Law of Variable Proportions - Stages of Operation and the Decision to Produce

Why not Stage III?

• In Stage III, marginal product (MP) of the variable factor is negative and total product falls when more units of the variable factor are used.​
• This means extra units of the variable factor reduce total output. Even if the variable factor were free, using more of it would be “economic nonsense” because the firm would get less output, not more. So Stage III is a region of economic absurdity.

Why not Stage I?

• In Stage I, average product (AP) and marginal product (MP) of the variable factor are rising and AP keeps increasing throughout this stage.​
• Stopping in Stage I means the firm is not using the fixed factor fully; by adding more units of the variable factor, it could still increase AP, reduce average cost, and increase profit. So a rational producer will not stop where profits can still be increased by using more variable input.

Why Stage II is rational

• In Stage II, TP is still rising, but at a diminishing rate; MP and AP are both positive but falling.​
• In this stage, the fixed factor is neither under‑utilized (as in Stage I) nor over‑utilized (as in Stage III). This is the “economic region” where the producer makes rational decisions about how many units of the variable factor to employ.
• Therefore, a rational producer will always choose to operate somewhere in Stage II. The exact point within Stage II depends on the prices of factor inputs and the price of the output.

1] Under‑utilization of fixed factor (reason for Stage I – increasing returns)

• In the beginning, the fixed factor (e.g., a machine or plot of land) is under‑utilized.
• Adding more units of the variable factor (like labour) improves the use of the fixed factor, so TP rises at an increasing rate and MP rises.​

2] Fixed factors of production (reason for diminishing returns)

• In the short run, some factors remain fixed. As more units of a variable factor are added to a fixed factor, after a point, the fixed factor becomes “crowded”.
• Because the fixed factor cannot increase in the same proportion, additional units of the variable factor add less and less to output, so MP starts declining.​

3] Optimum use of fixed factor

• There is an optimum combination of fixed and variable factors where the fixed factor is used most efficiently.
• For example, a machine (fixed factor) may work best with 4 workers; if a 5th worker is added, total output may rise only a little and MP falls. After the optimum point, the fixed–variable ratio becomes defective and MP diminishes.​

4] Imperfect substitutability of factors

• If factors could perfectly substitute for each other, the firm could keep increasing all factors in the right combination to maintain the same returns.
• In reality, factors are imperfect substitutes. After the fixed factor is optimally used, adding more of the variable factor without a matching increase in fixed factor leads to a non‑ideal ratio and falling MP.

• The law of variable proportions is a short‑run law and has universal application wherever at least one factor is fixed and others are variable.​
• Fixed factors are not only land; machines, plant, buildings, certain raw materials can also be fixed in the short run.

Agriculture

• Land is usually the fixed factor, while labour and capital (seeds, fertilizer, tools) are variable.
• When more and more labour and capital are applied to the same piece of land, TP at first rises faster, then more slowly, and finally may decline as the land becomes overcrowded. Hence the law applies strongly to agriculture.​​

Industries / manufacturing

• In manufacturing, plant and machinery may be fixed in the short run, while labour and some materials are variable.
• Initially, adding more labour to given machinery increases efficiency (increasing returns), but after a point, extra workers get in each other’s way, equipment is overused, and MP starts to diminish. Thus the law applies to industries as well.

1) Factory example (machines and workers)

One machine (fixed) and workers (variable):

• 1–2 workers: machine under‑used, output per worker rises (Stage I).
• 3–5 workers: machine used well, extra workers add less extra output than before (Stage II).
• 6+ workers: crowded around the machine, they obstruct each other, extra worker reduces total output (Stage III).​​

2) Farm example (land and labour)

One field (fixed land) and labour + capital:

• First few workers + inputs: better use of land, rapid rise in output (Stage I).
• More workers: less extra output from each additional worker, output rises slowly (Stage II).
• Too many workers: they step on each other’s work, output may even fall (Stage III).​​

• Law of variable proportions is a short‑run law explaining how output changes when one input varies and others are fixed.​
• There are three stages: Stage I (increasing returns), Stage II (diminishing returns), Stage III (negative returns).​
• Stages I and III are “non‑economic” regions; Stage II is the only rational region for a producer.
• A rational producer always operates in Stage II; the exact point depends on input and output prices.​
• The law applies to agriculture, industry, and any production where at least one factor is fixed in the short run.