Wikipedia
Final Utility is the utility of a good when applied to our least desirable use of it. It is the estimated utility of the last use of a supply, i.e., the least important use of that supply. For example, if a use of a good must be given up, it will logically be the last use of the good we would choose. This is because we give up the least important of our satisfactions first—which would be the uses satisfied by the last good since we satisfy our more important needs first.
For example, if we lost a unit of a good, the value of the loss would be the value of the least important use of the good. This last good, which represents its final utility, was being applied to our least important wants. In the case of the lost good, it is replaced and the value to which we can assign the loss is not the value of the first most important use of the good, but the least important—what we call the final utility.
According to the law of marginal utility, the value of each good in a stock of identical goods is utility of the last and most easily dispensable unit. That is why price is said to be determined by supply and demand: the price reflects the (approximate and average) value of the good, but most closely reflects the value of the last use. If there is a shortage of supply, the good will cease being applied to its least important uses. All else being equal, the price will increase and the increase in price represents, so to speak, the value we attribute to the new last use. Before, with a larger supply, the last use was of less value to us. With a smaller supply the value of the last use is necessarily more important because we always satisfy our more important wants first. Therefore the increase in price can be seen as a reflection of the increase in value we attribute to the last use of the supply.
Ludwig von Mises writes:
"When face with the problem of the value to be attached to one unit of a homogeneous supply, man decides on the basis of the value of the least important use he makes of the units of the whole supply; he decides on the basis of marginal utility."