Marginal Utility

This example makes several points.

First, the consumer's decision is not an all-or-nothing one. Instead, it is a decision to buy or not to buy just one more unit. That means it is a mistake to look at the total utility of the two goods as the basis for demand. The total utility is irrelevant to the decision to buy or not to buy one more unit of the good. What is relevant to any decision is what is gained or lost depending on how the decision is made; and only a part of the total utility is gained or lost as a result of the decision to buy, or not to buy, one more unit of the good. Economists call the part of utility that is gained or lost (in the decision to buy one more unit) the marginal utility.

So we should not look at the total utility but at the "marginal" utility of the good or service. Marginal utility is defined as the increase in utility as a result of consuming one more unit of the good. In other -- algebraic -- terms,

MU = U/Q dU/dQ

where U is utility and Q is the quantity of the good. In the numerical example, the MU of water is 1 and the MU of diamonds is 15, so the consumer is willing to pay 15 times as much for a diamond as for a gallon of water. (This example is, of course, not "realistic.") Despite that, the person gets about 67000 times as much total utility from water as from a diamond.

Let's see how the marginal utility of diamonds and water vary depending on how much of each good the person has.