Law of variable proportions and diminishing marginal product

Detail

Basic terms used in this section

• Production function: the link between inputs and output. It shows the most output a firm can get from given amounts of inputs, with a given technology.
• Short run: a period in which at least one input is fixed (for example land or a machine). Only the other input (usually labour) can change. The law of variable proportions belongs to the short run.
• Fixed factor: an input whose quantity cannot change in the short run (the farmer's 4 hectares).
• Variable factor: an input whose quantity can change (the number of workers).
• Total Product (TP): the total output produced with a given amount of the variable input.
• Marginal Product (MP): the extra output from one more unit of the variable input.

• Formula: MP_L = ΔTP / ΔL. For whole units, MP_L = TP_L − TP_(L−1).

• Average Product (AP): output per unit of the variable input.

• Formula: AP_L = TP / L.

Factor proportions: the mechanism

• Factor proportions are the ratio in which two inputs are combined, for example workers per hectare.
• If one factor is fixed and the other is increased, this ratio must change. That is why the law is called "variable proportions".
• Why MP first rises:
• At first the fixed factor is under-used. There is too much land for too few workers.
• Each new worker makes the proportion more suitable.

• So each extra worker adds more output than the one before. MP rises.

• Why MP later falls:

• After a point the fixed factor gets crowded.
• Each extra worker has less land (or fewer machines) to work with.

• So each extra worker adds less than the one before. MP falls.

• Farmer with 4 hectares (Class 12):

• With 1 worker there is too much land for one person to cultivate.

• From the 4th worker onwards the land gets crowded, and MP falls from 16 to 10.

• Same idea in everyday terms: a farmer with a fixed number of acres cannot get the biggest crop with too few workers. Adding workers raises output up to a limit. Past that limit, output starts to fall because there are too many workers and not enough land [2].

Worked example: NCERT Table 3.2 (land fixed at 4 hectares)

Labour (L)	TP	MP = ΔTP	AP = TP/L
0	0	–	–
1	10	10	10
2	24	14	12
3	40	16 (highest MP)	13.33 (highest AP)
4	50	10	12.5
5	56	6	11.2
6	57	1	9.5

• How to read the table:
• L = 1 → 3: MP rises (10 → 14 → 16). This is increasing returns to a factor.
• L = 4 onwards: MP falls (16 → 10 → 6 → 1). This is diminishing marginal product.

• TP keeps rising up to L = 6 because MP is still positive. It rises more and more slowly.

• NCERT error: the text says TP rises "by 10" (L = 1→2) and "by 12" (L = 2→3). Table 3.2 gives 14 and 16. Go by the table.

• How MP, AP and TP relate (rules that are often tested):
• When MP > AP, AP rises. (L = 1 to 3: MP 14 and 16 are above AP 12 and 13.33.)
• When MP < AP, AP falls. (L = 4: MP 10 is below AP 12.5.)
• MP cuts AP at the highest point of AP.
• When MP is positive, TP rises. When MP = 0, TP is at its maximum. When MP < 0, TP falls.
• Both the MP and AP curves are inverted-U shaped.

Two names, two meanings

• NCERT uses the two names as synonyms (words with the same meaning). The fact-checked definitions separate them:
• Law of variable proportions (LVP): the full path of MP as the proportions change. MP first rises with employment, then falls after a certain level.

• Law of diminishing marginal product (LDMP): only the falling phase. After a certain level of employment, MP falls as more of the variable input is added to the fixed inputs.

• Simple rule: LDMP is one part of LVP. LVP is the whole story.

• Diminishing returns here means that MP falls, not that TP falls. TP can keep rising while MP falls (L = 4 to 6 in the table).
• Assumptions of the law:
• Technology is fixed. A better seed or a new machine would shift the whole TP curve up.
• At least one input is fixed. If all inputs change together, the topic becomes returns to scale, which is a long-run idea.
• Units of the variable input are identical (homogeneous). Every worker is equally skilled. So MP falls because of crowding, not because later workers are weaker.

Three stages (beyond NCERT; two conventions exist)

Standard convention	Range	Feature
Stage I	Origin → maximum AP	MP > AP; the fixed factor is under-used
Stage II	Maximum AP → MP = 0	AP and MP both falling, both positive. This is the rational zone of production
Stage III	MP < 0	TP falls; too much of the variable factor

• Why Stage II is the "rational zone" (the only range a sensible producer chooses):
• In Stage I AP is still rising. Adding workers raises output per worker, so a firm should not stop there.
• In Stage III MP is negative. An extra worker reduces output, so no firm would pay for that worker.

• So a firm chooses a point in Stage II. The exact point depends on wages and the output price.

• In Table 3.2: Stage I ends near L = 3 (highest AP, 13.33). Stage II runs from L = 4 onwards. MP never becomes 0 in the table, so Stage III is not reached.

