Worked example 1
A student's total utility (TU) from consuming cups of coffee per day is shown in the table below.
| Cups of Coffee | Total Utility (utils) |
|---|---|
| 0 | 0 |
| --- | --- |
| 1 | 25 |
| 2 | 45 |
| 3 | 60 |
| 4 | 70 |
| 5 | 75 |
| 6 | 75 |
| 7 | 72 |
(a) Calculate the marginal utility (MU) for each cup of coffee consumed. (b) At which cup does diminishing marginal utility begin? (c) How many cups should be consumed to maximise total utility?
Show solution outline
(a) Calculating Marginal Utility (MU)
We calculate MU as the change in total utility from consuming one more unit (MU = ΔTU / ΔQ).
| Cups (Q) | TU | Marginal Utility (MU) | Calculation |
|---|---|---|---|
| 0 | 0 | - | - |
| --- | --- | --- | --- |
| 1 | 25 | 25 | 25 - 0 |
| 2 | 45 | 20 | 45 - 25 |
| 3 | 60 | 15 | 60 - 45 |
| 4 | 70 | 10 | 70 - 60 |
| 5 | 75 | 5 | 75 - 70 |
| 6 | 75 | 0 | 75 - 75 |
| 7 | 72 | -3 | 72 - 75 |
(b) Point of Diminishing Marginal Utility
The law of diminishing marginal utility states that MU falls as more units are consumed. In this case, the MU of the 1st cup is 25, and the MU of the 2nd cup is 20.
Answer: Diminishing marginal utility begins with the 2nd cup of coffee because this is the first point where the additional utility gained is less than the previous one.
(c) Maximising Total Utility
Total utility is maximised when marginal utility is zero. After this point, consuming more results in negative marginal utility, causing total utility to fall.
Answer: Total utility is maximised at 6 cups of coffee, where MU is 0 and TU is at its peak of 75 utils. Consuming the 7th cup would decrease total utility.