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9708 · 7.1

Utility — practice questions

Practice and worked examples for 9708 Utility. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

The table below shows the total utility (in utils) a student gains from consuming cups of coffee per day.

Cups of CoffeeTotal Utility (TU)
00
------
112
220
326
430
532
632
730

(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)TUMU (ΔTU)
00-
---------
11212
2208
3266
4304
5322
6320
730-2

(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.

Worked example 2

A consumer has £12 to spend. Good X costs £2 per unit (MU: 20, 16, 12, 8) and Good Y costs £3 per unit (MU: 18, 15, 12, 9).

Find the utility-maximising combination.

Show solution outline

Calculate MU/P for each unit:

UnitMU_x/P_xMU_y/P_y
1st20/2 = 1018/3 = 6
---------
2nd16/2 = 815/3 = 5
3rd12/2 = 612/3 = 4
4th8/2 = 49/3 = 3

Optimal bundle: Buy units with highest MU/P until budget exhausted.

  • 1st X (MU/P = 10): spend £2, left £10
  • 2nd X (MU/P = 8): spend £2, left £8
  • 1st Y (MU/P = 6): spend £3, left £5
  • 3rd X (MU/P = 6): spend £2, left £3
  • 2nd Y (MU/P = 5): spend £3, left £0

Optimum: 3X + 2Y — check: MU_x/P_x = 6 = MU_y/P_y ✓