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Let ∆ x 1 and ∆ x 2 be very small changes (e.g. The Marginal Rate of Substitution (MRS) is the rate at which a consumer would be willing to give up a very small amount of good 2 (which we call x 2) for some of good 1 (which we call x 1) in order to be exactly as happy after the trade as before the trade. Formal Definition of the Marginal Rate of Substitution The Marginal Rate of Substitution captures the rate at which I would be willing to exchange a tiny bit of jelly beans for M&Ms. The point is, a very small amount of M&Ms would make me equally as happy as I was before, and this amount of M&Ms is not necessarily equal to the amount of jelly beans I gave up. The amount of M&Ms that would make me exactly as happy might be one-third of an M&M, it might be two M&Ms, or maybe it would be half an M&M. But! The person could give me some amount of M&Ms that would make me exactly as happy as I was before I gave up that tiny bit of jelly beans. If I give the person half a jelly bean, I’m a little less happy than I was before.
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The point is that the person wants a very very small amount of jelly beans. Maybe this person only wants half a jelly bean. Now imagine someone comes along and wants one of my jelly beans. I like both types of candy and I like having the choice between fruity and chocolatey, so I’m pretty happy right now. Let’s imagine that I have some jelly beans and some M&Ms. Finally, I demonstrate that the Marginal Rate of Substitution has an advantage over Marginal Utility in terms of describing preferences and behavior (Section X), because it is less sensitive to the exact utility function you choose to use! Story Explanation of the Marginal Rate of Substitution After that, I connect the two concepts (Marginal Utility and Marginal Rate of Substitution) and show how they relate mathematically, first without calculus (Section VIII) and then with calculus (Section IX). In both cases, I start with a story explanation, then give a formal definition, and finally provide some other useful information about the concept. Then, I cover the concept of Marginal Utility (Sections V-VII). In this post, I start off by explaining the Marginal Rate of Substitution (Sections II-IV).