Production Function — Part 2: The Law of Variable Proportions and Returns to Scale: visual lesson, ISC Class 12 Economics

Lesson

Law of Variable Proportions and Returns to Scale

Part 2 — what happens to output as more of one input is added to a fixed input, and what happens when all inputs grow together.

In this lesson you will

State the Law of Variable Proportions with its assumptions
Explain the three stages with a diagram and their causes, and why a rational producer chooses Stage II
Explain the meaning of returns to scale and distinguish it from returns to a factor

Part 2 at a glance

Concept

The Law of Variable Proportions

As more units of a variable factor are combined with a fixed factor, the marginal product of the variable factor may rise at first but eventually diminishes, and may become negative.

It is also called the law of returns to a factor.

Imagined, smooth production function drawn from TP = 9L² − L³.

Concept

Assumptions of the law

Technology is unchanged.
At least one factor is fixed.
Units of the variable factor are homogeneous (equally efficient).
The period is short.

Table of the assumptions of the Law of Variable Proportions: unchanged technology, at least one fixed factor, homogeneous units of the variable factor and a short period, with why each matters
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

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