What is Cost Function? – GeeksforGeeks
The Cost Function is the relationship between the input costs and the output.
What is Cost of Production?
A firm produces goods and services using a variety of inputs. Such inputs are not free, the firm must pay for them. The cost of production refers to the expenditure incurred on these inputs.
The total expenditure incurred for producing a commodity is referred to as its cost. In economics, the cost includes:
- Explicit Cost: The actual expenditure made on the inputs or the payments made to the outsiders to hire their factor services is known as Explicit Cost. For example, paying the rent for the hired premises, paying for raw materials, or paying the employee’s wages.
- Implicit Cost: The estimated value of the inputs supplied by the owners along with the normal profits is known as Implicit Cost. For example, interest on own capital, rent of own land, salary for one’s services as an entrepreneur, etc. These are the costs associated with self-supplied factors.
Thus, cost in economics refers to both the actual money spent on inputs (also known as the explicit cost) and the imputed value of the inputs provided by the owners (also known as the implicit cost).
Difference between Explicit Cost and Implicit Cost
|
Basis |
Explicit Cost |
Implicit Cost |
|---|---|---|
|
Meaning |
Explicit Cost is a payment made to outside parties for hiring the factor services. |
Implicit Cost is the cost of self-supplied factors. |
|
Money Payment |
It includes paying with actual money to purchase and hire inputs. |
It consists of the firm’s imputed value of factors. There is no monetary payment involved. |
|
Example |
Payment of salaries, Rent, Insurance premiums, etc. |
Interest on capital, Rent of self-owned land, etc |
Cost Function
Cost Function refers to the relationship between input costs and output. In simple terms, the functional relationship between cost and output is referred to as the cost function. It is written as:
C = f(q)
{Where: C = Cost of Production; q = Quantity of Production; f = Functional Relationship}
Opportunity Cost
The cost of foregoing the next best alternative is called Opportunity Cost. The idea of opportunity cost is important as it serves as a basis for the concept of cost. When a company decides to produce a particular commodity, it always takes into account the value of the alternative commodity that is not produced. The value of the alternative commodity is the opportunity cost of the commodity that the firm is currently producing. For instance, suppose a farmer has the resources to grow either 20 quintals of maize or 30 quintals of wheat on his field. If he decides to grow wheat, he will forego the opportunity to grow 20 quintals of maize.
In the short run, some of the factors are fixed, while other factors are variable. In the same way, the short-run costs are also categorised into two different kinds of cost; viz., Fixed Costs and Variable Costs. The sum total of these costs is equal to the total cost.
1. Total Fixed Cost (TFC) or Fixed Cost (FC)
The costs on which the output level does not have a direct impact are known as Fixed Costs. For example, salary of staff, rent on office premises, interest on loans, etc. Other names of fixed costs are Supplementary Cost, Overhead Cost, Unavoidable Cost, Indirect Cost, or General Cost.
2. Total Variable Cost (TVC) or Variable Cost (VC)
The costs on which the output level has a direct impact are known as Variable Costs. For example, fuel, power, payment for raw materials, etc. Other names of variable costs are Prime Cost, Avoidable Cost, or Direct Cost.
3. Total Cost (TC)
The total expenditure incurred by an organisation on the factors of production which are required for the production of a commodity is known as Total Cost. In simple terms, total cost is the sum of total fixed cost and total variable cost at different output levels.
TC = TFC + TVC
Average Costs
Average costs are the per unit costs which explain the relationship between the cost and output in a realistic manner. These per-unit costs are obtained from Total Fixed Cost, Total Variable Cost, and Total Cost. The three different types of per-unit costs are as follows:
1. Average Fixed Cost (AFC)
The per unit fixed cost of production is known as Average Fixed Cost. The formula for calculating Average Fixed Cost is:
2. Average Variable Cost (AVC)
The per unit variable cost of production is known as Average Variable Cost. The formula for calculating Average Variable Cost is:
3. Average Total Cost (ATC) or Average Cost (AC)
The per unit total cost of production is known as Average Total Cost or Average Cost. The formula for calculating Average Total Cost is:
Another way to define Average Total Cost is by the sum of Average Fixed Cost and Average Variable Cost; i.e., AC = AFC + AVC.
