Introduction
In the theory of production, we study how output changes when the quantities of inputs (factors of production) are varied. In the short run, some factors are fixed and some are variable, and the behaviour of output is explained by the Law of Variable Proportions. In the long run, however, all factors become variable. The firm can change the size of its plant, scale of operation, and employ larger or smaller quantities of all inputs. The behaviour of output when all factors are increased in some proportion is analysed with the help of the Law of Returns to Scale.
In the B.Com (Semester I) syllabus of Panjab University, following Microeconomics by T.R. Jain & V.K. Ohri, the law of returns to scale is treated as a fundamental long-run production law and is usually explained with the help of a numerical table and isoquant diagrams.
Meaning and Definition of Returns to Scale
The term scale refers to the overall size of the firm or the level of operation, determined by the quantities of all factors used. Returns to scale describe how output changes when all inputs are increased in the same proportion.
The Law of Returns to Scale describes the behaviour of output when all inputs are increased in the same proportion. If, when all factors of production are increased by a certain percentage, output increases by a greater, equal, or smaller percentage, the firm is said to experience respectively increasing, constant or decreasing returns to scale.
Thus, while the law of variable proportions deals with the effect on output of changing one factor at a time (keeping others fixed), the law of returns to scale deals with the effect of changing all factors simultaneously and proportionally in the long run.
Assumptions of the Law of Returns to Scale
The standard assumptions under which the law operates are as follows:
- All factors are variable: The analysis is long-run in nature. The firm can change the scale of operations by varying all inputs together.
- Homogeneous factor units: Units of each factor (labour, capital, land, etc.) are identical in quality. Every additional unit added is of the same efficiency as previous units.
- Unchanged technology: The level of technology remains constant. Changes in output are due solely to changes in scale, not due to technical progress.
- Efficient organisation: The firm’s management is efficient and adjusts itself to the new scale of production without unnecessary wastage.
- Divisible inputs: Factors can be increased or decreased in small proportions to permit smooth changes in scale.
- Perfect competition: The firm is assumed to be operating under conditions of perfect competition in factor and product markets, so that external disturbances are minimal.
Illustrative Table Showing Returns to Scale
Consider a firm using two inputs: Labour (L) and Capital (K). In the long run, both L and K are varied in the same proportion. The resulting changes in output can be presented in a numerical schedule as follows (hypothetical figures for illustration, in the spirit of T.R. Jain & V.K. Ohri):
| Scale (Proportionate Change in L & K) |
Units of Labour (L) |
Units of Capital (K) |
Total Output (Q) |
Proportionate Change in Output |
Nature of Returns to Scale |
|---|---|---|---|---|---|
| Initial | 10 | 5 | 100 | – | Base situation |
| Double inputs | 20 | 10 | 230 | +130% output vs +100% inputs | Increasing Returns to Scale |
| Triple inputs | 30 | 15 | 300 | +200% output vs +200% inputs | Constant Returns to Scale |
| Quadruple inputs | 40 | 20 | 360 | +260% output vs +300% inputs | Decreasing Returns to Scale |
Interpretation of the table:
- When L and K are doubled (from 10 & 5 to 20 & 10), output increases from 100 to 230. Output has more than doubled → increasing returns to scale.
- When L and K are trebled (30 & 15), output rises to 300, exactly three times. Output increases in the same proportion as inputs → constant returns to scale.
- When L and K are quadrupled (40 & 20), output increases only to 360, less than four times. Output increases less than proportionately → decreasing returns to scale.
Diagrammatic Explanation using Isoquants
The law of returns to scale is conveniently explained with the help of isoquants. An isoquant is a curve showing different combinations of L and K that yield the same level of output. On a diagram with labour measured on the horizontal axis and capital on the vertical axis, higher isoquants represent higher levels of output.
Returns to scale are studied along a ray from the origin (also called an expansion path) where L and K are increased in the same proportion. The spacing of isoquants along this ray shows whether returns to scale are increasing, constant or decreasing.
Types of Returns to Scale
1. Increasing Returns to Scale (IRS)
When all inputs are increased in a given proportion and output increases by a greater proportion, the firm is said to experience increasing returns to scale.
- If inputs are doubled and output more than doubles → IRS.
