# What are Cost Functions and their types, factors, and Total, Average and Marginal Products

Hello everyone, in the previous topic we were talking about Cost Concepts and their Types. Today we are going to discuss Cost Functions and their types, factors, and Total, Average and Marginal Products.

Contents

## Cost Function

The Cost Function refers to the mathematical relation between the Cost of a Product and the various Determinants of Costs.

## Types of the Cost function

The types of the cost function are as follows-

### Short Run Function

In the short run, at least one of the factors i.e labor or capital cannot be varied, and therefore, they remain fixed.

To vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed factor whereas the other factor which the firm can vary is called the variable factor.

#### Cost output relationship in the short-run

In the short-run, a change in output is possible only by making changes in the variable inputs like raw materials, labor, etc. Inputs like land and buildings, plant and machinery, etc. are fixed in the short run. It means that the short-run is a period not sufficient enough to expand the number of fixed inputs.

Thus Total Cost (TC) in the short run is composed of two elements. They are – Total Fixed Cost (TFC) and Total Variable Cost (TVC)

TFC remains the same throughout the period and is not influenced by the level of activity. The firm will continue to incur these costs even if firm is temporarily shut down. Even though TFC remains the same fixed cost per unit varies with changes in the level of output. On the other hand, TVC increases with an increase in the level of activity and decreases with a decrease in the level of activity.

If the firm is shut down, there are no variable costs. Even though TVC is variable, the variable cost per unit is constant. So in the short-run, an increase in TC implies an increase in TVC only.

### Long Run Function

In the long run, all factors of production can be varied. A firm to produce different levels of output, in the long run, may vary both inputs simultaneously. So, in the long run, there is no fixed factor.

#### Cost output relationship in the long run-

To study the cost output relationship in the long run it is necessary to know the meaning of the long run. As known in the long run the size of an industry can be expanded to meet the increased demand for products as such in the long run all the factors of production can be varied according to the need.

Hence long-run costs are those which vary with the output when all the input factors including plant and equipment vary.

## Factors Of Cost Function

Factors that determine the cost function are-

#### Size

There is an inverse relationship between size and cost. As size increases, cost falls, and vice versa.

#### Level of Output

There is a direct relationship between output level and cost. More the level of output, more is the cost ( i. e., total cost) and vice Versa.

#### Price of Inputs

There is a direct relationship between the price of inputs and cost. As the price of inputs rise, cost rises and vice versa.

#### State of technology

The modern and upgraded technology implies lesser cost and vice versa.

Efficiency and cost are inversely related. More efficiency in management and administration better will be the product and less will be the cost. The cost will increase in case of inefficiencies in management and administration.

## Total Product

This relationship between the variable input and output, keeping all other inputs constant, is often referred to as the Total Product (TP) of the variable input.

## Average Product

Average product is defined as the output per unit of the variable input. We can calculate it as–

## Marginal Product

The marginal product of an input is defined as the change in output per unit of change in the input when all other inputs are held constant.

So, that is all for today guys see you in our next blog. If you like our article please don’t forget to share it with others & follow our Instagram page for your daily dose of Motivation.

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## General FAQ

### What is Cost Function?

The Cost Function refers to the mathematical relation between the Cost of a Product and the various Determinants of Costs.

### What are the types of the Cost function?

Following are the types of the Cost function-
a. Short Run Function
b. Long Run Function

### What is the short-run function?

In the short run, at least one of the factors i.e labor or capital cannot be varied, and therefore, they remain fixed. To vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed factor whereas the other factor which the firm can vary is called the variable factor.

### What is the long-run function?

In the long run, all factors of production can be varied. A firm to produce different levels of output, in the long run, may vary both the inputs simultaneously. So, in the long run, there is no fixed factor.

### What are the factors of cost function?

Factors that determine the cost function are-
1. Size
2. Level of Output
3. Price of Inputs
4. State of technology

### What is the Total Product?

This relationship between the variable input and output, keeping all other inputs constant, is often referred to as the Total Product (TP) of the variable input.

### What is the Average Product?

Average product is defined as the output per unit of the variable input.

### What is the Marginal Product?

The marginal product of an input is defined as the change in output per unit of change in the input when all other inputs are held constant.

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