How to Calculate Total Utility
Total utility is the sum of the marginal utilities of every unit consumed: TU = MU₁ + MU₂ + ... + MUn.
The Total Utility formula
Calculator
Enter the marginal utility of each unit to get total utility and see whether the extra utility is shrinking.
The first song is worth 30 utils in the worked example.
Extra utility from the second unit, on top of the first.
Extra utility from the third unit.
Extra utility from the fourth unit. Enter a negative number if the unit made things worse.
Summing the marginal utilities of all four units gives 82 utils of total satisfaction.
- Total utility after 3 units
- 72
- Utility added by the 4th unit
- 10
- Pattern of marginal utility
- Diminishing
The running total one unit earlier, which is what the fourth unit builds on.
Total utility rose by 10 utils on the last unit, which is the definition of its marginal utility.
Diminishing marginal utility is the normal case, and it is one reason demand curves slope downward.
How to calculate Total Utility, step by step
- 1List the marginal utility of each unit. Write down the extra utility from the first unit, the second unit, and so on.
- 2Add them together. TU = MU₁ + MU₂ + ... + MUn, summed over every unit actually consumed.
- 3Or build the running total. Total utility at quantity Q equals total utility at Q − 1 plus the marginal utility of unit Q.
- 4Find where total utility peaks. Total utility is highest at the quantity where marginal utility reaches zero, and it falls once MU goes negative.
Worked example: Total Utility
Marginal utility from the first four songs a listener buys is 30, 24, 18, and 10 utils. Total utility after four songs = 30 + 24 + 18 + 10 = 82 utils, and after three songs it was 30 + 24 + 18 = 72, so the fourth song added 82 − 72 = 10 utils. If a fifth song had MU = −4, total utility would drop to 82 − 4 = 78.
Total Utility questions
When is total utility at its maximum?
Total utility peaks where marginal utility equals zero, because every unit before that point adds satisfaction and every unit after it subtracts satisfaction.
Can total utility fall while marginal utility is positive?
No, total utility rises whenever marginal utility is positive. It only falls once marginal utility turns negative.
What is a util?
A util is an arbitrary unit invented for measuring satisfaction so bundles can be ranked. The numbers carry no real-world meaning on their own, only their relative sizes matter.
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