Sample Notes: Utility

A2 Level Economics – Topic 7.1: Utility

Definition and Calculation of Total Utility and Marginal Utility

Total Utility (TU)

• Definition: Total satisfaction gained from consuming a given quantity of a good or service.
• Example: If consuming 1 apple gives 20 utils, and 2 apples give 38 utils, total utility from 2 apples = 38 utils.

Marginal Utility (MU)

• Definition: Additional satisfaction from consuming one more unit of a good or service.
• Formula:
  MU = ΔTU / ΔQ
  where ΔTU = change in total utility, ΔQ = change in quantity consumed
• Example:
  If TU increases from 38 to 45 when a 3rd apple is eaten,
  MU of 3rd apple = (45 − 38) / (3 − 2) = 7 utils

Diminishing Marginal Utility

• Law of Diminishing Marginal Utility:
  As a person consumes more units of a good, the additional (marginal) utility from each extra unit decreases.
• Illustration:
  

  Apples Eaten	Total Utility (TU)	Marginal Utility (MU)
  1	20	20
  2	38	18
  3	45	7
  4	48	3
  5	48	0
  6	47	-1 (disutility)

• Implication: Consumers will stop consuming a good once marginal utility drops to zero or becomes negative.

Equi-Marginal Principle

• Definition:
  Consumers maximize total utility by allocating expenditure such that the last unit of money spent on each good yields the same marginal utility.
• Formula:
  MUₐ / Pₐ = MUᵦ / Pᵦ = MU𝚌 / P𝚌 …
  where MU = marginal utility and P = price of good
• Application Example:
  • Let:
    • MUₐ = 30, Pₐ = 3 → MUₐ/Pₐ = 10
    • MUᵦ = 60, Pᵦ = 6 → MUᵦ/Pᵦ = 10
    • MU𝚌 = 40, P𝚌 = 4 → MU𝚌/P𝚌 = 10
  • All equal → utility is maximized.

Derivation of an Individual Demand Curve

• Link with MU:
  As MU falls with more consumption, a consumer is willing to pay less for additional units → downward-sloping demand curve.
• Assumption: Consumers make purchasing decisions based on marginal utility and price.
• Explanation:
  • High MU → high willingness to pay → high price
  • Low MU → low willingness to pay → low price
• Demand Curve Representation:
  • X-axis: Quantity
  • Y-axis: Price or MU
  • Downward slope illustrates diminishing marginal utility

Limitations of Marginal Utility Theory and Its Assumptions

1. Measurement Problem

• Utility is subjective and cannot be measured objectively in “utils”.
• Assumes cardinal utility, but real preferences are ordinal.

2. Rationality Assumption

• Assumes all consumers behave rationally to maximize utility.
• Behavioral economics shows many decisions are influenced by emotions, biases, or incomplete information.

3. Constant Marginal Utility of Money

• Assumes the value of money remains constant as it is spent.
• In reality, marginal utility of money may change with income levels or preferences.

4. Independent Utility

• Assumes utility from one good is unaffected by consumption of another.
• Ignores complementary and substitute relationships between goods.

5. Ignorance of External Factors

• Ignores advertising, peer pressure, habits, and social factors.