Question

Difficulty: Very hardLaw of Diminishing Marginal Utility

A consumer's marginal utility (MUMU) for the first three consecutive glasses of fruit juice consumed is 2727 utils, 3535 utils, and 2323 utils respectively. If consuming the 4th4\text{th} glass brings total utility (TUTU) to 9797 utils, and the consumer reaches the satiety point at the 6th6\text{th} glass where total utility is maximized at 101101 utils (with TUTU for the 5th5\text{th} glass also equal to 101101 utils), which of the following correctly identifies the unit at which the Law of Diminishing Marginal Utility first sets in, the MUMU of the 4th4\text{th} glass, and the MUMU at the satiety point?

  1. 3rd glass, 1212 utils, and 00 utilsAnswer
  2. B
    2nd glass, 1212 utils, and 00 utils
  3. C
    3rd glass, 24.2524.25 utils, and 44 utils
  4. D
    4th glass, 1212 utils, and 44 utils

Answer

The Law of Diminishing Marginal Utility first sets in at the 3rd glass, the marginal utility of the 4th glass is 1212 utils, and the marginal utility at the satiety point is 00 utils.
The correct response accurately applies the principles of cardinal utility theory. First, diminishing marginal utility begins when marginal satisfaction starts decreasing; since MU1=27MU_1 = 27, MU2=35MU_2 = 35, and MU3=23MU_3 = 23, the decrease begins at the 3rd glass. Second, total utility after 3 glasses is 27+35+23=8527 + 35 + 23 = 85 utils; subtracting this from TU4=97TU_4 = 97 utils yields MU4=12MU_4 = 12 utils. Third, the satiety point occurs where total utility reaches its peak (101101 utils), corresponding to MU=0MU = 0 utils.

Step-by-Step Solution

1
Determine the unit where the Law of Diminishing Marginal Utility first sets in
The Law of Diminishing Marginal Utility sets in at the 3rd glass.
Marginal utility increases from the 1st glass (MU1=27MU_1 = 27 utils) to the 2nd glass (MU2=35MU_2 = 35 utils), but then decreases to the 3rd glass (MU3=23MU_3 = 23 utils). The law of diminishing marginal utility begins operating at the point where MUMU first starts to fall, which is at Q=3Q = 3.
2
Calculate total utility for 3 glasses (TU3TU_3) and derive the marginal utility of the 4th glass (MU4MU_4)
TU3=85TU_3 = 85 utils and MU4=12MU_4 = 12 utils.
TU3=MU1+MU2+MU3=27+35+23=85TU_3 = MU_1 + MU_2 + MU_3 = 27 + 35 + 23 = 85 utils. Given TU4=97TU_4 = 97 utils, MU4=TU4TU3=9785=12MU_4 = TU_4 - TU_3 = 97 - 85 = 12 utils.
3
Determine marginal utility at the point of satiety
MUsatiety=0MU_{\text{satiety}} = 0 utils.
The point of satiety is reached when Total Utility is at its maximum (TU5=101TU_5 = 101 utils and TU6=101TU_6 = 101 utils). At this point, additional consumption yields no added satisfaction, so MU6=TU6TU5=101101=0MU_6 = TU_6 - TU_5 = 101 - 101 = 0 utils.

Key Concept

Law of Diminishing Marginal Utility and Total Utility Relationship
Estimated Time:2m 0s
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