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.

**Table of content**

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**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(X_{1}, X_{2})

where Q represents the final output and X_{1 }and X_{2 }are inputs or factors of production.

**Browse more Topics under Production And Costs**

- Production Function
- Shapes of Total Product, Average Product and Marginal Product
- Return to scale and Cobb Douglas Function
- Behaviour of Cost in the Short Run
- Long-Run Cost Curves

*Learn more about Production Function here in more detail.*

**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

*Source: FreeEconHelp*

### 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 inflexion**. 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, 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 Average Product is declining, Marginal Product lies below Average Product.
- At the maximum of Average Product, Marginal and Average Product equal each other.

Learn more about the Shapes of Total Product, Average Product, and Marginal Product.

**Solved Example for You**

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

Answer: Returns to a Factor is used to explain the behaviour of physical output as only one factor is allowed to vary and all other factors are kept constant. This is a short-run concept.

The law of diminishing returns to a factor states that as the variable factor is allowed to vary (increase), keeping all other factors constant, the Marginal Product first increases, reaches its maximum and then declines and even becomes negative.