Total, average and marginal product

Detail

1. The setting: one input changes, the others stay fixed

• A production function shows the most output a firm can get from a given set of inputs, such as labour (L) and capital (K).
• This section studies the short run. In the short run only one input (usually labour) can change. The other inputs stay fixed.

• In Table 3.2 below, capital is fixed at K = 4. Only labour changes.

• The Class 8 chapter (Factors of Production) gives the base idea. Output comes from combining land, labour, physical capital and human capital, and technology decides how well they combine.

2. Total product (TP)

• Definition: the link between a variable input (an input the firm can change, like labour) and output, when all other inputs are held constant.
• NCERT's other names for it are total return to the variable input and total physical product of the variable input.
• Written as TP_L, meaning total product of labour.
• Example: at K = 4, 3 workers produce 40 units, so TP at L = 3 is 40.

3. Average product (AP)

• Definition: output for each unit of the variable input.
• Formula: AP_L = TP_L / L
• Worked example (Table 3.2): at L = 4, TP = 50, so AP_L = 50 / 4 = 12.5 units per worker.
• NCERT also calls AP the "average return".
• Real-world version: "labour productivity" in official data is basically AP at the level of the whole economy, meaning output divided by labour input.
• RBI's India KLEMS database (K = capital, L = labour, E = energy, M = materials, S = services; report dated 8 July 2024) measures labour productivity and total factor productivity (output growth that inputs alone cannot explain) for 27 industries covering the whole economy. The data runs from 1980-81 to 2022-23 [5].
• India KLEMS measures labour input as number of persons employed, adjusted by a labour-quality index based on education. OECD and EU KLEMS use output per hour worked instead [5][6].
• So India's "output per worker" is AP_L with persons as the unit, not hours. This matters when you compare India with other countries.
• KLEMS provisional estimates put employment at 64.33 crore in 2023-24, up from 47.5 crore in 2017-18 [7]. Productivity (AP) rises only if output grows faster than this labour input.

4. Marginal product (MP)

• Definition: the change in output when one more unit of an input is used, with all other inputs held constant.
• Formula: MP_L = ΔTP_L / ΔL = (TP at L units) − (TP at L − 1 units)

• Δ (delta) means "change in".

• Worked example: TP at L = 3 is 40 and TP at L = 2 is 24. So MP of the 3rd worker = 40 − 24 = 16.

• Britannica gives the same meaning: the extra output from adding one unit of an input (say labour) to the existing mix of inputs [2].
• MP is undefined at zero input. To find MP at L = 0 you would need TP at L = −1, and an input cannot be negative.
• NCERT also calls MP the "marginal return".

5. How TP, AP and MP connect

• TP = sum of all MPs up to that level of input.

• Check at L = 6: 10 + 14 + 16 + 10 + 6 + 1 = 57 = TP.

• AP = average of all MPs up to that level.

• Check at L = 3: (10 + 14 + 16) / 3 = 40 / 3 = 13.33 = AP.

• Why this works:

• TP is built by adding one worker's MP at a time.
• AP is TP ÷ L, so it is simply the mean of those MPs.

6. Table 3.2 (capital fixed at K = 4)

L	TP	MP_L	AP_L
0	0	–	–
1	10	10	10
2	24	14	12
3	40	16	13.33
4	50	10	12.5
5	56	6	11.2
6	57	1	9.5

• How to read it:
• L = 1 to 3: MP rises (10 → 14 → 16). TP rises at an increasing rate.
• L = 3 to 6: MP falls (16 → 10 → 6 → 1). TP still rises, but at a decreasing rate.
• AP peaks at 13.33 at L = 3, then falls.

7. Shapes of the curves

• TP curve: slopes upward.
• First it rises at an increasing rate, while MP is rising.
• Then it rises at a decreasing rate, while MP is falling.

• Beyond NCERT: TP is at its maximum where MP = 0. TP falls once MP turns negative.

• MP and AP curves: both are inverse-U shaped. They rise, reach a peak, then fall.

• Why MP falls in the end: each extra worker has less fixed capital to work with. Britannica puts it this way: under diminishing marginal productivity, each additional worker contributes less than the worker before [4]. This is the core of the Law of Variable Proportions (LVP), which says that when one input keeps rising and the others stay fixed, MP rises at first and then falls.

8. Relationship between marginal and average product

• At the first unit, MP = AP (10 = 10), because TP = MP = AP when L = 1.
• When MP > AP, AP rises. The new unit adds more than the current average, so the average goes up.
• When MP < AP, AP falls. The new unit adds less than the average, so it pulls the average down.
• So MP cuts AP from above at AP's maximum.

• In the table, AP peaks at 13.33 at L = 3. The next MP (10, at L = 4) is below 13.33, so AP falls to 12.5.

• AP stays positive as long as TP is positive, because TP/L > 0. MP can become zero or negative.

