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Difficulty: Very hardConcepts of Utility (Total, Average, and Marginal Utility)

Match each specific utility condition or phase of consumer satisfaction listed on the left with its exact mathematical relationship involving Total Utility (TUTU), Marginal Utility (MUMU), or Average Utility (AUAU) on the right.

  • Point of Total Saturation (Satiety)Marginal Utility is zero (MU=0MU = 0) while Total Utility (TUTU) reaches its absolute maximum.
  • Phase of Increasing Utility at a Decreasing RateMarginal Utility is positive but falling (0<MUn<MUn−10 < MU_{n} < MU_{n-1}), while Total Utility (TUTU) slope is positive and concave.
  • Point where Average Utility (AUAU) Reaches MaximumMarginal Utility equals Average Utility (MU=AUMU = AU), intersecting the AUAU curve at its peak.
  • Phase of Disutility (Dissatisfaction)Marginal Utility is negative (MU<0MU < 0), causing Total Utility (TUTU) to decline.

Answer

Point of Total Saturation matches MU=0MU = 0 with peak TUTU; Phase of Increasing Utility at a Decreasing Rate matches MU>0MU > 0 and falling; Point where AUAU Reaches Maximum matches MU=AUMU = AU; Phase of Disutility matches MU<0MU < 0 causing TUTU to decline.
The correct pairings accurately reflect the differential relationships governing total, average, and marginal utility: saturation corresponds to MU=0MU = 0 and peak TUTU; positive but declining MUMU causes TUTU to increase at a decreasing rate; maximum AUAU occurs where MU=AUMU = AU; and disutility occurs when MU<0MU < 0, causing TUTU to fall.

Step-by-Step Solution

1
Analyze the Saturation Point condition
Saturation occurs when consumption yields zero additional satisfaction (MU=0MU = 0). Beyond this, TUTU cannot increase, meaning TUTU is at its maximum.
By definition, the peak of TUTU occurs where the derivative or incremental gain (MUMU) is zero.
2
Analyze the Increasing Utility at a Decreasing Rate phase
As long as MU>0MU > 0, total satisfaction (TUTU) keeps growing. Because MUMU is falling, the rate of increase of TUTU slows down.
This reflects the core principle of diminishing marginal utility prior to reaching saturation.
3
Analyze the mathematical property of Average Utility (AUAU) peak
Average Utility (AU=TUQAU = \frac{TU}{Q}) rises when MU>AUMU > AU and falls when MU<AUMU < AU. Therefore, AUAU reaches its maximum at the point of intersection where MU=AUMU = AU.
This represents the classic mathematical relationship between average and marginal values.
4
Analyze the Disutility phase
Disutility occurs when additional units yield negative utility (MU<0MU < 0), causing the cumulative satisfaction (TUTU) to drop.
Negative marginal utility subtracts from total accumulated utility.

Key Concept

Interrelationships among Total Utility, Marginal Utility, and Average Utility
Estimated Time:1m 30s
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Topics

Concepts of Utility (Total, Average, and Marginal Utility)

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