Marginal Cost
The additional cost incurred to the total cost when one more unit of output is produced is known as Marginal Cost. For example, if the total cost of producing 2 units is ₹400 and the total cost of producing 3 units is ₹600, then the marginal cost will be 600 – 400 = ₹200.
{Where, n = Number of units produced; MCn = Marginal cost of the nth unit; TCn = Total cost of n units; TCn-1 = Total cost of (n-1) units}
Another way to calculate Marginal Cost:
When the change in the units produced is more than one unit, then the previous formula of calculating MC will not work. In that case, the formula for calculating Marginal Cost will be:
For example, if the total cost of producing 4 units is ₹300 and the total cost of producing 2 units is ₹50, then the marginal cost will be:
Marginal Cost = ₹125
Examples of Short-Run Costs
Example 1:
From the table below, calculate the missing figures.
|
Output (in units) |
TC (₹) |
TFC (₹) |
TVC (₹) |
|---|---|---|---|
|
0 |
– |
– |
– |
|
1 |
– |
– |
5 |
|
2 |
24 |
– |
– |
|
3 |
– |
– |
17 |
|
4 |
– |
15 |
28 |
|
5 |
57 |
– |
– |
Solution:
|
Output (in units) |
TC (₹) TC = TVC + TFC |
TFC (₹) |
TVC (₹) TVC = TC – TFC |
|---|---|---|---|
|
0 |
15 + 0 = 15 |
15 |
0 |
|
1 |
15 + 5 = 20 |
15 |
5 |
|
2 |
24 |
15 |
24 – 15 = 9 |
|
3 |
15 + 17 = 32 |
15 |
17 |
|
4 |
15 + 28 = 43 |
15 |
28 |
|
5 |
57 |
15 |
57 – 15 = 42 |
At all output levels, TFC remains constant at ₹15.
Example 2:
From the table below, calculate the missing number.
|
Output (in units) |
TC (₹) |
AC (₹) |
MC (₹) |
|---|---|---|---|
|
1 |
– |
– |
20 |
|
2 |
50 |
– |
– |
|
3 |
– |
– |
10 |
|
4 |
– |
– |
15 |
|
5 |
– |
17 |
– |
|
6 |
– |
– |
25 |
Solution:
|
Output (in units) Q |
TC (₹) TC = ΣMC + FC |
AC (₹) AC = TC ÷ Q |
MC (₹) MCn = TCn – TCn – 1 |
|---|---|---|---|
|
1 |
20 |
20 |
20 |
|
2 |
50 |
50 ÷ 2 = 25 |
30 |
|
3 |
60 |
60 ÷ 2 = 30 |
10 |
|
4 |
75 |
75 ÷ 4 = 18.75 |
15 |
|
5 |
17 x 5 = 85* |
17 |
10 |
|
6 |
110 |
110 ÷ 6 = 18.33 |
25 |
Working Notes:
1. In this example, fixed cost is assumed to be zero.
2. *TC = AC x Q
Example 3:
From the table given below, calculate the weekly TC and AVC.
|
Particulars |
|
|---|---|
| Number of workers employed |
70 |
| Number of units produced per week |
200 |
| Weekly rent of land |
₹ 500 |
| Weekly wage of each worker |
₹ 300 |
| Power |
₹ 350 |
| Raw materials used |
₹ 1,800 |
Solution:
TC = TVC + TFC
TVC = Raw materials used + Power + (Number of workers employed x Weekly wage)
TVC = 1,800 + 350 + (70 x 300)
TVC = ₹ 23,150
AVC = TVC/Units Produced per week
AVC = 23,150/200
AVC = ₹ 115.75
Last Updated :
23 Jun, 2023
Like Article
Save Article
The Cost Function is the relationship between the input costs and the output.
What is Cost of Production?
