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Total utility is the overall satisfaction or benefit that a consumer gets from consuming a certain amount of goods or services. It can be thought of as the sum of all the marginal utilities resulting from each additional unit consumed.

Marginal utility refers to the additional satisfaction or benefit that a consumer gets from consuming an additional unit of a good or service. It represents the change in total utility due to a one-unit increase in the quantity of the good consumed.

The relationship between total utility and marginal utility can be expressed as follows: Total Utility = Marginal Utility(1) + Marginal Utility(2) + ... + Marginal Utility(n), where n represents the number of units consumed.

The Law of Diminishing Marginal Utility states that as the consumption of a good or service increases, the marginal utility tends to decrease. This means that the satisfaction or benefit derived from consuming additional units of the good or service will be less than what was experienced by consuming previous units.

Let's use an example to illustrate this possibility. Suppose a consumer eats 1 slice of pizza and derives a satisfaction level of 10 utility points from it. When the consumer eats a second slice, the satisfaction level might increase to 18 utility points. The marginal utility from the second slice (8 points) is less than the marginal utility from the first slice (10 points), which demonstrates the Law of Diminishing Marginal Utility. However, the total utility increases from 10 to 18 points, showing that an increase in total utility is possible even when marginal utility is diminishing. This will continue until the marginal utility becomes zero or negative (at which point total utility will no longer increase). In conclusion, it is possible for total utility to increase while marginal utility diminishes due to the Law of Diminishing Marginal Utility. The total utility will increase as long as the marginal utility is positive, even if it is decreasing.