From the following data on a consumer's total utility derived from successive cups of tea, calculate the marginal utility of each cup and state at which cup the point of satiety is reached.
| Cups | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Total Utility (utils) | 10 | 18 | 24 | 24 | 20 |
Marginal utility of the n-th unit is calculated as MU_n = TU_n - TU_(n-1), taking TU_0 = 0.
| Cups (n) | TU | MU = TU_n - TU_(n-1) |
|---|---|---|
| 1 | 10 | 10 - 0 = 10 |
| 2 | 18 | 18 - 10 = 8 |
| 3 | 24 | 24 - 18 = 6 |
| 4 | 24 | 24 - 24 = 0 |
| 5 | 20 | 20 - 24 = -4 |
Marginal utility falls continuously from 10 to 8 to 6, confirming the Law of Diminishing Marginal Utility. It reaches zero at the 4th cup, which is exactly where total utility is at its maximum (24 utils) — this is the point of satiety. Beyond it, the 5th cup actually reduces total utility (from 24 to 20), so marginal utility turns negative, showing the consumer has over-consumed relative to what maximises satisfaction.
Independent verification: re-computing each difference separately — 18-10=8, 24-18=6, 24-24=0, 20-24=-4 — confirms the same marginal utility series, so the answer is verified.
MU series: 10, 8, 6, 0, -4 utils. The point of satiety (MU = 0, TU at its maximum) occurs at the 4th cup.
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