WEBVTT 00:00:11.679 --> 00:00:14.679 Um 00:00:12.640 --> 00:00:16.640 Uh today we're going to start talking 00:00:14.679 --> 00:00:17.679 about what's underneath the demand 00:00:16.640 --> 00:00:19.560 curve. 00:00:17.679 --> 00:00:21.679 So, basically what we did last time and 00:00:19.559 --> 00:00:24.159 what you did in section on Friday is 00:00:21.679 --> 00:00:25.839 talk about sort of the workhorse model 00:00:24.160 --> 00:00:27.640 uh of economics, which is the supply and 00:00:25.839 --> 00:00:30.039 demand model. And we always start the 00:00:27.640 --> 00:00:32.359 class with that cuz that's the the model 00:00:30.039 --> 00:00:34.119 in the course. But, I think as any good 00:00:32.359 --> 00:00:35.359 sort of scientist and inquisitive minds, 00:00:34.119 --> 00:00:37.039 you're probably immediately asking, 00:00:35.359 --> 00:00:38.880 "Well, where do these supply and demand 00:00:37.039 --> 00:00:41.039 curves come from? They don't just come 00:00:38.880 --> 00:00:42.080 out of thin air. Uh 00:00:41.039 --> 00:00:43.519 how do we think about them? Where do 00:00:42.079 --> 00:00:45.119 they come from?" And that's what we'll 00:00:43.520 --> 00:00:46.920 spend the base of the first half of the 00:00:45.119 --> 00:00:48.239 course going through. 00:00:46.920 --> 00:00:49.760 And so, we're going to start today with 00:00:48.240 --> 00:00:51.520 the demand curve. 00:00:49.759 --> 00:00:55.159 And the demand curve is going to come 00:00:51.520 --> 00:00:57.000 from how consumers make choices. 00:00:55.159 --> 00:00:58.759 Okay? And that will help us derive the 00:00:57.000 --> 00:01:01.000 demand curve. Then we'll turn next to 00:00:58.759 --> 00:01:04.640 supply curve, which will come from how 00:01:01.000 --> 00:01:06.040 firms make uh production decisions. 00:01:04.640 --> 00:01:07.159 But, let's start with the demand curve. 00:01:06.040 --> 00:01:09.480 And we're going to start by talking 00:01:07.159 --> 00:01:11.879 today about people's preferences 00:01:09.480 --> 00:01:12.960 and then the utility functions. 00:01:11.879 --> 00:01:14.839 Okay? 00:01:12.959 --> 00:01:16.199 So, our model of consumer 00:01:14.840 --> 00:01:18.200 decision-making 00:01:16.200 --> 00:01:21.200 is going to be a model of utility 00:01:18.200 --> 00:01:22.560 maximization. 00:01:21.200 --> 00:01:23.600 That's going to be our fundamental 00:01:22.560 --> 00:01:25.439 Remember, this course is all about 00:01:23.599 --> 00:01:26.599 constrained maximization. Our model 00:01:25.439 --> 00:01:28.039 today is going to be a model of utility 00:01:26.599 --> 00:01:29.199 maximization. 00:01:28.040 --> 00:01:30.680 And this model is going to have two 00:01:29.200 --> 00:01:31.760 components. 00:01:30.680 --> 00:01:34.760 There's going to be consumer 00:01:31.760 --> 00:01:34.760 preferences, 00:01:34.959 --> 00:01:39.399 which is what people want, and there's 00:01:37.439 --> 00:01:42.679 going to be a budget constraint, which 00:01:39.400 --> 00:01:42.680 is what they can afford. 00:01:43.239 --> 00:01:47.159 And we're going to put these two things 00:01:45.040 --> 00:01:49.320 together. We're going to maximize 00:01:47.159 --> 00:01:50.679 people's happiness or their choice or 00:01:49.319 --> 00:01:53.359 their their happiness given their 00:01:50.680 --> 00:01:55.000 preferences subject to the budget 00:01:53.359 --> 00:01:56.359 constraint they face. And that's going 00:01:55.000 --> 00:01:58.760 to be the constrained maximization 00:01:56.359 --> 00:02:00.040 exercise that actually through the magic 00:01:58.760 --> 00:02:01.560 of economics is going to yield the 00:02:00.040 --> 00:02:02.960 demand curve. And it's going to yield a 00:02:01.560 --> 00:02:05.400 very sensible demand curve that you'll 00:02:02.959 --> 00:02:07.159 understand intuitively. 00:02:05.400 --> 00:02:09.118 Now, so what we're going to do is do 00:02:07.159 --> 00:02:11.038 this in three steps. 00:02:09.118 --> 00:02:12.120 Step one over the next two lectures. 00:02:11.038 --> 00:02:13.319 Step one is we'll talk about 00:02:12.120 --> 00:02:16.360 preferences. 00:02:13.319 --> 00:02:18.039 How do we model people's tastes? 00:02:16.360 --> 00:02:19.520 We'll do that today. 00:02:18.039 --> 00:02:22.120 Step two is we'll talk about how we 00:02:19.520 --> 00:02:24.840 translate this to utility function. How 00:02:22.120 --> 00:02:26.439 we mathematically represent people's 00:02:24.840 --> 00:02:28.400 preferences in the utility function. 00:02:26.439 --> 00:02:30.840 We'll do that today as well. 00:02:28.400 --> 00:02:33.400 And then next time, we'll talk about the 00:02:30.840 --> 00:02:34.400 budget constraints that people face. 00:02:33.400 --> 00:02:36.560 So, today we're going to talk about the 00:02:34.400 --> 00:02:38.159 maximand. Next time we'll talk about the 00:02:36.560 --> 00:02:40.479 budget constraint. 00:02:38.159 --> 00:02:42.319 That means today's lecture is quite fun. 00:02:40.479 --> 00:02:44.239 Today's lecture is about unconstrained 00:02:42.319 --> 00:02:45.799 choice. We're not going to worry at all 00:02:44.240 --> 00:02:47.120 about what you can afford, what anything 00:02:45.800 --> 00:02:48.040 costs. 00:02:47.120 --> 00:02:48.719 We'll worry about what things cost. 00:02:48.039 --> 00:02:51.280 We're not going to worry about what you 00:02:48.719 --> 00:02:52.719 can afford. Okay? Today's the lecture 00:02:51.280 --> 00:02:55.000 where you won the lottery. 00:02:52.719 --> 00:02:57.120 Okay? You won the lottery, money is no 00:02:55.000 --> 00:02:58.319 object. How do you think about what you 00:02:57.120 --> 00:02:59.920 want? 00:02:58.319 --> 00:03:00.959 Okay? Next time we'll say, "Well, you 00:02:59.919 --> 00:03:02.079 didn't win the lottery." In fact, as 00:03:00.960 --> 00:03:03.520 we'll learn later in the semester, no 00:03:02.080 --> 00:03:07.160 one wins the lottery. Uh that's an 00:03:03.520 --> 00:03:08.360 incredibly bad deal. Um uh but basically 00:03:07.159 --> 00:03:10.400 next time we'll impose the budget 00:03:08.360 --> 00:03:13.120 constraints. But for today, we're just 00:03:10.400 --> 00:03:14.680 going to ignore that and talk about what 00:03:13.120 --> 00:03:17.039 do you want? 00:03:14.680 --> 00:03:20.159 Okay? And to start this, we're going to 00:03:17.039 --> 00:03:23.159 start with the series of preference 00:03:20.159 --> 00:03:23.159 assumptions. 00:03:25.400 --> 00:03:30.000 A series Remember, as I talked about 00:03:27.360 --> 00:03:31.240 last time, models rely on simplifying 00:03:30.000 --> 00:03:32.400 assumptions. Otherwise, we could never 00:03:31.240 --> 00:03:33.480 write down a model. It would go on 00:03:32.400 --> 00:03:36.640 forever. 00:03:33.479 --> 00:03:39.719 Okay? And the key question is, are those 00:03:36.639 --> 00:03:41.519 simplifying assumptions sensible? Uh do 00:03:39.719 --> 00:03:43.159 they do violence to reality in a way 00:03:41.520 --> 00:03:44.600 which makes you not believe the model? 00:03:43.159 --> 00:03:46.240 Or do are they roughly consistent with 00:03:44.599 --> 00:03:47.560 reality in a way that allows you to go 00:03:46.240 --> 00:03:49.560 on with the model? 00:03:47.560 --> 00:03:52.000 Okay? And we're going to impose three 00:03:49.560 --> 00:03:53.120 preference assumptions, which I hope 00:03:52.000 --> 00:03:54.639 will not violate your sense of 00:03:53.120 --> 00:03:58.960 reasonableness. 00:03:54.639 --> 00:03:58.959 The first is completeness. 00:04:00.599 --> 00:04:06.199 What I mean by that is you have 00:04:03.319 --> 00:04:08.319 preferences over any set of goods you 00:04:06.199 --> 00:04:10.239 might choose from. 00:04:08.319 --> 00:04:12.639 You might be indifferent. You might say, 00:04:10.240 --> 00:04:15.600 "I like A as much as B." But, you can't 00:04:12.639 --> 00:04:16.439 say, "I don't care." or "I don't know." 00:04:15.599 --> 00:04:17.879 You say, "I don't care." That's 00:04:16.439 --> 00:04:19.358 indifference. You can't say, "I don't 00:04:17.879 --> 00:04:21.399 know." You can't literally say, "I don't 00:04:19.358 --> 00:04:23.199 know how I feel about this." Um you 00:04:21.399 --> 00:04:25.000 might uh say you're indifferent to 00:04:23.199 --> 00:04:26.759 things, but you won't say, "I don't know 00:04:25.000 --> 00:04:28.160 uh how I feel about something." That's 00:04:26.759 --> 00:04:30.719 completeness. 00:04:28.160 --> 00:04:31.840 Okay? The second is the assumption we've 00:04:30.720 --> 00:04:33.360 all become familiar with since 00:04:31.839 --> 00:04:36.159 kindergarten math, which is 00:04:33.360 --> 00:04:36.160 transitivity. 00:04:38.040 --> 00:04:41.879 If you prefer A to B and B to C, you 00:04:40.360 --> 00:04:42.879 prefer A to C. 00:04:41.879 --> 00:04:44.120 Okay? 00:04:42.879 --> 00:04:46.199 Uh 00:04:44.120 --> 00:04:47.399 that's that's kind of um 00:04:46.199 --> 00:04:49.839 uh I'm sure that's pretty clear. You've 00:04:47.399 --> 00:04:51.759 done this a lot in other classes. 00:04:49.839 --> 00:04:53.239 So, these two are sort of standard 00:04:51.759 --> 00:04:54.480 assumptions you might make in any math 00:04:53.240 --> 00:04:55.800 class. 00:04:54.480 --> 00:04:57.560 The third assumption is the one where 00:04:55.800 --> 00:04:58.680 the economics comes in, 00:04:57.560 --> 00:05:01.680 which is the assumption of 00:04:58.680 --> 00:05:01.680 non-satiation, 00:05:02.639 --> 00:05:07.599 or the assumption of more is better. 00:05:08.839 --> 00:05:15.319 In this class, we will assume more is 00:05:12.360 --> 00:05:16.960 always better than less. 00:05:15.319 --> 00:05:19.279 Okay? We'll assume more is better than 00:05:16.959 --> 00:05:21.719 less. Now, to be clear, we're not going 00:05:19.279 --> 00:05:23.479 to say that the next unit makes you 00:05:21.720 --> 00:05:24.920 equally happy as the last unit. In fact, 00:05:23.480 --> 00:05:26.040 I'll talk about that in a few minutes. 00:05:24.920 --> 00:05:27.000 We'll in fact assume it makes you less 00:05:26.040 --> 00:05:29.760 happy. 