• Common confusion: AP can keep rising even after MP has started to fall, as long as MP is still above AP.
• Everyday analogy: your average marks rise only if your new test score (the marginal) is above your current average.
• Average of 60 over 3 tests, 4th test = 80 → new average = (180 + 80) / 4 = 65. The average rises.
• 4th test = 40 → (180 + 40) / 4 = 55. The average falls.

9. Stages of production (standard theory, beyond NCERT)

Stage	Range	What happens	Would a sensible firm produce here?
I	Start → AP maximum	AP rising, MP > AP	No. Fixed capital is under-used, and adding labour raises output per worker
II	AP maximum → MP = 0	AP and MP falling, both positive	Yes, this is the economic region
III	After MP = 0	TP falling, MP negative	No. Extra workers reduce output

10. When MP is zero: disguised unemployment

• Disguised unemployment: more workers are engaged than needed, so removing some of them does not reduce output. In other words, MP_L ≈ 0.
• Classic development theory argued that heavy population pressure on land pushed the MP of farm labour down to zero or close to zero in traditional agriculture [3].

• The joint family shared the farm's TP among all members, so everyone got some income even with near-zero MP [3].

• Caveat: Britannica notes it is doubtful that MP is really zero even in India or Pakistan. All available labour is needed at peak seasons such as harvest, so much of it is better described as seasonal unemployment [3].

• Link to this section: on such farms, AP stays positive (everyone gets a share) even when MP is about zero. This is exactly the AP > 0, MP ≈ 0 case from point 8.

11. NCERT drills (worked)

• Ex. 22, TP = 0, 15, 35, 50, 40, 48 (L = 0 to 5)
• MP = TP(L) − TP(L − 1) = 15, 20, 15, −10, 8
• AP = TP / L = 15/1, 35/2, 50/3, 40/4, 48/5 = 15, 17.5, 16.67, 10, 9.6
• Check: sum of MPs = 15 + 20 + 15 − 10 + 8 = 48 = TP at L = 5 ✓

• A negative MP followed by a positive MP is an odd pattern made up for the textbook. It does not follow the LVP, because under the LVP MP does not turn positive again once it has gone negative.

• Ex. 23, AP = 2, 3, 4, 4.25, 4, 3.5. Use TP = AP × L:

• TP = 2×1, 3×2, 4×3, 4.25×4, 4×5, 3.5×6 = 2, 6, 12, 17, 20, 21
• MP = 2, 4, 6, 5, 3, 1

• Check: AP peaks at 4.25 (L = 4). The next MP (3) is below it, so AP falls ✓

• Ex. 24, MP = 3, 5, 7, 5, 3, 1. Add the MPs one by one to get TP:

• TP = 3, 8, 15, 20, 23, 24
• AP = TP / L = 3, 4, 5, 5, 4.6, 4
• Check: at L = 4, MP (5) = AP (5), so AP is flat at its peak, then falls ✓

Prelims Hooks

• MP_L = TP(L) − TP(L − 1). AP_L = TP_L / L. TP = ΣMP. AP = average of the MPs.
• MP is undefined at zero input, because inputs cannot be negative.
• At L = 1, TP = AP = MP.
• MP cuts AP from above at AP's maximum. Trap: MP does not cut AP at MP's maximum.
• TP is at its maximum when MP = 0. TP falls when MP < 0.
• AP can never be negative while TP > 0. MP can be zero or negative.
• TP rises at a decreasing rate when MP is falling but still positive. Trap: falling MP does not mean falling TP.
• NCERT's other names: TP = total return / total physical product; AP = average return; MP = marginal return.
• India KLEMS is published by the RBI. It covers 27 industries, 1980-81 to 2022-23 (report of 8 July 2024), and measures labour input in persons, not hours [5][6].
• Disguised unemployment means the MP of labour is zero or close to zero [3].

Mains Points

• Productivity is AP, jobs are about MP. India's employment rose from 47.5 crore (2017-18) to 64.33 crore (2023-24) [7].
• Output per worker (AP) rises only if new workers add more than the current average (MP > AP).

• So job growth in low-MP sectors can pull average productivity down, even while total output rises.

• Structural transformation argument (GS-III, employment):

• Farm labour has a low MP, close to zero where there is disguised unemployment [3].
• Moving these workers to manufacturing and services does little to farm output.
• It adds more in the new sectors, so national TP rises.

• Caveat: peak-season labour needs [3] mean the move must fit the crop calendar.

• Measurement matters for policy:

• India measures labour productivity per person. OECD and EU KLEMS measure it per hour worked [5][6].
• In India, many workers are underemployed (working fewer hours than they want) or in informal jobs, so per-person AP understates productivity per hour.

• Be careful when comparing India's productivity with other countries.

• Diminishing MP and the case for investment:

• With capital fixed, each extra worker adds less output [4].
• More capital, skills and technology shift the whole TP curve up and raise MP at every level of labour.
• This supports capital expenditure, skilling missions and technology adoption over simply adding more workers.