1 00:00:00,000 --> 00:00:12,183 [SQUEAKING] [RUSTLING] [CLICKING] 2 00:00:12,183 --> 00:00:13,600 JONATHAN GRUBER: Today we're going 3 00:00:13,600 --> 00:00:17,790 to start talking about what's underneath the demand curve. 4 00:00:17,790 --> 00:00:19,490 So basically, what we did last time, 5 00:00:19,490 --> 00:00:21,590 and what you did in section on Friday 6 00:00:21,590 --> 00:00:23,150 is talk about sort of the workhorse 7 00:00:23,150 --> 00:00:26,528 model of economics, which is supply and demand model. 8 00:00:26,528 --> 00:00:28,820 And we always start the class with that, because that's 9 00:00:28,820 --> 00:00:30,680 the model in the course. 10 00:00:30,680 --> 00:00:33,800 But I think as any good sort of scientists and inquisitive 11 00:00:33,800 --> 00:00:35,957 minds, you're probably immediately asking, well, 12 00:00:35,957 --> 00:00:38,040 where do these supply and demand curves come from? 13 00:00:38,040 --> 00:00:40,895 They don't just come out of thin air. 14 00:00:40,895 --> 00:00:42,020 How do we think about them? 15 00:00:42,020 --> 00:00:43,100 Where do they come from? 16 00:00:43,100 --> 00:00:45,225 And that's what we'll spend basically the first 1/2 17 00:00:45,225 --> 00:00:47,000 of the course going through. 18 00:00:47,000 --> 00:00:49,820 And so we're going to start today with the demand curve, 19 00:00:49,820 --> 00:00:52,670 and the demand curve is going to come from how 20 00:00:52,670 --> 00:00:55,930 consumers make choices, OK? 21 00:00:55,930 --> 00:00:57,910 And that will help us drive the demand curve. 22 00:00:57,910 --> 00:01:00,090 Then we'll turn next to supply curve, which 23 00:01:00,090 --> 00:01:04,647 will come from how firms make production decisions. 24 00:01:04,647 --> 00:01:06,230 But let's start with the demand curve, 25 00:01:06,230 --> 00:01:07,688 and we're going to start by talking 26 00:01:07,688 --> 00:01:13,000 about people's preferences, and then the utility functions, OK? 27 00:01:13,000 --> 00:01:16,270 So our model of consumer decision making 28 00:01:16,270 --> 00:01:21,093 is going to be a model of utility maximization. 29 00:01:21,093 --> 00:01:23,010 That's going to be our fundamental-- remember, 30 00:01:23,010 --> 00:01:25,080 this course is all about constrain maximization. 31 00:01:25,080 --> 00:01:28,080 Our model today is going to be a model of utility maximization. 32 00:01:28,080 --> 00:01:30,830 And this model's going to have two components. 33 00:01:30,830 --> 00:01:35,330 There's going to be consumer preferences, which 34 00:01:35,330 --> 00:01:37,640 is what people want, and there's going 35 00:01:37,640 --> 00:01:40,580 to be a budget constraint, which is what they can afford. 36 00:01:43,340 --> 00:01:45,600 And we're going to put these two things together. 37 00:01:45,600 --> 00:01:49,280 We're going to maximize people's happiness, or their choice-- 38 00:01:49,280 --> 00:01:51,800 or their happiness given their preferences, 39 00:01:51,800 --> 00:01:54,367 subject to the budget constraint they face. 40 00:01:54,367 --> 00:01:56,450 And that's going to be the constraint maximization 41 00:01:56,450 --> 00:01:59,510 exercise that actually, through the magic of economics, 42 00:01:59,510 --> 00:02:00,997 is going to yield the demand curve, 43 00:02:00,997 --> 00:02:03,080 and yield a very sensible demand curve that you'll 44 00:02:03,080 --> 00:02:05,470 understand intuitively. 45 00:02:05,470 --> 00:02:09,289 Now, so what we're going to do is do this in three steps. 46 00:02:09,289 --> 00:02:11,110 Step one-- over the next two lectures. 47 00:02:11,110 --> 00:02:13,510 Step one is we'll talk about preferences, how 48 00:02:13,510 --> 00:02:16,410 do we model people's tastes. 49 00:02:16,410 --> 00:02:18,120 We'll do that today. 50 00:02:18,120 --> 00:02:20,460 Step two is we'll talk about how we translate this 51 00:02:20,460 --> 00:02:23,280 to utility function, how we mathematically 52 00:02:23,280 --> 00:02:26,580 represent people's preferences in utility function. 53 00:02:26,580 --> 00:02:28,470 We'll do that today as well. 54 00:02:28,470 --> 00:02:31,830 And then next time, we'll talk about the budget constraints 55 00:02:31,830 --> 00:02:33,450 that people face. 56 00:02:33,450 --> 00:02:35,670 So today, we're going to talk about the max demand. 57 00:02:35,670 --> 00:02:38,220 Next time we'll talk about the budget constraint. 58 00:02:38,220 --> 00:02:40,500 That means today's lecture is quite fun. 59 00:02:40,500 --> 00:02:42,827 Today's lecture is about unconstrained choice. 60 00:02:42,827 --> 00:02:44,910 We're not going to worry at all about what you can 61 00:02:44,910 --> 00:02:46,270 afford, what anything costs. 62 00:02:46,270 --> 00:02:48,270 We're not going to worry about what things cost. 63 00:02:48,270 --> 00:02:50,562 We're not going to worry about what you can afford, OK? 64 00:02:50,562 --> 00:02:53,340 Today's the lecture where you won the lottery, OK? 65 00:02:53,340 --> 00:02:54,390 You won the lottery. 66 00:02:54,390 --> 00:02:56,040 Money is no object. 67 00:02:56,040 --> 00:02:58,368 How do you think about what you want, OK? 68 00:02:58,368 --> 00:03:00,660 Next time, we'll say, well, you didn't win the lottery. 69 00:03:00,660 --> 00:03:02,040 In fact, as we learn later in the semester, 70 00:03:02,040 --> 00:03:03,340 no one wins the lottery. 71 00:03:03,340 --> 00:03:06,270 It's an incredibly bad deal. 72 00:03:06,270 --> 00:03:09,240 But next time, we'll impose the budget constraints. 73 00:03:09,240 --> 00:03:12,900 But for today, we're just going to ignore that and talk about 74 00:03:12,900 --> 00:03:15,560 what do you want, OK? 75 00:03:15,560 --> 00:03:17,490 And to start this, we're going to start 76 00:03:17,490 --> 00:03:21,140 with a series of preference assumptions. 77 00:03:25,500 --> 00:03:28,380 A series-- remember, as I talked about last time, 78 00:03:28,380 --> 00:03:30,375 models rely on simplifying assumptions. 79 00:03:30,375 --> 00:03:32,250 Otherwise, we could never write down a model. 