Marginal Product Formula

Formula to Calculate Marginal Product

The marginal product formula can be ascertained by calculating the change in quantity produced or change in production level and then divide the same by the change in the factor of production. The denominator in most of the cases is 1 as the formula that was initially made was based on every 1 unit of increment in a factor of production. Firms can in such case just find out the marginal product by deducting the previous quantity or level of production from the current production level.

Marginal Product can be defined as an increase in total production of a factor of production (capital, labor, land, etc.) which shall result from the increase in one unit in the factor of production while other factors of production are kept as constant. The Marginal Product (MP) formula is represented as below,

Marginal Product = (Qn – Qn-1) / (Ln – Ln-1)

Marginal-Product-Formula

Where,

  • Qn is the Total Production at time n
  • Qn-1 is the Total Production at time n-1
  • Ln is the Units at time n
  • Ln-1 is the Units at time n-1

Examples

You can download this Marginal Product Formula Excel Template here – Marginal Product Formula Excel Template

Example #1

QRP limited is a small shop and is in the business of washing the clothes for their customers. QRP limited wants to hire more employees to grow their business. 

Below are the details of the output and number of employees.

No of Employees No of Washes
1 10.00
2 19.00
3 26.00

You are required to compute the Marginal Product based on the above information.

Solution:

When 2 employees are hired:

Therefore, the calculation of marginal product is as follows,

Marginal Product Formula Example 1.1

= (19 – 10) /(2 – 1)

Marginal Product will be –

Marginal Product Formula Example 1.3

  • Marginal Product = 9

When 3 employees are hired:

Therefore, the calculation of marginal product is as follows,

 Example 1.4

=  (26 – 19) /(3 – 2)

Marginal Product will be –

Example 1.5

  • Marginal Product = 7

Example #2

VSP White Rock is a fund management and asset management company. Their managers are widely known for generating alpha and providing better returns than the market. Hence, most of the institutional investor’s choice is VSP white Rock and even retail individuals have started investing in this fund heavily. Within the past few months, it was observed that the returns are reducing by a minimum of 10 basis pointsBasis PointsBasis points or BPS is the smallest unit of bonds, notes and other financial instruments. BPS determines the slightest change in interest rate, to be precise. One basis point equals 1/100th part of 1%.read more. Below is the monthly summary for the returns of one of the schemes “SMC” that they have generated.

Investment Amount (million) Returns
0 0.00
100 15.89%
200 16.11%
300 16.34%
400 16.58%
500 16.83%
600 17.09%
700 17.30%
800 17.48%
900 17.56%
1000 17.56%

The team wants to analyze whether the funds need to be paused in “SMC” and instead create a new pool called “SMC 2” so that returns don’t look as vanish.

You are required to calculate the Marginal Product of Capital returns and advise whether the new fund should be created?

Solution

Here the managers are worried about more inflow of funds and because of which their returns are diminishing.

When 200 million were invested

Therefore, the calculation of marginal product is as follows,

Marginal Product Formula Example 2.1

= (16.11% – 15.89%)/(200 – 100)

Marginal Product will be –

Marginal Product Formula Example 2.2

  • Marginal Product = 0.0022%

When 300 million was invested

Therefore, the calculation of marginal product is as follows,

Marginal Product Formula Example 2.3

= (16.34% – 16.11%)/(200 – 100)

Marginal Product will be –

Marginal Product Formula Example 2.4

  • Marginal Product = 0.0023%

Similarly, we can calculate till 1000 million was invested.

Marginal Product Formula Example 2.5

As, can be seen from the above table when more funds were invested the Marginal Product of returns started diminishing meaning that the managers lack the opportunity to invest as most of their ideas would be sufficiently invested and therefore, they should start a new pool of funds called as “SMC 2”.

Example #3

B&B brothers are in the manufacturing of product ‘X’ and it requires a lot of labor work and hence they have hired almost 10-15 labors per week. Below are the details of output and number of employees:

Labor Hired Production (Kilo)
0 0
12 1000.00
21 2000.00
29 29000.00
35 3950.00
41 4880.00
51 5770.00
62 6600.00
74 7500.00

The management is concerned with the wages hike and their cost and hence they want to find out the optimal level of production and lay off the extra works.

You are required to calculate the Marginal Product of labor and advise accordingly.

Solution

When 21 labor was hired

Therefore, the calculation of marginal product is as follows,

Example 3.1

=  (2,000 – 1,000)/(21 – 12)

=1,000 / 9

Marginal Product will be –

Marginal Product Formula Example 3.2

  • Marginal Product = 111.11

When 29 labor was hired

Marginal Product will be –

Marginal Product Formula Example 3.4

=(2,900 – 2,000)/(29 – 21)

=  900 / 8

  • Marginal Product will be =  112.50

Similarly, we can calculate till 74 employees were hired.

 Example 3.5

It can be seen from the above table, that the optimal level of production is when 35 laborers were hired and post that the marginal product started diminishing. Hence, the management can lay off anything above 35 to 41 laborers.

Relevance and Uses of Marginal Product Formula

Calculating the marginal product shall allow firms to check for the increase in the level of production per one unit of a factor of production added. The definition of one factor of production unit can vary by firm. The objective for the firm is to search the optimal level of a number of employees (the type of factor of production) it must hire so as to achieve maximum revenue and production.

Too few labors shall mean they are not much productive. Several labors could mean they spend more on wages than the output they are bringing in. Hence, both situations are an issue for any business that is growing.

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