00:05:27.000 --> 00:05:31.519 But, we will say you always want more. 00:05:29.759 --> 00:05:33.839 The face of the chance of more or less, 00:05:31.519 --> 00:05:35.719 you'll always be happier with more. 00:05:33.839 --> 00:05:36.799 Okay? And that's the non-satiation 00:05:35.720 --> 00:05:38.640 assumption. 00:05:36.800 --> 00:05:40.240 Okay? I'll talk about that some during 00:05:38.639 --> 00:05:41.879 the lecture, but that's sort of what's 00:05:40.240 --> 00:05:43.160 going to give our models their power. 00:05:41.879 --> 00:05:45.040 That's the sort of new economics 00:05:43.160 --> 00:05:46.680 assumption that's going to give, beyond 00:05:45.040 --> 00:05:48.840 our typical math assumptions, that's 00:05:46.680 --> 00:05:49.920 going to give our models their power. 00:05:48.839 --> 00:05:51.560 Okay? 00:05:49.920 --> 00:05:54.080 So, that's our assumptions. 00:05:51.560 --> 00:05:55.720 So, armed with those, 00:05:54.079 --> 00:05:58.120 I want to start with the graphical 00:05:55.720 --> 00:05:59.360 representation of preferences. 00:05:58.120 --> 00:06:00.920 I want to graphically represent people's 00:05:59.360 --> 00:06:05.400 preferences. And I'll do so through 00:06:00.920 --> 00:06:05.400 something we call indifference curves. 00:06:07.800 --> 00:06:11.079 Indifference curves. 00:06:10.000 --> 00:06:12.759 Okay? 00:06:11.079 --> 00:06:15.120 These are base Indifference curves are 00:06:12.759 --> 00:06:16.319 basically preference maps. 00:06:15.120 --> 00:06:19.800 Essentially, indifference curves are 00:06:16.319 --> 00:06:20.800 graphical maps of preferences. 00:06:19.800 --> 00:06:23.879 Okay? 00:06:20.800 --> 00:06:26.319 So, for example, 00:06:23.879 --> 00:06:27.719 suppose your parents gave you some money 00:06:26.319 --> 00:06:29.040 at the beginning of the semester, and 00:06:27.720 --> 00:06:29.960 you can spend that money on two things. 00:06:29.040 --> 00:06:32.160 Your parents are rich. They give you 00:06:29.959 --> 00:06:33.199 tons of money. Spend that money on two 00:06:32.160 --> 00:06:34.760 things. 00:06:33.199 --> 00:06:38.360 Buying pizza 00:06:34.759 --> 00:06:39.879 or or um or eating cookies. 00:06:38.360 --> 00:06:42.199 Okay? 00:06:39.879 --> 00:06:43.759 So, consider your Consider preferences 00:06:42.199 --> 00:06:45.279 between pizza and cookies. That's your 00:06:43.759 --> 00:06:46.639 two things you can do. Once again, it's 00:06:45.279 --> 00:06:47.559 constrained model. Obviously, in life 00:06:46.639 --> 00:06:50.479 you can do a million things with your 00:06:47.560 --> 00:06:52.079 money. But, it turns out if we consider 00:06:50.480 --> 00:06:53.640 the contrast between doing two different 00:06:52.079 --> 00:06:55.639 things with your money, you get a rich 00:06:53.639 --> 00:06:57.120 set of intuition that you can apply to a 00:06:55.639 --> 00:06:57.959 much more multi-dimensional decision 00:06:57.120 --> 00:06:59.040 case. 00:06:57.959 --> 00:07:00.799 So, let's start with the two-dimensional 00:06:59.040 --> 00:07:02.120 decision case. You've got your money. 00:07:00.800 --> 00:07:03.480 You're going to have pizza or you're 00:07:02.120 --> 00:07:06.879 going to have cookies. 00:07:03.480 --> 00:07:09.080 Okay? Now, consider three choices. Okay? 00:07:06.879 --> 00:07:10.839 Choice A 00:07:09.079 --> 00:07:13.519 is two pizzas 00:07:10.839 --> 00:07:15.279 and one cookie. 00:07:13.519 --> 00:07:18.519 Choice B 00:07:15.279 --> 00:07:22.399 is one pizza, 00:07:18.519 --> 00:07:25.199 one pizza and two cookies, and choice C 00:07:22.399 --> 00:07:26.719 is two pizzas, two cookies. 00:07:25.199 --> 00:07:28.920 Okay? That's the three packages I want 00:07:26.720 --> 00:07:30.480 to compare. 00:07:28.920 --> 00:07:32.000 And I'm going to assume and I'll 00:07:30.480 --> 00:07:33.600 mathematically rationalize in a few 00:07:32.000 --> 00:07:37.839 minutes. But for now, I'm going to 00:07:33.600 --> 00:07:39.720 assume you are indifferent 00:07:37.839 --> 00:07:40.839 between these two packages. 00:07:39.720 --> 00:07:42.720 I'm going to assume you're equally happy 00:07:40.839 --> 00:07:45.599 with two slices of pizza and one cookie 00:07:42.720 --> 00:07:46.560 or two cookies and one slice of pizza. 00:07:45.600 --> 00:07:49.200 Okay? 00:07:46.560 --> 00:07:51.800 I'm going to assume that. But, I'm also 00:07:49.199 --> 00:07:53.759 going to assume you prefer option C to 00:07:51.800 --> 00:07:54.800 both of these. 00:07:53.759 --> 00:07:56.480 In fact, I'm not I'm going to assume 00:07:54.800 --> 00:07:57.759 that because that is what more is better 00:07:56.480 --> 00:07:59.080 gives you. 00:07:57.759 --> 00:08:00.120 Okay? So, you're indifferent between 00:07:59.079 --> 00:08:01.479 these. 00:08:00.120 --> 00:08:02.639 This indifference doesn't come from any 00:08:01.480 --> 00:08:04.720 property I wrote up there. That's an 00:08:02.639 --> 00:08:06.479 assumption. That's just a I just for 00:08:04.720 --> 00:08:07.640 this case I'm assuming that. This comes 00:08:06.480 --> 00:08:09.680 from the third property I wrote up 00:08:07.639 --> 00:08:11.839 there. You prefer package C cuz more is 00:08:09.680 --> 00:08:12.959 always better than less. 00:08:11.839 --> 00:08:15.279 Okay? 00:08:12.959 --> 00:08:18.399 So, now let's graph your preferences. 00:08:15.279 --> 00:08:20.879 And we do so in figure 2.1 00:08:18.399 --> 00:08:23.079 Okay? In the handout. Um 00:08:20.879 --> 00:08:24.439 Okay. So, um 00:08:23.079 --> 00:08:26.359 here's your indifference curve. So, 00:08:24.439 --> 00:08:28.959 we've graphed on the x-axis your number 00:08:26.360 --> 00:08:30.600 of number of cookies. On the y-axis, 00:08:28.959 --> 00:08:33.598 slices of pizza. 00:08:30.600 --> 00:08:36.120 Okay? Now, you have We've graphed the 00:08:33.599 --> 00:08:37.919 three choices I laid here. Choice A, 00:08:36.120 --> 00:08:39.279 which is two slices of pizza and one 00:08:37.918 --> 00:08:40.960 cookie. 00:08:39.279 --> 00:08:42.959 Choice B, which is two cookies and one 00:08:40.960 --> 00:08:44.440 slice of pizza. And choice C, which is 00:08:42.960 --> 00:08:45.840 two of both. 00:08:44.440 --> 00:08:47.440 And I have drawn on this graph your 00:08:45.840 --> 00:08:49.040 indifference curves. The way your 00:08:47.440 --> 00:08:51.600 indifference curves looks is there's one 00:08:49.039 --> 00:08:53.439 indifference curve between A and B 00:08:51.600 --> 00:08:54.879 because those are the points among which 00:08:53.440 --> 00:08:56.040 you're indifferent. 00:08:54.879 --> 00:08:59.120 So, what an indifference curve 00:08:56.039 --> 00:09:01.279 represents is all combinations of 00:08:59.120 --> 00:09:03.080 consumption among which you are 00:09:01.279 --> 00:09:03.959 indifferent. So, we call it indifference 00:09:03.080 --> 00:09:05.080 curve. 00:09:03.960 --> 00:09:07.280 So, an indifference curve, which will be 00:09:05.080 --> 00:09:09.000 sort of one of the big workhorses of 00:09:07.279 --> 00:09:12.000 this course. An indifference curve 00:09:09.000 --> 00:09:13.919 represents all combinations along which 00:09:12.000 --> 00:09:15.440 you are indifferent. You are indifferent 00:09:13.919 --> 00:09:17.599 between A and B. Therefore, they lie on 00:09:15.440 --> 00:09:19.520 the same curve. 00:09:17.600 --> 00:09:21.000 Okay? 00:09:19.519 --> 00:09:23.519 So, that's sort of our our our 00:09:21.000 --> 00:09:24.799 preference map, our indifference curves. 00:09:23.519 --> 00:09:27.240 And these indifference curves are going 00:09:24.799 --> 00:09:30.759 to have four properties. 00:09:27.240 --> 00:09:32.200 Four properties that you have to that 00:09:30.759 --> 00:09:33.439 follow naturally from this It's really 00:09:32.200 --> 00:09:35.040 three and a half. The third and fourth 00:09:33.440 --> 00:09:36.720 are really pretty much the same, but I 00:09:35.039 --> 00:09:38.959 like to write them out as four. 00:09:36.720 --> 00:09:41.160 Four properties that follow from the 00:09:38.960 --> 00:09:42.800 from these underlying assumptions. 00:09:41.159 --> 00:09:45.240 Property one 00:09:42.799 --> 00:09:46.559 is consumers prefer higher indifference 00:09:45.240 --> 00:09:49.840 curves. 00:09:46.559 --> 00:09:51.679 Consumers prefer 00:09:49.840 --> 00:09:53.399 higher 00:09:51.679 --> 00:09:55.039 indifference curves. 00:09:53.399 --> 00:09:56.879 Okay? And that just follow from more is 00:09:55.039 --> 00:09:58.159 better. That is, an indifference curve 00:09:56.879 --> 00:10:00.559 that's higher goes through the package 00:09:58.159 --> 00:10:02.559 that has at least as much of one thing 00:10:00.559 --> 00:10:03.839 and more of the other thing. Therefore, 00:10:02.559 --> 00:10:05.719 you prefer it. 00:10:03.840 --> 00:10:08.080 Okay? So, as indifference curves shift 00:10:05.720 --> 00:10:09.639 out, people are happier. 00:10:08.080 --> 00:10:11.639 Okay? So, on that higher indifference 00:10:09.639 --> 00:10:13.639 curve 00:10:11.639 --> 00:10:15.879 point C, you are happier than points A 00:10:13.639 --> 00:10:17.960 and B because more is better. 00:10:15.879 --> 00:10:19.360 Okay? 00:10:17.960 --> 00:10:21.320 The second 00:10:19.360 --> 00:10:23.600 is that 00:10:21.320 --> 00:10:27.000 indifference curves 00:10:23.600 --> 00:10:27.000 never cross. 00:10:27.559 --> 00:10:31.919 Indifference curves 00:10:29.279 --> 00:10:33.480 uh never cross. 00:10:31.919 --> 00:10:35.199 Okay, actually that's 00:10:33.480 --> 00:10:37.639 I'm going to that's third actually. I 00:10:35.200 --> 00:10:38.520 want to come to that in order. Second, 00:10:37.639 --> 00:10:39.960 third is indifference curves never 00:10:38.519 --> 00:10:43.000 cross. Second is indifference curves are 00:10:39.960 --> 00:10:43.000 downward sloping. 00:10:44.200 --> 00:10:47.280 Second is indifference curves are 00:10:45.480 --> 00:10:48.560 downward sloping. 