In economics, utility is a measure of personal satisfaction or level of meeting a need that a good or service meets. For example the initial cup of coffee in the morning meets a large need and provides a large amount of satisfaction (utility). Another example is go under water and hold your breath, keep holding it until you think you will pass out. Then come up out of the water, that first breath is wonderful -- tremendous utility. That is utility - the meeting of a need or being satisfied.
Now Marginal Utility is the change in utility from one more good or service being consumed. So the amount of utility from the first cup of coffee or that first breath is huge.
Diminishing Marginal Utility is the fact that each addition good or service consumed, creates a smaller and smaller amount of additional utility. In the examples above, that second cup of coffee in the morning or the second breath after the first will provide additional satisfaction or need meeting, but it will not provide near as much satisfaction (utility) as the first one did. The third cup or third breath has even less additional satisfaction or need meeting ability (utility) as the second and the first.
Some products or services may have some increasing marginal utility at first, but every good or service at some point provides decreasing additional utility (or diminishing marginal utility).
When the total utility curve stops increasing at an increasing rate and starts increasing at a decreasing rate, that is the point where the marginal utility curve reaches its max and starts decreasing -- this is the point of diminshing marginal utility.
Let me give you another example, if you had no shoes and someone gave you only one shoe, you would receive some utility. You can now hop through the sticker patch. But a second shoe that completes the pair might actually give you more utility than the first shoe, because you are clumsy and you keep falling down with only one shoe. But with two...
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