Why is the downward slope of the demand curve related to marginal utility?

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The reason for this is that when we consume more of a good or a service, the next unit of that product comes to have less utility for us (in general).  If I have not eaten, the first sandwich will have a great deal of utility for me because I am very hungry and it will really help to satisfy my hunger.  But after I've eaten two sandwiches, I'm no longer very hungry.  A third sandwich would not have much utility for me.  This is how decreasing marginal utility works.

So now think about how much I would pay for these sandwiches.  For the first one, I might pay a lot.  I'm very hungry and I really want the sandwich.  I'd pay a little less for the second sandwich because I'm less hungry.  By the third sandwich, I wouldn't pay much at all because I don't really need it that much.  Thus, as the quantity of sandwiches goes up, the price I will pay for them goes down.  This yields a downward sloping demand curve.

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