means for the greenhouse.
In the first case the 1st worker adds less than the 45-dollar wage. Explain why the greenhouse still hires workers, using revenue minus wages at 1 worker and at the number it does hire, and say which part of the schedule the hiring rule is read on.
Label the change from case 1 to case 2 and from case 1 to case 3 as a movement along the greenhouse's labor demand curve or a shift of it, with a reason for each. Then suppose many greenhouses in a region see the tray price rise to 8 dollars: describe what happens to labor demand in the region's market for greenhouse workers, and to the market wage and employment, in words.
Name one way this classroom model differs from a real greenhouse, such as workers who differ in skill, wages that include benefits, or a crop that takes weeks to grow, and say how it could change one of your answers.
Choose one reflection option and answer it: (a) describe a job you know where a new worker adds less than earlier ones, in words, and say why the employer might still hire that worker; or (b) describe a product whose price rose and made its makers hire more people, in words, and say which curve that change shifted. Both options carry the same weight.

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 labor markets in an introductory microeconomics course. In an illustrative example, not real data, a small greenhouse sells trays of seedlings to garden centers at a price it takes as given, and it hires workers at a daily wage it also takes as given. With 0 to 6 workers it fills 0, 8, 24, 36, 44, 50, and 54 trays a day. For each case, how many workers should it hire, and what is tray revenue minus the wage bill: (1) 5 dollars a tray and a 45-dollar wage; (2) 5 dollars a tray and a 25-dollar wage; (3) 8 dollars a tray and a 45-dollar wage? Then answer: when the wage falls from 45 to 25, does the greenhouse's demand for labor shift? When the tray price rises from 5 to 8, is that a change in the quantity of labor demanded? Should the greenhouse compare each worker's average output with the wage? What is the elasticity of the greenhouse's labor demand, and is it elastic or inelastic? Should the government require the greenhouse to pay more? Should the greenhouse grow only seedlings because its workers grow them faster than a rival's? Is the money left after wages the greenhouse's economic profit? Does the greenhouse set its wage where marginal revenue equals marginal cost, or where price equals marginal cost? If the town taxes each tray, who really pays? Is a legal minimum wage a price ceiling or a price floor? Does the greenhouse's water runoff impose a cost on neighbors that its hiring misses?

Test the response for these likely failures:

Chatbots often multiply the price by each worker count's average output, trays per worker, instead of by the marginal product, or say the greenhouse should hire until the average value equals the wage.
Chatbots sometimes say a fall in the wage from 45 to 25 dollars shifts the greenhouse's labor demand curve right.
Chatbots sometimes call the rise in the tray price from 5 to 8 dollars a change in the quantity of labor demanded.
Chatbots often add that the government should require the greenhouse to pay more, presenting a value judgment as a model result.
Chatbots sometimes read the steps of the labor demand schedule as an elasticity.
Chatbots sometimes label the greenhouse's labor demand elastic or inelastic without any calculation.
Chatbots sometimes say the greenhouse should grow only seedlings because its workers grow them faster than a rival's.
Chatbots often call tray revenue minus the wage bill the greenhouse's economic profit.
Chatbots sometimes say the greenhouse picks its workers where price equals marginal cost, borrowing the output rule.
Chatbots often say the greenhouse bears a per-tray tax in full because it hands the tax to the town.
Chatbots sometimes call a legal minimum wage a price ceiling.
Chatbots sometimes add a cost for water runoff on neighbors to the greenhouse's hiring decision.

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 13. 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 2 (explain how demand and supply determine a market's equilibrium price and quantity, and predict how a shift in demand or supply changes them), 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 greenhouse, printed here in full: "At 5 dollars a tray and a 45-dollar wage the greenhouse should hire no one, because the 1st worker adds only 40 dollars. It should compare each worker count's average output times the price with the wage, so at 3 workers it compares 5 × 12 = 60 with 45. When the wage falls to 25, its labor demand curve shifts right, and when the tray price rises to 8, that is only a change in the quantity of labor demanded. The money left after wages is its economic profit, and it hires where price equals marginal cost. The government should require it to pay more. Its labor demand is inelastic because the steps are steep, and it should grow only seedlings because its workers grow them fastest. A tray tax is paid entirely by the greenhouse, a minimum wage is a price ceiling, and it should count its water runoff in its hiring." Mark every slip, name the failure each shows, correct each one by hand against your own tables and Chapter 13, 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 greenhouse: two completed tables (the hiring table and the three-case decision table), written answers to six analysis questions, and a critique of a chatbot's answers about the same greenhouse, 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 value points and the wage lines 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
Hiring table built	Marginal product and the value of the marginal product at both tray prices are computed for 1 to 6 workers with each step shown, and the worker where diminishing returns set in is named with what the 3rd worker's value means.	The table is mostly complete, but one or two values are wrong, or diminishing returns are not located or explained.	No hiring table, or values computed from average output instead of marginal product.
Hiring decisions in three cases	In each case the workers are chosen by comparing each worker's value with the wage on the falling part of the schedule, tray revenue and the wage bill are shown, revenue minus wages is computed, and each result is read in a plain sentence.	Most cases are worked, but one hiring choice or one revenue-minus-wages figure is wrong, trays are compared with dollars once, or the plain sentences are missing.	No hiring choices, or trays compared with the wage throughout.
Movement, shift, and the market wage	The wage change is labelled a movement along labor demand and the tray-price change a shift right, each with its reason, and the regional answer names labor demand shifting right with the market wage and employment rising, with no figures invented.	One label is right and the other is missing or reversed, or the regional answer gives a direction for only one of the wage and employment.	No labels, or the wage change called a shift and the price change a movement, or no regional answer.
Rising-part reasoning	The answer compares revenue minus wages at 1 worker with the amount at the number hired and explains that the rule is read where marginal product falls, so a low first value does not mean hiring no one.	The answer says the greenhouse still hires but gives only one of the comparison or the falling-part reason.	No answer, or the greenhouse told to hire no one because the 1st worker adds less than the wage.
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; either route earns this band equally.	No critique on either route, or the chatbot's reply is pasted without any check.

Quality Gate

Every marginal product is a difference of two tray counts and every value is a marginal product times the tray price, shown by formula or by hand, never from memory or a chatbot.
Each hiring choice compares the value of the marginal product with the wage on the falling part of the schedule, never average output and never loaves or trays against dollars.
Every revenue-minus-wages figure subtracts the wage bill from tray revenue, and the best row matches the hiring rule.
The wage change is labelled a movement along labor demand and the tray-price change a shift of labor demand, each with its reason.
The regional market answer names labor demand as the curve that shifts and gives the direction of the market wage and employment, with no market wage or number employed invented.
Every judgment about what the greenhouse or a government ought to do is labelled normative.
No real-world wage, price, statistic, or study is invented anywhere in the submission.
The critique quotes the chatbot, or the printed flawed analysis, and corrects each slip by hand.

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