80 00:03:32,250 --> 00:03:34,380 It'll go on forever, OK? 81 00:03:34,380 --> 00:03:37,230 And the key question is, are those simplifying 82 00:03:37,230 --> 00:03:39,480 assumptions sensible? 83 00:03:39,480 --> 00:03:42,240 Do they do violence to reality in a way which makes you not 84 00:03:42,240 --> 00:03:44,097 believe the model, or are they roughly 85 00:03:44,097 --> 00:03:45,930 consistent with reality in a way that allows 86 00:03:45,930 --> 00:03:47,700 you to go on with the model? 87 00:03:47,700 --> 00:03:48,530 OK? 88 00:03:48,530 --> 00:03:51,270 And we're going to pose three preference assumptions, which 89 00:03:51,270 --> 00:03:54,720 I hope will not violate your sense of reasonableness. 90 00:03:54,720 --> 00:03:57,090 The first is completeness. 91 00:04:00,760 --> 00:04:04,560 What I mean by that is you have preferences 92 00:04:04,560 --> 00:04:08,500 over any set of goods you might choose from. 93 00:04:08,500 --> 00:04:09,900 You might be indifferent. 94 00:04:09,900 --> 00:04:12,060 You might say, "I like A as much as B," 95 00:04:12,060 --> 00:04:15,303 but you can't say, "I don't care," or, "I don't know." 96 00:04:15,303 --> 00:04:16,470 You can say, "I don't care." 97 00:04:16,470 --> 00:04:17,303 That's indifference. 98 00:04:17,303 --> 00:04:18,589 You can't say, "I don't know." 99 00:04:18,589 --> 00:04:19,964 You can't literally say, "I don't 100 00:04:19,964 --> 00:04:21,350 know how I feel about this." 101 00:04:21,350 --> 00:04:23,570 You might say you're indifferent to two things, 102 00:04:23,570 --> 00:04:26,600 but you won't say, "I don't know how I feel about something." 103 00:04:26,600 --> 00:04:29,000 That's completeness, OK? 104 00:04:29,000 --> 00:04:31,550 The second is the assumption we've all become familiar 105 00:04:31,550 --> 00:04:34,682 with since kindergarten math, which is transitivity. 106 00:04:38,130 --> 00:04:44,190 If you prefer A to B and B to C, you prefer A to C, OK? 107 00:04:44,190 --> 00:04:46,142 That's kind of-- 108 00:04:46,142 --> 00:04:47,350 I'm sure that's pretty clear. 109 00:04:47,350 --> 00:04:50,000 You've done this a lot in other classes. 110 00:04:50,000 --> 00:04:52,330 So these two are sort of standard assumptions 111 00:04:52,330 --> 00:04:54,550 you might make in any math class. 112 00:04:54,550 --> 00:04:57,710 The third assumption is the one where the economics comes in, 113 00:04:57,710 --> 00:05:02,730 which is the assumption of nonsatiation 114 00:05:02,730 --> 00:05:05,580 or the assumption of more is better. 115 00:05:08,940 --> 00:05:12,210 In this class, we will assume more 116 00:05:12,210 --> 00:05:15,860 is always better than less, OK? 117 00:05:15,860 --> 00:05:17,780 We'll assume more is better than less. 118 00:05:17,780 --> 00:05:19,390 Now, to be clear, we're not going 119 00:05:19,390 --> 00:05:21,830 to say that the next unit makes you 120 00:05:21,830 --> 00:05:23,182 equally happy as the last unit. 121 00:05:23,182 --> 00:05:25,140 In fact, I'll talk about that in a few minutes. 122 00:05:25,140 --> 00:05:27,223 Well, in fact, the next unit makes you less happy. 123 00:05:27,223 --> 00:05:29,810 But we will say you always want more, 124 00:05:29,810 --> 00:05:31,710 that faced with the chance of more or less, 125 00:05:31,710 --> 00:05:34,520 you'll always be happier with more, OK? 126 00:05:34,520 --> 00:05:37,518 And that's the nonsatiation assumption, OK? 127 00:05:37,518 --> 00:05:39,560 And I'll talk about that some during the lecture, 128 00:05:39,560 --> 00:05:42,185 but that's sort of what's going to give our models their power. 129 00:05:42,185 --> 00:05:44,068 That's a sort of new economics assumption. 130 00:05:44,068 --> 00:05:46,610 That's going to give-- beyond your typical math assumptions-- 131 00:05:46,610 --> 00:05:49,970 this is going to give our models their power, OK? 132 00:05:49,970 --> 00:05:51,590 So that's our assumptions. 133 00:05:51,590 --> 00:05:54,800 So armed with those, I want to start 134 00:05:54,800 --> 00:05:57,992 with a graphical representation of preferences. 135 00:05:57,992 --> 00:06:00,200 I want to graphically represent people's preferences, 136 00:06:00,200 --> 00:06:03,155 and I'll do so through something we call indifference curves. 137 00:06:07,900 --> 00:06:11,150 Indifference curves, OK? 138 00:06:11,150 --> 00:06:15,230 These are-- indifference curves are basically preference maps. 139 00:06:15,230 --> 00:06:18,080 Essentially, indifference curves are graphical maps 140 00:06:18,080 --> 00:06:20,850 of preferences, OK? 141 00:06:20,850 --> 00:06:26,430 So for example, suppose your parents gave you some money 142 00:06:26,430 --> 00:06:29,160 to begin the semester, and you spent that money on two things. 143 00:06:29,160 --> 00:06:29,790 Your parents are rich. 144 00:06:29,790 --> 00:06:30,957 They gave you tons of money. 145 00:06:30,957 --> 00:06:36,570 You spent your money on two things, buying pizza 146 00:06:36,570 --> 00:06:39,930 or eating cookies, OK? 147 00:06:39,930 --> 00:06:43,433 So consider preferences between pizza and cookies. 148 00:06:43,433 --> 00:06:44,850 That's your two things you can do. 149 00:06:44,850 --> 00:06:46,050 Once again, this is a constrained model. 150 00:06:46,050 --> 00:06:48,717 Obviously, in life, you can do a million things with your money. 151 00:06:48,717 --> 00:06:51,528 But it turns out, if we consider the contrast between doing 152 00:06:51,528 --> 00:06:53,070 two different things with your money, 153 00:06:53,070 --> 00:06:54,737 you get a rich set of intuition that you 154 00:06:54,737 --> 00:06:57,210 can apply to a much more multi-dimensional decision 155 00:06:57,210 --> 00:06:57,990 case. 156 00:06:57,990 --> 00:07:00,210 So let's start with a two dimensional decision case. 157 00:07:00,210 --> 00:07:01,127 You've got your money. 158 00:07:01,127 --> 00:07:04,350 Either you can have pizza or you can have cookies, OK? 159 00:07:04,350 --> 00:07:06,960 Now, consider three choices, OK? 160 00:07:06,960 --> 00:07:13,560 Choice A is two pizzas and one cookie. 