1/17/12

Equation for total, and marginal utility



This article describes the difference between total, marginal, and average utility and gives an example of how to find each of them given an initial table.

Utility Table



Quantity
Consumed
Total Utility (sum of utility from consumption)
Marginal Utility (change in total utility divided by change in quantity consumed)
Average Utility (total utility divided by total quantity consumed)
1
50
50
50
2
90
40
45
3
120
30
40
4
140
20
35
5
150
10
30
6
155
5
25.83
10
160
1.25
16

The difference between total utility, marginal utility and average utility is pretty intuitive but it takes some practice to learn.


Most problems in economics will give you a table showing the quantity consumed/purchased, and an associated column showing total utility from these purchases.  Total utility shows the total amount of utility (satisfaction or happiness) achieved from the consumption of ALL of the goods or services consumed. 

Using the above table as an example, the total amount of happiness you get from consuming 1 good is 50, but if you consume 2 goods you will have a total utility of 90.  If you happen to consume 10 goods, your total utility from the consumption of these 10 goods will be 160. 

Marginal utility is calculated by taking the difference in total utilities, and dividing by the change in quantity consumed.  Most of the time the change in quantity consumed will be 1, but this is not always the case.  Using the table above as an example, calculating the marginal utility is done by taking the difference between total utility (and dividing by 1, which gives the same number).  However, when we move from consuming 6 units to 10 units, we have to divide the change in total utility (5) by the change in quantity (4) to get 1.25, which means that each good provides 1.25 utility.

To get average utility, we take total utility and divide it by the number of goods being consumed.  Using the table above as an example, you can see that each row in the average utility column can be confirmed by taking the amount in the total utility column and dividing by the amount in the quantity column.

Also keep in mind the idea of diminishing marginal utility.  The table above adheres to these rules, and for more information on diminishing marginal utility look here.

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