GRADE 11 ECONOMICS

Chapter 5: Theory of Production.

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Meaning of Production

Production refers to the transformation of inputs (resources or factors of production) into outputs (goods and services).

Example: Inputs like sugarcane (raw material), capital (machines), and labour (workers) are used to produce sugar.

Production Function

A production function shows the technical relationship between inputs (factors of production) and output, under a given technology.

Q = f(L, K)
where,
Q = Quantity of output
L = Labour
K = Capital

It shows how much output can be produced from different combinations of labour and capital.

Types of Production Function

Short-run Production Function

In the short run, the law of variable proportions studies the input–output relationship where only one factor of production is variable while others remain fixed.

Q = f(L, K̅)

Where labor (L) is variable factor and capital (K̅) is fixed factor.

Long-run Production Function

The input and output relationship in the long run is studied under the law of return to scale. It is also known as production function with two variable input.

Q = f(L, K)

Where labor (L) and capital (K) are variable factor.

Product Concepts

a. Total Product (TP)

Total Product refers to the total quantity of goods produced using a given quantity of inputs in a specific period.

TP = ΣMP
or
TP = AP × L

It increases as more of the variable factor (like labour) is added — but at different rates.

b. Average Product (AP)

Average Product is the output per unit of the variable factor.

AP = TP / L

c. Marginal Product (MP)

Marginal Product is the additional output produced by employing one more unit of the variable factor.

MP = TPn - TPn-1
or
MP = ΔTP / ΔL

Relationship between MP and AP

↑
When MP > AP, AP is rising.
→
When MP = AP, AP is at its maximum.
↓
When MP < AP, AP is falling.
±
MP may be positive, negative, or zero but AP is always positive.
↗
When MP is rising, AP must rise but when MP is falling, AP may rise or fall.
[Graph showing TP, AP, and MP curves with their relationships]

4. Law of Variable Proportions / Law of Diminishing Returns

The Law of Variable Proportions explains how output changes when one input is varied, while others are kept constant.

[Three stages of production graph showing TP, AP, MP curves]
Applies to: Short run, where at least one factor (like capital) is fixed.
Behavior: As more units of the variable factor (like labour) are added, output passes through three stages.

Stages of Production:

Stage Name Behavior of TP, AP, MP Cause
I Increasing Returns TP ↑ at increasing rate, MP ↑ Efficient use of fixed and variable factors
II Diminishing Returns TP ↑ at decreasing rate, MP ↓ but positive Optimum stage (rational producer operates here) where scarcity of fixed factor occurs
III Negative Returns TP ↓, MP becomes negative Overuse of variable factor
Rational Stage of Production:
Stage II (Diminishing Returns)

5. Isoquant and Isoquant Map

[Isoquant map showing different isoquant curves with labels Q1, Q2, Q3]
Isoquant: Curve showing different combinations of two inputs (L and K) that produce the same level of output.
Isoquant Map: A set of isoquants representing different levels of output (similar to contour lines on a map).

6. Returns to Scale

Returns to scale describe how output changes when all inputs are changed in the same proportion.

(It is a long-run concept.)
Increasing Returns to Scale:

Output increases more than proportionately to inputs.

e.g., Inputs ↑ by 50%, Output ↑ by 80%
[Upward sloping convex curve]
Constant Returns to Scale:

Output increases in the same proportion as inputs.

e.g., Inputs ↑ by 50%, Output ↑ by 50%
[Straight 45° line]
Decreasing Returns to Scale:

Output increases less than proportionately to inputs.

e.g., Inputs ↑ by 50%, Output ↑ by 30%
[Upward sloping concave curve]
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