161 00:07:13,560 --> 00:07:21,230 Choice B is one pizza and two cookies, 162 00:07:21,230 --> 00:07:25,310 and choice C is two pizzas, two cookies. 163 00:07:25,310 --> 00:07:29,010 OK, that's the three packages I want to compare. 164 00:07:29,010 --> 00:07:30,360 And I am going to assume-- 165 00:07:30,360 --> 00:07:32,920 and I'll mathematically rationalize in a few minutes-- 166 00:07:32,920 --> 00:07:34,830 but for now, I'm going to assume you 167 00:07:34,830 --> 00:07:39,293 are indifferent between these two packages. 168 00:07:39,293 --> 00:07:40,710 I'm going to assume you're equally 169 00:07:40,710 --> 00:07:43,530 happy with two slices of pizza and one cookie or two cookies 170 00:07:43,530 --> 00:07:46,620 and one slice of pizza, OK? 171 00:07:46,620 --> 00:07:47,730 I'm going to assume that. 172 00:07:47,730 --> 00:07:50,790 But I'm also going to assume you prefer 173 00:07:50,790 --> 00:07:53,770 option C to both of these. 174 00:07:53,770 --> 00:07:55,360 In fact, I'm going to assume that, 175 00:07:55,360 --> 00:07:58,290 because that is what more is better gives you, OK? 176 00:07:58,290 --> 00:07:59,910 So you're indifferent between this. 177 00:07:59,910 --> 00:08:02,410 This indifference doesn't come from any property I wrote up. 178 00:08:02,410 --> 00:08:03,520 That's an assumption. 179 00:08:03,520 --> 00:08:06,040 That's just-- for this case, I'm assuming that. 180 00:08:06,040 --> 00:08:08,208 This comes to the third property I wrote up there. 181 00:08:08,208 --> 00:08:10,000 You prefer package C because more is always 182 00:08:10,000 --> 00:08:13,000 better than less, OK? 183 00:08:13,000 --> 00:08:15,370 So now, let's graph your preferences, 184 00:08:15,370 --> 00:08:20,950 and we do so in figure 2-1, OK, in the handout. 185 00:08:20,950 --> 00:08:24,430 OK, so here's your indifference curve. 186 00:08:24,430 --> 00:08:28,330 So we've graphed on the x-axis your number of cookies, 187 00:08:28,330 --> 00:08:31,630 on the y-axis slices of pizza, OK? 188 00:08:31,630 --> 00:08:34,809 Now, you have-- we've graphed the three choices I laid here, 189 00:08:34,809 --> 00:08:37,720 choice A, which is two slices of pizza 190 00:08:37,720 --> 00:08:41,049 and one cookie, choice B, which is two cookies and one 191 00:08:41,049 --> 00:08:44,530 slice of pizza, and choice C, which is two of both. 192 00:08:44,530 --> 00:08:46,817 And I've drawn on this graph your indifference curves. 193 00:08:46,817 --> 00:08:48,400 The way your indifference curves looks 194 00:08:48,400 --> 00:08:51,610 is there's one indifference curve between A and B, 195 00:08:51,610 --> 00:08:54,940 because those are the points among which you're indifferent. 196 00:08:54,940 --> 00:08:57,430 So what an indifference curve represents 197 00:08:57,430 --> 00:09:01,000 is all combinations of consumption among which 198 00:09:01,000 --> 00:09:02,240 you are indifferent. 199 00:09:02,240 --> 00:09:04,030 That's why we call it indifference curve. 200 00:09:04,030 --> 00:09:05,530 So an indifference curve, which will 201 00:09:05,530 --> 00:09:08,460 be sort of one of the big workhorses of this course, 202 00:09:08,460 --> 00:09:12,070 an indifference curve represents all combinations along which 203 00:09:12,070 --> 00:09:13,123 you are in different. 204 00:09:13,123 --> 00:09:15,040 You're indifferent between A and B. Therefore, 205 00:09:15,040 --> 00:09:19,580 they lie on the same curve, OK? 206 00:09:19,580 --> 00:09:23,395 So that's sort of our preference map, our indifference curves. 207 00:09:23,395 --> 00:09:24,770 And these indifference curves are 208 00:09:24,770 --> 00:09:28,670 going to have four properties, four properties 209 00:09:28,670 --> 00:09:29,730 that you have to-- 210 00:09:29,730 --> 00:09:31,817 that follow naturally from this-- 211 00:09:31,817 --> 00:09:32,900 it's really three and 1/2. 212 00:09:32,900 --> 00:09:35,108 The third and fourth are really pretty much the same, 213 00:09:35,108 --> 00:09:36,700 but I like to write them out as four. 214 00:09:36,700 --> 00:09:41,180 Four properties that follow from these underlying assumptions-- 215 00:09:41,180 --> 00:09:45,290 Property one is, consumers prefer higher indifference 216 00:09:45,290 --> 00:09:46,610 curves. 217 00:09:46,610 --> 00:09:53,910 Consumers prefer higher indifference curves, OK? 218 00:09:53,910 --> 00:09:55,617 And that's just all from more is better. 219 00:09:55,617 --> 00:09:57,450 That is, an indifference curve that's higher 220 00:09:57,450 --> 00:10:00,630 goes through package that has at least as much of one thing 221 00:10:00,630 --> 00:10:02,220 and more of the other thing. 222 00:10:02,220 --> 00:10:04,290 Therefore, you prefer it, OK? 223 00:10:04,290 --> 00:10:08,550 So as indifference curve shifts out, people are happier, OK? 224 00:10:08,550 --> 00:10:12,580 So on that higher indifference curve, point C, 225 00:10:12,580 --> 00:10:14,170 you are happier than points A and B, 226 00:10:14,170 --> 00:10:18,030 because more is better, OK? 227 00:10:18,030 --> 00:10:24,610 The second is that indifference curves never cross. 228 00:10:27,670 --> 00:10:32,330 Indifference curves never cross, OK? 229 00:10:32,330 --> 00:10:35,127 Actually, that's third, actually. 230 00:10:35,127 --> 00:10:36,460 I want to come to that in order. 231 00:10:36,460 --> 00:10:38,625 Second-- third is the indifference curves never-- 232 00:10:38,625 --> 00:10:40,750 Second is indifference curves are downward sloping. 233 00:10:44,280 --> 00:10:47,582 Second is indifference curves are downward sloping. 234 00:10:47,582 --> 00:10:49,290 Indifference curves are downward sloping. 235 00:10:49,290 --> 00:10:52,260 Let's talk about that first, OK? 236 00:10:52,260 --> 00:10:57,120 That simply comes from the principle of nonsatiation. 237 00:10:57,120 --> 00:10:59,370 So look at figure 2-2. 