00:10:47.279 --> 00:10:51.079 Okay? Indifference curves are downward 00:10:48.559 --> 00:10:52.199 sloping. Let's talk about that first. 00:10:51.080 --> 00:10:54.960 Okay? 00:10:52.200 --> 00:10:57.040 That simply comes from the principle of 00:10:54.960 --> 00:10:59.320 non-satiation. 00:10:57.039 --> 00:11:00.838 So, look at figure 2.2. 00:10:59.320 --> 00:11:03.200 Here's an upward sloping indifference 00:11:00.839 --> 00:11:05.160 curve. 00:11:03.200 --> 00:11:06.400 Okay? Why does that violate the 00:11:05.159 --> 00:11:07.480 principle of non-satiation? Why does 00:11:06.399 --> 00:11:09.600 that violate that? Yeah. 00:11:07.480 --> 00:11:11.080 Well, either if you're either you're 00:11:09.600 --> 00:11:13.720 somehow less happy if you have more 00:11:11.080 --> 00:11:16.160 cookies, like or you're less happy if 00:11:13.720 --> 00:11:18.360 you have more pizza. Yeah, but 00:11:16.159 --> 00:11:20.360 And like there's 00:11:18.360 --> 00:11:22.039 and that violates non-satiation. 00:11:20.360 --> 00:11:23.600 Exactly. So, basically you're 00:11:22.039 --> 00:11:24.838 indifferent on this curve you're 00:11:23.600 --> 00:11:26.159 indifferent between one of each and two 00:11:24.839 --> 00:11:27.440 of each. You can't be indifferent. Two 00:11:26.159 --> 00:11:28.360 of each has got to be better than one of 00:11:27.440 --> 00:11:29.680 each. 00:11:28.360 --> 00:11:31.720 So, an upward sloping indifference curve 00:11:29.679 --> 00:11:32.838 would violate non-satiation. 00:11:31.720 --> 00:11:34.080 So, that's the second property of 00:11:32.839 --> 00:11:35.240 indifference curve. 00:11:34.080 --> 00:11:37.560 The third property of indifference curve 00:11:35.240 --> 00:11:40.039 is indifference curves never cross. 00:11:37.559 --> 00:11:42.399 Okay? We can see that 00:11:40.039 --> 00:11:44.199 in figure 2.3. 00:11:42.399 --> 00:11:45.559 Okay? Someone else tell me why this 00:11:44.200 --> 00:11:48.240 violates the properties I wrote up there 00:11:45.559 --> 00:11:49.359 indifference curves crossing. 00:11:48.240 --> 00:11:51.159 Yeah. 00:11:49.360 --> 00:11:53.279 Because B and C 00:11:51.159 --> 00:11:54.838 What's that? Because B and C are 00:11:53.279 --> 00:11:56.360 strictly better. 00:11:54.839 --> 00:11:58.880 Because the B and C, B is strictly 00:11:56.360 --> 00:12:00.800 better. That's right. 00:11:58.879 --> 00:12:03.559 But but they're they're also but they're 00:12:00.799 --> 00:12:04.519 also both on the same curve as A. So, 00:12:03.559 --> 00:12:06.439 you're saying they're both you're 00:12:04.519 --> 00:12:07.679 indifferent with A for both B and C, but 00:12:06.440 --> 00:12:09.200 you can't be because B is strictly 00:12:07.679 --> 00:12:10.679 better than C. So, it violates 00:12:09.200 --> 00:12:12.800 transitivity. 00:12:10.679 --> 00:12:13.838 Okay? So, the problem with crossing 00:12:12.799 --> 00:12:16.599 indifference curves they violate 00:12:13.839 --> 00:12:16.600 transitivity. 00:12:17.320 --> 00:12:22.400 And then finally, the fourth 00:12:20.120 --> 00:12:24.480 is sort of a cute extra assumption, but 00:12:22.399 --> 00:12:27.399 I think it's important to clarify, 00:12:24.480 --> 00:12:29.480 which is that there is only one 00:12:27.399 --> 00:12:33.039 indifference curve through every 00:12:29.480 --> 00:12:33.039 possible consumption bundle. 00:12:33.240 --> 00:12:36.360 Only one 00:12:34.799 --> 00:12:37.679 IC 00:12:36.360 --> 00:12:40.560 through 00:12:37.679 --> 00:12:40.559 every bundle. 00:12:42.279 --> 00:12:45.759 Okay? You can't have two indifference 00:12:43.839 --> 00:12:47.680 curves going through the same bundle. 00:12:45.759 --> 00:12:49.360 Okay? Uh and that's because of 00:12:47.679 --> 00:12:50.079 completeness. If you have two 00:12:49.360 --> 00:12:51.120 indifference curves going through the 00:12:50.080 --> 00:12:52.320 same bundle, you wouldn't know how you 00:12:51.120 --> 00:12:54.039 felt. 00:12:52.320 --> 00:12:55.160 Okay? So, there can only be one going 00:12:54.039 --> 00:12:56.199 through every bundle cuz you know how 00:12:55.159 --> 00:12:57.600 you feel. 00:12:56.200 --> 00:12:59.080 You may feel indifferent, but you know 00:12:57.600 --> 00:13:00.240 how you feel. You can't say I don't 00:12:59.080 --> 00:13:01.920 know. 00:13:00.240 --> 00:13:03.240 Okay? So, that's sort of a extra 00:13:01.919 --> 00:13:05.360 assumption that sort of completes the 00:13:03.240 --> 00:13:06.360 link to the properties. 00:13:05.360 --> 00:13:08.759 Okay? 00:13:06.360 --> 00:13:10.000 So, that's basically how indifference 00:13:08.759 --> 00:13:11.559 curves work. 00:13:10.000 --> 00:13:14.279 Now, 00:13:11.559 --> 00:13:15.759 I find when I I took this course 00:13:14.279 --> 00:13:16.879 before you were 00:13:15.759 --> 00:13:18.200 God, maybe before your parents were 00:13:16.879 --> 00:13:19.679 born. I don't know. Certainly before you 00:13:18.200 --> 00:13:20.800 guys were born. Okay, when I took this 00:13:19.679 --> 00:13:22.279 course, 00:13:20.799 --> 00:13:23.599 I found this course full of a lot of 00:13:22.279 --> 00:13:24.799 lightbulb moments. That is stuff was 00:13:23.600 --> 00:13:26.600 just sort of confusing then boom an 00:13:24.799 --> 00:13:27.719 example really make it work for me. And 00:13:26.600 --> 00:13:29.600 the example that made indifference 00:13:27.720 --> 00:13:31.080 curves work to me was actually during my 00:13:29.600 --> 00:13:33.000 first year up. 00:13:31.080 --> 00:13:34.680 When my year up was with a grad student 00:13:33.000 --> 00:13:35.759 and that grad student had to decide 00:13:34.679 --> 00:13:36.959 where he was going to accept a job. He 00:13:35.759 --> 00:13:38.838 had a series of job offers and he had to 00:13:36.960 --> 00:13:40.320 decide. And basically said, here's the 00:13:38.839 --> 00:13:42.080 way I'm thinking about it. I'm 00:13:40.320 --> 00:13:44.080 indifferent I've I've indifference map 00:13:42.080 --> 00:13:47.440 and I care about two things. I care 00:13:44.080 --> 00:13:47.440 about school location 00:13:47.839 --> 00:13:52.240 and I care about economics department 00:13:49.679 --> 00:13:52.239 quality. 00:13:53.000 --> 00:13:55.839 Okay? I care about the quality of my 00:13:54.480 --> 00:13:57.839 colleagues and the research that's done 00:13:55.839 --> 00:13:59.800 there and the location. And basically 00:13:57.839 --> 00:14:02.040 he's he had two offers. 00:13:59.799 --> 00:14:03.439 One was from Princeton, which he put up 00:14:02.039 --> 00:14:04.759 here. No offense to New Jerseyans, but 00:14:03.440 --> 00:14:06.800 Princeton as a young single person 00:14:04.759 --> 00:14:08.559 sucks. Okay, fine when you're married 00:14:06.799 --> 00:14:10.439 and have kids, but deadly as a young 00:14:08.559 --> 00:14:13.439 single person. And the other so, that's 00:14:10.440 --> 00:14:15.160 Princeton. Down here was Santa Cruz. 00:14:13.440 --> 00:14:17.360 Okay? Awesome can have the most 00:14:15.159 --> 00:14:19.199 beautiful university in America. Okay? 00:14:17.360 --> 00:14:20.480 But not as good an economics department. 00:14:19.200 --> 00:14:23.079 And he decided he was roughly 00:14:20.480 --> 00:14:25.360 indifferent between the two. 00:14:23.078 --> 00:14:27.559 But he had a third offer 00:14:25.360 --> 00:14:29.919 from the IMF, which is a research 00:14:27.559 --> 00:14:31.559 institution in DC, which as he had a lot 00:14:29.919 --> 00:14:32.838 of good colleagues and DC is way better 00:14:31.559 --> 00:14:34.679 than Princeton, New Jersey even if it's 00:14:32.839 --> 00:14:35.880 not as good as Santa Cruz. So, he 00:14:34.679 --> 00:14:37.399 decided he would take the offer at the 00:14:35.879 --> 00:14:39.759 IMF. 00:14:37.399 --> 00:14:41.480 Okay? Even though the IMF had worse 00:14:39.759 --> 00:14:43.879 colleagues than Princeton 00:14:41.480 --> 00:14:45.519 and worse location than Santa Cruz, 00:14:43.879 --> 00:14:47.720 it was still better in combination the 00:14:45.519 --> 00:14:48.879 two of them given his preferences. 00:14:47.720 --> 00:14:50.879 And that's how he used indifference 00:14:48.879 --> 00:14:52.279 curves to help make his decision. 00:14:50.879 --> 00:14:54.360 Okay? 00:14:52.279 --> 00:14:55.720 So, that's sort of an example of uh of 00:14:54.360 --> 00:14:57.720 applying it. Let's see no offense to the 00:14:55.720 --> 00:14:59.639 New Jerseyans in the room, of which I'm 00:14:57.720 --> 00:15:00.720 one, but believe me you'd rather be in 00:14:59.639 --> 00:15:02.919 Santa Cruz. 00:15:00.720 --> 00:15:05.879 Um okay. Uh 00:15:02.919 --> 00:15:09.838 so, now let's go from preferences 00:15:05.879 --> 00:15:09.838 to utility functions. 00:15:12.480 --> 00:15:15.079 Okay? So, now we're going to move from 00:15:13.679 --> 00:15:17.519 preferences, 00:15:15.078 --> 00:15:19.639 which we've represented graphically, 00:15:17.519 --> 00:15:21.799 to utility functions, which we're going 00:15:19.639 --> 00:15:22.799 to represent mathematically. Remember, I 00:15:21.799 --> 00:15:23.838 want you to understand everything in 00:15:22.799 --> 00:15:25.838 this course at three levels: 00:15:23.839 --> 00:15:28.320 graphically, mathematically, and most 00:15:25.839 --> 00:15:30.400 importantly of all intuitively. Okay? 00:15:28.320 --> 00:15:31.400 So, graphic is indifference curves. Now 00:15:30.399 --> 00:15:34.120 we'll come to the mathematical 00:15:31.399 --> 00:15:36.519 representation, which utility function. 00:15:34.120 --> 00:15:38.679 Okay? And the idea is that every 00:15:36.519 --> 00:15:41.879 individual, all of you in this room, 00:15:38.679 --> 00:15:43.559 have a stable, well-behaved underlying 00:15:41.879 --> 00:15:44.919 mathematical representation of your 00:15:43.559 --> 00:15:47.399 preferences, 00:15:44.919 --> 00:15:49.319 which we call utility function. 