• Older CBSE convention: the three phases are increasing, diminishing and negative returns to a factor. Here the first phase ends at maximum MP, not maximum AP.
• In Table 3.2 both points happen to fall at L = 3. In general they differ: MP peaks before AP does.

• State which convention you are using in answers.

• Causes of the rising phase:

• The fixed factor is indivisible: it cannot be split into smaller parts (a tractor cannot be halved). It gives its full benefit only when enough workers use it.

• More workers allow specialisation (division of labour). Each worker does one task and does it better.

• Causes of the falling phase:

• Over-crowding of the fixed factor.

• Factors are imperfect substitutes (one input cannot fully replace another). Extra labour cannot make up for missing land.

• History:

• Turgot first stated diminishing returns on land.
• Ricardo's theory of rent rests on it. As farming spreads to worse land, or more work goes onto the same land, extra output falls. The better land then earns rent.
• Malthus's population argument also rests on it. Food output meets diminishing returns while population keeps growing.

Disguised unemployment link

• Disguised unemployment: people who look employed but add nothing to output. Their MP is zero.
• When too many family members work a fixed plot, the MP of labour is zero (or near zero). Taking some workers away leaves output unchanged.
• Worked example:
• 5 family members work 2 acres and produce 20 quintals of wheat.
• One member leaves for a city job. The other 4 still produce 20 quintals.

• The 5th worker's MP = 20 − 20 = 0. That person was disguisedly unemployed.

• Stage link: this is the Stage II/III boundary (MP = 0), where TP is at its maximum.

• Lewis (1954) surplus-labour model:
• Farm workers with zero MP can move into industry.
• Farm output does not fall.
• Industry gets cheap labour, and the economy grows.

• (Cross-refer employment-informal-sector and growth-theories-business-cycles.)

• India's data:

• According to PLFS, more than 45% of India's workforce is in agriculture. The rest: 11.4% in manufacturing, 28.9% in services and 13.0% in construction. The total workforce is about 56.5 crore (2022-23) [3].
• The share of agriculture in the workforce was 45.8% (2023). The Economic Survey assumes it will slowly fall to one-fourth by 2047 [3].
• Agriculture produced 17.7% of GVA at current prices in FY24. Industry produced 27.6% and services 54.7% [4]. (Scaffold: "about 46% of workers but about 16–18% of GVA", PLFS 2023-24 / NSO.)
• Agriculture and allied sectors grew at an average of about 5% a year (FY17–FY23) [5].

• What this means: about 46% of workers produce under one-fifth of output. So output per farm worker is low, which is a sign of disguised unemployment.

• The policy response: move workers out of farming. India needs to create about 78.5 lakh non-farm jobs every year until 2030 to absorb a growing workforce and the workers leaving agriculture [3].

Prelims Hooks

• LVP is a short-run law: at least one input is fixed. Returns to scale is a long-run idea in which all inputs change.
• MP = ΔTP/ΔL; AP = TP/L. MP cuts AP at the highest point of AP.
• TP is at its maximum when MP = 0. TP falls only when MP is negative, not when MP is merely falling.
• Diminishing returns ≠ falling TP. In the falling-MP phase, TP still rises, but at a slower rate.
• Rational zone = Stage II (from maximum AP to MP = 0). There, both AP and MP are falling but positive.
• Convention trap: in the standard convention Stage I ends at maximum AP. In the older CBSE convention it ends at maximum MP.
• Assumptions: fixed technology, at least one fixed input, and homogeneous (identical) units of the variable input.
• Disguised unemployment = MP of labour zero. This is linked to the Lewis (1954) surplus-labour model.
• Turgot first stated diminishing returns. Ricardo (rent) and Malthus (population) built on it.
• Agriculture's share of GVA at current prices was 17.7% in FY24, against more than 45% of the workforce (PLFS) [4][3].

Mains Points

• Structural transformation (the shift of workers from farming to industry and services):
• With about 46% of workers on farms but only 17.7% of GVA (FY24) [3][4], many farm workers have near-zero MP.
• Moving them into non-farm jobs raises national output without lowering farm output. This is the Lewis argument.

• Hence the Economic Survey's target of about 78.5 lakh non-farm jobs every year until 2030 [3].

• Land fragmentation and diminishing returns:

• Small plots with large families push farms towards the Stage II/III boundary.

• Ways to raise the MP of labour: consolidate landholdings, move workers into agro-processing and rural non-farm jobs, and raise capital per worker (irrigation, farm machines).

• Technology offsets diminishing returns:

• The law assumes fixed technology. HYV seeds, irrigation and the Green Revolution shifted the whole TP curve up.

• This is why Malthus's forecast of food shortage failed. Farm R&D and extension services are therefore GS-III priorities.

• Caveat for answers:

• Zero MP is an extreme case. In peak seasons (sowing, harvest) farm labour is often scarce.
• So "disguised unemployment" is better written as seasonal underemployment with low MP, not strictly zero MP all year.