Law of Marginal Utility

Introduction

The term Marginal Utility can be defined as a very broad term. Thus, to understand the same we need to understand the term Utility first. The term Utility, in economics it is defined as the amount of expectation that is fulfilled by the consumption of a product or a service by a consumer. In layman's language, the same can be said as the ability to satisfy the want. For example, say a consumer who is a smoker, the product cigarette is having utility to him but not to a consumer who is a non-smoker.
 In the field of economics, based on the above discussion, the term Marginal Utility can be defined as the extra amount of satisfaction that is received by a consumer on consuming an extra amount of the product that he or she is intending to. Economics also says that the utility received by a consumer on consuming more than one unit of the product or service goes on decreasing when compared to the utility obtained from the former one. In other words, the utility of an additional unit of consumption is inversely related to the number of units consumed. This can be illustrated with the help of an example, say a consumer is very hungry and he is given only a piece of chapati from 10 chapatis prepared for him. The utility received by him on having the first chapati is the highest when he is consuming a second chapati and so on, as shown in the figure, he is not that much hungry that he was when he was consuming the first one. Hence the utility from the second piece onward decreases for him/her. When ultimately he is consuming the 6th chapati it is seen that he is not at all absorbing any utility from the same. Even after the 6th one if he goes on consuming it is seen that the utility receive has become negative. In other words, he is not receiving any utility rather consumption of the same is harming him.
Types Of Marginal Utility 
Marginal Utility can again be divided into 3 parts. They are discussed as follows:
 Positive Marginal Utility: This is nothing but the utility that the consumer receives on having the 1st chapati. In simple terms, he is very hungry and he is relieved in getting at least a single chapati to eat. So, in this case, the utility thus received by him is very high which is termed as Positive Marginal Utility.
 Zero-Marginal Utility: By the time the consumer is having the 5th chapati it is seen that is hunger phase has passed and he is full. Now when he is consuming the 6th chapati he is very much reluctant and is not receiving g any utility from the same. This is known as Zero-Marginal Utility.
 Negative Marginal Utility: At this stage, he consuming unwanted chapatis i.e. he is not having any requirement to have the chapatis but he is still having them. This at a point in time can harm him and he may end up vomiting. This phase is known as the Negative Marginal Utility.
Mathematical Deviation Of Utility
Marginal Utility is of utmost importance in economics and so to save time formula has been derived for easy calculation of the same.
MU_x=(δTU_x)/(δQ_x )
In the above equation, 
MU_x is the marginal utility of the commodity.
δTU_x is the change in Total Utility of a product or a service in this case a chapati.
δQ_x is the change in the quantity of the commodity.
To derive the above one needs to know the concept of Total Utility. Now, Total Utility (TU_X) is nothing but the summation of the utilities thus received by consuming all the units of a certain product or service. The mathematical derivation of total utility can be shown as follows:
TU_x=∑MU_x
∑MU_x is the sum of all the marginal utilities.
Assumptions of Marginal Utility
While learning the concept of Marginal Utility it should be clearly remembered that the same is based on certain assumptions. Without knowing the assumption(s) the whole concept of Marginal Utility can be considered vague or irrelevant. Thus the assumptions are as follows:
 It assumed that utility can be measured in terms of a specific unit. The units mainly used in this case is 'util'.
 It is considered that the money is having a constant Marginal Utility, even though a person keeps on spending on any kind of service or product he/she is obtaining.
 Lastly, the concept of Complimentary Goods is obliterated i.e each commodity is having its utility and the same cannot be complemented with others.
Illustration 
Lastly, to understand the concept of Marginal Utility as discussed above an example is very much required. Thus the following illustration:
 Say today is a very bright and sunny day. A person has returned home from the market, walking. Now as a result of this he has become very thirsty and hence on returning home he grabbed a bottle of cold water from the fridge. As he grabbed the bottle he quickly took 2 sips from the bottle after that he again 2 few sips but this time he was a bit slow in having the same. Lastly, after waiting for a few moments he took the last sip and kept the bottle back in the fridge. This activity when expressed in the terms of Marginal Utility and Total Utility as discussed above, the following can be noticed.

It is clearly understood from the above table that in the 1st sip the person is having the highest level of satisfaction. In this case MU=TU. Now at having the 2nd and the 3rd sip it is seen that the level of satisfaction is decreasing but on the other hand Total Utility is increasing. This is the stage of Positive Marginal Utility.
 The 4th stage is the level of Zero-Marginal Utility, which in this context means that the person is not thirsty any more. The 5th or the last sip results in a decline of Marginal Utility. In this stage, even the Total Utility is declining to show the phase of Negative Marginal Utility.
Conclusion
Utility Schedule
Units Consumed (Sip of Water) Marginal Utility (MU) [In Utils] Total Utility (TU=∑MU_x) [In Utils]
1st Sip 10 10
2nd Sip 7 17
3rd Sip 4 21
4th Sip 0 21
5th Sip -4 17
Thus from the above discussion, it can be said that Marginal Utility is an integral part of economics and the same is linked to Total Utility. Also, the following can be concluded:
 Increase in Total Utility = Positive Marginal Utility
 Maximum Total Utility = Zero Marginal Utility
 Negative Marginal Utility = Diminishing Total Utility

 Total Utility Increases at a diminishing rate.