The total utility derived by a consumer from successive units of a commodity is given below. Calculate marginal utility at each level and state whether the Law of Diminishing Marginal Utility holds.
| Units | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Total Utility | 15 | 27 | 36 | 42 |
Using MU_n = TU_n - TU_(n-1) with TU_0 = 0:
| Units (n) | TU | MU |
|---|---|---|
| 1 | 15 | 15 - 0 = 15 |
| 2 | 27 | 27 - 15 = 12 |
| 3 | 36 | 36 - 27 = 9 |
| 4 | 42 | 42 - 36 = 6 |
Marginal utility falls continuously — 15, then 12, then 9, then 6 — with each successive unit adding less to total utility than the one before it, and total utility itself keeps rising throughout (it has not yet reached its maximum in this data, since MU has not yet fallen to zero).
Independent verification: summing the MU series, 15+12+9+6 = 42, which matches the given TU of the 4th unit exactly, confirming the MU values are correctly derived.
MU = 15, 12, 9, 6 utils for units 1 to 4 respectively. Since MU falls continuously with every additional unit, the Law of Diminishing Marginal Utility clearly holds for this consumer's data.
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