Difficulty: Introductory | Prerequisites: Basic algebra, understanding of total product. Chapter 5 of Cabral's textbook.
This topic sits at the heart of production theory in introductory microeconomics. Before a firm can decide how much to produce or how many workers to hire, it needs to understand how output responds to changes in a single input, holding everything else fixed. The concepts of average product and marginal product give you that understanding. If you have covered total product curves and the idea of a production function, you are ready for this. If not, start with Chapter 5's opening sections on inputs and outputs.
When Kim adds more hours to her taco truck's day, total tacos sold rises but each extra hour adds fewer tacos than the last. Average sales per hour fall steadily, and marginal sales fall even faster. The total product curve is concave, which is the graphical signature of diminishing marginal returns.
Total product (TP)
The total quantity of output produced for a given level of a variable input (here, total tacos sold for a given number of hours open).
In simple terms, this is the raw number in the "Number of Tacos" column.
Average product (AP)
Total product divided by the quantity of the variable input: AP = TP / hours.
Think of it as: how many tacos does Kim sell per hour, on average, across all the hours she has been open?
Marginal product (MP)
The change in total product resulting from a one-unit increase in the variable input: MP = ΔTP / ΔHours.
In simple terms, this is the number of extra tacos Kim gets from opening for one more hour.
Diminishing marginal returns (diminishing marginal product)
The principle that, as successive units of a variable input are added (holding other inputs fixed), the marginal product of that input eventually declines.
Think of it as: the first hour is the most productive, and every hour after that adds less and less. Kim gets tired, foot traffic thins out, or both.
Concave function
A function whose graph curves downward (bows toward the x-axis). On a total product curve, concavity means the slope is positive but decreasing, which corresponds to positive but falling marginal product.
In simple terms, the curve rises quickly at first and then flattens out.
Average product at any hour = total tacos ÷ hours open.
At 1 hour: 18.0 / 1 = 18.0 tacos per hour.
At 5 hours: 42.7 / 5 = 8.54 tacos per hour.
Marginal product of an hour = change in total tacos when that hour is added.
Going from 0 to 1 hour: 18.0 - 0 = 18.0 tacos.
Going from 1 to 2 hours: 31.6 - 18.0 = 13.6 tacos.
Going from 9 to 10 hours: 46.1 - 46.1 = 0 tacos.
Hours | Total tacos | Average product (tacos/hr) | Marginal product (tacos) |
|---|---|---|---|
0 | 0 | 0 | 0 |
1 | 18.0 | 18.0 | 18.0 |
2 | 31.6 | 15.8 | 13.6 |
3 | 37.4 | 12.5 | 5.80 |
4 | 40.7 | 10.2 | 3.30 |
5 | 42.7 | 8.54 | 2.00 |
6 | 44.2 | 7.36 | 1.50 |
7 | 45.2 | 6.46 | 1.00 |
8 | 46.0 | 5.75 | 0.800 |
9 | 46.1 | 5.12 | 0.100 |
10 | 46.1 | 4.61 | 0 |
Marginal product falls continuously from 18.0 (hour 1) to 0 (hour 10).
Every additional hour adds fewer tacos than the one before.
This is diminishing marginal returns in action.
Both decline as hours increase, but marginal product falls faster.
Key rule: when MP < AP, AP is falling. Here MP drops below AP from the very first interval, so AP declines throughout.
Intuition: if the "extra" hour is less productive than the current average, it drags the average down.
Plotting total tacos (y) against hours (x) produces a concave curve.
The curve rises steeply at first, then flattens.
Concavity = the slope (which is marginal product) is positive but decreasing.
A linear curve would mean constant MP. A convex curve would mean increasing MP. Neither fits here.
The pattern reflects the law of diminishing marginal returns (sometimes called diminishing marginal product).
Holding other inputs constant (truck size, equipment, Kim's skills), adding more of one input (hours) eventually yields smaller and smaller increments to output.
This is not the same as diminishing marginal utility, which applies to consumption. The problem set is about production. The student answer in the source PDF uses the phrase "diminishing marginal utility" loosely; the precise term for a production context is diminishing marginal returns or diminishing marginal product.
AP = \frac{TP}{L}where TP = total product and L = quantity of the variable input (hours).