238 00:10:59,370 --> 00:11:04,120 Here's an upward sloping indifference curve, OK? 239 00:11:04,120 --> 00:11:06,300 Why does that violate the principle of nonsatiation? 240 00:11:06,300 --> 00:11:07,425 Why does that violate that? 241 00:11:07,425 --> 00:11:08,220 Yeah. 242 00:11:08,220 --> 00:11:10,880 AUDIENCE: Either, if you're-- either you're less happy with 243 00:11:10,880 --> 00:11:14,680 you have more cookies, or you're less happy if you have more 244 00:11:14,680 --> 00:11:16,130 pizza. 245 00:11:16,130 --> 00:11:20,378 And like there's-- and that violates nonsatiation. 246 00:11:20,378 --> 00:11:21,420 JONATHAN GRUBER: Exactly. 247 00:11:21,420 --> 00:11:23,610 So basically, you're indifferent-- on this curve, 248 00:11:23,610 --> 00:11:25,290 you're indifferent with one of each and two of each. 249 00:11:25,290 --> 00:11:26,332 You can't be indifferent. 250 00:11:26,332 --> 00:11:28,440 Two of each has got to be better than one of each. 251 00:11:28,440 --> 00:11:30,065 So an upward sloping indifference curve 252 00:11:30,065 --> 00:11:31,800 would violate nonsatiation. 253 00:11:31,800 --> 00:11:34,140 So that's the second property of indifference curve. 254 00:11:34,140 --> 00:11:35,807 The third property of indifference curve 255 00:11:35,807 --> 00:11:38,310 is the indifference curves never cross, OK? 256 00:11:38,310 --> 00:11:43,020 We could see that in figure 2-3, OK? 257 00:11:43,020 --> 00:11:44,700 Someone else tell me why this violates 258 00:11:44,700 --> 00:11:48,036 the properties I wrote up there, indifference curves crossing. 259 00:11:48,036 --> 00:11:49,423 Yeah. 260 00:11:49,423 --> 00:11:51,340 AUDIENCE: Because B and C [is strictly better. 261 00:11:51,340 --> 00:11:52,548 JONATHAN GRUBER: What's that? 262 00:11:52,548 --> 00:11:54,548 AUDIENCE: Because B and C, B is strictly better. 263 00:11:54,548 --> 00:11:57,006 JONATHAN GRUBER: Because the B and C, B is strictly better. 264 00:11:57,006 --> 00:11:57,757 That's right. 265 00:11:57,757 --> 00:11:59,070 AUDIENCE: [INAUDIBLE] 266 00:11:59,070 --> 00:12:01,250 JONATHAN GRUBER: But they're also 267 00:12:01,250 --> 00:12:03,633 both on the same curve as A. So you're 268 00:12:03,633 --> 00:12:06,050 saying they're both-- you're indifferent with A for both B 269 00:12:06,050 --> 00:12:08,690 and C, but you can't be, because B is strictly better than C. 270 00:12:08,690 --> 00:12:11,300 So it violates transitivity, OK? 271 00:12:11,300 --> 00:12:13,430 So the problem with crossing indifference curves 272 00:12:13,430 --> 00:12:17,420 is they violate transitivity. 273 00:12:17,420 --> 00:12:20,570 And then finally, the fourth is sort 274 00:12:20,570 --> 00:12:22,610 of a cute extra assumption, but I 275 00:12:22,610 --> 00:12:24,860 think it's important to clarify, which 276 00:12:24,860 --> 00:12:28,070 is that there is only one indifference 277 00:12:28,070 --> 00:12:33,380 curve through every possible consumption bundle, 278 00:12:33,380 --> 00:12:38,620 only one IC through every bundle. 279 00:12:42,270 --> 00:12:44,270 OK, you can't have two indifference curves going 280 00:12:44,270 --> 00:12:47,120 through the same bundle, OK? 281 00:12:47,120 --> 00:12:49,010 And that's because of completeness. 282 00:12:49,010 --> 00:12:49,910 If you have two indifference curves 283 00:12:49,910 --> 00:12:51,327 going through the same bundle, you 284 00:12:51,327 --> 00:12:52,619 wouldn't know how you felt, OK? 285 00:12:52,619 --> 00:12:54,785 So there can only be one going through every bundle, 286 00:12:54,785 --> 00:12:56,300 because you know how you feel. 287 00:12:56,300 --> 00:12:58,550 You may feel indifferent, but you know how you feel. 288 00:12:58,550 --> 00:13:00,640 You can't say I don't know, OK? 289 00:13:00,640 --> 00:13:02,240 So that's sort of a extra assumption 290 00:13:02,240 --> 00:13:06,420 that sort of completes the link to the properties, OK? 291 00:13:06,420 --> 00:13:10,160 So that's basically how indifference curves work. 292 00:13:10,160 --> 00:13:15,472 Now, I find-- when I took this course, before you were-- 293 00:13:15,472 --> 00:13:17,180 god, maybe before your parents were born, 294 00:13:17,180 --> 00:13:19,305 I don't know, certainly before you guys were born-- 295 00:13:19,305 --> 00:13:21,562 when I took this course, I found this course 296 00:13:21,562 --> 00:13:23,270 full of a lot of light bulb moments, that 297 00:13:23,270 --> 00:13:24,290 is, stuff was just sort of confusing, 298 00:13:24,290 --> 00:13:26,600 and then boom, an example really made it work for me. 299 00:13:26,600 --> 00:13:29,030 And the example that made indifference curves work to me 300 00:13:29,030 --> 00:13:31,160 was actually doing my first UROP. 301 00:13:31,160 --> 00:13:33,805 When my UROP was with a grad student, and that grad student 302 00:13:33,805 --> 00:13:35,930 had to decide whether he was going to accept a job. 303 00:13:35,930 --> 00:13:38,120 He had a series of job offers, so he had to decide. 304 00:13:38,120 --> 00:13:40,200 And basically, he said, "Here's the way I'm thinking about it. 305 00:13:40,200 --> 00:13:42,230 I am indifferent-- I have an indifference map 306 00:13:42,230 --> 00:13:43,950 and I care about two things. 307 00:13:43,950 --> 00:13:48,150 I care about school location and I 308 00:13:48,150 --> 00:13:50,005 care about economics department quality. 309 00:13:53,370 --> 00:13:55,140 I care about the quality of my colleagues, 310 00:13:55,140 --> 00:13:57,360 and the research it's done there, and the location." 311 00:13:57,360 --> 00:13:59,880 And basically, he had two offers. 312 00:13:59,880 --> 00:14:02,210 One was from Princeton, which he put up here. 313 00:14:02,210 --> 00:14:03,960 No offense to New Jerseyans, but Princeton 314 00:14:03,960 --> 00:14:05,880 as a young single person sucks. 315 00:14:05,880 --> 00:14:08,220 OK, fine when you're married and have kids, but deadly 316 00:14:08,220 --> 00:14:09,690 as a young single person. 317 00:14:09,690 --> 00:14:11,460 And the other-- so that's Princeton. 