Worked example 1
The table below shows the total utility (in utils) a student gains from consuming cups of coffee per day.
| Cups of Coffee | Total Utility (TU) |
|---|---|
| 0 | 0 |
| --- | --- |
| 1 | 12 |
| 2 | 20 |
| 3 | 26 |
| 4 | 30 |
| 5 | 32 |
| 6 | 32 |
| 7 | 30 |
(a) Calculate the marginal utility for each cup consumed. (b) At which cup of coffee is total utility maximised? (c) After which cup does the law of diminishing marginal utility set in?
Show solution outline
(a) Calculation of Marginal Utility (MU)
Marginal Utility is the change in total utility from consuming one more unit (MU = ΔTU / ΔQ).
| Cups (Q) | TU | MU (ΔTU) |
|---|---|---|
| 0 | 0 | - |
| --- | --- | --- |
| 1 | 12 | 12 |
| 2 | 20 | 8 |
| 3 | 26 | 6 |
| 4 | 30 | 4 |
| 5 | 32 | 2 |
| 6 | 32 | 0 |
| 7 | 30 | -2 |
(b) Maximising Total Utility
Total utility is maximised at 32 utils. This occurs when the student consumes the 5th and 6th cups of coffee. Specifically, TU is at its peak when the 6th cup is consumed, as this is the point where marginal utility becomes zero.
(c) Law of Diminishing Marginal Utility
The law of diminishing marginal utility begins after the first cup. The MU from the first cup is 12, but the MU from the second cup falls to 8. From this point onwards, each additional cup provides less marginal utility than the one before it.