MP = \frac{\Delta TP}{\Delta L}where ΔTP is the change in total product and ΔL is the change in the input (here, always 1 hour).
Concavity check: if MP is positive but declining, the TP curve is concave. If MP were constant, TP would be linear. If MP were rising, TP would be convex.
Diminishing marginal returns is why restaurants stop adding wait staff after a point: the kitchen becomes the bottleneck, and extra servers just crowd each other. It is also why farms see falling yields per additional worker once land and equipment are fully utilised. Any business owner deciding "should I stay open another hour?" is weighing marginal revenue against marginal cost, and the answer depends on how quickly marginal product is falling.
Students often say "diminishing marginal utility" when they mean "diminishing marginal returns." Utility is about consumption (how much satisfaction you get from eating one more taco). Returns are about production (how much extra output you get from one more hour of work). In a production problem like this one, the correct term is diminishing marginal returns.
Students sometimes think diminishing marginal returns means total output is falling. It does not. Total output is still rising here (from 0 to 46.1 tacos); it is the rate of increase that is shrinking.
A common error is computing marginal product as total product divided by hours. That gives you average product, not marginal product. Marginal product is the change in total product from the previous level.
Some students assume that because marginal product is falling, the firm should stop producing. Whether to stop depends on comparing marginal revenue to marginal cost, not on marginal product alone.
⚠️ You will almost certainly be asked to compute AP and MP from a table. Know the formulas cold.
⚠️ Expect a question asking you to identify whether a total product curve is concave, convex, or linear, and to explain what that shape implies about marginal product.
⚠️ The relationship "when MP < AP, AP is falling" is a classic exam point. Be ready to explain the intuition (the batting-average analogy works well: if today's game is worse than your season average, your season average drops).
⚠️ Diminishing marginal returns is a short-run concept (at least one input is fixed). Do not confuse it with returns to scale, which is a long-run concept where all inputs change proportionally.
True or false: Marginal product is total product divided by the number of input units. (False. That is average product.)
Fill in the blank: When the total product curve is concave, marginal product is ______ . (Positive but declining.)
True or false: Diminishing marginal returns means total output is decreasing. (False. Total output can still be increasing; only the rate of increase is falling.)
Fill in the blank: If MP < AP, then AP is ______ . (Falling.)
True or false: The tenth hour of Kim's truck adds zero tacos, so total product at 10 hours equals total product at 9 hours. (True. Both are 46.1.)
Q: If Kim sells 40.7 tacos in 4 hours, what is her average product? Show your working.
A: AP = TP / L = 40.7 / 4 = 10.175, rounded to 10.2 tacos per hour.
Q: Kim's total product rises from 42.7 tacos (5 hours) to 44.2 tacos (6 hours). What is the marginal product of the sixth hour?
A: MP = ΔTP / ΔL = (44.2 - 42.7) / (6 - 5) = 1.5 tacos.
Q: Is the relationship between hours and total tacos linear, concave, or convex? Explain how you know from the marginal product data.
A: Concave. Marginal product is positive but declining throughout, which means the slope of the total product curve is falling. A graph of total tacos against hours rises steeply at first and then flattens.
Q: Explain, using the data in the table, why average product is falling at every hour.
A: Marginal product is below average product at every hour after the first. When the marginal unit adds less than the current average, it pulls the average down. Since MP < AP from hour 2 onward, AP falls continuously.
Q: A student writes that Kim's data illustrates "diminishing marginal utility." What is wrong with this statement, and what is the correct term?
A: Diminishing marginal utility describes consumption (each additional unit consumed gives less satisfaction). Kim's data describes production (each additional hour of work produces fewer additional tacos). The correct term is diminishing marginal returns, or equivalently, diminishing marginal product.
This connects directly to cost theory: marginal cost is the mirror image of marginal product. When MP is high, MC is low, and vice versa. You will see this when the course moves to cost curves in the next chapter.
The average-marginal relationship reappears throughout the course. The rule "when marginal is below average, average falls" applies to average cost, average revenue, and average product alike. Master it once here and it carries forward.
Diminishing marginal returns is a short-run phenomenon. When the course reaches long-run production and returns to scale (where all inputs change), the logic shifts. Keep the two distinct.
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