In the illustration in § 23, when the boy had eaten the first apple, he experienced a certain amount of gratification, the result of a certain definite utility. The second apple had a smaller utility than the first. As the number of apples consumed was increased the total utility, that is, the sum of the utilities of the individual apples consumed, was increased. But the more apples he ate, the less was the satisfaction received from, or the utility of, the last apple consumed. When he had consumed the fifth apple his desire for apples was fully satisfied. If now being given a sixth apple he consumed it he would receive no satisfaction from it. Its utility would be nothing. Sometimes the utility of this sixth apple is spoken of as the marginal, utility of the apples and in this sense the marginal utility is always zero.

But the term marginal utility is most commonly used in another sense. It is used to indicate the utility of the last unit of the good which is actually consumed. Thus if the boy ate three apples only, the utility of the third apple would be called the marginal utility of the apples, whereas, if he ate four apples the utility of the fourth apple would be called the marginal utility of the apples. If, then, the boy with the five-apple appetite had only three apples, we shall say that the marginal utility of his supply was the utility of the third apple. The actual utilities of these three apples were all different but their potential utilities were the same for the reason that the second apple could have been substituted for the first or for the third without inconvenience to the boy. To sum up: as we increase the number of units consumed we increase the total utility, but we diminish the marginal utility.

The foregoing principle may be illustrated graphically by the accompanying figures. The units of the supply of the good (apples in this case) are measured along the line OX of the first figure and the utilities of the different units are represented by rectangles parallel to OY. Thus area a represents the amount of utility received from the consumption of the first unit consumed (the first apple), area b the amount of utility received from the consumption of the second unit, and so on for the five units. If a sixth unit were to be consumed, it would not give satisfaction to the consumer, i.e. it would not possess utility. This is represented in the figure by placing one half of the sixth rectangle above the line OX and one half below. The consumption of the first half of the sixth unit represents a utility or the satisfaction of a desire; the consumption of the second half of the sixth unit represents a discomfort or a disutility. Assuming that the disutility just equals the utility, it is a matter of indifference to the consumer whether or not the sixth unit is consumed.

When two units of the good have been consumed the total utility received is represented by the area a plus the area b, while the marginal utility of the first two units is the utility of the marginal or last of the two units, or area b. When three units have been consumed, the total utility is represented by the sum of areas a, 6, and c. The marginal utility is represented by area c. In other words the total utility is the sum of the utilities of all of the units consumed; the marginal utility is the utility of the last unit consumed.

In Figure I the rectangles are all of the same breadth but of varying heights. Therefore the different utilities and the areas of the different rectangles are to each other as the heights of the rectangles. Thus in Figure II the utility curve mn is drawn to connect the tops of imaginary rectangles representing utilities. When the supply of the good is measured by the line O'f, the total utility of the supply is represented by the area O'fim. When the supply of the good is measured by the line O'g the total utility of the supply is represented by the area O'ghm. The total utilities of the two supplies O'f and O'g are to each other as the areas O'fim and O'ghm. The marginal utility of O'f is represented by the line fi erected perpendicular to O'X' at / and intersecting the utility curve mn at i. Similarly the marginal utility of supply O'g is represented by the line gh. The marginal utilities of the two supplies O'f and O'g are to each other as fi and gh.

Figure II. - Utility Curve.