Which best describes the relationship between total utility and marginal utility?

BlackTom题目解析

Question

Which best describes the relationship between total utility and marginal utility?

BlackTom题目解析

BlackTom AI · Accepted Answer

The question asks about how total utility and marginal utility are related. This requires comparing each statement to the standard economic relationship between total utility (the overall satisfaction from consuming a good) and marginal utility (the additional satisfaction from consuming one more unit).
Option 1: 'Total utility reflects the changes in marginal utility.' This is inaccurate because total utility is the aggregate level of satisfaction, while marginal utility measures the incremental change at the margin. It is marginal utility, not total utility, that describes the changes in total utility as more units are consumed.
Option 2: 'Marginal utility reaches zero when total utility is at a minimum.' Here the logic is flawed: marginal utility declines as consumption increases, and it can reach zero at the point where adding another unit provides no additional satisfaction, but that situation does not correspond to total utility being at a minimum; total utility typically decreases with negative marginal utility, not zero marginal utility, and in standard concave utility functions marginal utility approaches zero as total utility increases, not as it reaches a minimum. This statement confuses the direction and interpretation of the relationship.
Option 3: 'Total utility is negative when marginal utility is positive.' This runs counter to the definitions: marginal utility being positive means each additional unit adds to total utility, so total utility would not be negative due to a positive marginal value. The claim reverses the intuitive and mathematical connection between the two concepts.
Option 4: 'Marginal utility reflects the changes in total utility.' This correctly captures the core relationship: marginal utility measures how total utility changes when consumption increases by one unit. If marginal utility is positive, total utility increases; if marginal utility is negative, total utility decreases; and when marginal utility is zero, total utility is at a peak with respect to small changes in quantity. The wording aligns with standard microeconomic definitions and the slope interpretation of total utility with respect to quantity.
In summary, the only option that accurately describes the standard relationship is option 4, since marginal utility is the derivative-like measure of how total utility changes as more units are consumed, while the other statements mix up cause and effect or rely on incorrect implications about sign and minima/maxima of total utility.

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