A consumer obtains an average utility (AU) of 15 utils from consuming 4 units of bottled w… — JAMB UTME

A consumer obtains an average utility ( $AU$ ) of $15$ utils from consuming $4$ units of bottled water. When the $5^{\text{th}}$ unit is consumed, the marginal utility ( $MU$ ) derived is $25$ utils. If consuming the $6^{\text{th}}$ unit brings the consumer's total utility ( $TU$ ) to $96$ utils, what is the average utility ( $AU$ ) per unit, in utils, when $6$ units are consumed?

Answer: 16 utils

Answer

The average utility per unit when 6 units are consumed is 16 utils.

To find the average utility after 6 units, determine total utility at 4 units (

15 \times 4 = 60

utils). Adding the marginal utility of the 5th unit (

25

utils) gives a total utility of

85

utils for 5 units. Since total utility for 6 units is given as

96

utils, dividing by quantity (

96 / 6

) yields an average utility of

16

utils.

Step-by-Step Solution

Calculate Total Utility for 4 units (

TU_4

)

TU_4 = 60

utils

Total utility is calculated by multiplying average utility by the quantity consumed:

TU_4 = AU_4 \times 4 = 15 \times 4 = 60

utils.

Calculate Total Utility for 5 units (

TU_5

)

TU_5 = 85

utils

Total utility of 5 units equals total utility of 4 units plus the marginal utility of the 5th unit:

TU_5 = TU_4 + MU_5 = 60 + 25 = 85

utils.

Identify Total Utility for 6 units (

TU_6

)

TU_6 = 96

utils

The total utility after consuming 6 units is given directly in the problem description as 96 utils.

Calculate Average Utility for 6 units (

AU_6

)

AU_6 = 16

utils

Average utility is calculated by dividing total utility by total units consumed:

AU_6 = \frac{TU_6}{6} = \frac{96}{6} = 16

utils.

Key Concept

Mathematical interrelationships between Total Utility (TU), Average Utility (AU), and Marginal Utility (MU)

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