# Relationship between total utility and marginal utility

From the data in the table and the diagram below, we can establish the following relationship between total utility and marginal utility:

### Total and marginal utility schedule

Number of chocolates consumed Total utility (utils) Marginal utility (utils)
0 0 0
1 8 8
2 14 6
3 19 5
4 23 4
5 26 3
6 28 2
7 29 1
8 29 0
9 25 -4

The relationship between total utility and marginal utility is as follows:

1. As total utility increases at a decreasing rate, then marginal utility decreases.

2. When total utility is at a maximum point, then marginal utility is zero.

3. When total utility starts to decline, then marginal utility becomes negative.

#### Activity

Do the following activity on marginal and total utility.

### The table below is based on William's consumption of units of beer. Complete the table by calculating his marginal utility for units of beer.

Units of beer Total utility (utils) Marginal utility (utils)
0 0 0
1 12 12
2 22
3 30 8
4 37
5 42 5
6 45
7 46 1
8 46 0
9 42

How to calculate MU:

Second unit: 22 – 12 = 10
Fourth unit: 37 – 30 = 7
Sixth unit: 45 – 42 = 3
Ninth unit: 42 – 46 = -4

The completed table should look like this:

Units of beer Total utility (utils) Marginal utility (utils)
0 0 0
1 12 12
2 22 10
3 30 8
4 37 7
5 42 5
6 45 3
7 46 1
8 46 0
9 42 -4

### The following diagrams are based on William's consumption of beer:

Study these diagrams and answer the questions:

As the units of beer consumed by William increase, his total utility _______

Think again.

His total utility does increase but not his marginal utility.

Think again.

His marginal utility does decrease but not his total utility.

Correct.

As William consumes more beer, his total utility will increase while his marginal utility will decrease.

### Indicate whether the following statement is true or false:

Since the marginal utility of the first beer is the highest, William should only consume one beer in order to maximise his utility.

Think again.

William wants to maximise his total utility.

Correct.

The statement is false.

William wants to maximise his total utility, and he does so when he consumes seven beers.

### Choose the correct words in brackets.

The relationship between total utility and marginal utility indicates that when marginal utility decreases, total utility (increases, decreases) at a(n) (increasing, decreasing) rate, and when total utility is at a (maximum, minimum) point, marginal utility is zero and total utility starts to decline if marginal utility is (negative, positive).

The relationship between total utility and marginal utility indicates that when marginal utility decreases, total utility increases at a decreasing rate, and when total utility is at a maximum point, marginal utility is zero and total utility starts to decline if marginal utility is negative.

### Choose the correct words in brackets.

The law of diminishing marginal utility states that the marginal utility or extra satisfaction gained from consuming an additional good or service (declines, increases) as people consume (more, less) of the good or service in a given period.

The law of diminishing marginal utility states that the marginal utility or extra satisfaction gained from consuming an additional good or service declines as people consume more of the good or service in a given period.