Business Economics · Theory of Production and Cost

Total, Average and Marginal Product: Relationship and Numericals

Q: What is the relationship between AP and MP?

When MP is above AP, AP rises. When MP is below AP, AP falls. The MP curve cuts the AP curve at the maximum point of AP.

Q: How do I calculate marginal product from a table?

Subtract the previous row's TP from the current row's TP when input rises by one unit. If input changes by more than one unit, divide the change in TP by the change in input.

Q: Can MP be negative?

Yes. If adding more of the variable input reduces total output, MP is negative and TP falls. This happens when the fixed factor is overcrowded.

Q: Why does AP never become zero before MP does?

MP falls first and cuts AP at its peak. AP keeps falling afterwards but stays positive as long as TP is positive. MP can turn zero and negative while AP is still positive.

Updated 1 October 2026 · Fact-checked

Total product (TP) is the full output from given inputs. Average product (AP) is TP ÷ units of the variable input. Marginal product (MP) is the extra TP from one more unit of that input. To solve table questions, compute MP as the change in TP, AP as TP ÷ units, then compare.

Understand Total, Average and Marginal Product

Production uses inputs such as labour, land and capital. In the short run, at least one input is fixed, say machines or land. You vary only one input, usually labour. The three product concepts measure what happens to output as you add more of that variable input.

Total product (TP) is the total quantity of output produced with a given amount of the variable input. If 5 workers make 60 units, TP is 60.

Average product (AP) is output per unit of the variable input. It tells you how productive each worker is on average. Marginal product (MP) is the addition to TP when you employ one more unit of the variable input. It tells you what the last worker added.

The three are linked. TP is the running total of all MPs. AP is the average of all the units so far. As long as MP is above AP, each new worker pulls the average up, so AP rises. When MP is below AP, AP falls. So MP cuts AP at AP's maximum point. This is the same logic as a cricket batting average: a score above your average raises it, a score below lowers it.

TP rises as long as MP is positive. TP is at its maximum when MP is zero. If MP turns negative, TP falls. In the usual short-run pattern, MP first rises, then falls because of diminishing returns. AP also rises, reaches a peak, then falls, but MP falls first. This pattern is the base of the Law of Variable Proportions.

Key formulas to remember

Total product: TP = AP × L; L is the number of units of the variable input. Also TP = sum of all MPs up to that unit.
Average product: AP = TP ÷ L; Divide TP at that level by the units of the variable input at that level.
Marginal product: MP = ΔTP ÷ ΔL = TPn − TPn−1; When input rises by exactly one unit, MP is simply the difference between successive TP values.
TP as sum of MP: TPn = MP1 + MP2 + … + MPn; Holds when TP is zero at zero input and input rises one unit at a time.
AP-MP rule: MP > AP → AP rises; MP = AP → AP at maximum; MP < AP → AP falls; MP curve cuts AP curve from above at AP's highest point.
TP-MP rule: MP > 0 → TP rises; MP = 0 → TP maximum; MP < 0 → TP falls; TP rises at an increasing rate while MP rises, and at a decreasing rate while MP falls but stays positive.

How to solve Total, Average and Marginal Product questions

Use this order for any table or relationship question. It keeps your arithmetic clean and stops sign errors.

1Read what is given: TP, AP or MP, and the units of the variable input. Note whether input rises by 1 unit each row.
2If TP is given, find MP by subtracting the previous TP from the current TP. The first MP equals the first TP when TP at zero input is 0.
3Find AP by dividing TP by the number of units of the input in that row.
4If AP is given, find TP by multiplying AP by units. Then find MP from the TP difference.
5If MP is given, find TP by adding MPs cumulatively.
6Compare MP with AP row by row to see whether AP is rising, at maximum or falling.
7Check where MP is zero or negative to locate maximum TP.
8Match your result with the option. Recheck one row by a second method before marking.

Quickest way: Quick checks for MCQs

When to use it: Use when the table is short and options are close in value. Saves time and avoids full table calculation.

