Cardinal Utility Approach: Total and Marginal Utility

Alfred Marshall's cardinal approach treats utility as a measurable quantity, expressed in imaginary units called utils, in the same way that weight is measured in kilograms or length in metres. While no instrument can literally weigh satisfaction, the cardinal approach is a useful simplifying assumption that allows a consumer's behaviour to be analysed with numbers and formulae.

Two related concepts follow from this assumption. Total Utility (TU) is the sum of the utility a consumer derives from consuming all the units of a commodity taken together. Marginal Utility (MU) is the additional utility gained from consuming one more (the last) unit of the commodity, holding the consumption of everything else constant. Marginal utility is calculated as the change in total utility resulting from a one-unit change in the quantity consumed:

$MU_n = TU_n - TU_{n-1}$

where $TU_n$ is the total utility from $n$ units and $TU_{n-1}$ is the total utility from $(n-1)$ units. Equivalently, total utility up to the $n$-th unit is the sum of the marginal utilities of every unit consumed up to and including that unit: $TU_n = MU_1 + MU_2 + ... + MU_n$.

Consider a student consuming successive glasses of buttermilk on a hot afternoon: