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2281 · 3.2

Households — practice questions

Practice and worked examples for 2281 Households. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A student's total utility (TU) from consuming cups of coffee per day is shown in the table below.

Cups of CoffeeTotal Utility (utils)
00
------
125
245
360
470
575
675
772

(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)TUMarginal Utility (MU)Calculation
00--
------------
1252525 - 0
2452045 - 25
3601560 - 45
4701070 - 60
575575 - 70
675075 - 75
772-372 - 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.

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.

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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 ✓