318 00:14:11,460 --> 00:14:13,470 Down here was Santa Cruz. 319 00:14:13,470 --> 00:14:14,067 OK, awesome. 320 00:14:14,067 --> 00:14:15,900 [INAUDIBLE] is the most beautiful university 321 00:14:15,900 --> 00:14:17,430 in America, OK? 322 00:14:17,430 --> 00:14:19,290 But not as good an economics department. 323 00:14:19,290 --> 00:14:23,090 And he decided he was roughly indifferent between the two. 324 00:14:23,090 --> 00:14:27,110 But he had a third offer from the IMF, which 325 00:14:27,110 --> 00:14:29,217 is a research institution in DC, which 326 00:14:29,217 --> 00:14:30,800 has-- he had a lot of good colleagues, 327 00:14:30,800 --> 00:14:32,660 and DC is way better than Princeton, New Jersey, 328 00:14:32,660 --> 00:14:34,460 even though it's not as good as Santa Cruz. 329 00:14:34,460 --> 00:14:37,960 So he decided he would take the offer at the IMF, OK? 330 00:14:37,960 --> 00:14:41,590 Even though the IMF had worse colleagues than Princeton 331 00:14:41,590 --> 00:14:43,750 and worse location than Santa Cruz, 332 00:14:43,750 --> 00:14:46,000 it was still better in combination of the two of them, 333 00:14:46,000 --> 00:14:47,520 given his preferences. 334 00:14:47,520 --> 00:14:49,270 And that's how he used indifference curves 335 00:14:49,270 --> 00:14:52,360 to make his decision, OK? 336 00:14:52,360 --> 00:14:54,625 So that's sort of an example of applying it. 337 00:14:54,625 --> 00:14:56,000 Once again, no offense to the New 338 00:14:56,000 --> 00:14:59,320 Jerseyans in the room, of which I am one, but believe me, 339 00:14:59,320 --> 00:15:01,550 you'd rather be in Santa Cruz. 340 00:15:01,550 --> 00:15:05,990 OK, so now, let's go from preferences 341 00:15:05,990 --> 00:15:08,363 to utility functions. 342 00:15:12,710 --> 00:15:15,580 OK, so now, we're going to move from preferences, which we've 343 00:15:15,580 --> 00:15:19,650 represented graphically, to utility functions, which we're 344 00:15:19,650 --> 00:15:21,067 going to represent mathematically. 345 00:15:21,067 --> 00:15:23,358 Remember, I want you understand, everything this course 346 00:15:23,358 --> 00:15:25,590 at three levels, graphically, mathematically, 347 00:15:25,590 --> 00:15:28,380 and most importantly of all, intuitively, OK? 348 00:15:28,380 --> 00:15:30,360 So graphic is indifference curves. 349 00:15:30,360 --> 00:15:32,550 Now we come to the mathematical representation, 350 00:15:32,550 --> 00:15:34,890 which is utility function, OK? 351 00:15:34,890 --> 00:15:37,740 And the idea is that every individual, all of you 352 00:15:37,740 --> 00:15:41,370 in this room, have a stable, well behaved, 353 00:15:41,370 --> 00:15:43,500 underlying mathematical representation 354 00:15:43,500 --> 00:15:47,912 of your preferences, which we call utility function. 355 00:15:47,912 --> 00:15:50,120 Now, once again, that's going to be very complicated, 356 00:15:50,120 --> 00:15:52,040 your preference over lots of different things. 357 00:15:52,040 --> 00:15:53,495 We're going to make things simple by writing out 358 00:15:53,495 --> 00:15:56,570 a two dimensional representation for now of your indifference 359 00:15:56,570 --> 00:15:57,200 curve. 360 00:15:57,200 --> 00:15:59,480 We're going to say, how do we act mathematically 361 00:15:59,480 --> 00:16:03,950 represent your feelings about pizza versus cookies? 362 00:16:03,950 --> 00:16:04,550 OK? 363 00:16:04,550 --> 00:16:06,508 Imagine that's all you care about in the world, 364 00:16:06,508 --> 00:16:07,670 is pizza and cookies. 365 00:16:07,670 --> 00:16:09,590 How do we mathematically represent that? 366 00:16:09,590 --> 00:16:11,750 So for example, we could write down 367 00:16:11,750 --> 00:16:15,050 that your utility function is equal to the square root 368 00:16:15,050 --> 00:16:18,268 of the number of slices of pizza times the number of cookies. 369 00:16:18,268 --> 00:16:19,310 We could write that down. 370 00:16:19,310 --> 00:16:20,150 I'm not saying that's right. 371 00:16:20,150 --> 00:16:22,190 I'm not saying it works for anyone in this room 372 00:16:22,190 --> 00:16:25,400 or even everyone this room, but that is a possible way 373 00:16:25,400 --> 00:16:29,110 to represent utility, OK? 374 00:16:29,110 --> 00:16:30,340 What this would say-- 375 00:16:30,340 --> 00:16:31,270 this is convenient. 376 00:16:31,270 --> 00:16:33,580 We will use-- we'll end up using square root form a lot 377 00:16:33,580 --> 00:16:35,997 for utility functions and a lot of convenient mathematical 378 00:16:35,997 --> 00:16:36,820 properties. 379 00:16:36,820 --> 00:16:39,358 And it happens to jive with our example, right? 380 00:16:39,358 --> 00:16:41,900 Because in this example, you're indifferent between two pizza 381 00:16:41,900 --> 00:16:44,140 and one cookie or one pizza and two cookie. 382 00:16:44,140 --> 00:16:45,762 They're both square root of 2. 383 00:16:45,762 --> 00:16:47,470 And you prefer two pizza and two cookies. 384 00:16:47,470 --> 00:16:49,510 That's two, OK? 385 00:16:49,510 --> 00:16:53,710 So this gives you a high utility for two pizza and two cookies, 386 00:16:53,710 --> 00:16:59,050 OK, than one pizza and two cookie, 387 00:16:59,050 --> 00:17:02,080 or two pizza and one cookie. 388 00:17:02,080 --> 00:17:04,520 So now, the question is, what does this mean? 389 00:17:04,520 --> 00:17:06,670 What is utility? 390 00:17:06,670 --> 00:17:10,000 Well, utility doesn't actually mean anything. 391 00:17:10,000 --> 00:17:14,140 There's not really a thing out there called utiles OK? 392 00:17:14,140 --> 00:17:16,930 In other words, utility is not a cardinal concept. 393 00:17:16,930 --> 00:17:19,930 It is only an ordinal concept. 394 00:17:19,930 --> 00:17:23,290 You cannot say your utility, you are-- 395 00:17:23,290 --> 00:17:26,470 you cannot literally say, "My utility is x% higher than 396 00:17:26,470 --> 00:17:29,230 your utility," but you can rank them. 397 00:17:29,230 --> 00:17:32,140 So we're going to assume that utility can be ranked 398 00:17:32,140 --> 00:17:34,840 to allow you to rank choices. 