Marginal utility and total utility

What I want to do in this video is think about a concept that we've already thought about multiple times in the context of many, many videos. And this is the idea of utility-- utility, which is really just a way of saying how much benefit or satisfaction or value do you get out of getting a good or service. But the angle that we're going to take in this video is going to be slightly different. In the past, when we were measuring benefit or value, we either measured in terms of dollars, where we said, hey, the benefit of getting an incremental Honda Civic was $5,000. And we talk about the incremental-- we're talking about, and we've heard the word many times-- we were talking about the marginal benefit. Or early on, when we talked about the production possibilities frontier and we talked about the marginal benefit of another squirrel, we were talking about it in terms of berries. We were talking about it in terms of another good or service. What we're going to do in this video is just think about it in absolute terms. We're just going to think of some arbitrary way of measuring utility and then just assign values to. What's the value of getting one chocolate bar? And then what's the value that we give to the next chocolate bar and then the chocolate bar after that? And we're going to do the same things about fruit. And from that, we're going to see if we can build up some of the things that we already know about demand curves and how things relate to price and the price of other goods and things like that. And in particular, we're going to focus on marginal utility. So obviously, you could have total utility. If I have four chocolate bars, you could say the total utility I'm getting from all four of them. Or, you could think about marginal utility, the utility I'm getting from the next incremental chocolate bar or the next incremental pound of fruit. And before I move on, there's one thing-- and this was a point of confusion for me when I first learned this-- is OK, I'm using the word marginal utility now. In the past, I've used the word marginal benefit. They sound very similar. In fact, I even used the word benefit when I defined the word utility. How are these two things different? And the simple answer is, conceptually, they aren't. Conceptually, they are the exact same thing. The difference is how the words tend to be used in the context of a traditional microeconomics class. So when people talk about utility, they tend to measure it in terms of some type of absolute measure that they just came up with. You can view them as utility unit, some type of satisfaction units. While when they talk about marginal benefit, they tend to measure it either in dollars or in terms of some other goods. But I've seen either term used either way. So they really do mean the exact same thing. But in this video, we're going to use the term utility, and we're going to come up with a measuring scale, and it's a somewhat arbitrary one. And we're going to use that to come up with some conclusions about the basket of goods someone might purchase depending on different prices. So as you could imagine, I pre-wrote these two things. We're going to talk about chocolate bars, and we are going to talk about fruit. So right here in these little tables here, I've shown the marginal utility of each incremental. In the case of chocolate bars, each incremental bar, and in the case of fruit, each incremental pound of fruit. So this is saying that first chocolate bar-- obviously, if I have no chocolate bars I'm getting no utility from chocolate bars-- and this is saying that that first chocolate bar has a marginal utility. So the utility of that next incremental one is 100. I'm not saying $100. I'm not saying it's equivalent to 100 pounds of fruit. I'm not saying it's equivalent to 100 berries. I'm just arbitrarily saying it is 100. And what matters is not that this is 100 or 1,000 or a million. What matters is how this compares to other things. So for example, if I-- let's say this is 100, and if I know that I like fruit-- a pound of fruit-- 20% more than that first-- Or if I like an incremental-- my first pound of fruit-- 20% more, then I would have to say that the marginal utility of my first pound of fruit is 120. And this is what we said right over here. And if, another way to think about it is, if the marginal utility of the second chocolate bar I get-- because I've already enjoyed a little bit of chocolate bar, and I'm a little chocolated out-- is 20% less than that, then if this is 100, then this would have to be 80. I could have set this to be 1,000 and this to be 800 and this to be 1,200. I could have set this to be 10 and this to be 8 and this to be 12. What matters is, is that they really just have the same ratios between them that really do reflect my actual preferences. So let's just think about this a little bit. My first chocolate bar, I'm pretty excited. I just call it 100. The next chocolate bar, I'm a little bit less excited about it. I've already had some chocolate. My craving has been satiated to some degree, but I still like chocolate. So I'll call that an 80. We could call it 80 satisfaction units, whatever you want to call it. Then the next chocolate bar after this-- now I'm starting to get pretty stuffed, and I'm really chocolated out. And so I'm not getting as much benefit from it. And then finally if you give me another chocolate bar, it's even less. And if we were to list a fifth chocolate bar, I might not want it at all. My marginal utility might go to 0 maybe for that fifth chocolate bar. Maybe that sixth chocolate bar, I have to somehow get rid of it somehow, because I'm so tired of chocolate bars. Maybe it'll have a negative marginal utility. And we could think about the same thing with fruit. The first pound of fruit, I'm pretty excited about fruit. I have a fruit craving. I like that first pound of fruit even more than that first chocolate bar. I like it 20% more. So I get to 120, you could call it utility points or whatever arbitrary unit you want to call it. Then my next pound of fruit, once again I'm having diminishing utility, diminishing benefit as I get more and more incremental pounds of