- In the table above, going from (L=10, K=5, Q=100) to (L=20, K=10, Q=230) shows IRS.
- On the isoquant diagram, as we move along the expansion path, isoquants are closer together.
Reasons: Increasing returns to scale usually arise due to internal economies of scale such as better specialisation of labour and management, technical indivisibilities (larger machines being more efficient), economies in buying and selling, and improved use of by-products.
2. Constant Returns to Scale (CRS)
When all inputs are increased in a given proportion and output increases in exactly the same proportion, the firm experiences constant returns to scale.
- If inputs are trebled and output also becomes three times → CRS.
- In the table, moving from (L=10, K=5, Q=100) to (L=30, K=15, Q=300) illustrates CRS.
- On the isoquant diagram, isoquants are equally spaced along the expansion path.
At constant returns to scale, the firm is operating at a stage where internal economies have been largely exhausted and diseconomies have not yet set in. Many textbooks describe this as the “balanced” zone of long-run production.
3. Decreasing Returns to Scale (DRS)
When all inputs are increased in a given proportion and output increases by a smaller proportion, the firm faces decreasing returns to scale.
- If inputs are quadrupled but output increases less than four times → DRS.
- In the table, moving from (L=10, K=5, Q=100) to (L=40, K=20, Q=360) shows DRS.
- On the isoquant diagram, isoquants are farther apart along the expansion path.
Reasons: Decreasing returns to scale arise mainly due to internal diseconomies: difficulties of coordination and control in a very large organisation, overburdened management, communication delays, and possible labour–management problems. As scale becomes too large, these factors reduce the proportional increase in output.
Difference between Law of Variable Proportions and Law of Returns to Scale (Brief)
Since both laws relate to production, examiners often expect a brief comparison:
| Basis | Law of Variable Proportions | Law of Returns to Scale |
|---|---|---|
| Time Period | Short run — at least one factor is fixed. | Long run — all factors are variable. |
| Change in Inputs | Only one factor is varied, others kept constant. | All factors are varied in the same proportion. |
| Main Concept | Explains TP, MP, AP of a single variable factor. | Explains proportional changes in output when the scale changes. |
| Stages | Three stages: Increasing, Diminishing and Negative returns to a factor. | Three phases: Increasing, Constant and Decreasing returns to scale. |
| Practical Use | Guides optimum use of variable factor for a given plant size. | Guides decision on optimum size of plant or firm in the long run. |
Importance of the Law of Returns to Scale
The law of returns to scale is important both theoretically and practically:
By studying the pattern of returns to scale, a firm can identify the range over which increasing returns and then constant returns prevail, and avoid the region of decreasing returns. This helps in deciding the optimum size of the plant in the long run.
Returns to scale are closely related to the shape of the long-run average cost (LAC) curve. Increasing returns to scale are associated with falling LAC, constant returns with flat LAC, and decreasing returns with rising LAC. Thus, the law provides the theoretical foundation for long-run cost analysis.
Internal economies (technical, managerial, financial, marketing, etc.) and internal diseconomies are reflected in the pattern of returns to scale. The law translates these qualitative aspects into a clear quantitative relationship between inputs and output.
For economic planners and industrial policy-makers, understanding returns to scale is important in deciding whether an industry should be developed on a large scale (where increasing returns are significant) or on a more decentralised basis.
In Panjab University B.Com (Sem I) examinations, this question frequently appears in the form: “Explain the Law of Returns to Scale with the help of suitable table and diagrams.” A clear schedule, well-labelled isoquant diagrams, and a systematic explanation of IRS, CRS and DRS almost always fetch high marks.
Conclusion
To sum up, the Law of Returns to Scale explains how output responds when all factors of production are increased in the same proportion in the long run. Depending on whether output increases more than proportionately, in the same proportion, or less than proportionately, the firm experiences respectively increasing, constant or decreasing returns to scale. Graphically, this is reflected in the spacing of isoquants along the expansion path. The law, as presented in the prescribed text of T.R. Jain & V.K. Ohri for B.Com Semester I, provides a rigorous theoretical basis for understanding long-run production behaviour, economies and diseconomies of scale, and the shape of long-run cost curves, and is therefore of high examination importance.