00:15:47.399 --> 00:15:50.199 Okay? Now, once again, that's going to 00:15:49.320 --> 00:15:51.240 be very complicated and you have 00:15:50.200 --> 00:15:52.680 preference over lots of different 00:15:51.240 --> 00:15:54.120 things. We're going to make things 00:15:52.679 --> 00:15:56.120 simple by writing out two-dimensional 00:15:54.120 --> 00:15:58.078 representation for now of your 00:15:56.120 --> 00:16:00.959 indifference curve. We're going to say, 00:15:58.078 --> 00:16:03.919 how do we mathematically represent your 00:16:00.958 --> 00:16:05.599 feelings about pizza versus cookies? 00:16:03.919 --> 00:16:07.599 Okay? Imagine that's all you care about 00:16:05.600 --> 00:16:09.519 in the world is pizza and cookies. 00:16:07.600 --> 00:16:11.639 How do we mathematically represent that? 00:16:09.519 --> 00:16:14.039 So, for example, we could write down 00:16:11.639 --> 00:16:15.799 that your utility function is equal to 00:16:14.039 --> 00:16:18.480 the square root of the number of slices 00:16:15.799 --> 00:16:19.599 of pizza times the number of cookies. 00:16:18.480 --> 00:16:21.360 We could write that down. I'm not saying 00:16:19.600 --> 00:16:22.600 that's right. I'm not saying it works 00:16:21.360 --> 00:16:25.279 for anyone in this room or even everyone 00:16:22.600 --> 00:16:28.360 in this room, but that is a possible way 00:16:25.279 --> 00:16:30.559 to represent utility. 00:16:28.360 --> 00:16:32.159 Okay? What this would say, this is 00:16:30.559 --> 00:16:33.879 convenient. We will use we'll end up 00:16:32.159 --> 00:16:34.919 using square root form a lot for utility 00:16:33.879 --> 00:16:36.720 functions, a lot of convenient 00:16:34.919 --> 00:16:39.039 mathematical properties. 00:16:36.720 --> 00:16:40.639 And it happens to jive with our example, 00:16:39.039 --> 00:16:42.078 right? Because in this example you're 00:16:40.639 --> 00:16:44.000 indifferent between two pizza and one 00:16:42.078 --> 00:16:45.759 cookie or one pizza and two cookie. 00:16:44.000 --> 00:16:47.000 They're both square root of two. 00:16:45.759 --> 00:16:48.600 And you prefer two pizza and two 00:16:47.000 --> 00:16:50.600 cookies, that's two. 00:16:48.600 --> 00:16:53.560 Okay? So, this gives you a higher 00:16:50.600 --> 00:16:55.800 utility for two pizza and two cookies 00:16:53.559 --> 00:16:57.838 okay? Um uh 00:16:55.799 --> 00:16:59.679 then uh one pizza 00:16:57.839 --> 00:17:02.000 than one pizza and two cookie or two 00:16:59.679 --> 00:17:03.838 pizza and one cookie. 00:17:02.000 --> 00:17:05.920 So, now the question is what does this 00:17:03.839 --> 00:17:08.799 mean? What is utility? 00:17:05.920 --> 00:17:10.560 Okay? Well, utility doesn't actually 00:17:08.799 --> 00:17:12.919 mean anything. There's not really a 00:17:10.559 --> 00:17:14.039 thing out there called utils. 00:17:12.920 --> 00:17:15.600 Okay? 00:17:14.039 --> 00:17:18.039 In other words, utility is not a 00:17:15.599 --> 00:17:19.838 cardinal concept. It is only an ordinal 00:17:18.039 --> 00:17:23.279 concept. 00:17:19.838 --> 00:17:26.119 You cannot say your utility you are you 00:17:23.279 --> 00:17:27.838 cannot literally say my utility is X% 00:17:26.119 --> 00:17:29.119 higher than your utility, but you can 00:17:27.838 --> 00:17:31.279 rank them. 00:17:29.119 --> 00:17:33.079 So, we're going to assume that utility 00:17:31.279 --> 00:17:34.720 can be ranked to allow you to rank 00:17:33.079 --> 00:17:36.720 choices. 00:17:34.720 --> 00:17:38.319 Even if generally we might slip some and 00:17:36.720 --> 00:17:41.319 sort of pretend utility is cardinal for 00:17:38.319 --> 00:17:42.319 some cute examples, but by and large 00:17:41.319 --> 00:17:44.559 we're going to think of utility as 00:17:42.319 --> 00:17:46.279 purely ordinal. It's just a way to rank 00:17:44.559 --> 00:17:47.720 your choices. It's just when you have a 00:17:46.279 --> 00:17:49.799 set of choices out there over many 00:17:47.720 --> 00:17:51.679 dimensions. Like if your choice in life 00:17:49.799 --> 00:17:53.200 is always over one dimension 00:17:51.679 --> 00:17:54.840 and more was better, it would always be 00:17:53.200 --> 00:17:56.960 easy to rank it, right? You never ever 00:17:54.839 --> 00:17:58.519 problem. Once your choice over more than 00:17:56.960 --> 00:18:00.039 one dimension, 00:17:58.519 --> 00:18:01.839 now if you want to rank them, you need 00:18:00.039 --> 00:18:03.599 some way to combine them. That's what 00:18:01.839 --> 00:18:05.359 this function does. It allows you 00:18:03.599 --> 00:18:07.439 essentially to weight the different 00:18:05.359 --> 00:18:09.199 elements of your consumption bundle so 00:18:07.440 --> 00:18:11.759 you can rank them um 00:18:09.200 --> 00:18:14.319 when it comes time to choose. 00:18:11.759 --> 00:18:15.679 Okay? Now, this is obviously incredibly 00:18:14.319 --> 00:18:17.200 simple, 00:18:15.679 --> 00:18:19.200 but it turns out to be amazingly 00:18:17.200 --> 00:18:20.480 powerful in explaining real world 00:18:19.200 --> 00:18:21.840 behavior. 00:18:20.480 --> 00:18:23.240 Okay? 00:18:21.839 --> 00:18:24.519 And so, what I want to do today is work 00:18:23.240 --> 00:18:25.720 with the underlying mathematics of 00:18:24.519 --> 00:18:26.879 utility 00:18:25.720 --> 00:18:28.319 and then we'll come back we'll see in 00:18:26.880 --> 00:18:31.240 the next few lectures how it could 00:18:28.319 --> 00:18:33.519 actually be used to explain decisions. 00:18:31.240 --> 00:18:34.839 So, a key concept we're going to talk 00:18:33.519 --> 00:18:38.119 about 00:18:34.839 --> 00:18:39.678 in this class is marginal utility. 00:18:38.119 --> 00:18:41.719 Marginal utility is just the derivative 00:18:39.679 --> 00:18:43.560 of the utility function with respect to 00:18:41.720 --> 00:18:45.880 one of the elements. So, the marginal 00:18:43.559 --> 00:18:48.279 utility for cookies of cookies is 00:18:45.880 --> 00:18:50.560 utility of the next cookie 00:18:48.279 --> 00:18:52.480 given how many cookies you've had. 00:18:50.559 --> 00:18:55.039 This class can be very focused on 00:18:52.480 --> 00:18:56.679 marginal decision making. 00:18:55.039 --> 00:18:58.559 In economics, it's all about how you 00:18:56.679 --> 00:19:00.679 think about the next unit. Turns out 00:18:58.559 --> 00:19:02.039 that makes life a ton easier. Turns out 00:19:00.679 --> 00:19:03.720 it's way easier to say, do you want the 00:19:02.039 --> 00:19:06.200 next cookie? Than to say, how many 00:19:03.720 --> 00:19:07.159 cookies do you want? 00:19:06.200 --> 00:19:09.159 Because if you want the next cookie, 00:19:07.159 --> 00:19:10.159 that's sort of a very isolated decision. 00:19:09.159 --> 00:19:12.159 You say, okay, I've had this many 00:19:10.159 --> 00:19:13.400 cookies, do I want the next cookie? 00:19:12.159 --> 00:19:14.360 Whereas before you start eating you say, 00:19:13.400 --> 00:19:16.759 how many cookies do you want? That's 00:19:14.359 --> 00:19:18.799 sort of a harder more global decision. 00:19:16.759 --> 00:19:20.720 So, we're going to focus on the stepwise 00:19:18.799 --> 00:19:22.399 decision making process of do you want 00:19:20.720 --> 00:19:24.440 the next unit, the next cookie or the 00:19:22.400 --> 00:19:28.120 next slice of pizza? 00:19:24.440 --> 00:19:29.559 Okay? And the key feature of utility 00:19:28.119 --> 00:19:31.000 functions we'll work with throughout the 00:19:29.559 --> 00:19:35.440 semester 00:19:31.000 --> 00:19:35.440 is that they will feature diminishing 00:19:36.359 --> 00:19:41.599 diminishing marginal utility. 00:19:39.079 --> 00:19:43.319 Marginal utility will fall as you have 00:19:41.599 --> 00:19:45.439 more of a good. 00:19:43.319 --> 00:19:47.079 The more of a good you've had, the less 00:19:45.440 --> 00:19:48.799 happiness you'll derive from the next 00:19:47.079 --> 00:19:50.599 unit. 00:19:48.799 --> 00:19:52.839 Okay? 00:19:50.599 --> 00:19:55.199 Now, we can see that graphically in 00:19:52.839 --> 00:19:58.039 figure 2-4. 00:19:55.200 --> 00:20:00.200 Figure 2-4 graphs on the x-axis the 00:19:58.039 --> 00:20:01.720 number of cookies holding constant 00:20:00.200 --> 00:20:04.279 pizza. So, let's say you're having two 00:20:01.720 --> 00:20:05.799 pizza slices and you want to say, 00:20:04.279 --> 00:20:07.559 "What's my benefit from the next 00:20:05.799 --> 00:20:09.879 cookie?" 00:20:07.559 --> 00:20:11.799 And on the on the left axis, violating 00:20:09.880 --> 00:20:13.360 what I just said like 15 seconds ago, we 00:20:11.799 --> 00:20:14.799 graph utility. 00:20:13.359 --> 00:20:16.000 Now, once again, the util numbers don't 00:20:14.799 --> 00:20:18.039 mean anything. It's just to give you an 00:20:16.000 --> 00:20:19.519 ordinal sense. 00:20:18.039 --> 00:20:20.960 What you see here is that if you have 00:20:19.519 --> 00:20:23.879 one cookie, 00:20:20.960 --> 00:20:25.400 your utility is 1.4, square root of 2 * 00:20:23.880 --> 00:20:26.760 1. 00:20:25.400 --> 00:20:28.200 If you have two cookies, your utility 00:20:26.759 --> 00:20:30.119 goes up 00:20:28.200 --> 00:20:32.039 to square root of 4, which is 2. You are 00:20:30.119 --> 00:20:34.599 happier with two cookies. 00:20:32.039 --> 00:20:36.440 But you are less happy from the second 00:20:34.599 --> 00:20:39.119 cookie than the first cookie. 00:20:36.440 --> 00:20:40.600 Okay? And you can see that in figure if 00:20:39.119 --> 00:20:43.519 you flip back and forth between 2-4 and 00:20:40.599 --> 00:20:46.159 2-5, you can see that. 00:20:43.519 --> 00:20:48.440 Okay? The first cookie, 00:20:46.160 --> 00:20:50.400 going from zero to one cookie, gave you 00:20:48.440 --> 00:20:53.440 one So, in this case, we're not graphing 00:20:50.400 --> 00:20:56.200 the marginal utility. So, figure 2-4 is 00:20:53.440 --> 00:20:57.480 the level of utility, 00:20:56.200 --> 00:20:59.559 which is not really something you can 00:20:57.480 --> 00:21:00.519 measure, in fact. Figure 2-5 is 00:20:59.559 --> 00:21:02.079 something you can measure, which is 00:21:00.519 --> 00:21:03.680 marginal utility. What's your happiness? 00:21:02.079 --> 00:21:05.240 And we'll talk about measuring this from 00:21:03.680 --> 00:21:06.880 the next cookie. You see, the first 00:21:05.240 --> 00:21:08.640 cookie 00:21:06.880 --> 00:21:10.960 gives you 00:21:08.640 --> 00:21:13.040 um a utility and a utility increment of 00:21:10.960 --> 00:21:15.480 1.4. 00:21:13.039 --> 00:21:17.480 Okay? You go from utility of zero 00:21:15.480 --> 00:21:18.640 to utility of 1.4. 00:21:17.480 --> 00:21:21.120 The next cookie gives you a utility 00:21:18.640 --> 00:21:23.600 increment of 0.59. 00:21:21.119 --> 00:21:25.239 Okay, you go from utility of 1.41 00:21:23.599 --> 00:21:26.519 to utility of 2. 00:21:25.240 --> 00:21:28.960 The next cookie gives you a utility 00:21:26.519 --> 00:21:30.759 increment of 0.45, the square root of 3. 00:21:28.960 --> 00:21:32.360 So, now we flip back to the previous 00:21:30.759 --> 00:21:34.359 page. We're going from the square root 00:21:32.359 --> 00:21:35.439 of 4 to We're going from the square root 00:21:34.359 --> 00:21:36.839 of 4, I'm sorry, to the square root of 00:21:35.440 --> 00:21:39.080 6. 00:21:36.839 --> 00:21:40.799 Square root of 6 is only 0.45 more than 00:21:39.079 --> 00:21:42.279 the square root of 4. 00:21:40.799 --> 00:21:44.440 And so on. 00:21:42.279 --> 00:21:46.480 So, each additional cookie 00:21:44.440 --> 00:21:48.519 makes you less and less happy. It makes 00:21:46.480 --> 00:21:50.400 you happier. It has to cuz more is 00:21:48.519 --> 00:21:51.879 better. But it makes you less and less 00:21:50.400 --> 00:21:54.640 happy. 00:21:51.880 --> 00:21:56.360 Okay? And this makes sense. 00:21:54.640 --> 00:21:58.080 Just think about any decision in life 00:21:56.359 --> 00:22:00.479 starting with nothing of something and 00:21:58.079 --> 00:22:02.480 having the first one. Slice of pizza, a 00:22:00.480 --> 00:22:03.319 cookie, deciding on which movie to go 00:22:02.480 --> 00:22:04.880 to. 00:22:03.319 --> 00:22:06.599 The first movie, the one you want to see 00:22:04.880 --> 00:22:08.720 the most, 00:22:06.599 --> 00:22:09.919 okay, is going to make you happier than 00:22:08.720 --> 00:22:11.360 you want to see the one you want to see 00:22:09.920 --> 00:22:12.640 not quite as much. 00:22:11.359 --> 00:22:15.039 The first cookie when you're hungry will 00:22:12.640 --> 00:22:16.120 make you happier than the second cookie. 00:22:15.039 --> 00:22:17.960 The first slice of pizza will make you 00:22:16.119 --> 00:22:19.159 happier. Now, you may be close to 00:22:17.960 --> 00:22:20.600 indifferent where that second slice of 00:22:19.160 --> 00:22:21.840 pizza makes you almost as happy as the 00:22:20.599 --> 00:22:23.759 first. 00:22:21.839 --> 00:22:25.639 But the first will make you happier. 00:22:23.759 --> 00:22:27.000 Okay, if you think about that's really 00:22:25.640 --> 00:22:27.960 sort of that first step. You were hungry 00:22:27.000 --> 00:22:29.519 and that first one makes you feel 00:22:27.960 --> 00:22:32.160 happier. 00:22:29.519 --> 00:22:33.920 Now, but you got to remember you always 00:22:32.160 --> 00:22:35.080 want more cookies. 00:22:33.920 --> 00:22:36.400 Now, you might say, "Wait a second, this 00:22:35.079 --> 00:22:38.119 is stupid. Okay, once I've had 10 00:22:36.400 --> 00:22:39.480 cookies, I'm going to barf." 00:22:38.119 --> 00:22:42.079 The 11th cookie could actually make me 00:22:39.480 --> 00:22:43.360 worse off cuz I don't like barfing. 00:22:42.079 --> 00:22:45.480 But 00:22:43.359 --> 00:22:47.240 in economics, we have to remember you 00:22:45.480 --> 00:22:49.000 don't have to eat the 11th cookie. You 00:22:47.240 --> 00:22:50.120 could give it away. 00:22:49.000 --> 00:22:52.240 So, if I say you want to buy the 11th 00:22:50.119 --> 00:22:53.959 cookie, you could save it for later. You 00:22:52.240 --> 00:22:56.039 could give it to a friend. 00:22:53.960 --> 00:22:57.880 So, you always want it. In the worst 00:22:56.039 --> 00:22:59.799 case, you throw it out. 00:22:57.880 --> 00:23:01.880 It can't make you worse off. 00:22:59.799 --> 00:23:03.159 It can only make you better off. 00:23:01.880 --> 00:23:04.640 And that's what where our sort of more 00:23:03.160 --> 00:23:05.840 is better assumption comes from. 00:23:04.640 --> 00:23:07.160 Obviously, in the limit, you know, if 00:23:05.839 --> 00:23:08.678 you get a million cookies, your garbage 00:23:07.160 --> 00:23:09.759 can gets full, you have no friends to 00:23:08.679 --> 00:23:12.240 give them to. I understand the limit 00:23:09.759 --> 00:23:13.640 these things fall apart. Okay? But 00:23:12.240 --> 00:23:15.000 that's the basic idea of more is better 00:23:13.640 --> 00:23:16.640 and the basic idea of of diminishing 00:23:15.000 --> 00:23:17.960 marginal utility. Okay, any questions 00:23:16.640 --> 00:23:20.320 about that? 00:23:17.960 --> 00:23:20.319 Yeah. 00:23:20.880 --> 00:23:25.520 Utility function can never be negative 00:23:22.559 --> 00:23:26.879 because we have Well, utility Once 00:23:25.519 --> 00:23:28.119 again, utility is not an ordinal 00:23:26.880 --> 00:23:29.200 concept. You can set up utility 00:23:28.119 --> 00:23:31.678 functions such that the number is 00:23:29.200 --> 00:23:34.360 negative. You can set that up. Okay? The 00:23:31.679 --> 00:23:35.920 marginal utility is always positive. You 00:23:34.359 --> 00:23:37.079 always get some benefit from the next 00:23:35.920 --> 00:23:38.400 unit. 00:23:37.079 --> 00:23:39.480 Utility, once again, the measurement is 00:23:38.400 --> 00:23:40.759 irrelevant. So, it can be negative. You 00:23:39.480 --> 00:23:42.240 can set it up. Yeah, I could write my 00:23:40.759 --> 00:23:43.920 utility function like this, you know, 00:23:42.240 --> 00:23:45.440 something like that. So, it could be 00:23:43.920 --> 00:23:47.279 negative. That's just a sort of scaling 00:23:45.440 --> 00:23:49.440 factor. But marginal utility is always 00:23:47.279 --> 00:23:51.240 positive. You're always happier or it's 00:23:49.440 --> 00:23:53.160 not it's not negative. You're always 00:23:51.240 --> 00:23:54.640 happier at least indifferent to getting 00:23:53.160 --> 00:23:56.840 the next unit. 00:23:54.640 --> 00:23:58.240 Yeah. So, when you're looking at 2-5, 00:23:56.839 --> 00:23:59.839 you can't look at the function of the 00:23:58.240 --> 00:24:02.039 pizza and the marginal utility, so it's 00:23:59.839 --> 00:24:04.678 going to go down. 00:24:02.039 --> 00:24:05.519 Uh I'm sorry. You look Figure 2-5, no, 00:24:04.679 --> 00:24:06.640 the marginal utility is going to go 00:24:05.519 --> 00:24:07.960 down. 00:24:06.640 --> 00:24:09.200 Each fraction of cookie, the marginal 00:24:07.960 --> 00:24:11.000 utility Marginal utility is always 00:24:09.200 --> 00:24:12.840 diminishing. So, if you start with zero, 00:24:11.000 --> 00:24:14.279 then you can get half of the pizza in 00:24:12.839 --> 00:24:15.720 this graph. 00:24:14.279 --> 00:24:17.279 Well, it's really hard to do it from 00:24:15.720 --> 00:24:19.000 zero. That's really tricky. It's sort of 00:24:17.279 --> 00:24:20.720 much easier to start from one. 00:24:19.000 --> 00:24:21.759 So, corner solutions, we'll talk a lot 00:24:20.720 --> 00:24:23.519 about corner solutions in this class. 00:24:21.759 --> 00:24:25.000 They get ugly. Think of it starting from 00:24:23.519 --> 00:24:26.240 one. Starting from that first cookie, 00:24:25.000 --> 00:24:27.559 every fraction of a cookie makes you 00:24:26.240 --> 00:24:29.799 happier but less and less happy with 00:24:27.559 --> 00:24:31.919 each fraction. It's a good question. 00:24:29.799 --> 00:24:35.720 All right. Good questions. All right. 00:24:31.920 --> 00:24:38.920 So, now let's let's talk about Let's 00:24:35.720 --> 00:24:40.640 flip back from the math to the graphics 00:24:38.920 --> 00:24:42.600 and talk about where indifference curves 00:24:40.640 --> 00:24:44.640 come from. I just drew them out. But in 00:24:42.599 --> 00:24:46.519 fact, indifference curves are the 00:24:44.640 --> 00:24:49.000 graphical representation of what comes 00:24:46.519 --> 00:24:51.359 out of utility function. 00:24:49.000 --> 00:24:54.480 Okay? And indeed, the slope of the 00:24:51.359 --> 00:24:58.439 indifference curve we are going to call 00:24:54.480 --> 00:24:59.920 the marginal rate of substitution. 00:24:58.440 --> 00:25:02.600 The rate essentially at which you're 00:24:59.920 --> 00:25:04.240 willing to substitute 00:25:02.599 --> 00:25:05.919 one good for the other. The rate at 00:25:04.240 --> 00:25:09.559 which you're willing to substitute 00:25:05.920 --> 00:25:11.160 cookies for pizza is your marginal rate 00:25:09.559 --> 00:25:14.480 of substitution. 00:25:11.160 --> 00:25:16.519 And we'll define that as the slope of 00:25:14.480 --> 00:25:18.679 the indifference curve, delta P over 00:25:16.519 --> 00:25:19.720 delta C. 00:25:18.679 --> 00:25:20.960 That is your marginal rate of 00:25:19.720 --> 00:25:22.839 substitution. Literally, the 00:25:20.960 --> 00:25:23.880 indifference curve tells you the rate at 00:25:22.839 --> 00:25:25.959 which you're willing to substitute. You 00:25:23.880 --> 00:25:28.480 just follow along and say, "Look, I'm 00:25:25.960 --> 00:25:30.920 willing to give up um So, in other 00:25:28.480 --> 00:25:33.679 words, if you look at figure 2-6, 00:25:30.920 --> 00:25:35.720 you say, "Look, I'm indifferent between 00:25:33.679 --> 00:25:37.759 point A and point B. 00:25:35.720 --> 00:25:39.120 One cook- one slice of pizza and I'm 00:25:37.759 --> 00:25:40.160 sorry, one cookie and four slices of 00:25:39.119 --> 00:25:42.479 pizza 00:25:40.160 --> 00:25:44.560 is the same to me as two cookies and two 00:25:42.480 --> 00:25:45.799 slices of pizza. Why is it the same? 00:25:44.559 --> 00:25:47.759 Because they both give me utility square 00:25:45.799 --> 00:25:49.079 root of 4, right? So, given this 00:25:47.759 --> 00:25:50.480 mathematical rep- I'm not saying you 00:25:49.079 --> 00:25:52.000 are. I'm saying given this mathematical 00:25:50.480 --> 00:25:54.079 representation, 00:25:52.000 --> 00:25:55.440 okay, you are indifferent between point 00:25:54.079 --> 00:25:57.119 A and point B. 00:25:55.440 --> 00:25:58.519 So, what that says and what's the slope 00:25:57.119 --> 00:26:01.039 of the indifference curve? What's the 00:25:58.519 --> 00:26:04.119 arc slope between point A and point B? 00:26:01.039 --> 00:26:05.440 The slope is -2. 