399 00:17:34,840 --> 00:17:36,940 Even if generally, we might slip some and sort 400 00:17:36,940 --> 00:17:40,120 of pretend utility is cardinal for some cute examples, 401 00:17:40,120 --> 00:17:41,910 but by and large, we're going to think 402 00:17:41,910 --> 00:17:43,630 of utility as purely ordinal. 403 00:17:43,630 --> 00:17:45,503 It's just a way to rank your choices. 404 00:17:45,503 --> 00:17:47,170 It's just when you have a set of choices 405 00:17:47,170 --> 00:17:49,900 out there over many dimensions-- like if your choice in life 406 00:17:49,900 --> 00:17:52,770 was always over one dimension and more was better, 407 00:17:52,770 --> 00:17:54,520 it would always be easy to rank it, right? 408 00:17:54,520 --> 00:17:55,810 You'd never have a problem. 409 00:17:55,810 --> 00:17:58,605 Once your choice is over more than one dimension, 410 00:17:58,605 --> 00:17:59,980 now if you want to rank them, you 411 00:17:59,980 --> 00:18:01,600 need some way to combine them. 412 00:18:01,600 --> 00:18:03,220 That's what this function does. 413 00:18:03,220 --> 00:18:05,830 It allows you essentially to weight the different elements 414 00:18:05,830 --> 00:18:07,600 of your consumption bundle, so you 415 00:18:07,600 --> 00:18:12,520 can rank them when it comes time to choose, OK? 416 00:18:12,520 --> 00:18:15,730 Now, this is obviously incredibly simple, 417 00:18:15,730 --> 00:18:18,910 but it turns out to be amazingly powerful in explaining 418 00:18:18,910 --> 00:18:21,665 real world behavior, OK? 419 00:18:21,665 --> 00:18:23,040 And so what I want to do today is 420 00:18:23,040 --> 00:18:25,628 work with the underlying mathematics of utility, 421 00:18:25,628 --> 00:18:26,670 and then we'll come back. 422 00:18:26,670 --> 00:18:28,087 We'll see in the next few lectures 423 00:18:28,087 --> 00:18:31,350 how it could actually be used to explain decisions. 424 00:18:31,350 --> 00:18:36,000 So a key concept we're going to talk about in this class 425 00:18:36,000 --> 00:18:38,160 is marginal utility. 426 00:18:38,160 --> 00:18:39,780 Marginal utility is just a derivative 427 00:18:39,780 --> 00:18:43,180 of the utility function with respect to one of the elements. 428 00:18:43,180 --> 00:18:45,840 So the marginal utility for cookies, of cookies, 429 00:18:45,840 --> 00:18:48,380 is the utility of the next cookie, 430 00:18:48,380 --> 00:18:50,670 given how many cookies you've had. 431 00:18:50,670 --> 00:18:52,350 This class is going to be very focused 432 00:18:52,350 --> 00:18:55,140 on marginal decision making. 433 00:18:55,140 --> 00:18:58,260 In economics, it's all about how you think about the next unit. 434 00:18:58,260 --> 00:19:00,110 Turns out, that makes life a ton easier. 435 00:19:00,110 --> 00:19:01,860 Turns out, it's way easier to say, "Do you 436 00:19:01,860 --> 00:19:04,380 want the next cookie," than to say, "How many cookies do you 437 00:19:04,380 --> 00:19:05,770 want?" 438 00:19:05,770 --> 00:19:07,270 Because if you want the next cookie, 439 00:19:07,270 --> 00:19:09,280 that's sort of a very isolated decision. 440 00:19:09,280 --> 00:19:10,840 You say, OK, I had this many cookies. 441 00:19:10,840 --> 00:19:12,310 Do I want the next cookie? 442 00:19:12,310 --> 00:19:13,510 Whereas before you start eating, if you say, 443 00:19:13,510 --> 00:19:15,010 how many cookies do you want, that's 444 00:19:15,010 --> 00:19:16,900 sort of a harder, more global decision. 445 00:19:16,900 --> 00:19:19,570 So we're going to focus on this stepwise decision making 446 00:19:19,570 --> 00:19:22,380 process of do you want the next unit, the next cookie, 447 00:19:22,380 --> 00:19:25,360 or the next slice of pizza, OK? 448 00:19:25,360 --> 00:19:28,660 And the key feature of utility functions 449 00:19:28,660 --> 00:19:31,120 we'll work with throughout the semester 450 00:19:31,120 --> 00:19:39,210 is that they will feature diminishing marginal utility. 451 00:19:39,210 --> 00:19:43,440 Marginal utility will fall as you have more of a good. 452 00:19:43,440 --> 00:19:45,540 The more of a good you've had, the less 453 00:19:45,540 --> 00:19:50,690 happiness you'll derive from the next unit, OK? 454 00:19:50,690 --> 00:19:55,250 Now, we can see that graphically in figure 2-4. 455 00:19:55,250 --> 00:19:58,400 Figure 2-4 graphs on the x-axis the number 456 00:19:58,400 --> 00:20:01,090 of cookies holding constant pizza. 457 00:20:01,090 --> 00:20:03,170 So let's say you're having two pizza slices, 458 00:20:03,170 --> 00:20:07,630 and you want to say, what's my benefit from the next cookie? 459 00:20:07,630 --> 00:20:10,330 And on the left axis, violating what I just 460 00:20:10,330 --> 00:20:13,108 said like 15 seconds ago, we graph utility. 461 00:20:13,108 --> 00:20:15,400 Now, once again, the utile numbers don't mean anything. 462 00:20:15,400 --> 00:20:18,110 It's just to give you an ordinal sense. 463 00:20:18,110 --> 00:20:21,050 What you see here is that if you have 1 cookie, 464 00:20:21,050 --> 00:20:25,412 your utility is 1.4, square root of 2 times 1. 465 00:20:25,412 --> 00:20:26,870 If you have 2 cookies, your utility 466 00:20:26,870 --> 00:20:29,990 goes up to square root of 4, which is 2. 467 00:20:29,990 --> 00:20:32,450 You are happier with 2 cookies, but you 468 00:20:32,450 --> 00:20:36,540 are less happy from the second cookie than the first cookie, 469 00:20:36,540 --> 00:20:37,490 OK? 470 00:20:37,490 --> 00:20:39,140 And you could see that in figure-- 471 00:20:39,140 --> 00:20:41,690 if you flip back and forth between 2-4 and 2-5, 472 00:20:41,690 --> 00:20:44,550 you can see that, OK? 473 00:20:44,550 --> 00:20:47,970 The first cookie, going from 0 to 1 cookie, 474 00:20:47,970 --> 00:20:50,040 gave you one-- so in this case, we're now 475 00:20:50,040 --> 00:20:51,990 graphing the marginal utility. 