Production and marginal product
Learning goals
After this page, you can:
- Compute the marginal product of each worker from an output table, and find the worker with whom diminishing marginal returns begin.
- Tell the short run (at least one input is fixed) from the long run (everything can change), and classify a business decision as one or the other.
- Explain in one plain paragraph how diminishing marginal returns (one input fixed) differ from returns to scale (all inputs grow together).
The idea
A pie shop has one oven and one small kitchen. The first baker does everything alone: rolls the dough, fills the pies, watches the oven. A second baker helps a lot. Now one person rolls while the other fills. A third baker helps even more: one rolls, one fills, one runs the oven. But by the sixth baker, people are waiting for the oven and stepping around each other. Each baker costs the same wage. The sixth one simply adds fewer pies.
That story is the whole page. Let’s give its parts names.
The production function. A production function is a table (or a rule) that says how much output you get from a given set of inputs. Our pie shop’s table, with one oven:
| Bakers | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Pies per day | 0 | 12 | 28 | 48 | 64 | 76 | 84 | 88 |
Marginal product: what one more worker adds. The marginal product (MP) of a worker is the extra output that worker brings. You get it by subtraction: output with that worker minus output without them. The 3rd baker’s MP is 48 − 28 = 20 pies. The 7th baker’s MP is 88 − 84 = 4 pies.
Do not mix this up with the average product: total output divided by the number of workers. With 3 bakers, the average is 48 ÷ 3 = 16 pies per baker. The average tells you how the team does as a whole. The marginal tells you what the next hire does. Hiring decisions run on the marginal.
Why MP rises at first. With one or two bakers, the oven sits idle part of the day and each person does many different jobs. Adding a person lets the team split the work. Each baker gets faster at one task. So the 2nd baker adds more than the 1st, and the 3rd adds more than the 2nd.
Why MP falls later: diminishing marginal returns. The oven does not grow when you hire. It is a fixed input: you cannot change it this month. Every new baker shares the same oven and the same counter. Sooner or later, each extra baker adds less than the one before. This is called diminishing marginal returns.
Two traps to avoid:
- Diminishing returns begin with the first worker whose MP is smaller than the previous worker’s MP. In our table the MPs are 12, 16, 20, 16, 12, 8, 4. The 3rd baker adds 20, the 4th adds only 16. So diminishing returns begin with baker 4.
- Diminishing returns do not mean total output falls. Here total output keeps rising, all the way to 88 pies. It only rises more slowly. Output would fall only if a worker got in the way so badly that their MP turned negative.
Is one more worker worth it? Compare what the worker adds with what the worker costs. If a baker costs $160 a day and each pie sells for $20, a baker who adds 4 pies brings in $80 of pies for $160 of wages. Total output still rises, but the shop loses money on that hire.
Short run and long run. Economists split decisions by one question: what can I change this month?
- In the short run, at least one input is fixed. The pie shop can call in more bakers or add a shift, but it is stuck with one oven and one kitchen.
- In the long run, every input can change. The shop can move to a bigger kitchen, buy a second oven, or open a new location.
The short run and long run are not fixed lengths of time. A food truck may reach its long run in a few weeks. A steel mill or an airline may need years.
Returns to scale: when everything grows together. In the long run, you can ask a different question: if I double every input, what happens to output?
- Output more than doubles → increasing returns to scale. A bigger shop lets people specialize even more.
- Output exactly doubles → constant returns to scale.
- Output less than doubles → decreasing returns to scale. Coordination gets harder.
Suppose a two-oven kitchen makes 108 pies with 6 bakers. The one-oven shop made 48 pies with 3 bakers. Twice the inputs, 2.25 times the pies: increasing returns to scale at that size.
The mix-up to avoid. Diminishing marginal returns and returns to scale sound alike, but they answer different questions. Diminishing returns: one input grows while another stays fixed (more bakers, same oven). It is a short-run idea. Returns to scale: all inputs grow together (more bakers and more ovens). It is a long-run idea. A shop can have diminishing returns to bakers and increasing returns to scale at the same time.
MP of worker n = q(n) − q(n − 1) · Average product = q ÷ L
Diminishing returns begin with the first worker whose MP is smaller than the previous worker’s MP — not where total output falls.
Double every input: output more than doubles = increasing, exactly doubles = constant, less than doubles = decreasing returns to scale.
Try it
The table below the charts is the one-oven pie shop. You can type over the pies column.
- Move the slider from 0 to 7 bakers. Watch the bars. Which baker adds the most pies? With which baker do the bars start to shrink?
- Find the baker whose bar is the shortest. Does total output fall when that baker joins?
- Turn on the second oven. Where do diminishing returns begin now? Read the “double everything” box: is the shop showing increasing or decreasing returns to scale?
- Type a new number for 5 bakers (for example, 70). Does the start of diminishing returns move?
Worked example
Problem. The one-oven pie shop makes 0, 12, 28, 48, 64, 76, 84 and 88 pies a day with 0 to 7 bakers. A baker costs $160 a day and a pie sells for $20. (1) Find each baker’s marginal product. (2) With which baker do diminishing returns begin? (3) Is the 7th baker worth hiring? (4) A second oven is available in the long run. Two ovens with 6 bakers make 108 pies, and two ovens with 8 bakers make 124 pies. What kind of returns to scale does the shop show?
Step 1. Marginal products. Subtract each row from the one below it: 12 − 0 = 12, 28 − 12 = 16, 48 − 28 = 20, 64 − 48 = 16, 76 − 64 = 12, 84 − 76 = 8, 88 − 84 = 4.
Step 2. Where diminishing returns begin. MP peaks with baker 3 (20 pies). Baker 4 adds only 16. So diminishing returns begin with baker 4, at 48 → 64 pies. Total output still rises all the way to 88. Diminishing returns are about the extra output, not the total.
Step 3. The 7th baker. Baker 7 adds 4 pies. 4 × $20 = $80 of pies, for a $160 wage. The shop loses $80 a day on that hire. Do not hire baker 7.
Step 4. Returns to scale. Double everything from (1 oven, 3 bakers): two ovens and 6 bakers make 108 pies. 108 ÷ 48 = 2.25: more than double, so increasing returns to scale at that size. Double from (1 oven, 4 bakers): two ovens and 8 bakers make 124 pies. 124 ÷ 64 = 1.94: a bit less than double, so slightly decreasing returns to scale at that bigger size.
Check yourself
A pie shop with one oven makes 28 pies a day with 2 bakers and 48 pies a day with 3 bakers. What is the marginal product of the 3rd baker?
MP of worker n = output with n workers − output with n − 1 workers.
The one-oven pie shop’s bakers have marginal products of 12, 16, 20, 16, 12, 8 and 4 pies, and total output never falls. With which baker do diminishing marginal returns begin?
Diminishing returns begin with the first worker whose MP is smaller than the previous worker’s.
Which of these is a long-run decision for the pie shop?
Short run: at least one input (the oven, the building) is fixed. Long run: everything can change.
The pie shop adds a 6th baker to its one oven, and output rises by only 8 pies. The owner calls this ‘decreasing returns to scale.’ What is the correct name?
One input fixed → diminishing marginal returns; all inputs grow together → returns to scale.
A baker costs $160 a day and a pie sells for $20. The 7th baker would add 4 pies a day. Is the 7th baker worth hiring?
Hire while the extra output is worth more than the extra wage.
Video
Video coming soon.