Utility Bills Chapter Notes | Applied Mathematics for Class 11 - Commerce PDF Download

Definition of Utility

• Utility refers to the satisfaction or pleasure that consumers derive from consuming goods and services.
• It is a subjective concept and varies from person to person.

Total Utility (TU)

• Total utility is the total satisfaction obtained from consuming a certain quantity of a good or service.
• Formula: TU = U₁ + U₂ + U₃ + ... + Uₙ, where U₁, U₂, ..., Uₙ are the individual utilities derived from consuming each unit of the good or service.

Example

Suppose a person consumes three apples and derives the following utilities: 10, 8, and 6.
Ans: Total Utility = 10 + 8 + 6 = 24

Marginal Utility (MU)

• Marginal utility is the additional satisfaction obtained from consuming one additional unit of a good or service.
• Formula: MU = ΔTU / ΔQ, where ΔTU is the change in total utility and ΔQ is the change in quantity consumed.

Example

Using the previous example, if consuming the third apple increases total utility to 24, and consuming the second apple increased total utility from 10 to 18:
Ans: Marginal Utility of the third apple = (24 - 18) / (3 - 2) = 6

Law of Diminishing Marginal Utility

• According to the law of diminishing marginal utility, as a person consumes more of a good or service, the marginal utility derived from each additional unit decreases.
• This principle reflects the idea that as consumption increases, the satisfaction derived from each additional unit tends to diminish.

Utility Maximization

• Consumers aim to maximize their total utility subject to their budget constraints.
• They allocate their limited income among different goods and services in such a way that the marginal utility per dollar spent is equal across all goods.
• This condition is known as the equal marginal utility per dollar rule or the equimarginal principle.

Equimarginal Principle

Formula: MU₁ / P₁ = MU₂ / P₂ = ... = MUᵢ / Pᵢ, where MUᵢ is the marginal utility of the i-th good or service, and Pᵢ is its price.

Example

Suppose a person has a budget of Rs. 100 to spend on apples (Rs. 10 each) and oranges (Rs. 5 each).
Ans: If the marginal utility of the last apple consumed is 20 and the marginal utility of the last orange consumed is 10:
Equimarginal Principle: 20 / 10 = 10 / 5