Consumer's Equilibrium

Why does a consumer buy what he buys? Because goods give him satisfaction. In economics, the want-satisfying power of a good is called its utility. Utility is subjective — it differs from person to person and place to place (water has high utility to a thirsty traveller in a desert, low utility beside a river).

Two measures of utility are central:

• Total Utility (TU) — the total satisfaction a consumer gets from consuming a given quantity of a good.
• Marginal Utility (MU) — the additional satisfaction from consuming one more unit of the good. MU = change in TU when one more unit is consumed.

As a person consumes more and more units of the same good, the extra satisfaction from each successive unit falls. This universal tendency is the Law of Diminishing Marginal Utility (DMU): as the consumption of a good increases, its marginal utility goes on decreasing. The first slice of pizza gives great satisfaction, the second a little less, the third even less.

The table below shows this for slices of pizza:

Notice MU keeps falling (20, 15, 10, 5, 0). TU rises as long as MU is positive, is maximum when MU = 0 (the 5th unit, the point of satiety), and would fall if MU became negative.

A consumer is in equilibrium when he gets the maximum total satisfaction from his given income and the given prices, and has no wish to change what he buys. The utility (cardinal) approach explains this using marginal utility.

One good: if a consumer is buying a single good, he is in equilibrium where the marginal utility of the good equals its price (both measured in money):

MU = Price (P)

If MU > P, the good gives more satisfaction than it costs, so he buys more; as he buys more, MU falls (law of DMU) until MU = P. If MU < P, he buys less. Equilibrium is where they are equal.

Two or more goods: when income is spent on several goods, the consumer maximises satisfaction by the Law of Equi-Marginal Utility — he arranges his spending so that the marginal utility of the last rupee spent on each good is equal:

MUₓ ÷ Pₓ = MUₐ ÷ Pₐ = … = MU of money

In words, the satisfaction from the last rupee spent on good X should equal the satisfaction from the last rupee spent on good Y. If one good gives more utility per rupee, the consumer shifts spending toward it (its MU falls) until the ratios are equal. At that point total satisfaction is maximum and the consumer is in equilibrium. This neatly explains how a consumer with limited money divides it among many goods.

A more modern approach explains the consumer without needing to measure utility in numbers — it only asks the consumer to rank combinations. It uses two tools: the indifference curve and the budget line.

An indifference curve (IC) joins all the combinations of two goods that give the consumer the same total satisfaction — so he is "indifferent" between them. Its features: it slopes downward (to keep satisfaction the same, more of one good means less of the other), it is convex to the origin, and a higher IC means more satisfaction. A set of such curves is an indifference map.

The budget line shows all the combinations of two goods a consumer can afford with his given income at the given prices. The combinations he can buy (on or below the line) form the budget set. The budget line slopes downward and its slope depends on the price ratio of the two goods.

The consumer is in equilibrium at the point where the budget line just touches (is tangent to) the highest possible indifference curve — point E below. There he buys the affordable combination that gives the maximum satisfaction.