A consumer's total utility (TU) from consuming 3 units of commodity X is 45 utils. Consumi… — JAMB UTME

A consumer's total utility ( $TU$ ) from consuming $3$ units of commodity X is $45$ utils. Consuming the $4^{\text{th}}$ unit provides a marginal utility ( $MU$ ) of $9$ utils. The $5^{\text{th}}$ unit brings the consumer to the point of satiety (saturation), while consuming the $6^{\text{th}}$ unit results in a marginal utility of $-3$ utils. What is the average utility ( $AU$ ) derived from consuming $5$ units of commodity X?

$10.8$ utilsAnswer
B
$12.6$ utils
C
$9.0$ utils
D
$10.2$ utils

Answer

The average utility derived from consuming 5 units of commodity X is

10.8

utils.

The correct answer of

10.8

utils is obtained because total utility at

3

units (

45

utils) plus the marginal utility of the

4^{\text{th}}

unit (

9

utils) equals

54

utils. At the point of satiety (

5^{\text{th}}

unit), marginal utility is

0

, leaving total utility unchanged at

54

utils. Dividing

54

utils by

5

units yields an average utility of

10.8

utils.

Step-by-Step Solution

Calculate Total Utility for 4 units (

TU_4

)

TU_4 = TU_3 + MU_4 = 45 + 9 = 54

utils

Total utility at

n

units is the sum of total utility at

n-1

units and the marginal utility of the

n^{\text{th}}

unit.

Determine Marginal Utility (

MU_5

) and Total Utility (

TU_5

) at the point of satiety

MU_5 = 0

utils, so

TU_5 = TU_4 + MU_5 = 54 + 0 = 54

utils

At the point of satiety (saturation point), Total Utility reaches its maximum, which means Marginal Utility is exactly zero.

Compute Average Utility for 5 units (

AU_5

)

AU_5 = \frac{TU_5}{5} = \frac{54}{5} = 10.8

utils

Average utility is defined as total utility divided by the quantity consumed (

AU = \frac{TU}{Q}

Key Concept

Relationship between Total Utility, Marginal Utility at the point of satiety, and Average Utility calculation.

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