The concept of utility and its measurement

Utility represents the satisfaction or happiness that an individual gains from consuming a good or service.

Key measures of utility

• Total utility - The overall satisfaction obtained from consuming all units of a good over a specific period.
• Marginal utility (MU) - The extra satisfaction gained from consuming one additional unit of a good.

Utility is often measured in arbitrary units, allowing economists to quantify satisfaction in a way similar to counting units of goods consumed.

The law of diminishing marginal utility

The law of diminishing marginal utility states that as a consumer increases consumption of a good, the additional satisfaction (marginal utility) from each extra unit decreases, assuming other factors remain constant.

If total utility after one pear is 12 units and after two is 18 units, the marginal utility of the second pear is 6 units (18 - 12).

Application to purchasing decisions

Consumers are more willing to buy goods when prices are below their expected value, such as during sales, but less likely when prices exceed expectations. For instance, a shopper might pay $2.50 for the first dessert bar when hungry, but only $1.75 for a second and $1.20 for a third, reflecting decreasing marginal utility.

The equi-marginal principle and consumer equilibrium

The equi-marginal principle explains how consumers allocate their limited income to maximise total utility across different goods. It occurs when the marginal utility per unit of currency spent is equal for all goods.

Formula for the equi-marginal principle

$\frac{{\text{MU}}_1}{{\text{P}}_1}=\frac{{\text{MU}}_2}{{\text{P}}_2}=\cdots =\frac{{\text{MU}}_n}{{\text{P}}_n}$

Where:

• MU = Marginal utility for each good (subscripts denote different goods)
• P = Price of each good

When this equality holds, reallocating spending cannot increase total utility further.

Assumptions of the equi-marginal principle

• Consumers have limited incomes.
• Consumers behave rationally.
• Consumers aim to maximise their utility.

Understanding consumer equilibrium

Consumer equilibrium is achieved when a consumer has distributed their income to maximise utility, following the equi-marginal principle. At this point, no further adjustments in spending will yield higher satisfaction.

Worked example - Applying the equi-marginal principle

A consumer has $10 to spend on fizzy drinks (priced at $3 per can, MU of 15 for the next can) and juice (priced at $5 per carton, MU of 25 for the next carton). Check if they are in equilibrium and suggest any adjustments.

Step 1: Identify the values

• Price of fizzy drinks (P₁) = $3, MU of fizzy drinks = 15
• Price of juice (P₂) = $5, MU of juice = 25

Step 2: Calculate MU per pound for each

MU per $ for fizzy drinks = 15 / 3 = 5

MU per $ for juice = 25 / 5 = 5

Step 3: Check equilibrium

Since 5 = 5, the ratios are equal, so the consumer is in equilibrium.

Step 4: Interpretation

No reallocation is needed, as utility is maximised.

Deriving the individual demand curve from marginal utility

An individual demand curve shows the quantity of a good a consumer is willing to buy at different prices, derived from marginal utility theory. As price changes while income stays constant, the consumer's equilibrium shifts, leading to a new quantity demanded.

Limitations of marginal utility theory

Marginal utility theory has several shortcomings, as it relies on assumptions that may not always hold in real-world scenarios.

Key limitations

• Measurement challenges - It assumes consumers can precisely rank preferences and assign numerical values to satisfaction, which is often unrealistic.
• Rationality assumption - It presumes consumers always act rationally, ignoring impulsive or irrational decisions.
• Influence of other factors - Empirical evidence shows purchases are affected by psychological elements, such as habits or advertising, beyond just utility calculations.