Question

Difficulty: HardLaw of Diminishing Marginal Utility

The table below presents the Total Utility (TUTU) and Marginal Utility (MUMU) derived by a consumer from drinking successive bottles of fruit juice on a warm day:

Quantity Consumed (QQ)Total Utility (TUTU) in utilsMarginal Utility (MUMU) in utils
12424
24218
3XX12
460YY
5600
652-8

Based on the table, what are the values of XX and YY, and at which quantity consumed is the consumer's point of satiety reached?

  1. X=54X = 54, Y=6Y = 6, and satiety is reached at the 5th unit.Answer
  2. B
    X=54X = 54, Y=18Y = 18, and satiety is reached at the 4th unit.
  3. C
    X=42X = 42, Y=6Y = 6, and satiety is reached at the 6th unit.
  4. D
    X=54X = 54, Y=0Y = 0, and satiety is reached at the 3rd unit.

Answer

X=54X = 54, Y=6Y = 6, and the point of satiety is reached at the 5th unit of consumption.
To find XX, add the marginal utility of the 3rd unit (1212) to the total utility of the 2nd unit (4242), giving X=54X = 54. To find YY, subtract the total utility of the 3rd unit (5454) from the total utility of the 4th unit (6060), giving Y=6Y = 6. The point of satiety is the level of consumption where marginal utility reaches zero and total utility is maximized (6060 utils at 55 units). Thus, the option stating X=54X = 54, Y=6Y = 6, and satiety at the 5th unit is correct.

Step-by-Step Solution

1
Calculate the unknown Total Utility XX at Q=3Q = 3.
X=TU3=TU2+MU3=42+12=54X = TU_3 = TU_2 + MU_3 = 42 + 12 = 54 utils.
Total Utility at any level of consumption is the cumulative sum of Marginal Utilities up to that level.
2
Calculate the unknown Marginal Utility YY at Q=4Q = 4.
Y=MU4=TU4TU3=6054=6Y = MU_4 = TU_4 - TU_3 = 60 - 54 = 6 utils.
Marginal Utility is the change in Total Utility resulting from consuming one additional unit (MUn=TUnTUn1MU_n = TU_n - TU_{n-1}).
3
Identify the point of satiety.
Satiety occurs at Q=5Q = 5 units.
The point of satiety (saturation point) is reached where Marginal Utility equals zero (MU=0MU = 0) and Total Utility attains its peak value (TU=60TU = 60).

Key Concept

Relationship between Total Utility and Marginal Utility; Point of Satiety
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