1. The production function
A production function is the technical relationship between physical inputs and the maximum physical output, given technology: Q = f(L, K).
- Fixed factor: cannot be changed in the period (plant, heavy machines).
- Variable factor: can be changed (labour, raw materials).
| Input at an imagined Bhagalpur silk shed | Short run | Why |
|---|---|---|
| Looms | Fixed | Take months to buy and install |
| Shed | Fixed | Cannot be enlarged quickly |
| Weavers | Variable | Can be hired within days |
| Silk yarn | Variable | Bought as output changes |
Key terms
- Production function
The technical relation between physical inputs and maximum physical output, for given technology.
- Fixed factor
An input whose quantity cannot be changed in the period considered.
2. Short run and long run
- Short run: at least one factor fixed; output changes by changing the variable factor, so the factor proportion changes. This gives returns to a factor.
- Long run: all factors variable; inputs can change in the same proportion. This gives returns to scale.
| Short-run production function | Long-run production function | |
|---|---|---|
| Factors | At least one fixed | All variable |
| Factor proportion | Changes | Can stay the same |
| Law that applies | Returns to a factor (variable proportions) | Returns to scale |
| Example | More moulders, same kiln | A second kiln with its own crew |
Key terms
- Short run
A period in which at least one factor of production is fixed.
- Long run
A period long enough for all factors of production to be varied.
3. Total, average and marginal product
- TP = total output of the variable factor = ΣMP.
- AP = TP ÷ L.
- MP = TPn − TPn−1 (= ΔTP ÷ ΔL).
Example: an imagined Nagpur packing shed packs 51 crates with 3 workers and 68 with 4, so the fourth worker's MP is 17 and AP with 4 workers is 17.
| Workers | TP (crates) | MP | AP |
|---|---|---|---|
| 1 | 12 | 12 | 12 |
| 2 | 30 | 18 | 15 |
| 3 | 51 | 21 | 17 |
| 4 | 68 | 17 | 17 |
| 5 | 80 | 12 | 16 |
| 6 | 84 | 4 | 14 |
| Concept | Meaning | Formula |
|---|---|---|
| Total product (TP) | Total output of all units of the variable factor | ΣMP |
| Average product (AP) | Output per unit of the variable factor | TP ÷ L |
| Marginal product (MP) | Addition to TP from one more unit | TPn − TPn−1 |
| Labourers | MP (rows) | TP = running total |
|---|---|---|
| 1 | 6 | 6 |
| 2 | 10 | 16 |
| 3 | 13 | 29 |
| 4 | 9 | 38 |
| 5 | 5 | 43 |
| 6 | 2 | 45 |
| 7 | 0 | 45 |
| 8 | -3 | 42 |
Key terms
- Average product
Output per unit of the variable factor, TP ÷ L.
- Marginal product
The change in total product from one more unit of the variable factor.
4. Relationships among TP, AP and MP
TP and MP: MP rising → TP rises at an increasing rate (to the point of inflexion); MP falling but positive → TP rises at a diminishing rate; MP = 0 → TP maximum; MP negative → TP falls.
AP and MP: MP > AP → AP rises; MP = AP → AP maximum (MP cuts AP at its peak); MP < AP → AP falls. MP can be negative; AP stays positive while TP is positive.
| Marginal product | Total product |
|---|---|
| Rising | Rises at an increasing rate |
| Maximum | Point of inflexion |
| Falling but positive | Rises at a diminishing rate |
| Zero | Maximum |
| Negative | Falls |
| Marginal product compared with average product | Average product |
|---|---|
| MP > AP | Rises |
| MP = AP | At its maximum |
| MP < AP | Falls |
| MP negative | Still positive while TP is positive |
Key terms
- Point of inflexion
The point on the TP curve where it changes from rising at an increasing rate to rising at a diminishing rate; MP is maximum there.
5. The Law of Variable Proportions and its stages
Statement: as more units of a variable factor are combined with a fixed factor, MP may rise at first but eventually diminishes and can become negative.
Assumptions: constant technology; at least one fixed factor; homogeneous units of the variable factor; short period.
Stages (convention used here): I — increasing returns, to the maximum of AP; II — diminishing returns, to the maximum of TP (MP = 0); III — negative returns. Some books end Stage I at the point of inflexion.
Causes: indivisibility of the fixed factor and division of labour; scarcity of the fixed factor and imperfect substitution; overcrowding.
Rational producer: operates in Stage II, where both factors have positive marginal products; the exact point depends on prices.
| Stage | Total product | Marginal product | Average product | Ends where |
|---|---|---|---|---|
| I: increasing returns | Rises (first at an increasing rate) | Rises, then falls; above AP | Rises | AP is maximum (MP = AP) |
| II: diminishing returns | Rises at a diminishing rate | Falls, stays positive | Falls | TP is maximum (MP = 0) |
| III: negative returns | Falls | Negative | Falls | — |
| Assumption | Why it matters |
|---|---|
| Technology unchanged | Better methods would shift the whole TP curve |
| At least one factor fixed | The law is about changing factor proportions |
| Units of the variable factor homogeneous | Diminishing MP is not due to weaker workers |
| Short period | The fixed factor cannot be increased |
| Returns | Main causes |
|---|---|
| Increasing | Fuller use of an indivisible fixed factor; division of labour |
| Diminishing | Fixed factor becomes scarce relative to the variable factor; factors are imperfect substitutes |
| Negative | Overcrowding and overuse of the fixed factor |
Key terms
- Law of Variable Proportions
In the short run, the marginal product of a variable factor added to a fixed factor eventually diminishes.
- Negative returns
The stage in which an extra unit of the variable factor reduces total product.
6. Returns to scale (meaning only)
Returns to scale: the response of output when all inputs change in the same proportion in the long run.
- Increasing: output rises more than in proportion.
- Constant: in the same proportion.
- Diminishing: less than in proportion.
Returns to scale differ from returns to a factor (short run, one input varied).
| Factory (imagined) | Output before | After doubling all inputs | Rise in output | Returns to scale |
|---|---|---|---|---|
| Kolhapur sugar mill | 400 | 960 | 140 per cent | Increasing returns to scale |
| Ankleshwar paint plant | 250 | 500 | 100 per cent | Constant returns to scale |
| Ludhiana cycle-parts unit | 300 | 480 | 60 per cent | Diminishing returns to scale |
| Returns to a factor | Returns to scale | |
|---|---|---|
| Period | Short run | Long run |
| Inputs changed | One, others fixed | All, in the same proportion |
| Factor proportion | Changes | Unchanged |
| Types | Increasing, diminishing, negative | Increasing, constant, diminishing |
Key terms
- Returns to scale
How output changes when all inputs are changed in the same proportion in the long run.
Exam tips
Common mistakes
- Writing that TP falls when MP falls; TP falls only when MP is negative.
- Drawing MP cutting AP anywhere other than AP's highest point.
- Saying AP becomes negative; only MP can.
- Explaining diminishing returns by "less efficient workers"; the law assumes homogeneous units.
- Mixing returns to a factor (short run, one input) with returns to scale (long run, all inputs).
How marks are usually awarded
- 1 mark: one correct option or term.
- 2 marks: two points, or a calculation with its formula.
- 3 marks: three explained points, or a schedule with an interpretation.
- 5 marks: parts in order, with a described diagram and reasons.