When consumption is expanded beyond the point of satiety, the total utility starts falling because marginal utility turns negative. In the present example, the consumer gets negative marginal utilities of Rs. 2 and Rs. 4, when he decides to consume seventh and eighth units of the commodity respectively.

Fig. 4.1: Relation among MU, TU and AU

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The relationship between total utility and marginal utility can also be verified mathematically by using the concept of slope. We know that the slope of the total utility curve at each point indicates the marginal utility derived from the corresponding level of consumption. This has been shown in Fig. 4.2.

Fig. 4.2: Marginal Utility though Slope of Total Utility

In Fig. 4.2, four points ‘A’, ‘B’ ‘C’ and ‘D’ are considered on the total utility curve. The slopes at these points are measured by the slopes of the tangents drawn at these points. The slope of the total utility curve at point ‘A’ is AF/EF, while the slope of the total utility curve at point ‘B’ is BH/GH. Since AF/EF > BH/GH, marginal utility for the unit corresponding to point ‘A’ is greater than for the unit corresponding to point ‘B’.

Thus, initially, marginal utility falls, as total utility rises at diminishing rate. Further, at maximum point ‘C’ on the total utility curve, the tangent is parallel to X-axis. So, its slope is zero. Therefore, marginal utility is zero, when total utility is maximum. Again, slope of the tangent after point ‘C’ becomes negative (e.g., point ‘D’ in the figure). This shows that marginal utility turns negative, after total utility reaches its maximum point.

Unlike marginal utility, average utility is always positive, since it is a ratio of two non- negative values. So, the graph of average utility always remains above X-axis. When average utility attains maximum value, it is equal to marginal utility. Like marginal utility curve, average utility curve is also downward sloping.