# Total Utility, Marginal Utility, and their Relationship

### Concept of Cardinal Utility: Total Utility and Marginal Utility

In economics, the term utility refers to ‘the pleasure or satisfaction that individuals get from their economic activity.’ It is essentially a subjective and psychological phenomenon and varies from one person to another, one place to another, and one time to another. All those goods and services which have the capacity to satisfy human wants are said to contain utility in the viewpoint of economics.

### Basic Terminologies/Concepts

#### Total Utility (TU)

Total satisfaction gained by the consumer from the consumption of all the available units of the commodity is known as total utility. It is the sum of all the marginal utilities associated with each unit of consumption.

If we sum the utilities obtained from the consumption of different units of a particular commodity at a given time, then we get the numerical value of total utility.

Mathematically,

TU= ∑MU= MU1+MU2+ ……….  +  MUn

Where TU= Total Utility; MU1= Marginal utility obtained from the consumption of 1st unit of a particular commodity (so on…. Up to nth unit)

For example, if A consumes 3 biscuits and obtains 5, 4, and 3 utils of utility from the first, second, and third biscuits respectively then the total utility is 5+4+3=12 utils.

#### Marginal Utility (MU)

The marginal utility can be defined as an extra utility drawn from an extra unit of a commodity. Hence, it is the change in total utility while consuming one more unit of commodity. In other words, it is the ratio of change in total utility with the change in units of a commodity (normally one unit).

Mathematically,

MU= ∆𝑻𝑼/∆𝑸

Where ∆TU= change in total utility; ∆Q = change in the unit of commodity consumed by consumer

Alternatively,

MU= TUn-TUn-1

Where TUn= total utility at n unit of consumption; TNn-1total utility at the n-1 unit of consumption

For example, a consumer obtains 100 units of total utility from the consumption of three biscuits, and if he consumes a fourth biscuit total utility becomes 105 units then his marginal utility= 105-100= 5 units. (TUn= 4th biscuit and TUn-1=3rd biscuit)

### Relationship between Total Utility and Marginal Utility

There is a direct relationship between total utility and marginal utility. Total utility is always based on marginal utility as a total utility (TU) is the summation of marginal utilities. The relationship between TU and MU can be explained with help of the following table.

In the above table, there are three forms of marginal utility (MU) as positive, zero, and negative marginal utility. Up to 5 units of consumption, marginal utility (MU) is decreasing and remains positive. Until the marginal utility (MU) is positive, total utility (TU) surges/rises at a declining rate.

When a consumer consumes the 6th unit of the commodity, s/he gets no utility or there is zero utility and as a result, total utility (TU) remains constant and becomes maximum.

After the 6th unit, if the consumer keeps consuming or if s/he consumes the 7th unit of the commodity, marginal utility (MU) becomes negative and with negative marginal utility (MU), total utility (TU) starts to decline.

It can be graphically explained as below.

In the diagram, TU is the total utility curve and MU is the marginal utility curve.  As the consumer consumes the first unit of commodity, s/he obtains 10 utils of utility. Here both TU and MU are the same.

When the consumer consumes 2nd unit of goods, TU increases to 18 utils from 10 utils and MU decreases to 8 utils. By adding MUs TU is obtained. Accordingly, when the consumer consumes the 6th unit of goods, MU decreases to zero where TU becomes maximum (30 utils). After the 6th unit consumption of goods, MU is negative (-2) and due to negative MU, total utility declines to 28 utils from 30 utils. Thus, the consumer gets maximum satisfaction when MU is zero and that point is known as the point of saturation.

Therefore, total Utility, marginal Utility, and their relationship can be summarized as below.

• The TU curve begins from the origin, increases at a decreasing rate, reaches a maximum, and then starts falling.
• MU curve is the slope of the TU curve and given by MU=∆𝑇𝑈/∆Q
• When TU is maximum, MU is zero. It is referred to as the saturation point. It indicates that units of the good are consumed till the saturation point.
• Until the TU curve is concave, the MU curve is downward sloping and remains above the x-axis.
• Once When TU curve is falling, the MU curve becomes negative.
• The falling part of the MU curve demonstrates the law of diminishing marginal utility.
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