# Total Product, Average Product and Marginal Product: Formulae, Examples

The compilation of these Production and Costs Notes makes students exam preparation simpler and organised.

## Total Product, Average Product and Marginal Product

What is the production function in economics? Let us study the definitions of Total Product, Average Product and Marginal Product in simple economic terms along with the methods of calculation for each. We will also look at the law of variable proportions and the relationship between Marginal product and Total Product.

### Production Function

The function that explains the relationship between physical inputs and physical output (final output) is called the production function. We normally denote the production function in the form:

Q = f(X1, X2)

where Q represents the final output and X1 and X2 are inputs or factors of production.

Total Product
In simple terms, we can define Total Product as the total volume or amount of final output produced by a firm using given inputs in a given period of time.

Marginal Product
The additional output produced as a result of employing an additional unit of the variable factor input is called the Marginal Product. Thus, we can say that marginal product is the addition to Total Product when an extra factor input is used.

Marginal Product = Change in Output/Change in Input

Thus, it can also be said that Total Product is the summation of Marginal products at different input levels.

Total Product = Ʃ Marginal Product

Average Product
It is defined as the output per unit of factor inputs or the average of the total product per unit of input and can be calculated by dividing the Total Product by the inputs (variable factors).

Average Product = Total Product/Units of Variable Factor Input

Relationship between Marginal Product and Total Product
The law of variable proportions is used to explain the relationship between Total Product and Marginal Product. It states that when only one variable factor input is allowed to increase and all other inputs are kept constant, the following can be observed:

When the Marginal Product (MP) increases, the Total Product is also increasing at an increasing rate. This gives the Total product curve a convex shape in the beginning as variable factor inputs increase. This continues to the point where the MP curve reaches its maximum.

• When the MP declines but remains positive, the Total Product is increasing but at a decreasing rate. Thisgiveends the Total product curve a concave shape after the point of inflection. This continues until the Total product curve reaches its maximum.
• When the MP is declining and negative, the Total Product declines.
• When the MP becomes zero, the Total Product reaches its maximum.

Relationship between Average Product and Marginal Product
There exists an interesting relationship between Average Product and Marginal Product. We can summarize it as under:

• When Average Product is rising, Marginal Product lies above Average Product.
• When the Average Product is declining, the Marginal Product lies below the Average Product.
• At the maximum of Average Product, Marginal and Average Product equal each other.

Example:

Question:
What are Returns to a Factor? What do you mean by the Law of Diminishing Returns?