476 00:20:51,990 --> 00:20:56,300 So figure 2-4 is the level of utility, 477 00:20:56,300 --> 00:20:58,713 which is not really something you can measure, in fact. 478 00:20:58,713 --> 00:21:00,380 Figure 2-5 is something you can measure, 479 00:21:00,380 --> 00:21:02,210 which is marginal utility, what's your happiness-- 480 00:21:02,210 --> 00:21:03,752 and we'll talk about measuring this-- 481 00:21:03,752 --> 00:21:04,700 from the next cookie. 482 00:21:04,700 --> 00:21:13,150 You see, the first cookie gives you a utility increment of 1.4, 483 00:21:13,150 --> 00:21:13,740 OK? 484 00:21:13,740 --> 00:21:17,550 You go from utility of 0 to utility of 1.4. 485 00:21:17,550 --> 00:21:21,190 The next cookie gives you utility increment of 0.59. 486 00:21:21,190 --> 00:21:25,340 OK, you go from utility of 1.41 to utility of 2. 487 00:21:25,340 --> 00:21:27,770 The next cookie gives utility increment of 0.45, 488 00:21:27,770 --> 00:21:29,090 the square root of 3. 489 00:21:29,090 --> 00:21:31,720 So now we flip back to the previous page. 490 00:21:31,720 --> 00:21:33,770 We're going from the square root of 4, 491 00:21:33,770 --> 00:21:35,395 we're going from the square root of 4-- 492 00:21:35,395 --> 00:21:36,920 I'm sorry-- to the square root of 6. 493 00:21:36,920 --> 00:21:40,880 Square root of 6 is only 0.45 more than the square root of 4, 494 00:21:40,880 --> 00:21:42,450 and so on. 495 00:21:42,450 --> 00:21:46,300 So each additional cookie makes you less and less happy. 496 00:21:46,300 --> 00:21:49,400 It makes you happier, it has to, because more is better, 497 00:21:49,400 --> 00:21:52,540 but it makes you less and less happy, OK? 498 00:21:52,540 --> 00:21:54,680 And this makes sense. 499 00:21:54,680 --> 00:21:56,420 Just think about any decision life 500 00:21:56,420 --> 00:21:58,100 starting with nothing of something 501 00:21:58,100 --> 00:22:00,520 and having the first one, slice of pizza, 502 00:22:00,520 --> 00:22:03,380 a cookie, deciding on which movie to go to. 503 00:22:03,380 --> 00:22:07,120 The first movie, the one you want to see the most, 504 00:22:07,120 --> 00:22:09,760 is going to make you happier than the one you 505 00:22:09,760 --> 00:22:11,182 want to see not quite as much. 506 00:22:11,182 --> 00:22:12,640 The first cookie when you're hungry 507 00:22:12,640 --> 00:22:14,808 will make you happier than the second cookie. 508 00:22:14,808 --> 00:22:16,600 The first slice of pizza make you happier-- 509 00:22:16,600 --> 00:22:18,440 Now, you may be close to indifferent. 510 00:22:18,440 --> 00:22:20,565 Maybe the second slice of pizza makes you almost as 511 00:22:20,565 --> 00:22:21,950 happy as the first. 512 00:22:21,950 --> 00:22:24,070 But the first will make you happier, OK? 513 00:22:24,070 --> 00:22:25,007 If you think about-- 514 00:22:25,007 --> 00:22:26,590 that's really sort of that first step. 515 00:22:26,590 --> 00:22:29,590 You were hungry, and that first one makes you feel happier. 516 00:22:29,590 --> 00:22:33,592 Now, but you got to remember, you always want more cookies. 517 00:22:33,592 --> 00:22:35,050 Now, you might say, "Wait a second. 518 00:22:35,050 --> 00:22:36,050 This is stupid. 519 00:22:36,050 --> 00:22:38,102 Once I've had 10 cookies, I'm going to barf. 520 00:22:38,102 --> 00:22:40,060 The 11th cookie can actually make me worse off, 521 00:22:40,060 --> 00:22:42,140 because I don't like barfing." 522 00:22:42,140 --> 00:22:45,530 But in economics, we have to remember, 523 00:22:45,530 --> 00:22:47,240 you don't have to eat the 11th cookie. 524 00:22:47,240 --> 00:22:48,812 You can give it away. 525 00:22:48,812 --> 00:22:50,770 So if like say, you don't want the 11th cookie, 526 00:22:50,770 --> 00:22:52,370 you can save it for later. 527 00:22:52,370 --> 00:22:54,040 You can give it to a friend. 528 00:22:54,040 --> 00:22:55,660 So you always want it. 529 00:22:55,660 --> 00:22:58,000 In the worst case, you throw it out. 530 00:22:58,000 --> 00:23:01,762 It can't make you worse off, it can only make you better off. 531 00:23:01,762 --> 00:23:03,970 And that's what our sort of more is better assumption 532 00:23:03,970 --> 00:23:04,470 comes from. 533 00:23:04,470 --> 00:23:07,053 Obviously, the limit-- you know, if you get a million cookies, 534 00:23:07,053 --> 00:23:08,220 your garbage can gets full. 535 00:23:08,220 --> 00:23:09,190 You have no friends to give them to. 536 00:23:09,190 --> 00:23:11,860 I understand at the limit, these things fall apart, OK? 537 00:23:11,860 --> 00:23:13,780 But that's the basic idea of more is better 538 00:23:13,780 --> 00:23:16,180 and the basic idea of diminishing marginal utility. 539 00:23:16,180 --> 00:23:17,780 OK, any questions about that? 540 00:23:17,780 --> 00:23:18,280 Yeah. 541 00:23:18,280 --> 00:23:20,950 AUDIENCE: Can the utility function ever be negative? 542 00:23:20,950 --> 00:23:22,325 JONATHAN GRUBER: Utility function 543 00:23:22,325 --> 00:23:24,970 can never be negative because we have-- well, 544 00:23:24,970 --> 00:23:27,328 utility-- once again, utility is not an ordinal concept. 545 00:23:27,328 --> 00:23:28,870 You can set up utility functions such 546 00:23:28,870 --> 00:23:30,250 that the number is negative. 547 00:23:30,250 --> 00:23:31,310 You can set that up. 548 00:23:31,310 --> 00:23:34,360 OK, the marginal utility is always positive. 549 00:23:34,360 --> 00:23:36,890 You always get some benefit from the next unit. 550 00:23:36,890 --> 00:23:38,890 Utility, once again, the measurement's relevant. 551 00:23:38,890 --> 00:23:39,620 So it could be negative. 552 00:23:39,620 --> 00:23:40,440 You could set it up-- 553 00:23:40,440 --> 00:23:42,080 I could write my utility function like this, 554 00:23:42,080 --> 00:23:43,330 you know, something like that. 555 00:23:43,330 --> 00:23:44,390 So it could be negative. 556 00:23:44,390 --> 00:23:46,430 That's just a sort of scaling factor. 557 00:23:46,430 --> 00:23:48,190 But marginal utility is always positive. 558 00:23:48,190 --> 00:23:51,040 You're always happier, or it's non-negative. 