Which one of the following statements about total utility and marginal utility is not correct according to the law of diminishing marginal utility?

Introduction / Context:
In microeconomic theory of consumer behaviour, total utility and marginal utility are used to explain how satisfaction changes as a consumer consumes more units of a good. The law of diminishing marginal utility is a fundamental principle that describes how marginal utility typically falls as consumption increases. This question asks you to identify which given statement about the relationship between total utility and marginal utility is not correct.

Given Data / Assumptions:

• Total utility is the sum of satisfaction from all units consumed.
• Marginal utility is the additional satisfaction from one more unit of the good.
• The law of diminishing marginal utility is assumed to hold.
• Average utility is total utility divided by the number of units consumed.

Concept / Approach:
According to the law of diminishing marginal utility, as a consumer consumes more units of a good, the marginal utility obtained from each additional unit generally decreases. Total utility rises as long as marginal utility is positive, reaches a maximum when marginal utility becomes zero, and starts falling when marginal utility becomes negative. Average utility, however, does not necessarily equal marginal utility when total utility is at its maximum. Instead, at the point of maximum total utility, marginal utility is zero while average utility is positive and less than its earlier peak value.

Step-by-Step Solution:
Step 1: Recall that when total utility is increasing, marginal utility must be positive, since each extra unit still adds to total satisfaction. Step 2: Remember that when total utility is decreasing, marginal utility is negative, because the extra unit reduces total satisfaction. Step 3: Understand that total utility is maximized at the point where marginal utility becomes zero, after which further consumption lowers total utility. Step 4: Recognize that at maximum total utility, marginal utility is zero while average utility is still positive, so they are not equal to each other at that point.

Verification / Alternative check:
You can sketch a simple numerical example. Suppose marginal utility values for successive units decline from 10 to 8, 6, 4, 2, 0, and then negative values. Total utility is the cumulative sum and peaks when marginal utility becomes zero. At that unit, average utility is total utility divided by the number of units, which remains positive. Marginal utility is zero. Since average utility is positive and not zero, they cannot be equal at the maximum of total utility, confirming that the statement claiming equality is incorrect.

Why Other Options Are Wrong:
When total utility is maximum, marginal utility is zero: This is correct and comes directly from the relationship between total and marginal utility.
When total utility is decreasing, marginal utility is negative: This is also correct, because a negative marginal utility means each additional unit reduces total satisfaction.
When total utility is increasing, marginal utility is positive: This is correct, since total utility can only increase when each extra unit adds positive utility.

Common Pitfalls:
A frequent confusion is between average and marginal concepts. Students sometimes think that at a maximum point for total utility, both marginal and average utility must be equal or must both be zero. This is not true. Marginal utility is zero at the maximum of total utility, but average utility can still be positive. Another pitfall is ignoring the sign of marginal utility when total utility begins to fall; remembering that negative marginal utility pulls total utility down helps avoid that error.

Final Answer:
The statement that is not correct is that when total utility is maximum, marginal and average utility are equal to each other.