Marginal Utility Formula (Table of Contents)
What is the Marginal Utility Formula?
The term “Marginal Utility” refers to the satisfaction gained by a consumer on consuming an additional unit of a good or service. Basically, a consumer’s perceived total satisfaction or benefit changes for every additional unit of a good, i.e. it may increase until a certain point in time and then the trend reverses. The concept of marginal utility helps us in assessing this change in consumer perception in terms of different levels of satisfaction in a more scientific way (law of diminishing marginal utility).
The formula for marginal utility is expressed as a change in total utility (ΔTU) divided by the change in the number of units of the good or service consumed (ΔQ). Mathematically, it is represented as,
The above formula for marginal utility can also be expressed as,
Where,
 TU_{i}: Total Utility at Q_{i} Units
 TU_{f}: Total Utility at Q_{f} Units
 Q_{i}: No. of Units Consumed Initially
 Q_{f}: No. of Units Consumed Finally
Example of Marginal Utility Formula (With Excel Template)
Let’s take an example to understand the calculation of Marginal Utility in a better manner.
Marginal Utility Formula – Example #1
Let us take the example of John who purchased a chocolate cake with 4 pieces. Now, the following information is available regarding his perceived utility after consumption of each piece of the cake. Calculate the marginal utility of each piece of the chocolate cake.
Solution:
Marginal Utility is calculated using the formula given below
Marginal Utility = (TU_{f} – TU_{i}) / (Q_{f} – Q_{i})
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For 1^{st} Piece of the Cake
 Marginal Utility_{1} = (150 – 0) / (1 – 0)
 Marginal Utility_{1 }= 150
For 2^{nd} Piece of the Cake
 Marginal Utility_{2} = (225 – 150) / (2 – 1)
 Marginal Utility_{2 }= 75
For 3^{rd} Piece of the Cake
 Marginal Utility_{3} = (250 – 225) / (3 – 2)
 Marginal Utility_{3 }= 25
For 4^{th} Piece of the Cake
 Marginal Utility_{4} = (220 – 250) / (4 – 3)
 Marginal Utility_{4 }= 30
Therefore, here we can see how the marginal utility of a piece of cake declines after the consumption of the previous one. Here, the highest utility is reached at the consumption of the 3^{rd} piece beyond which the total declined. This is a classic example of diminishing marginal utility.
Marginal Utility Formula – Example #2
Let us take the example of David who purchased four pastries for $8 each. Now, the bakery offers him a deal that if he purchases one more pastries then he would be given 10% on the entire purchase. If David agreed to buy the additional unit, then calculate the marginal utility of the 5^{th} piece for him.
Solution:
Initial Total Utility is calculated as
Final Total Utility is calculated as
Marginal Utility is calculated using the formula given below
Marginal Utility = (TU_{f} – TU_{i}) / (Q_{f} – Q_{i})
 Marginal Utility = ($36 – $32) / (5 – 4)
 Marginal Utility = $4
Therefore, the marginal utility of each piece of pastry declined from $8 until the 4^{th} piece to $4 for the 5^{th} piece.
Explanation
The formula for Marginal Utility can be calculated by using the following steps:
Step 1: Firstly, ascertain the number of units of the good or service consumed initially and the total satisfaction (utility) gained by the consumer with that. The consumer’s willingness to pay is an indicator of the perceived value and hence can be used as a proxy for total utility. The number of units consumed initially and the total utility at that level are denoted by Q_{i} and TU_{i} respectively.
Step 2: Next, ascertain the number of units consumed finally and the total utility at that level, which are denoted by Q_{f} and TU_{f} respectively.
Step 3: Next, determine the change in total utility by deducting the initial total utility(step 1) from the final total utility (step 2).
Change in Total Utility, ΔTU = TU_{f} – TU_{i}
Step 4: Next, determine the change in the number of units consumed by deducting the initial number of units consumed (step 1) from the final number of units consumed (step 2).
Change in No. of Units Consumed, ΔQ = Q_{f} – Q_{i}
Step 5: Finally, the formula for marginal utility can be derived by dividing the change in total utility (step 3) by the change in the number of units consumed (step 4) as shown below.
Marginal Utility = Change in Total Utility (ΔTU) / Change in No. of Units Consumed (ΔQ)
Marginal Utility = (TU_{f} – TU_{i}) / (Q_{f} – Q_{i})
Relevance and Use of Marginal Utility Formula
Marginal utility is an important economic concept that is based on the law of diminishing marginal returns. This theory states that perceived satisfaction gained by a consumer increases with the consumption of each additional unit until a certain level and then it starts to decrease which indicates that the consumer is losing interest in the good or service. Now, this concept is used by sellers to understand consumer behavior and determine the price point and different levels of consumption. One of the best examples of the seller using marginal utility theory to lure consumers is at shopping malls where we come across offers on larger packs rather than the smaller ones.
Marginal Utility Formula Calculator
You can use the following Marginal Utility Formula Calculator
Change in Total Utility (ΔTU)  
Change in No. of Units Consumed (ΔQ)  
Marginal Utility  
Marginal Utility  = 


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