00:26:04.119 --> 00:26:07.439 So, your marginal rate of substitution 00:26:05.440 --> 00:26:09.279 is -2. 00:26:07.440 --> 00:26:10.279 You are indifferent. 00:26:09.279 --> 00:26:13.240 Okay? 00:26:10.279 --> 00:26:15.079 Um you're indifferent between 1-4 and 00:26:13.240 --> 00:26:18.200 2-2. Therefore, you're willing to 00:26:15.079 --> 00:26:22.119 substitute or give away 00:26:18.200 --> 00:26:24.120 two slices of pizza to get one cookie. 00:26:22.119 --> 00:26:25.639 Delta P delta C 00:26:24.119 --> 00:26:28.399 is uh 00:26:25.640 --> 00:26:31.240 is -2. 00:26:28.400 --> 00:26:32.440 Okay? Now, it turns out you can define 00:26:31.240 --> 00:26:34.519 the marginal rate of substitution over 00:26:32.440 --> 00:26:36.920 any segment of indifference curve. And 00:26:34.519 --> 00:26:39.119 what's interesting is it changes. It 00:26:36.920 --> 00:26:42.640 diminishes. Look what happens when we 00:26:39.119 --> 00:26:44.919 move from two pizzas and two cookies 00:26:42.640 --> 00:26:46.280 to from point B to point C. 00:26:44.920 --> 00:26:47.920 Now, the marginal rate of substitution 00:26:46.279 --> 00:26:50.039 is only -1/2. 00:26:47.920 --> 00:26:52.320 Now, I'm only willing to give up one 00:26:50.039 --> 00:26:53.839 slice of pizza to get two cookies. 00:26:52.319 --> 00:26:55.359 What's happening? First, I was willing 00:26:53.839 --> 00:26:57.000 to give up two slices of pizza to get 00:26:55.359 --> 00:26:58.319 one cookie. 00:26:57.000 --> 00:27:00.000 Now, I'm only willing to give up willing 00:26:58.319 --> 00:27:02.240 to give up one slice of pizza to get two 00:27:00.000 --> 00:27:03.880 cookies. What's happening? 00:27:02.240 --> 00:27:05.640 Yeah. You don't want a cookie as much. 00:27:03.880 --> 00:27:07.679 Because of? Diminishing marginal 00:27:05.640 --> 00:27:10.400 utility. Exactly. Diminishing marginal 00:27:07.679 --> 00:27:12.840 utility has caused the marginal rate of 00:27:10.400 --> 00:27:13.960 substitution itself itself to diminish. 00:27:12.839 --> 00:27:15.720 For those of you who are really kind of 00:27:13.960 --> 00:27:17.960 better at math than I am, it turns out 00:27:15.720 --> 00:27:19.799 technically, mathematically, marginal 00:27:17.960 --> 00:27:22.000 utility isn't always diminishing. You 00:27:19.799 --> 00:27:23.279 can draw cases. MRS is always 00:27:22.000 --> 00:27:24.640 diminishing. 00:27:23.279 --> 00:27:25.678 So, you can think of marginal utility as 00:27:24.640 --> 00:27:27.040 always diminishing. It's fine for this 00:27:25.679 --> 00:27:28.080 class. When you get to higher level math 00:27:27.039 --> 00:27:30.200 and economics, you'll see marginal 00:27:28.079 --> 00:27:32.039 utility doesn't have to diminish. MRS 00:27:30.200 --> 00:27:35.000 has to diminish. 00:27:32.039 --> 00:27:36.519 Okay? MRS is always diminishing. 00:27:35.000 --> 00:27:40.200 As you go along the indifference curve, 00:27:36.519 --> 00:27:40.200 that slope is always falling. 00:27:40.319 --> 00:27:43.759 Okay? 00:27:41.679 --> 00:27:46.640 So, basically, 00:27:43.759 --> 00:27:48.559 what we can write now is how the MRS 00:27:46.640 --> 00:27:50.600 relates to utility function, 00:27:48.559 --> 00:27:53.720 our first sort of mind-blowing result, 00:27:50.599 --> 00:27:56.599 is that the MRS is equal to the negative 00:27:53.720 --> 00:27:59.519 of the marginal utility of cookies over 00:27:56.599 --> 00:28:02.119 the marginal utility of pizza. 00:27:59.519 --> 00:28:04.279 That's our first key definition. 00:28:02.119 --> 00:28:05.599 It's equal to the negative of the 00:28:04.279 --> 00:28:07.720 marginal utility of the good on the 00:28:05.599 --> 00:28:10.519 x-axis over the marginal utility of the 00:28:07.720 --> 00:28:13.079 good on the y-axis. 00:28:10.519 --> 00:28:16.240 Okay? Essentially, the marginal rate of 00:28:13.079 --> 00:28:19.039 substitution tells you how your relative 00:28:16.240 --> 00:28:22.039 marginal utilities evolve as you move 00:28:19.039 --> 00:28:25.720 down the indifference curve. 00:28:22.039 --> 00:28:28.599 When you start at point A, 00:28:25.720 --> 00:28:30.799 you have lots of pizza and not a lot of 00:28:28.599 --> 00:28:33.119 cookies. 00:28:30.799 --> 00:28:36.879 When you have lots of pizza, 00:28:33.119 --> 00:28:38.839 your marginal utility is small. 00:28:36.880 --> 00:28:40.560 Here's the key insight. This is the 00:28:38.839 --> 00:28:41.678 thing which, once again, it's a light 00:28:40.559 --> 00:28:43.799 bulb thing. If you get this, it'll make 00:28:41.679 --> 00:28:46.320 your life so much easier. Marginal 00:28:43.799 --> 00:28:47.759 utilities are negative functions of 00:28:46.319 --> 00:28:50.279 quantity. 00:28:47.759 --> 00:28:53.079 The more you have of a thing, the less 00:28:50.279 --> 00:28:54.879 you want the next unit of it. 00:28:53.079 --> 00:28:55.918 That's why, for example, cookies is now 00:28:54.880 --> 00:28:58.440 in the numerator and pizza is in the 00:28:55.919 --> 00:29:00.679 denominator, flipping from this side. 00:28:58.440 --> 00:29:02.120 Okay? The more you have a good, the less 00:29:00.679 --> 00:29:04.679 you want it. 00:29:02.119 --> 00:29:07.199 So, start at point A. You have lots of 00:29:04.679 --> 00:29:09.120 pizza and not a lot of cookies. 00:29:07.200 --> 00:29:10.640 You don't really want more pizza. You 00:29:09.119 --> 00:29:13.479 want more cookies. 00:29:10.640 --> 00:29:16.800 That means the denominator is small. 00:29:13.480 --> 00:29:18.319 The marginal utility of pizza is small. 00:29:16.799 --> 00:29:19.759 You don't really want it. 00:29:18.319 --> 00:29:21.559 But the marginal utility of cookies is 00:29:19.759 --> 00:29:24.279 high. You don't have many of them. So, 00:29:21.559 --> 00:29:26.720 this is a big number. 00:29:24.279 --> 00:29:28.599 Now, let's move to point B. 00:29:26.720 --> 00:29:30.240 And think about your next decision. 00:29:28.599 --> 00:29:33.119 Well, now 00:29:30.240 --> 00:29:34.200 your marginal utility of pizza, 00:29:33.119 --> 00:29:35.759 if you're going to go from two to one 00:29:34.200 --> 00:29:37.519 slice of pizza, now pizza is worth a lot 00:29:35.759 --> 00:29:38.879 more than cookies. So, now it gets 00:29:37.519 --> 00:29:40.960 smaller. 00:29:38.880 --> 00:29:43.080 So, essentially, as you move along that 00:29:40.960 --> 00:29:44.400 indifference curve, because of this you 00:29:43.079 --> 00:29:45.678 want because diminishing marginal 00:29:44.400 --> 00:29:47.519 utility, 00:29:45.679 --> 00:29:49.720 it leads this issue of a diminishing 00:29:47.519 --> 00:29:52.000 marginal rate of substitution. 00:29:49.720 --> 00:29:53.559 Okay? So, basically, as you move along 00:29:52.000 --> 00:29:55.640 the indifference curve, you're more and 00:29:53.559 --> 00:29:57.480 more willing to give up 00:29:55.640 --> 00:29:59.280 the good on the x-axis to get the good 00:29:57.480 --> 00:30:00.960 on the y-axis. As you move from the 00:29:59.279 --> 00:30:03.599 upper left to the lower right on that 00:30:00.960 --> 00:30:04.960 indifference map, figure 2.6, 00:30:03.599 --> 00:30:06.199 you're more you're more willing to give 00:30:04.960 --> 00:30:08.680 up 00:30:06.200 --> 00:30:11.000 the good on the on the x-axis to get the 00:30:08.680 --> 00:30:13.160 good on the y-axis. 00:30:11.000 --> 00:30:16.039 And what this implies is that 00:30:13.160 --> 00:30:17.759 indifference curves are con- 00:30:16.039 --> 00:30:21.119 indifference curves 00:30:17.759 --> 00:30:22.680 are uh convex to the origin. 00:30:21.119 --> 00:30:23.959 Indifference curves are convex to the 00:30:22.680 --> 00:30:26.720 origin. 00:30:23.960 --> 00:30:28.440 It's very important. Okay, the 00:30:26.720 --> 00:30:29.799 Let's see. The They are They are not 00:30:28.440 --> 00:30:31.240 concave. They're either convex or 00:30:29.799 --> 00:30:33.079 straight. Let's say they're They're not 00:30:31.240 --> 00:30:34.960 concave to the origin. 00:30:33.079 --> 00:30:36.159 Okay, to be technical. 00:30:34.960 --> 00:30:37.799 Indifference curves can be linear. We'll 00:30:36.160 --> 00:30:39.160 come to that. 00:30:37.799 --> 00:30:40.919 But they can't be concave to the origin. 00:30:39.160 --> 00:30:43.480 Why? Well, let's look at the next 00:30:40.920 --> 00:30:44.840 figure, the last figure, figure 2.7. 00:30:43.480 --> 00:30:47.640 What would happen if indifference curves 00:30:44.839 --> 00:30:51.879 were concave to the origin? 00:30:47.640 --> 00:30:54.280 Then that would say moving from 00:30:51.880 --> 00:30:55.920 one pizza, so now I've drawn a a concave 00:30:54.279 --> 00:30:57.440 indifference curve. And with this 00:30:55.920 --> 00:31:00.200 indifference curve, moving from point A 00:30:57.440 --> 00:31:02.920 to point B leaves you indifferent. 00:31:00.200 --> 00:31:04.720 So, you're happy to give up one slice of 00:31:02.920 --> 00:31:06.400 pizza to get one cookie. 00:31:04.720 --> 00:31:07.720 Starting with four slices of pizza and 00:31:06.400 --> 00:31:09.920 one cookie, 00:31:07.720 --> 00:31:12.480 you were happy to give up one slice of 00:31:09.920 --> 00:31:15.519 pizza to get one cookie. 00:31:12.480 --> 00:31:16.920 Now, starting from two and three, you're 00:31:15.519 --> 00:31:19.160 now willing to give up two slices of 00:31:16.920 --> 00:31:20.519 pizza to get one cookie. 00:31:19.160 --> 00:31:23.080 What does that violate? Why Why does 00:31:20.519 --> 00:31:25.000 that not make sense? Yeah. 00:31:23.079 --> 00:31:26.119 Law of diminishing marginal returns. 