A firm produces goods and services using a variety of inputs. Such inputs are not free, the firm must pay for them. The cost of production refers to the expenditure incurred on these inputs.
The total expenditure incurred for producing a commodity is referred to as its cost. In economics, the cost includes:
- Explicit Cost: The actual expenditure made on the inputs or the payments made to the outsiders to hire their factor services is known as Explicit Cost. For example, paying the rent for the hired premises, paying for raw materials, or paying the employee’s wages.
- Implicit Cost: The estimated value of the inputs supplied by the owners along with the normal profits is known as Implicit Cost. For example, interest on own capital, rent of own land, salary for one’s services as an entrepreneur, etc. These are the costs associated with self-supplied factors.
Thus, cost in economics refers to both the actual money spent on inputs (also known as the explicit cost) and the imputed value of the inputs provided by the owners (also known as the implicit cost).
Difference between Explicit Cost and Implicit Cost
|
Basis |
Explicit Cost |
Implicit Cost |
|---|---|---|
|
Meaning |
Explicit Cost is a payment made to outside parties for hiring the factor services. |
Implicit Cost is the cost of self-supplied factors. |
|
Money Payment |
It includes paying with actual money to purchase and hire inputs. |
It consists of the firm’s imputed value of factors. There is no monetary payment involved. |
|
Example |
Payment of salaries, Rent, Insurance premiums, etc. |
Interest on capital, Rent of self-owned land, etc |
Cost Function
Cost Function refers to the relationship between input costs and output. In simple terms, the functional relationship between cost and output is referred to as the cost function. It is written as:
C = f(q)
{Where: C = Cost of Production; q = Quantity of Production; f = Functional Relationship}
Opportunity Cost
The cost of foregoing the next best alternative is called Opportunity Cost. The idea of opportunity cost is important as it serves as a basis for the concept of cost. When a company decides to produce a particular commodity, it always takes into account the value of the alternative commodity that is not produced. The value of the alternative commodity is the opportunity cost of the commodity that the firm is currently producing. For instance, suppose a farmer has the resources to grow either 20 quintals of maize or 30 quintals of wheat on his field. If he decides to grow wheat, he will forego the opportunity to grow 20 quintals of maize.
In the short run, some of the factors are fixed, while other factors are variable. In the same way, the short-run costs are also categorised into two different kinds of cost; viz., Fixed Costs and Variable Costs. The sum total of these costs is equal to the total cost.
1. Total Fixed Cost (TFC) or Fixed Cost (FC)
The costs on which the output level does not have a direct impact are known as Fixed Costs. For example, salary of staff, rent on office premises, interest on loans, etc. Other names of fixed costs are Supplementary Cost, Overhead Cost, Unavoidable Cost, Indirect Cost, or General Cost.
2. Total Variable Cost (TVC) or Variable Cost (VC)
The costs on which the output level has a direct impact are known as Variable Costs. For example, fuel, power, payment for raw materials, etc. Other names of variable costs are Prime Cost, Avoidable Cost, or Direct Cost.
3. Total Cost (TC)
The total expenditure incurred by an organisation on the factors of production which are required for the production of a commodity is known as Total Cost. In simple terms, total cost is the sum of total fixed cost and total variable cost at different output levels.
TC = TFC + TVC
Average Costs
Average costs are the per unit costs which explain the relationship between the cost and output in a realistic manner. These per-unit costs are obtained from Total Fixed Cost, Total Variable Cost, and Total Cost. The three different types of per-unit costs are as follows:
1. Average Fixed Cost (AFC)
The per unit fixed cost of production is known as Average Fixed Cost. The formula for calculating Average Fixed Cost is:
2. Average Variable Cost (AVC)
The per unit variable cost of production is known as Average Variable Cost. The formula for calculating Average Variable Cost is:
3. Average Total Cost (ATC) or Average Cost (AC)
The per unit total cost of production is known as Average Total Cost or Average Cost. The formula for calculating Average Total Cost is:
Another way to define Average Total Cost is by the sum of Average Fixed Cost and Average Variable Cost; i.e., AC = AFC + AVC.
