Law of Variable Proportions

1) Meaning and scope

The Law of Variable Proportions (LVP) explains the behavior of output when:

• one input is variable (e.g., labour L), and
• at least one input is fixed (e.g., capital K),
• technology is given (no change in technique).

In short-run production:

We study how output changes as we increase L while K remains fixed.

Alternate name: “Law of Diminishing Returns” (more precisely, diminishing marginal returns to the variable input).

2) The key idea in one sentence

As we keep adding more and more units of a variable input to a fixed input, marginal product will:

• initially rise (often),
• then fall (diminishing returns),
• and may eventually become negative.

This is not a moral statement; it is a technological/organizational regularity due to fixed factor constraint.

3) Assumptions (very exam-relevant)

LVP holds under these standard assumptions:

1. Technology is constant (no innovation during analysis).
2. At least one factor is fixed (short run).
3. Units of the variable factor are homogeneous (identical).
4. Inputs are divisible (can add small increments, conceptually).
5. Production is measured over a relevant time period where fixed factor truly cannot adjust.

CUET trap: If technology changes or fixed factor changes, observed output changes may not reflect LVP.

4) Total, marginal, and average product in LVP

Let:

• TP = Total Product $Q$
• MP = Marginal Product $\Delta Q/\Delta L$
• AP = Average Product $Q/L$

4.1 Typical numerical pattern (illustrative)

As L increases from low levels:

• TP increases at increasing rate → MP rising Then:
• TP increases at decreasing rate → MP falling but still positive Finally:
• TP may fall → MP negative

This pattern is the basis of the three “stages of production.”

5) Three stages of production (must-know classification)

Stage I: Increasing returns to the variable factor

• TP increases at an increasing rate.
• MP rises and MP > AP.
• AP rises.

Why MP rises initially?

• better division of labour and specialization,
• fixed capital underutilized at first; adding labour uses it more effectively.

Why Stage I is not optimal for firms? Because AP is still rising—adding more labour increases efficiency (output per unit labour). A firm would not stop where it can still raise average productivity easily.

Stage II: Diminishing returns to the variable factor (Rational stage)

• TP increases at a decreasing rate.
• MP falls but remains positive: $MP>0$.
• AP falls.
• Stage II starts at the maximum of AP (where MP = AP) and ends where MP = 0.