00:31:25.000 --> 00:31:28.799 Yeah, it's law of diminishing marginal 00:31:26.119 --> 00:31:30.319 utility. Here, you were you were you 00:31:28.799 --> 00:31:31.879 were only You were happy to have one 00:31:30.319 --> 00:31:32.799 slice of pizza to get one cookie. Now 00:31:31.880 --> 00:31:33.760 you were willing to have two slices of 00:31:32.799 --> 00:31:35.799 pizza to get one cookie, even though you 00:31:33.759 --> 00:31:37.720 have less pizza and more cookies. That 00:31:35.799 --> 00:31:40.200 can't be right. As you have less pizza 00:31:37.720 --> 00:31:42.480 and more cookies, cookies pizza should 00:31:40.200 --> 00:31:43.960 become more valuable, not less valuable. 00:31:42.480 --> 00:31:45.480 And cookies should become less valuable, 00:31:43.960 --> 00:31:47.559 not more valuable. 00:31:45.480 --> 00:31:49.519 So, a concave to the origin indifference 00:31:47.559 --> 00:31:50.519 curve would violate the principle of 00:31:49.519 --> 00:31:51.279 diminishing marginal utility and 00:31:50.519 --> 00:31:53.079 diminishing marginal rate of 00:31:51.279 --> 00:31:55.359 substitution. 00:31:53.079 --> 00:31:56.480 Okay? Yeah. What if it's like trading 00:31:55.359 --> 00:31:58.719 cards? 00:31:56.480 --> 00:32:00.000 Okay. I mean, theory and 00:31:58.720 --> 00:32:01.000 I mean, I think you get more of trading 00:32:00.000 --> 00:32:03.240 cards, 00:32:01.000 --> 00:32:04.079 you you you have fewer cards than you 00:32:03.240 --> 00:32:05.200 want to 00:32:04.079 --> 00:32:06.639 trade that. 00:32:05.200 --> 00:32:08.000 That's very interesting. So, in some 00:32:06.640 --> 00:32:10.160 sense, 00:32:08.000 --> 00:32:11.720 what that is saying is that your utility 00:32:10.160 --> 00:32:12.720 function is really over sets. You're 00:32:11.720 --> 00:32:15.319 saying your utility function is over 00:32:12.720 --> 00:32:17.480 trading cards. It's over sets. 00:32:15.319 --> 00:32:19.720 So, basically, that's what sort of you 00:32:17.480 --> 00:32:22.039 know, what's sort of a bit 00:32:19.720 --> 00:32:23.400 you know, our models are flexible. One 00:32:22.039 --> 00:32:26.279 way to say they're loose, another way to 00:32:23.400 --> 00:32:27.920 say they're flexible. So, one But one of 00:32:26.279 --> 00:32:30.119 the challenges you'll face on this 00:32:27.920 --> 00:32:31.480 course is thinking about what is 00:32:30.119 --> 00:32:32.879 decision set over which I'm writing my 00:32:31.480 --> 00:32:34.880 utility function. You're saying it's 00:32:32.880 --> 00:32:36.440 sets, not trading cards. So, that's why 00:32:34.880 --> 00:32:38.240 it happens. 00:32:36.440 --> 00:32:39.759 Okay? Other questions? Good question. 00:32:38.240 --> 00:32:41.599 Yeah, in the back. What about like 00:32:39.759 --> 00:32:43.759 addictive things where like the more you 00:32:41.599 --> 00:32:45.399 have of it, the more you want to buy? 00:32:43.759 --> 00:32:46.920 Yeah, that's that's a really really good 00:32:45.400 --> 00:32:48.759 question. I spent a lot of my research 00:32:46.920 --> 00:32:50.640 life, actually. I do a lot of I did a 00:32:48.759 --> 00:32:52.559 lot of research for a number of years on 00:32:50.640 --> 00:32:54.800 thinking about how you properly model 00:32:52.559 --> 00:32:56.759 addictive decisions like smoking. 00:32:54.799 --> 00:32:59.960 Addictive decisions like smoking, 00:32:56.759 --> 00:33:02.359 essentially, it really is that your 00:32:59.960 --> 00:33:03.920 utility function itself shifts as you 00:33:02.359 --> 00:33:06.519 get more addictive. 00:33:03.920 --> 00:33:07.960 It's not that your marginal utility, the 00:33:06.519 --> 00:33:09.720 next cigarette is still worth less than 00:33:07.960 --> 00:33:10.799 the first cigarette. It's just that as 00:33:09.720 --> 00:33:12.079 you get more addicted, that first 00:33:10.799 --> 00:33:13.359 cigarette gets worth more and more to 00:33:12.079 --> 00:33:14.678 you. 00:33:13.359 --> 00:33:16.559 So, when you wake up in the morning 00:33:14.679 --> 00:33:17.880 feeling crappy, that first cigarette 00:33:16.559 --> 00:33:19.559 still does more for you than the second 00:33:17.880 --> 00:33:21.600 cigarette. It's just the next day you 00:33:19.559 --> 00:33:23.119 wake up feeling crappier. 00:33:21.599 --> 00:33:26.559 Okay? So, we model addiction as 00:33:23.119 --> 00:33:28.079 something where essentially each day 00:33:26.559 --> 00:33:29.799 cigarettes do less and less for you. You 00:33:28.079 --> 00:33:31.960 get essentially adjusted to new You get 00:33:29.799 --> 00:33:33.119 habituated to higher levels. 00:33:31.960 --> 00:33:34.400 And this is why, you know, I do a lot of 00:33:33.119 --> 00:33:36.559 work, you know, this is why, 00:33:34.400 --> 00:33:37.960 unfortunately, we saw last year the 00:33:36.559 --> 00:33:39.440 number of the highest number of deaths 00:33:37.960 --> 00:33:42.160 from accidental overdose in US history, 00:33:39.440 --> 00:33:43.279 72,000 people died from drug overdoses 00:33:42.160 --> 00:33:44.840 last year, more than ever died in 00:33:43.279 --> 00:33:45.920 traffic accidents in our nation's 00:33:44.839 --> 00:33:47.799 history. 00:33:45.920 --> 00:33:49.400 Okay? Why? 00:33:47.799 --> 00:33:51.119 Because people get habituated to certain 00:33:49.400 --> 00:33:52.360 levels. And they used to be used to 00:33:51.119 --> 00:33:54.119 certain levels. So, people get hooked on 00:33:52.359 --> 00:33:55.479 OxyContin. 00:33:54.119 --> 00:33:57.039 They get habituated to a certain level. 00:33:55.480 --> 00:33:58.400 They maybe switch to heroin. And they're 00:33:57.039 --> 00:33:59.960 habituated to a certain level. And now 00:33:58.400 --> 00:34:01.720 there's this thing called fentanyl, 00:33:59.960 --> 00:34:03.360 which is synthetic opioid brought over 00:34:01.720 --> 00:34:05.519 from China, which is incredibly 00:34:03.359 --> 00:34:07.799 powerful. And dealers are mixing the 00:34:05.519 --> 00:34:09.878 fentanyl in with the heroin. 00:34:07.799 --> 00:34:11.159 And the people shoot up not realizing at 00:34:09.878 --> 00:34:12.279 their habituated level, not realizing 00:34:11.159 --> 00:34:14.159 they have this dangerous substance, and 00:34:12.280 --> 00:34:15.000 they overdose and die. 00:34:14.159 --> 00:34:16.280 And that's because they've got 00:34:15.000 --> 00:34:17.159 habituated to higher levels. They didn't 00:34:16.280 --> 00:34:18.320 realize they're getting a different 00:34:17.159 --> 00:34:19.760 product. So, it's not about not 00:34:18.320 --> 00:34:22.399 diminishing marginal utility. It's about 00:34:19.760 --> 00:34:23.560 different underlying different products. 00:34:22.398 --> 00:34:25.599 All right? 00:34:23.559 --> 00:34:27.279 Other questions? 00:34:25.599 --> 00:34:28.319 Sorry for that depressing note, but it's 00:34:27.280 --> 00:34:29.240 important to be thinking about That's 00:34:28.320 --> 00:34:30.600 why, once again, we're the dismal 00:34:29.239 --> 00:34:33.519 science. We have to think about these 00:34:30.599 --> 00:34:34.918 things. Okay. Now, let's come to a great 00:34:33.519 --> 00:34:36.519 example 00:34:34.918 --> 00:34:37.759 that I hope you've wondered about, and 00:34:36.519 --> 00:34:39.679 maybe you've already figured out in your 00:34:37.760 --> 00:34:41.200 life. But I hope you've at least stopped 00:34:39.679 --> 00:34:44.679 and wondered about, 00:34:41.199 --> 00:34:45.878 which is the prices of different sizes 00:34:44.679 --> 00:34:48.480 of goods 00:34:45.878 --> 00:34:49.519 in a convenience store, say. 00:34:48.480 --> 00:34:51.519 Okay? 00:34:49.519 --> 00:34:53.440 Take Starbucks. 00:34:51.519 --> 00:34:55.358 You can get a tall iced coffee for 00:34:53.440 --> 00:34:56.679 $2.25. 00:34:55.358 --> 00:35:00.119 Or the next size, whatever the hell they 00:34:56.679 --> 00:35:03.000 call it, bigger. Okay? You can get for 00:35:00.119 --> 00:35:05.279 70 more cents. So, $2.25 and you can 00:35:03.000 --> 00:35:09.119 double it for 70 more cents. Or take 00:35:05.280 --> 00:35:11.519 McDonald's. A small drink is $1.22 00:35:09.119 --> 00:35:14.079 at the local McDonald's. But for 50 more 00:35:11.519 --> 00:35:16.320 cents, you can double the size. 00:35:14.079 --> 00:35:18.400 Okay? What's going on here? 00:35:16.320 --> 00:35:19.640 It Why do they give you twice as much 00:35:18.400 --> 00:35:20.800 liquid? 00:35:19.639 --> 00:35:22.519 Or if you go for ice cream, it's the 00:35:20.800 --> 00:35:25.080 same thing. Why do they give you twice 00:35:22.519 --> 00:35:26.320 as much for much less than twice as much 00:35:25.079 --> 00:35:27.679 money? 00:35:26.320 --> 00:35:30.519 What's going on? Yeah. 00:35:27.679 --> 00:35:33.079 Um since your marginal utility is is 00:35:30.519 --> 00:35:34.880 diminishing as you have more coffee 00:35:33.079 --> 00:35:37.799 available to you, you're willing to pay 00:35:34.880 --> 00:35:39.599 less for it. So, they make like the 00:35:37.800 --> 00:35:41.280 additional coffee cheaper. 00:35:39.599 --> 00:35:43.079 Exactly. That's a great way to explain 00:35:41.280 --> 00:35:45.080 it. The point is it's all about 00:35:43.079 --> 00:35:47.119 diminishing marginal utility. 00:35:45.079 --> 00:35:48.960 Okay? When you come in to McDonald's on 00:35:47.119 --> 00:35:50.358 a hot day, you are desperate for that 00:35:48.960 --> 00:35:51.400 soda. 00:35:50.358 --> 00:35:52.960 But you're not as desperate to have 00:35:51.400 --> 00:35:54.200 twice as much soda. You'd like it. 00:35:52.960 --> 00:35:56.159 You're probably willing to pay more for 00:35:54.199 --> 00:35:58.358 it. But you don't like it nearly as much 00:35:56.159 --> 00:36:00.239 as that first bit of soda. 00:35:58.358 --> 00:36:02.759 So, those prices simply reflect the 00:36:00.239 --> 00:36:04.759 market's reaction to understanding 00:36:02.760 --> 00:36:06.120 diminishing marginal utility. 