Hiring by the Margin: One More Worker?
Should a pizza shop hire a third worker? Compare what each extra worker adds against what they cost, and the decision becomes arithmetic.
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What this means
The marginal rule is one sentence, and it works for eating, studying, and running a business. As long as the additional benefit of doing more is larger than the additional cost, do more. The moment the additional cost is larger than the additional benefit, do less.
Businesses run this rule when they decide how many people to employ. The additional benefit of a worker is marginal revenue, meaning the extra money coming in because that person is there. The additional cost is what the business pays them, which for an hourly job is the wage.
Take a pizza shop where every worker is paid twenty dollars an hour. With one worker, the shop brings in one hundred dollars of revenue per hour. Add a second and total revenue rises to one hundred forty. Add a third and total revenue rises to one hundred fifty.
Read those as totals, then convert them to marginal amounts, because totals hide the decision. The first worker adds one hundred dollars. The second adds forty, since one hundred forty minus one hundred is forty. The third adds only ten, since one hundred fifty minus one hundred forty is ten.
Now compare each against the twenty dollar wage. The first worker brings in one hundred and costs twenty, so hire. The second brings in forty and costs twenty, so hire, because forty is greater than twenty. The third brings in ten and costs twenty, so do not hire, because ten is less than twenty. The right answer is two workers.
Check it with profit if you want proof. One worker leaves eighty dollars after wages. Two workers leave one hundred. Three workers leave ninety. Two is the best, which is exactly what the marginal comparison told you without having to compute every profit.
Why did each worker add less than the one before? The shop has one kitchen, one oven, and one counter. A second person splits the work sensibly. A third starts waiting for the oven and reaching around people. That pattern has a name: diminishing marginal returns.
Why it matters
This is the same rule you use on yourself. Should you pick up another shift, join another club, or study another hour? Not maybe. Compare what that additional hour gives you against what that additional hour costs you, and the answer stops being a mood and starts being a decision.
It also explains something that looks unfair from the outside. When a business will not hire another person, the reason is usually not stinginess. It is that the next worker would not add more than they cost, given the space and equipment the business already has. This is also why an employer who buys a second oven may suddenly be able to hire that third worker profitably. The worker did not change. What the worker had to work with did.
Real-world example
Watch a busy fast food counter during a lunch rush and then again at three in the afternoon. Same store, same equipment, different number of people on shift. During the rush, another worker on the register clearly adds sales, because customers are standing in line and some would leave without being served. At three, an extra worker would mostly stand around, adding almost no revenue while still earning a wage. That is why schedules are built around rushes, and it is a marginal decision being made hour by hour.
Try it
- Build a table with five columns: Number of workers, Total revenue per hour, Marginal revenue of that worker, Marginal cost of that worker, and Hire or not.
- Fill in the totals given: one worker produces $100 per hour, two workers produce $140 per hour, and three workers produce $150 per hour. Every worker is paid $20 per hour.
- Calculate the marginal revenue column yourself by subtracting each total from the one before it. Do not copy the totals into this column. You should get $100, then $40, then $10.
- Write $20 in the marginal cost column for all three rows, since each worker earns the same wage.
- Go row by row and decide hire or not by comparing only that row's two numbers. Write out the comparison in words, for example "the third worker adds $10 and costs $20, so no."
- State your answer and defend it in one sentence: how many workers should this shop hire?
- Verify with profit. Add a column for total revenue minus total wages. One worker: $100 minus $20. Two workers: $140 minus $40. Three workers: $150 minus $60. Confirm that the largest profit sits at the same number of workers your marginal comparison chose.
- Change the wage to $8 per hour and redo the decision. The marginal revenues do not change, only the wage. How many workers now, and why did the answer move?
- Change the wage to $50 per hour instead and redo it again. Then answer the question that matters: what does this tell you about how a rise in wages affects hiring, and what would happen to your answers if the shop bought a second oven so the third worker no longer had to wait?
Teacher note
The mistake to expect in step 3 is comparing the totals to the wage instead of the marginal amounts. A student who compares $150 to $20 concludes the third worker is obviously worth it and hires everyone in sight. Catch this early by asking what the third worker specifically added, and make them point at the subtraction. Requiring the comparison to be written in words in step 5 makes this error visible instead of buried in a table.
The second confusion is over the second worker. Some students see revenue growth slowing from $100 to $40 and read the slowdown itself as a reason to stop. Slowing is not the test. Forty dollars is still greater than the twenty dollar wage, so that worker is still worth hiring, and the shop earns more with two than with one. Step 7 settles the argument, because a student who wants to stop at one worker has to explain why $80 of profit beats $100.
Steps 8 and 9 are where the concept generalizes, so do not cut them for time. At a wage of $8 the third worker becomes worth hiring, since $10 is greater than $8, and profit does peak at three workers. At a wage of $50 only the first worker clears the bar. Students who work all three wages usually reach the generalization on their own, which lands far better than being told it.
A student has this concept when they can state the rule without the pizza shop attached, and when they can explain why the answer is two rather than three by naming the third worker's specific marginal revenue rather than by saying three is too many.
Check yourself
One worker generates $100 per hour in revenue and two workers generate $140 per hour. What is the marginal revenue of the second worker?
With a wage of $20 per hour, and totals of $100 for one worker, $140 for two, and $150 for three, how many workers should the shop hire?
Why does each additional worker at the pizza shop add less revenue than the one before?
Suppose the wage falls to $8 per hour while the revenue totals stay at $100, $140, and $150. What happens to the hiring decision?
Do more while the next step adds more than it costs, and stop when it does not, which is why a business hires the worker who adds forty dollars and turns down the one who adds ten.