The table below presents the utility schedule of a consumer consuming successive portions of roasted maize: | Quantity (Q) | Total Utility (TU) in utils | Marginal Utility (MU) in utils | | :---: | :---: | :---: | | 1 | 18 | 18 | | 2 | 34 | 16 | | 3 | P | 12 | | 4 | 54 | Q_m | | 5 | 58 | 4 | | 6 | 5

The table below presents the utility schedule of a consumer consuming successive portions … — JAMB UTME

The table below presents the utility schedule of a consumer consuming successive portions of roasted maize:

Quantity ( $Q$ )	Total Utility ( $TU$ ) in utils	Marginal Utility ( $MU$ ) in utils
1	18	18
2	34	16
3	$P$	12
4	54	$Q_m$
5	58	4
6	58	0
7	52	-6

Based on the table, what is the combined value of $P + Q_m$ , and at which unit of consumption does the consumer reach the point of satiety?

$54$ utils and the 6th unitAnswer
B
$54$ utils and the 5th unit
C
$50$ utils and the 6th unit
D
$58$ utils and the 7th unit

Answer

The combined value of

P + Q_m

54

utils, and the point of satiety is reached at the 6th unit.

To find

P

, add the marginal utility of the 3rd unit (

12

) to the total utility of the 2nd unit (

34

), yielding

P = 46

. To find

Q_m

, subtract the total utility of the 3rd unit (

46

) from the total utility of the 4th unit (

54

), yielding

Q_m = 8

. Summing these gives

46 + 8 = 54

utils. The point of satiety is the quantity at which marginal utility is zero (

MU = 0

), which occurs at the 6th unit where total utility peaks at

58

utils.

Step-by-Step Solution

Calculate the unknown Total Utility

P

at the 3rd unit.

P = TU_2 + MU_3 = 34 + 12 = 46

utils.

Total utility at quantity

Q

equals total utility at

Q-1

plus marginal utility at

Q

Calculate the unknown Marginal Utility

Q_m

at the 4th unit.

Q_m = TU_4 - TU_3 = 54 - 46 = 8

utils.

Marginal utility at quantity

Q

is the change in total utility resulting from consuming that unit.

Sum

P

and

Q_m

P + Q_m = 46 + 8 = 54

utils.

Simple addition of the calculated values.

Identify the point of satiety.

The 6th unit.

The point of satiety (maximum total satisfaction) occurs at the consumption level where Marginal Utility equals zero (

MU = 0

) and Total Utility reaches its maximum.

Key Concept

Law of Diminishing Marginal Utility and Relationship between Total Utility and Marginal Utility

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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