00:36:04.760 --> 00:36:07.760 Now, we haven't talked about the supply 00:36:06.119 --> 00:36:09.000 side of the market yet. I'm not getting 00:36:07.760 --> 00:36:11.080 to how providers make decisions. That's 00:36:09.000 --> 00:36:12.719 a much deeper issue. I'm just saying 00:36:11.079 --> 00:36:14.000 that this is diminishing marginal 00:36:12.719 --> 00:36:17.239 utility in action, how it works in the 00:36:14.000 --> 00:36:21.280 market. And that's why you see this. 00:36:17.239 --> 00:36:23.559 Okay? So, basically, um what you see is 00:36:21.280 --> 00:36:25.440 that uh that first bite of ice cream, 00:36:23.559 --> 00:36:27.000 for example, is worth more, and that's 00:36:25.440 --> 00:36:30.440 why the ice cream is twice as big 00:36:27.000 --> 00:36:34.000 doesn't cost uh twice as much. 00:36:30.440 --> 00:36:36.079 Now, so basically, what this means is if 00:36:34.000 --> 00:36:37.480 you think about our demand and supply 00:36:36.079 --> 00:36:40.358 model, 00:36:37.480 --> 00:36:43.679 on a hot day, or any day, 00:36:40.358 --> 00:36:46.239 the demand for the first 16 oz 00:36:43.679 --> 00:36:48.559 is higher than the demand for the second 00:36:46.239 --> 00:36:50.719 16 oz. 00:36:48.559 --> 00:36:52.840 But the cost of producing 16 oz is the 00:36:50.719 --> 00:36:54.358 same. So, let's think about this. It's 00:36:52.840 --> 00:36:56.358 always risky when I try to draw a graph 00:36:54.358 --> 00:36:57.759 on the board, but let's bear with me. 00:36:56.358 --> 00:36:59.759 Okay? So, let's say we have this sort of 00:36:57.760 --> 00:37:01.960 simple supply and demand model. 00:36:59.760 --> 00:37:04.240 You have this You have this supply 00:37:01.960 --> 00:37:06.679 function for soda. And let's assume it's 00:37:04.239 --> 00:37:08.319 roughly flat. Okay, let's assume sort of 00:37:06.679 --> 00:37:10.358 the cost of firm producing each, you 00:37:08.320 --> 00:37:13.039 know, within some range, the firm 00:37:10.358 --> 00:37:14.759 basically every incremental 16 oz costs 00:37:13.039 --> 00:37:17.159 them the same. So, that's sort of their 00:37:14.760 --> 00:37:18.800 supply curve. Okay? And then you have 00:37:17.159 --> 00:37:20.599 some demand curve. 00:37:18.800 --> 00:37:23.240 Okay? You have some demand curve, which 00:37:20.599 --> 00:37:25.319 is downward sloping. Okay? And they set 00:37:23.239 --> 00:37:27.358 some price. And this is the demand for 00:37:25.320 --> 00:37:29.039 16 oz. 00:37:27.358 --> 00:37:31.519 Now, you have What's the demand for the 00:37:29.039 --> 00:37:32.880 next 16 oz? 00:37:31.519 --> 00:37:34.280 Okay? 00:37:32.880 --> 00:37:35.400 Yeah, this isn't going to work. 00:37:34.280 --> 00:37:36.680 We have to have an upward sloping supply 00:37:35.400 --> 00:37:38.800 curve. Sorry about that. We have a 00:37:36.679 --> 00:37:40.839 slightly upward sloping supply curve. 00:37:38.800 --> 00:37:42.560 Okay? Now we have the demand for the 00:37:40.840 --> 00:37:46.519 next So, So, here's your Here's your 00:37:42.559 --> 00:37:46.519 price. Here's your $1.22. 00:37:46.559 --> 00:37:52.440 Okay? Now you say, "Well, what's my 00:37:49.358 --> 00:37:53.759 demand when I sell 32 oz?" 00:37:52.440 --> 00:37:55.200 Well, it turns out demand doesn't shift 00:37:53.760 --> 00:37:56.920 out twice as much. It just shifts out a 00:37:55.199 --> 00:38:00.119 little bit more. So, you can only charge 00:37:56.920 --> 00:38:01.480 $1.72 for the next 16 oz. Probably, if 00:38:00.119 --> 00:38:03.358 you want to go to the big If you go to 00:38:01.480 --> 00:38:05.559 the 7-Eleven where you can get sizes up 00:38:03.358 --> 00:38:07.840 to, you know, as big as your house, 00:38:05.559 --> 00:38:09.679 okay? They keep These curves keep 00:38:07.840 --> 00:38:11.079 getting closer and closer to each other. 00:38:09.679 --> 00:38:12.759 So, those price increments get smaller 00:38:11.079 --> 00:38:14.719 and smaller. And that's why you get the 00:38:12.760 --> 00:38:16.080 monster, you know, ginormous gulp at 00:38:14.719 --> 00:38:18.599 7-Eleven 00:38:16.079 --> 00:38:20.000 is really just not that not that 00:38:18.599 --> 00:38:21.880 different from the price of getting the 00:38:20.000 --> 00:38:23.480 small little mini size. 00:38:21.880 --> 00:38:24.880 Okay? Because of diminishing marginal 00:38:23.480 --> 00:38:27.079 utility. 00:38:24.880 --> 00:38:29.840 All right? And so, that's how the market 00:38:27.079 --> 00:38:32.480 That's essentially how we can take this 00:38:29.840 --> 00:38:34.400 abstract concept, this sort of crazy 00:38:32.480 --> 00:38:36.559 math, and turn it into literally what 00:38:34.400 --> 00:38:38.760 you see in the store you walk into. 00:38:36.559 --> 00:38:39.719 Okay? Questions about that? 00:38:38.760 --> 00:38:41.600 Yeah. 00:38:39.719 --> 00:38:44.000 Um so, how does 00:38:41.599 --> 00:38:45.759 this play into buying in bulk versus 00:38:44.000 --> 00:38:48.039 buying like a single item? 00:38:45.760 --> 00:38:49.359 Like if, for example, like you wanted to 00:38:48.039 --> 00:38:51.320 buy a snack, but you were going to have 00:38:49.358 --> 00:38:52.960 the breakfast every day. Awesome. 00:38:51.320 --> 00:38:54.359 Awesome question. And then every single 00:38:52.960 --> 00:38:57.960 day it was going to be your first 00:38:54.358 --> 00:39:00.159 granola bar, right? So, so it I I think 00:38:57.960 --> 00:39:02.199 that its utility would be diminished 00:39:00.159 --> 00:39:04.079 like every single time. But it's still 00:39:02.199 --> 00:39:06.358 cheaper to buy in bulk than it would be 00:39:04.079 --> 00:39:08.319 to buy a single granola bar every Great 00:39:06.358 --> 00:39:10.199 great question. Yeah. I think that has 00:39:08.320 --> 00:39:11.720 more to do with packaging costs than 00:39:10.199 --> 00:39:13.159 with utility. 00:39:11.719 --> 00:39:15.079 Well, I mean, 00:39:13.159 --> 00:39:16.519 the risk of my going to this model is, 00:39:15.079 --> 00:39:17.639 you know, once we once we get non-linear 00:39:16.519 --> 00:39:18.599 in the world we do things in this class, 00:39:17.639 --> 00:39:20.239 we have to start talking about supply 00:39:18.599 --> 00:39:21.880 factors I want to talk to. But there's 00:39:20.239 --> 00:39:24.639 two answers. One is packaging 00:39:21.880 --> 00:39:27.119 efficiencies. But the other is if you 00:39:24.639 --> 00:39:28.879 actually go to Costco 00:39:27.119 --> 00:39:29.920 and look at their prices, for many 00:39:28.880 --> 00:39:31.519 things they're not actually better than 00:39:29.920 --> 00:39:33.440 the supermarket. 00:39:31.519 --> 00:39:36.358 So, actually, the price of buying the 00:39:33.440 --> 00:39:40.079 giant like 8,000 bars of granola 00:39:36.358 --> 00:39:41.799 is actually not that much more 00:39:40.079 --> 00:39:43.519 than not that much less than a thousand 00:39:41.800 --> 00:39:44.519 time buying eight pack of eight granola 00:39:43.519 --> 00:39:46.199 bars. 00:39:44.519 --> 00:39:47.599 It turns out it's less. 00:39:46.199 --> 00:39:49.679 But it's not nearly as much less as 00:39:47.599 --> 00:39:51.920 these examples as sodas and McDonald's. 00:39:49.679 --> 00:39:53.839 Which is exactly your point. Utility 00:39:51.920 --> 00:39:55.920 diminishes less. 00:39:53.840 --> 00:39:57.840 So, they don't want to charge as much 00:39:55.920 --> 00:39:59.440 less for multiple packages. 00:39:57.840 --> 00:40:01.120 So, you can actually if you compare 00:39:59.440 --> 00:40:03.800 perish the gap in perishable product 00:40:01.119 --> 00:40:05.239 pricing by size, it's much larger than 00:40:03.800 --> 00:40:07.600 the gap in non-perishable pricing by 00:40:05.239 --> 00:40:09.639 size. Great point. Yeah. Is there also 00:40:07.599 --> 00:40:11.400 just like a different time frame for 00:40:09.639 --> 00:40:13.279 which the utilities start diminishing 00:40:11.400 --> 00:40:15.360 for every product? Cuz like you gave the 00:40:13.280 --> 00:40:17.120 example of soda, but it's like would 00:40:15.360 --> 00:40:19.120 that reset like later in the day if you 00:40:17.119 --> 00:40:20.719 wanted like were thirsty then? Or 00:40:19.119 --> 00:40:22.039 Awesome. And that is why they don't let 00:40:20.719 --> 00:40:23.439 you walk back in with the same cup and 00:40:22.039 --> 00:40:25.239 refill it. 00:40:23.440 --> 00:40:27.119 Right? That's exactly right. And that 00:40:25.239 --> 00:40:29.919 comes this point. It's sort of like it's 00:40:27.119 --> 00:40:32.799 non-perishable as you get longer apart. 00:40:29.920 --> 00:40:34.639 Uh so, um but you know, it's all this 00:40:32.800 --> 00:40:37.519 really interesting thing. So, at Fenway, 00:40:34.639 --> 00:40:39.359 okay? You can get You get like a regular 00:40:37.519 --> 00:40:40.800 size soda. It's like crazy. It's like 00:40:39.360 --> 00:40:42.920 six bucks. 00:40:40.800 --> 00:40:44.760 Then for like eight bucks, you get a big 00:40:42.920 --> 00:40:48.079 soda. Then for 10 bucks, you get a 00:40:44.760 --> 00:40:49.040 refillable big soda. Okay? Now, the 00:40:48.079 --> 00:40:50.400 question is can you bring that 00:40:49.039 --> 00:40:51.559 refillable soda back to additional 00:40:50.400 --> 00:40:54.800 games? 00:40:51.559 --> 00:40:57.880 Technically not, but I do. 00:40:54.800 --> 00:40:59.160 Uh and um and basically they sort of 00:40:57.880 --> 00:41:00.119 understand. So, so there's an 00:40:59.159 --> 00:41:02.199 interesting question of sort of the 00:41:00.119 --> 00:41:04.079 perishability of things and how that's 00:41:02.199 --> 00:41:05.480 and how that's going to affect uh things 00:41:04.079 --> 00:41:07.239 going on. It's a really it's it's a 00:41:05.480 --> 00:41:08.719 really it's an interesting question. 00:41:07.239 --> 00:41:10.119 Other comments? 00:41:08.719 --> 00:41:11.399 Okay, I'm going to stop there. Those are 00:41:10.119 --> 00:41:13.359 great comments. Thanks everyone for 00:41:11.400 --> 00:41:14.960 participating and we'll come back next 00:41:13.360 --> 00:41:16.480 time and talk about the sad reality that 00:41:14.960 --> 00:41:19.360 we haven't won the lottery and we have 00:41:16.480 --> 00:41:19.360 limited amounts of money.