Utility and diminishing marginal utility

Utility is a good's power to satisfy a want. It is subjective: it differs from person to person, and with place and time (a room heater gives great utility in a cold winter, and almost none in summer).

Cardinal utility analysis measures utility in numbers (units called utils).

• Total utility (TU): the satisfaction from all the units consumed.
• Marginal utility (MU): the extra satisfaction from one more unit: MUn = TUn − TU(n−1). TU is the sum of all the MUs.

Example: eating chapatis, a person's TU is 10, 17, 21, 23, 23 and 21 for 1 to 6 chapatis. MU = 10, 7, 4, 2, 0, −2.

The law of diminishing marginal utility: as you consume more units of a good, the MU of each extra unit falls. When TU reaches its maximum and stays constant, MU is zero; after that, MU becomes negative, and TU falls.

Three links between the two to remember: while MU falls but stays positive, TU rises; when MU is zero, TU is at its maximum (the point of satiety, or saturation point); when MU turns negative, TU falls.

If quantity jumps by more than one unit (from 1 to 3, say), use MU = ΔTU ÷ ΔQ. TU going from 10 to 18 over 2 units gives MU = 8 ÷ 2 = 4.

The law holds only under some assumptions:

• Continuous consumption, with no time gap. A burger at 9 a.m. and another at 6 p.m. may please just as much, because you are hungry again.
• Standard units: a glass of water, a normal chapati, not a spoonful at a time.
• Identical units: all the chapatis the same, not one paneer paratha and then an aloo one.

Hobbies (collecting stamps or coins) and money itself are often given as exceptions: for many people, more of them seems to please more, not less.

This explains the law of demand: since each extra unit is worth less to the consumer, she will buy more only at a lower price.