What is the Relationship between Total Utility and Marginal Utility

Theory of Consumer Behaviour: Cardinal Utility Analysis

As discussed, Economics deals with how economic units make decisions in order to maximize their welfare given the limited resources in hand. So, when studying consumer behaviour, we try to find out of the various goods and services available in the market which goods and services the consumer decides to buy and how much quantity of the goods and services the consumer buys, given his/her limited resources. Which goods and services the consumer decides to buy depends on the preferences of the consumers, and how much of the preferred goods and services the consumer buys depends upon the income of the consumer and prices of the goods and services.

Consumers buy goods and services as the consumption of these goods and services gives consumers satisfaction or ‘utility’. Utility is a subjective concept and varies from consumer to consumer. Therefore, two consumers may have different preferences for a good. A person who likes tea derives a greater satisfaction or utility from it compared to another consumer who doesn’t like tea. Utility may also change with a change in place and time. For example, ice-cream may give more utility in summers as compared to winters. An air conditioner provides more utility in a hotter region compared to a colder region.

Cardinal Utility Analysis:

The cardinal utility analyses assumes that utility can be quantified and measured in numbers. For example you can state in number terms how much utility you get after consuming a piece of chocolate, say 1 piece of chocolate gives you 5 units of utility, the second piece gives 4 units. Utility is measured by a unit utils. So, the consumption of two pieces of chocolates gives you 5 utils and 4 utils respectively. Utility is a subjective concept. The piece of chocolate can give different amounts of utility to different people. It depends upon the tastes and preferences of the people.

The cardinal utility analysis is one of the methods used to determine consumer’s equilibrium. Before, we determine consumer’s equilibrium it is important to discuss concepts like Total utility and Marginal utility.

Total Utility

It is the sum of all the utilities derived from consuming a given number of units of a commodity. So, for example, if the consumption of the 1^st piece of a chocolate gives you 3 utils, the second one 5 utils and the third one 4 utils, then the total utility derived from consuming all the three units is the sum of 3, 5 and 4 which is 12 utils.

Marginal Utility

It is that extra or additional utility that a consumer derives when he/she consumes an additional unit of the commodity. If the 6^th unit of the commodity gives a utility of 17 utils and the 7^th unit gives 20 utils, then marginal utility is the 20-17 utils i.e 3 utils.

MU = MU _{7th unit} – MU _{6th unit}

       = 20-17

       = 3 utils

In general form, the Marginal Utility can be found using the following form

 MU _{nth unit} = TU _{nth unit} – TU _{(n-1) th unit}

We can express the Total and Marginal Utility with the help of a table

Units of Commodity X	Total Utility	Marginal Utility
1	10	10
2	18	8
3	24	6
4	28	4
5	30	2
6	30	0
7	28	-2

Relationship Between Total Utility and Marginal Utility

The above table shows the relationship between marginal and total utility. The following observations can be drawn from the above table.

1. As long as MU is positive, TU is increasing
2. When MU is zero, TU at that point is maximum.
3. When MU becomes negative, TU starts to decline.
4. TU is the sum of MU. As can be seen from the table, adding all the MU terms i.e 10 + 8+6+4+2+0+(-2) = 28.
5. When MU is declining, that means that TU is increasing but at a decreasing rate. Since, MU is the addition made to TU, therefore a declining MU means that TU  is increasing but at a declining rate.

 The relationship can be shown with the help of a diagram:

As can be seen from the diagram, the TU is maximum where MU is zero.