Marginal utility vs Total utility [closed]

If marginal utility is positive, consuming an additional unit of a product will cause total utility to decline. Is that statement true and why?

Marginal utility is, by definition, the additional utility that comes from consuming an additional unit of a good (more precisely, this holds if we consider discrete units of the good, if we have a continuous differentiable utility function marginal utility is the derivative of the function, but the intuitive concept is the same).

Therefore, if marginal utility is (strictly, that is not zero) positive, this means that the consumption of an additional unit of the good increases total utility.

In order to have a decrease of total utility, we must have a (strictly) negative marginal utility.

Therefore, the correct statement is just the contrary of what you said: if marginal utility is positive, an additional unit of a product will cause the total utility to increase.

• If I consider the Law of diminishing marginal utility, then is the statement still false? Commented Mar 13, 2023 at 17:43
• Yes, that Law doesn't change the fact that the mariginal utility is positive, it means that it is positive, but decreasing, smaller as long as the consumption increases, but still positive. From a technical point of view this law involves the second derivative, not the derivative: the first derivative is positive, the second derivative is negative (but the second derivative only). Commented Mar 13, 2023 at 17:48
• That means, Total Utility increases but in a declining rate if i consider Law of diminishing utility ? Commented Mar 14, 2023 at 0:20
• Yes, exactly. That's the meaning of the law of diminishing marginal utility. Commented Mar 14, 2023 at 0:30

The statement is not true. Consider trivial example of following utility function:

$$U= 2x^{0.5}$$

Marginal utility will be always positive for this for this function (given that x is a good so $$x\geq 0$$, you can check that MU is

$$MU = \frac{1}{x^{0.5}}$$

which will always be positive in this case yet consuming additional units of x causes $$U$$ to increase not decrease.