Equalizing Marginal Utility per Dollar Spent발음듣기
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Equalizing Marginal Utility per Dollar Spent
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In the last video we thought about how we would allocate our five dollars between chocolate bars and fruit.발음듣기
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And the way we did it was very rational: we thought about how much bang we would get for each buck.발음듣기
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So we got a lot of utility per price starting off with that first chocolate bar, a little less for that next chocolate bar, but still more than we would get for a pound of fruit.발음듣기
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I want to think about maybe a more continuous case where we can buy very, very small increments of each of the products.발음듣기
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And what I'm going to do is plot the marginal utility per price, which is really bang for your buck, on the vertical axis.발음듣기
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In the case of fruit, the more pounds of fruit you get the more tired you get of fruit, the less fruit you need or the less you want fruit for that next incremental pound.발음듣기
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And I'm assuming I can buy these in super-small chunks, as small as maybe the penny or even fractions of a penny.발음듣기
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So if I just had a penny, and I think about 'where am I getting the best bang for my buck for that penny?'발음듣기
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So my first dollar, I'll spend on A. And the total utility I'll get is actually going to be the area under this curve.발음듣기
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The reason why it wouldn't be the area of this larger rectangle - it would just be the area under the curve - is you're not getting the 100 marginal utility per price for the entire dollar.발음듣기
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Actually, even after we already spent a dollar our next penny we'd still want to spend on Product A because we're still getting more bang for the buck.발음듣기
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We spent our first two dollars all on Product A because we're getting more bang for our buck, even though that bang was diminishing every penny or fraction of a penny that we spent.발음듣기
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Well, we get about the same marginal utility whether we spend it on a little bit more of Product B or a little bit more of Product A.발음듣기
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If we spend a little bit too much on Product A then we could have gotten more marginal utility spending on Product B.발음듣기
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So what we would do is, once we've gotten to this threshold right about here we actually are going to spend every incremental fraction of a penny we're actually going to want a split between Product A and Product B.발음듣기
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If we spend too much on one and we go down this curve we could've gotten higher utility on this one.발음듣기
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If we spent too much on this one we could get higher utility spending on this one right over here.발음듣기
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Assuming that we eventually spent enough that we buy some of both - obviously we started just buying Product A because it had higher utility, at least for those first few dollars.발음듣기
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But assuming that we end up buying some mix of the two, which we do end up spending if we spend more than $2, there's an interesting thing: the marginal utility for a project - the marginal utility for B or the marginal utility for price for B that I spent on that last little increment is going to be the same as the marginal utility per price for that last increment of A.발음듣기
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So if B was, I don't know, if it was fruit and let's say A was chocolate but we could buy it in very, very small increments we're saying for that last fraction of a pound of fruit you're spending or getting the same marginal utility per price as you're getting for that last fraction of a bar or fraction of a pound of chocolate.발음듣기
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So there's a general principle, and it really just comes from this very straightforward thing: that as soon as you can get better marginal utility on the other one you start spending there.발음듣기
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So the general principal: if you're allocating money between two goods for that last increment - not across the board, just that last increment (that's why the word marginal is so important) - for that last ounce of chocolate vs. that very last ounce of fruit the marginal utility per price for that last increment of one good would be the same as the marginal utility per price of the second good.발음듣기
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This is just saying as you spend money - let's say you spend enough money to buy both - at some point you're going to get to a threshold where you're neutral between the two, where the marginal utility per price is the same for an incremental of B vs. an incremental of A.발음듣기
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Because obviously if you focus too much on this right over here - let's say you focus, at that point you switch and just start buying a bunch of Product B over here.발음듣기
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Well, that didn't make sense because you were buying Product B when you could have gotten higher marginal utility buying some of product A.발음듣기
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And that's the same reason why you didn't just keep going down A, because you could've gotten higher marginal utility over here.발음듣기
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