Ask only for the row the question needs. Do not fill the whole table.
For MP, subtract two TP values. For AP, divide one TP by its input.
Use the shortcut: MP of the nth unit = TPn − TPn−1. Never divide for MP when input rises by 1.
For theory MCQs, remember the one line: MP cuts AP at AP's maximum; MP is zero at TP's maximum.
If AP is at maximum, say MP equals AP. If AP is rising, say MP is above AP.
Eliminate options where AP is negative or where MP is zero while TP is still rising. These cannot be right.
If a numerical looks long, check the last digits of your answer against the options first.

Common mistakes in Total, Average and Marginal Product

Dividing TP by input to get MP.
AP and MP look similar, and both use TP.
Fix: MP is a difference, not a ratio. MP = change in TP ÷ change in input. AP is the ratio.
Saying MP equals AP when TP is maximum.
Mixing up two different turning points.
Fix: MP = 0 at maximum TP. MP = AP at maximum AP. These are different points.
Thinking AP falls as soon as MP starts falling.
Assuming both curves turn together.
Fix: MP falls first. AP keeps rising as long as MP is still above AP. AP only falls once MP drops below it.
Using the wrong input change when units jump by more than 1.
Students automatically subtract TP values without checking the input column.
Fix: Divide the change in TP by the change in input. If input goes from 2 to 4 and TP rises by 20, MP per unit is 10.
Assuming TP falls when MP falls.
Confusing the fall of MP with a fall of TP.
Fix: TP falls only when MP is negative. If MP is falling but positive, TP still rises, at a decreasing rate.
Computing AP at zero input.
Filling every row mechanically.
Fix: AP is undefined at zero units of input because you cannot divide by zero. Start from the first unit.

Worked examples

Example 1

A firm's total product with labour is: 1 worker = 10, 2 workers = 24, 3 workers = 36, 4 workers = 44. What is the marginal product of the 3rd worker?
(a) 8
(b) 12
(c) 14
(d) 36

Show the solution

Input rises by 1 unit each row, so MP = TP3 − TP2.
TP3 = 36 and TP2 = 24.
MP = 36 − 24 = 12.

Answer: (b) 12

Example 2

For a firm, TP at 5 units of labour is 90 and MP of the 6th unit is 6. What is AP at 6 units of labour?
(a) 14
(b) 15
(c) 16
(d) 18

Show the solution

TP6 = TP5 + MP6 = 90 + 6 = 96.
AP6 = TP6 ÷ 6 = 96 ÷ 6 = 16.
Check: AP5 = 90 ÷ 5 = 18. MP6 = 6 is below AP, so AP falls from 18 to 16. This is consistent.

Answer: (c) 16

Example 3

When marginal product is greater than average product, which statement is correct?
(a) Average product is falling
(b) Average product is rising
(c) Total product is falling
(d) Average product is at its maximum

Show the solution

If the additional unit produces more than the current average, it pulls the average up.
So AP is rising when MP > AP.
AP falls when MP < AP, and is at maximum when MP = AP.
TP cannot fall here, since MP above AP means MP is positive.

Answer: (b) Average product is rising

Exam tips

Most questions ask for one cell of a table. Compute only that cell.
Learn the three rules: MP > AP means AP rises, MP = AP means AP maximum, MP < AP means AP falls.
Remember that MP is zero at maximum TP, and negative when TP falls.
Watch the input column. If it does not rise by 1 each row, divide by the change in input.
With 0.25 negative marking, skip a long table only if you cannot finish it quickly. Most take under a minute.

Practice questions from Theory of Production and Cost

Total, Average and Marginal Product: frequently asked questions

What is the relationship between AP and MP?

When MP is above AP, AP rises. When MP is below AP, AP falls. The MP curve cuts the AP curve at the maximum point of AP.

How do I calculate marginal product from a table?

Subtract the previous row's TP from the current row's TP when input rises by one unit. If input changes by more than one unit, divide the change in TP by the change in input.

Can MP be negative?

Yes. If adding more of the variable input reduces total output, MP is negative and TP falls. This happens when the fixed factor is overcrowded.

Why does AP never become zero before MP does?

MP falls first and cuts AP at its peak. AP keeps falling afterwards but stays positive as long as TP is positive. MP can turn zero and negative while AP is still positive.