Marginal Cost
The additional cost incurred to the total cost when one more unit of output is produced is known as Marginal Cost. For example, if the total cost of producing 2 units is ₹400 and the total cost of producing 3 units is ₹600, then the marginal cost will be 600 – 400 = ₹200.
{Where, n = Number of units produced; MCn = Marginal cost of the nth unit; TCn = Total cost of n units; TCn-1 = Total cost of (n-1) units}
Another way to calculate Marginal Cost:
When the change in the units produced is more than one unit, then the previous formula of calculating MC will not work. In that case, the formula for calculating Marginal Cost will be:
For example, if the total cost of producing 4 units is ₹300 and the total cost of producing 2 units is ₹50, then the marginal cost will be:
Marginal Cost = ₹125
Examples of Short-Run Costs
Example 1:
From the table below, calculate the missing figures.
|
Output (in units) |
TC (₹) |
TFC (₹) |
TVC (₹) |
|---|---|---|---|
|
0 |
– |
– |
– |
|
1 |
– |
– |
5 |
|
2 |
24 |
– |
– |
|
3 |
– |
– |
17 |
|
4 |
– |
15 |
28 |
|
5 |
57 |
– |
– |
Solution:
|
Output (in units) |
TC (₹) TC = TVC + TFC |
TFC (₹) |
TVC (₹) TVC = TC – TFC |
|---|---|---|---|
|
0 |
15 + 0 = 15 |
15 |
0 |
|
1 |
15 + 5 = 20 |
15 |
5 |
|
2 |
24 |
15 |
24 – 15 = 9 |
|
3 |
15 + 17 = 32 |
15 |
17 |
|
4 |
15 + 28 = 43 |
15 |
28 |
|
5 |
57 |
15 |
57 – 15 = 42 |
At all output levels, TFC remains constant at ₹15.
Example 2:
From the table below, calculate the missing number.
|
Output (in units) |
TC (₹) |
AC (₹) |
MC (₹) |
|---|---|---|---|
|
1 |
– |
– |
20 |
|
2 |
50 |
– |
– |
|
3 |
– |
– |
10 |
|
4 |
– |
– |
15 |
|
5 |
– |
17 |
– |
|
6 |
– |
– |
25 |
Solution:
|
Output (in units) Q |
TC (₹) TC = ΣMC + FC |
AC (₹) AC = TC ÷ Q |
MC (₹) MCn = TCn – TCn – 1 |
|---|---|---|---|
|
1 |
20 |
20 |
20 |
|
2 |
50 |
50 ÷ 2 = 25 |
30 |
|
3 |
60 |
60 ÷ 2 = 30 |
10 |
|
4 |
75 |
75 ÷ 4 = 18.75 |
15 |
|
5 |
17 x 5 = 85* |
17 |
10 |
|
6 |
110 |
110 ÷ 6 = 18.33 |
25 |
Working Notes:
1. In this example, fixed cost is assumed to be zero.
2. *TC = AC x Q
Example 3:
From the table given below, calculate the weekly TC and AVC.
|
Particulars |
|
|---|---|
| Number of workers employed |
70 |
| Number of units produced per week |
200 |
| Weekly rent of land |
₹ 500 |
| Weekly wage of each worker |
₹ 300 |
| Power |
₹ 350 |
| Raw materials used |
₹ 1,800 |
Solution:
TC = TVC + TFC
TVC = Raw materials used + Power + (Number of workers employed x Weekly wage)
TVC = 1,800 + 350 + (70 x 300)
TVC = ₹ 23,150
AVC = TVC/Units Produced per week
AVC = 23,150/200
AVC = ₹ 115.75
Last Updated :
23 Jun, 2023
Like Article
Save Article
Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to the primary source is specified. All trademarks belong to their rightful owners, all materials to their authors. If you are the owner of the content and do not want us to publish your materials, please contact us by email – [email protected]. The content will be deleted within 24 hours.