diminishing marginal utility

Utility

1. Definition

Utility is the satisfaction or pleasure a consumer derives from consuming a good or service. It is a subjective, personal measure and can differ from one individual to another.

2. Types of Utility

• Total Utility (TU): the overall satisfaction obtained from consuming a given quantity of a good.
• Marginal Utility (MU): the additional satisfaction obtained from consuming one more unit of that good.

3. Key Assumptions of the Cardinal Utility Approach

4. Limitations of the Marginal‑Utility Theory

• Cardinality: In reality utility cannot be measured in exact “utils”; the scale is arbitrary and cannot be compared across individuals.
• Perfect rationality: Consumers often act on habits, emotions or incomplete information, which deviates from the rational‑maximisation assumption.
• Static analysis: The theory assumes a single decision‑making moment and ignores inter‑temporal choices.
• Ordinal alternatives: Modern consumer theory (indifference curves, utility‑maximisation with a utility function) treats utility as an ordering of preferences rather than a measurable quantity. This addresses many of the above shortcomings.

5. Calculating Total and Marginal Utility

Marginal Utility is the change in total utility when consumption rises by one unit:

$$ MU = \frac{\Delta TU}{\Delta Q} $$

Total Utility can be built up by adding successive marginal utilities:

$$ TU_n = \sum_{i=1}^{n} MU_i $$

In words, the total utility after the n‑th unit equals the sum of the marginal utilities of the first n units.

6. Law of Diminishing Marginal Utility

All else equal, as a consumer consumes more units of a good, the marginal utility derived from each additional unit eventually falls.

1. MU may rise at first as the consumer becomes familiar with the good.
2. Beyond a certain quantity, each extra unit adds less satisfaction than the previous one.
3. When MU reaches zero, total utility is at its maximum; any further consumption makes MU negative and total utility falls.

7. Numerical Illustration – Pizza Slices

The table shows how total and marginal utility change as a consumer eats successive slices of pizza. The negative MU in the last row demonstrates the “beyond‑optimal” point where additional consumption reduces welfare.

8. Graphical Representation (ceteris paribus)

9. Utility Maximisation – The Equi‑marginal Principle

9.1 Definition

A consumer maximises total utility by allocating a limited budget so that the last unit of money spent on each good yields the same marginal utility per unit of cost.

9.2 Formal optimisation condition

For any two goods A and B (and similarly for any number of goods):

$$ \frac{MU_A}{P_A} = \frac{MU_B}{P_B} = \dots = \frac{MU_n}{P_n} = \lambda $$

where λ is the marginal utility of income (the “utility price”). Equivalently, the condition can be written as MU_i = λP_i for every good i.

9.3 Two‑good numerical example

Because MU/P for pizza (3.0) exceeds that for soda (2.0), the consumer should purchase one more slice of pizza and one less soda. After the adjustment, suppose the next slice of pizza gives MU = 4 utils; the new ratio is 4/2 = 2, equal to soda’s 2/1 = 2. At this point the equi‑marginal condition holds and total utility is maximised.

10. Economic Implications

• Downward‑sloping demand curve: Diminishing MU explains why, as the price of a good falls, consumers are willing to buy additional units – the lower price compensates for the lower MU of those extra units.
• Consumer‑choice behaviour: The equi‑marginal principle provides a simple rule for allocating a fixed budget across many goods.
• Firm pricing strategies: Understanding that MU falls with each extra unit, firms may offer bulk‑purchase discounts, bundling or tiered pricing to capture more consumer surplus.
• Behavioural insights: Real‑world consumers do not always behave perfectly rationally; habits, advertising, and bounded information can cause deviations from the predictions of marginal‑utility theory.
• Link to modern theory: While marginal‑utility theory underpins the basic intuition behind demand, the Cambridge syllabus expects students to recognise its limitations and the subsequent move to ordinal utility and indifference‑curve analysis.

11. Summary

• Utility measures satisfaction; TU is the total, MU is the extra satisfaction from one more unit.
• The law of diminishing marginal utility states that MU falls as consumption rises, eventually reaching zero (maximum TU) and then becoming negative.
• Consumers maximise total utility by equalising the marginal utility per dollar spent across all goods (the equi‑marginal principle):
  $$\frac{MU_i}{P_i} = \lambda \quad \forall i$$
• This behaviour explains the downward‑sloping demand curve and informs firms’ pricing decisions.
• However, the theory rests on strong assumptions (cardinality, perfect rationality, ceteris paribus) and has been superseded by ordinal approaches such as indifference‑curve analysis.