Theory of Production
Production is the transformation of inputs (land, labour, capital, materials) into output. The production function Q = f(L, K, ...) is a technical relationship. In the short run, at least one factor is fixed — the Law of Variable Proportions operates with three stages (increasing, diminishing, negative returns). In the long run, all factors vary and the Laws of Returns to Scale (increasing, constant, decreasing) apply.
In this chapter
Meaning of Production
Production is the process of transforming inputs into output — converting raw materials, labour, capital, and other factors into goods and services that satisfy human wants. Example from Nepal: a sugar mill in Birgunj takes sugarcane (raw material), machines (capital), workers (labour) and land, and produces sugar (output). Production creates form utility (changes the form of inputs), place utility (moves goods to where they are needed), and time utility (stores goods for future use).
Production Function
A production function is a technical relationship between inputs and the maximum output that can be produced from them, given the state of technology. It depends on land (Lb), labour (L), capital (K), raw materials (M), technology (T) and time (t). In the short run, at least one factor is fixed (usually capital) — written Q = f(L, K̄). In the long run, all factors are variable — written Q = f(L, K).
Production function (general → short run → long run)
Total, Average and Marginal Product
Total Product (TP) is the total output from a given combination of inputs. Average Product (AP) is output per unit of the variable factor: AP = TP/L. Marginal Product (MP) is the additional output from one more unit of the variable factor: MP = ΔTP/ΔL = TP_n − TP_{n−1}. Example: a Terai rice farmer adds more labour to fixed land — the first few workers raise TP fast, but eventually each extra worker adds less and less.
TP, AP and MP — definitions
TP, AP and MP schedule — adding labour to a fixed ropani of land
| Labour (L) | TP (kg) | AP = TP/L | MP = ΔTP/ΔL |
|---|---|---|---|
| 1 | 10 | 10.0 | 10 |
| 2 | 24 | 12.0 | 14 |
| 3 | 39 | 13.0 | 15 |
| 4 | 52 | 13.0 | 13 |
| 5 | 61 | 12.2 | 9 |
| 6 | 66 | 11.0 | 5 |
| 7 | 66 | 9.4 | 0 |
| 8 | 64 | 8.0 | −2 |
Relationship between TP, AP and MP (Four Key Rules)
- When MP rises, TP rises at an increasing rate (Stage I begins).
- When MP falls but is positive, TP rises at a decreasing rate (Stage II — the rational stage).
- When MP = 0, TP is maximum.
- When MP is negative, TP falls (Stage III — irrational).
- MP cuts AP at AP's maximum — when MP > AP, AP rises; when MP < AP, AP falls.
Law of Variable Proportions
- Increasing returns to factor
- Diminishing returns
- Negative returns. A rational producer operates in Stage II.
Three Stages Explained (with Terai rice farm example)
- Stage I — Increasing Returns: MP rises because fixed factor (land) is under-utilised. Adding more workers allows specialisation. Example: 1 → 3 workers in a 1-ropani field — TP rises fast (10 → 39 kg).
- Stage II — Diminishing Returns: MP falls but stays positive. The ideal stage — TP keeps rising but at a slower pace. Example: 4 → 7 workers — TP rises 52 → 66 kg, MP falls 13 → 0.
- Stage III — Negative Returns: MP turns negative. Too many workers on too little land cause crowding and inefficiency. Example: 8th worker reduces TP from 66 → 64 kg. A rational producer never operates here.
Why a Garment Factory in Kathmandu Should Not Over-Hire
A garment factory in Baluwatar has fixed machines (capital) but can hire workers (labour). Initially more workers means more output. But after some point — when there are not enough machines for everyone — workers wait, get in each other's way, and the marginal product falls. If they over-hire, MP becomes negative (Stage III): extra workers actually reduce total output. The manager must operate in Stage II where TP is rising and MP is positive.
In the long run all factors are variable. The laws of returns to scale describe how output changes when all inputs are changed in the same proportion. Increasing returns to scale: output rises by a larger proportion than inputs (e.g., doubling inputs triples output) — due to specialisation and economies of scale. Constant returns to scale: output rises in the same proportion (doubling inputs doubles output). Decreasing returns to scale: output rises by a smaller proportion (doubling inputs raises output by less than double) — due to management complexities.
Mathematical form of the three returns to scale (t > 1)
Practice Problem
From the following TP data of a garment factory in Kathmandu, calculate AP and MP for each level of labour. State which stage the firm is operating in at L=7. Labour (L): 1, 2, 3, 4, 5, 6, 7, 8 TP (units/day): 6, 14, 24, 32, 38, 42, 42, 40
Practice Problem
A Nepali tea-processing factory in Ilam doubles its inputs (labour and machines) and finds output rises from 100 kg/day to 250 kg/day. (a) Identify the returns to scale. (b) If a second doubling (inputs ×4 from original) raises output only to 360 kg/day, identify the new returns to scale and explain.
Quick Revision
- Production = transformation of inputs into output.
- Production function: Q = f(L, K, ...). Short run: Q = f(L, K̄); Long run: Q = f(L, K).
- TP = ΣMP = AP × L; AP = TP/L; MP = ΔTP/ΔL = TP_n − TP_{n−1}.
- MP > 0 → TP rising; MP = 0 → TP max; MP < 0 → TP falling.
- Law of Variable Proportions: 3 stages — Increasing, Diminishing, Negative returns.
- Rational producer operates in Stage II.
- Returns to scale: IRS, CRS, DRS (long run).