Understanding Utility & the Equi-Marginal Principle (Cambridge International A-Level Economics)

What utility means

Utility theory

• Utility is the satisfaction gained from consumption

  • Marginal utility is the additional utility (satisfaction) gained from the consumption of an additional product

• The utility gained from consuming the first unit is usually higher than the utility gained from consuming the next unit

  • For example, a hungry consumer gains high utility from eating their first hamburger. They are still hungry and purchase a second hamburger but gain less satisfaction from eating it than they did from the first hamburger

• To calculate total utility, the marginal utility of each unit consumed is added together

  • This means that total utility keeps increasing even while marginal utility is decreasing

• The Law of Diminishing Marginal Utility states that as additional products are consumed, the utility gained from t he next unit is lower than the utility gained from the previous unit

• A consumer achieves utility maximisation when they spend their limited income in such a way that they will achieve the most satisfaction from their money

Understanding diminishing marginal utility

Spec point — 7.1.2

Diminishing marginal utility

• The law of diminishing marginal utility states that as additional products are consumed, the utility gained from the next unit is lower than the utility gained from the previous unit

• The law of diminishing marginal utility helps to explain why the demand curve is downward sloping

  • When the first unit is purchased, the utility is high and consumers are willing to pay a high price
  • When subsequent units are purchased, each one offers less utility and the willingness of the consumer to pay the initial price decreases
  • Lowering the price makes it a more attractive proposition for the consumer to keep consuming additional units
  • This is one reason why firms offer discounts such as '50% off the second item'

The marginal utility decreases with every additional bite

• A consumer achieves utility maximisation when they spend their limited income in such a way that they will achieve the most satisfaction from their money
• When marginal utility is zero, total utility is maximised

The equi-marginal principle

Spec point — 7.1.3

• The equi-marginal principle helps explain how a rational consumer allocates their limited budget to gain the most utility from their spending

• A person is in consumer equilibrium when they cannot rearrange their spending to gain more total enjoyment

• In economic terms, this happens when:

• $\frac{\mathrm{MUa}}{\mathrm{Pa}}=\frac{\mathrm{MUb}}{\mathrm{Pb}}$

• Where

  • MU = marginal utility (extra satisfaction from one more unit)
  • P = price of the product
  • a and b are different products

Worked Example

• Imagine a consumer has £10 to spend and is choosing between:

  • Bubble tea (£2 per cup)
  • Spotify Premium (£1 per day)

• They want to gain the m ost enjoyment from their money. The table below shows how much satisfaction (utility) they gain from each extra unit of bubble tea or Spotify, and how much satisfaction per £1 spent

Finding consumer equilibrium

Bubble Tea (£2 each)

Quantity	MU	MU/£
1	40	20
2	36	18
3	30	15
4	20	10
5	10	5

Spotify (£1/day)

Quantity	MU	MU/£
1	30	30
2	24	24
3	18	18
4	12	12
5	6	6

Analysis

• The consumer maximises utility by applying the equi-marginal principle
• Utility is maximised when:

$\frac{\mathrm{MUa}}{\mathrm{Pa}}=\frac{\mathrm{MUb}}{\mathrm{Pb}}$

• The optimal bundle within the £10 budget is:

  • 3 Bubble Teas (£6)
  • 4 Spotify days (£4)

• At this combination:

  • MU/£ of the last bubble tea = 15
  • MU/£ of the last Spotify day = 12

• Perfect equality is not achieved because:

  • Goods are indivisible
  • Prices differ (£2 vs £1)
  • The budget constraint prevents further fine adjustment

• Consumer equilibrium is therefore defined as the point where:

  • No reallocation of expenditure increases total utility

• If £2 were reallocated from bubble tea to Spotify:

  • The marginal utility gained from additional Spotify would be less than the marginal utility lost from bubble tea
  • Total utility would fall

• Hence, the chosen bundle represents constrained utility maximisation

Exam Hint You should remember that this concept assumes the consumer is rational, wants to maximise happiness and has a fixed budget