fruit. Now, it's very important to realize this is marginal utility, not total utility. This is a utility I'm getting from each incremental pound. It's positive, so I'm still enjoying that next incremental pound. I'm just enjoying it a little bit less than the pound before. And to realize what total utility is, if I were to have two pounds of fruit, I would have 120 of utility from that first pound. And then I would have 100 from the second pound. And so you would say I had a total utility of 220, you could call them utility units, from both pounds. Now with just the information that I've given here, there's a few things you could say. You could say, well look, my first pound of fruit I enjoy more, 20% more than my first chocolate bar. You could also say that my second pound of fruit, I enjoy it or I could derive about the same amount of value as my first chocolate bar. You could say that my second chocolate bar I enjoy less than my first chocolate bar. You could even say 20% less if these numbers are good. But this still doesn't give you a lot of information about how you would actually spend your money. You might say, well, obviously wouldn't you want to just buy fruit over chocolate bars, or at least that first pound of fruit over that first chocolate bar? Well, you might, but it depends on how much that fruit actually costs. Just looking at this alone, we can just make relative judgments about how much we prefer each incremental bar or each incremental pound or them relative to each other. But it really doesn't tell us how we would spend our actual money. So let's think about things. Let's put some prices on some of these goods and think about how we would actually allocate our dollar given these marginal utility numbers right over here. So let's say that the chocolate bars are $1 per bar. And let's say that the fruit is $2 per pound. So this is going to be per pound. This is going to be per bar. And what we're going to think about is we're going to think about marginal utility for that incremental chocolate bar per price of that incremental chocolate bar. And here the price is going to be at $1 per pound. So here, for that first bar, I'm going to be spending $1, and I'm getting 100 marginal utility points, whatever you want to call it. So I'm getting 100 marginal utility points for that dollar. So I'm getting 100 marginal utility points per dollar. Here, same logic. I'm getting 80 marginal utility points per dollar. This is pretty simple math. Here I'm getting 60 marginal utility points for the dollar. Here I'm getting 40. So that doesn't seem too interesting. It might be a little bit more interesting here. What is the marginal utility per incremental fruit that I'm getting per dollar, per price, or actually per price of the incremental fruit here? Well here, that first pound of fruit I'm getting 120 marginal utility points we could call them. But I paid $2 for it. So 120-- let me write it over here. So for that first incremental fruit, the marginal utility for that first fruit is 120. And the price of that first pound of fruit is equal to 2. So I'm getting 60 marginal utility points per dollar. I'm getting 60. Here, 100 marginal utility points, but I'm spending $2. So that's 50 points per dollar. This is 25 points per dollar. This is 10 points per dollar. Now this makes things a little bit more interesting. If I had $5 to spend, how would I want to spend my $5? What you really just want to think about, where are you getting the most satisfaction for each dollar? Where are you getting the most bang for your buck? So where am I going to spend my first dollar? So dollar one. So let's think about it a little bit. My first dollar, where am I going to get the most satisfaction per dollar? Well, I get the most satisfaction per dollar right over here. I get 100 satisfaction units for a dollar. Even though I like a pound of fruit, I'm getting less satisfaction per dollar. So I'm getting less bang for my buck. So my first dollar is going to go right over there. I'm going to buy one candy bar. Then where am I going to spend my second dollar? So once again, I just want to look at all of my options, and we're going to assume that I'm going to spend my $5 on either of these two just to limit our universe. Once again, I'm going to maximize my bang for buck. I get 80 satisfaction points or marginal utility points over here per dollar. I only get 60 over here. So I'm going to buy even a second chocolate bar. Let's keep going. Where am I going to spend my third dollar? Now, it gets a little bit interesting. I could spend my third dollar right over here and get 60 points per dollar, or I could spend it over here and get 60 points per dollar. I'd actually get the same amount. There are both 60 points per dollar. So I'm kind of neutral. I'm going to get the same bang for my buck whether I get another chocolate bar or whether I get another fruit. So just for simplicity, let's say I get another chocolate bar. I could have got the fruit too. It's really a toss up. I could flip a coin, and I choose to get another chocolate bar. So I first spent my first $3 on three chocolate bars. Now where am I going to spend my fourth dollar? Well, my fourth dollar, now my best bang for my buck isn't to get another chocolate bar. I'm only going to get 40 units per buck there. Now it is to spend it on fruit. So now the next dollar I could spend on half a pound of fruit, and I would get this. So my fourth dollar I could spend on this for half a pound of fruit because it's $2 per pound. And then I could spend my fifth dollar there too. So this is my fourth and my fifth dollar because it's $2. You could think of it that we're spending $2 for one pound of fruit. And we're getting 60 utility points per dollar. So we're getting the best bang for our buck right over there. But what was useful about this is it allowed us without thinking about money to say how much do we like these things irrespective of their actual price and then give it a certain price. It allowed us to think rationally about, well, how would we actually spend our money. In this case, when chocolate bars are $1 and fruit is $2 per pound, we decided to buy three chocolate bars and only one pound of fruit.