Production with one variable input: stages and diminishing returns
With one input fixed, adding more of a variable input eventually adds less and less output. This gives the three stages of production.
The production function
A production function shows the maximum output a firm can make from each combination of inputs, with given technology: Q = f(L, K), where L is labour and K is capital. In the short run, at least one input (such as land, buildings or machines) is fixed, so output can only be changed by using more of the variable input, usually labour. Three measures are used: total product (TP), the total output; average product (AP) = TP ÷ L; and marginal product (MP) = ΔTP ÷ ΔL, the extra output from one more worker.
Worked example: TP, AP and MP on a tea estate plot
A fixed plot of tea land is worked by 1 to 8 pluckers. Total product (kg of green leaf a day) is: 10, 30, 54, 72, 85, 90, 90, 84. Find MP and AP, and the stages of production.
- MP: 10, 30 − 10 = 20, 54 − 30 = 24, 72 − 54 = 18, 85 − 72 = 13, 90 − 85 = 5, 90 − 90 = 0, 84 − 90 = −6.
- AP: 10 ÷ 1 = 10, 30 ÷ 2 = 15, 54 ÷ 3 = 18, 72 ÷ 4 = 18, 85 ÷ 5 = 17, 90 ÷ 6 = 15, 90 ÷ 7 = 12.86, 84 ÷ 8 = 10.5.
- MP is highest (24) at the 3rd worker; diminishing marginal returns begin with the 4th worker.
- AP is highest (18) at 3-4 workers, where MP = AP = 18 for the 4th worker. Stage I ends here.
- TP is highest (90) when MP = 0 at the 7th worker. Stage II ends here.
- From the 8th worker MP is negative and TP falls: Stage III.
Stage I: up to 4 workers (AP rising). Stage II: 4 to 7 workers (AP falling, MP positive). Stage III: beyond 7 workers (MP negative). A rational estate hires within Stage II.
The three stages of production
| Stage | Range | What happens | Rational? |
|---|---|---|---|
| I: increasing returns to the variable input | From zero to maximum AP (MP = AP) | MP > AP, AP rising; the fixed input is under-used | No: adding workers raises output per worker |
| II: diminishing returns | From maximum AP to MP = 0 | AP and MP falling, MP still positive; TP rising to its peak | Yes: the firm operates here |
| III: negative returns | Beyond MP = 0 | MP negative, TP falling; too many workers for the fixed input | No: removing workers would raise output |
The law of diminishing returns
- Statement: when more and more units of a variable input are added to a fixed input, marginal product eventually falls.
- Assumptions: at least one input fixed, technology unchanged, units of the variable input are identical, short run.
- Reason: each extra worker has less of the fixed input (land, machines) to work with.
- Links between the curves: when MP > AP, AP rises; when MP = AP, AP is at its maximum; when MP = 0, TP is at its maximum; when MP < 0, TP falls.
- Diminishing returns in the short run cause marginal cost to rise, which is why short-run cost curves are U-shaped.
Applying it to a hiring decision
Using the tea plot above, suppose green leaf is worth Rs. 250 per kg and each plucker costs Rs. 1,500 a day (illustrative figures). How many pluckers should be hired?
- Value of the marginal product (MP × Rs. 250) of each worker: 2,500; 5,000; 6,000; 4,500; 3,250; 1,250; 0; −1,500.
- Hire a worker as long as the value of their marginal product is at least the wage of Rs. 1,500.
- Worker 5 adds Rs. 3,250 > Rs. 1,500: hire. Worker 6 adds Rs. 1,250 < Rs. 1,500: do not hire.
Hire 5 pluckers. This is inside Stage II, as theory predicts.
On a tea estate, the land and bushes are fixed in the short run. Adding pluckers raises green leaf output at first, but after a point each extra worker adds less, because there are only so many bushes to pluck. Managers of regional plantation companies must find the best number to hire.
Short answer: “State the law of diminishing returns.” When more units of a variable input are added to a fixed input, with technology unchanged, the marginal product of the variable input eventually falls.
Structured question: “Given a total product schedule, calculate AP and MP and identify the three stages of production.” AP = TP ÷ L, MP = ΔTP ÷ ΔL. Stage I ends at maximum AP (MP = AP), Stage II ends at MP = 0, Stage III has negative MP.
Essay: “Explain the law of diminishing returns and the three stages of production. Why does a rational firm operate in Stage II?” Define the production function, TP, AP and MP, state the law with a table and diagram, describe each stage, and explain why Stages I and III are irrational.
Stage II is the sweet spot: AP falling, MP still positive. Stage I = Increasing AP (keep hiring); Stage III = Idiotic (too many workers, MP below zero).