Revise Households for Cambridge 2281 (3.2)

In economics, utility refers to the satisfaction, happiness, or economic welfare a consumer derives from consuming a good or service. It is a subjective concept, meaning the utility gained from a product varies greatly from person to person. To analyse consumer behaviour, economists use a hypothetical unit of measurement called 'utils'. While we cannot practically measure satisfaction in this way, it provides a useful model. The fundamental assumption underpinning utility theory is that consumers are rational and will always attempt to maximise their total utility, given their limited income and the prices of goods. This principle of utility maximisation is the cornerstone of modern microeconomic demand theory.

Total Utility (TU) is the aggregate satisfaction a consumer receives from consuming a specific quantity of a good. For example, the total utility of drinking three cups of coffee is the sum of the satisfaction from all three. Marginal Utility (MU), on the other hand, is the additional satisfaction gained from consuming one more unit of that good. It is the change in total utility resulting from a one-unit increase in consumption (MU = ΔTU / ΔQ). As a person consumes more of a good, their total utility will typically increase, but the marginal utility from each extra unit tends to be smaller than the previous one.

This fundamental law states that, ceteris paribus, as a consumer consumes successive units of a particular good, the marginal utility derived from each additional unit will eventually decline. The first unit of a good typically satisfies the most pressing need or desire, making its MU high. Subsequent units are consumed to satisfy less urgent wants, so they add progressively less to our total satisfaction. For instance, the first glass of water on a hot day is extremely satisfying (high MU), but the fifth glass provides much less additional satisfaction (low MU). Total utility is maximised at the point where marginal utility becomes zero. Consuming beyond this point would lead to negative marginal utility, causing total utility to fall.

The law of diminishing marginal utility is crucial for explaining why the individual demand curve is downward sloping. A rational consumer will continue to purchase a good as long as the marginal utility gained is greater than or equal to the price they must pay (MU ≥ P). Since the marginal utility of each additional unit decreases, a consumer is only willing to buy more units if the price falls. For a lower price to be paid, the consumer must be persuaded to consume an extra unit which they value less. Therefore, the marginal utility curve, when expressed in monetary terms, plots the price a consumer is willing to pay for each quantity, effectively becoming the individual's demand curve.

When faced with choices between different goods, a rational consumer aims to maximise their total utility by allocating their limited income according to the equi-marginal principle. This principle states that a consumer will be in equilibrium, maximising their total utility, when the ratio of marginal utility to price is the same for all goods they purchase. The formula is: MUa/Pa = MUb/Pb. If the ratio is higher for good A than for good B, the consumer would get more satisfaction per pound spent by buying more of A and less of B. They will continue to substitute until the ratios are equal, at which point no further reallocation of spending can increase total utility.

Total utility (TU) measures overall satisfaction from consumption. It typically rises at a decreasing rate as more is consumed.

Marginal utility (MU) is the extra satisfaction from one more unit:

MU = ΔTU / ΔQ

The law of diminishing marginal utility states that MU eventually falls as consumption increases — the 10th slice of pizza adds less satisfaction than the 1st.

A rational consumer with a fixed budget allocates spending so that marginal utility per pound is equal across all goods:

MU_x / P_x = MU_y / P_y

If MU_x/P_x > MU_y/P_y, the consumer should buy more X and less Y until equality is restored. This is the equi-marginal principle.

Utility-maximising condition: $\frac{MU_x}{P_x} = \frac{MU_y}{P_y}$

Consumer buys more of a good until MU per pound equals that of all other goods.

As price of good X falls, MU_x/P_x rises relative to other goods → consumer buys more X. As quantity of X rises, MU falls (diminishing MU). The consumer only demands more X at lower prices — hence the downward-sloping demand curve.