559 00:23:51,040 --> 00:23:52,930 You're always happier or at least indifferent 560 00:23:52,930 --> 00:23:54,570 to getting the next unit. 561 00:23:54,570 --> 00:23:55,253 Yeah. 562 00:23:55,253 --> 00:23:56,920 AUDIENCE: So when you're looking at 2-5, 563 00:23:56,920 --> 00:23:58,545 if you get like a fraction of a cookie, 564 00:23:58,545 --> 00:24:02,497 is the marginal utility still going to go up? 565 00:24:02,497 --> 00:24:04,080 JONATHAN GRUBER: I'm sorry, you look-- 566 00:24:04,080 --> 00:24:06,528 figure 2-5-- no, the marginal is going to go down. 567 00:24:06,528 --> 00:24:08,570 Each fraction of a cookie, the marginal utility-- 568 00:24:08,570 --> 00:24:09,770 marginal utility is always diminishing. 569 00:24:09,770 --> 00:24:11,270 AUDIENCE: So if you start with zero, 570 00:24:11,270 --> 00:24:13,762 and you get 1/2 a cookie based on this graph-- 571 00:24:13,762 --> 00:24:16,220 JONATHAN GRUBER: Well, it's really hard to do it from zero. 572 00:24:16,220 --> 00:24:17,095 That's really tricky. 573 00:24:17,095 --> 00:24:19,050 It's sort of much easier to start from one. 574 00:24:19,050 --> 00:24:21,530 So corner solutions, we'll talk about corner solutions 575 00:24:21,530 --> 00:24:22,910 in this class, they get ugly. 576 00:24:22,910 --> 00:24:24,220 Think of it starting from one. 577 00:24:24,220 --> 00:24:26,090 Starting with that first cookie, every fraction of a cookie 578 00:24:26,090 --> 00:24:28,700 makes you happier, but less and less happy with each fraction. 579 00:24:28,700 --> 00:24:29,930 Good question. 580 00:24:29,930 --> 00:24:31,190 All right, good questions. 581 00:24:31,190 --> 00:24:35,510 All right, so now, let's talk about-- 582 00:24:35,510 --> 00:24:39,050 let's flip back from the math to the graphics, 583 00:24:39,050 --> 00:24:41,180 and talk about where indifference curves come from. 584 00:24:41,180 --> 00:24:42,510 I just drew them out. 585 00:24:42,510 --> 00:24:44,630 But in fact, indifference curves are 586 00:24:44,630 --> 00:24:46,910 the graphical representation of what comes out 587 00:24:46,910 --> 00:24:50,000 of utility function, OK? 588 00:24:50,000 --> 00:24:51,980 And indeed, the slope of the indifference 589 00:24:51,980 --> 00:24:58,470 curve, we're going to call the marginal rate of substitution, 590 00:24:58,470 --> 00:24:59,970 the rate essentially at which you're 591 00:24:59,970 --> 00:25:04,000 willing to substitute one good for the other. 592 00:25:04,000 --> 00:25:08,130 The rate at which you're willing to substitute cookies for pizza 593 00:25:08,130 --> 00:25:11,250 is your marginal rate of substitution. 594 00:25:11,250 --> 00:25:15,180 And we'll define that as the slope of the indifference 595 00:25:15,180 --> 00:25:18,780 curve, delta p over delta c. 596 00:25:18,780 --> 00:25:20,700 That is your marginal rate of substitution. 597 00:25:20,700 --> 00:25:21,540 Literally, the indifference curve 598 00:25:21,540 --> 00:25:23,915 tells you the rate at which you're willing to substitute. 599 00:25:23,915 --> 00:25:25,800 You just follow along and say, "Look, 600 00:25:25,800 --> 00:25:28,240 I'm willing to give up--" 601 00:25:28,240 --> 00:25:31,920 So in other words, if you look at figure 2-6, you say, "Look, 602 00:25:31,920 --> 00:25:36,480 I'm indifferent between point A to point B. 603 00:25:36,480 --> 00:25:37,800 One slice of pizza-- 604 00:25:37,800 --> 00:25:40,290 I'm sorry-- one cookie and four slices of pizza 605 00:25:40,290 --> 00:25:43,170 is the same to me as two cookies and two slices of pizza." 606 00:25:43,170 --> 00:25:44,480 Why is it the same? 607 00:25:44,480 --> 00:25:46,730 Because they both give me utility square root of four, 608 00:25:46,730 --> 00:25:47,250 right? 609 00:25:47,250 --> 00:25:48,512 So given this mathematical-- 610 00:25:48,512 --> 00:25:49,470 I'm not saying you are. 611 00:25:49,470 --> 00:25:52,160 I'm saying, given this mathematical representation, 612 00:25:52,160 --> 00:25:54,600 OK, you are indifferent between point A and point 613 00:25:54,600 --> 00:25:56,730 B. So what that says-- and what's 614 00:25:56,730 --> 00:25:58,390 the slope with the indifference curve? 615 00:25:58,390 --> 00:26:01,170 What's the arc slope between point A and point B? 616 00:26:01,170 --> 00:26:04,210 The slope is negative 2. 617 00:26:04,210 --> 00:26:07,570 So your marginal rate of substitution is negative 2. 618 00:26:07,570 --> 00:26:10,810 You are indifferent, OK? 619 00:26:10,810 --> 00:26:14,140 You are indifferent between 1, 4 and 2, 2. 620 00:26:14,140 --> 00:26:18,040 Therefore, you're willing to substitute or give away 621 00:26:18,040 --> 00:26:22,200 two slices of pizza to get one cookie. 622 00:26:22,200 --> 00:26:29,310 Delta p delta c is negative 2, OK? 623 00:26:29,310 --> 00:26:31,860 Now, it turns out you can define the marginal rate 624 00:26:31,860 --> 00:26:34,500 of substitution over any segment of indifference curve, 625 00:26:34,500 --> 00:26:36,960 and what's interesting is it changes. 626 00:26:36,960 --> 00:26:38,160 It diminishes. 627 00:26:38,160 --> 00:26:41,340 Look what happens when we move from two pizzas and two 628 00:26:41,340 --> 00:26:44,608 cookies, from point B to point C. 629 00:26:44,608 --> 00:26:46,150 Now the marginal rate of substitution 630 00:26:46,150 --> 00:26:48,030 is only negative of 1/2. 631 00:26:48,030 --> 00:26:50,790 Now I'm only willing to give up one slice of pizza 632 00:26:50,790 --> 00:26:52,410 to get two cookies. 633 00:26:52,410 --> 00:26:53,260 What's happening? 634 00:26:53,260 --> 00:26:55,260 First, I was willing give up two slices of pizza 635 00:26:55,260 --> 00:26:57,120 to get one cookie. 636 00:26:57,120 --> 00:26:59,730 Now I'm only willing to give up one slice of pizza 637 00:26:59,730 --> 00:27:01,050 to get two cookies. 638 00:27:01,050 --> 00:27:02,050 What's happening? 639 00:27:02,050 --> 00:27:02,550 Yeah. 640 00:27:02,550 --> 00:27:03,930 AUDIENCE: You don't want a cookie as much? 641 00:27:03,930 --> 00:27:05,130 JONATHAN GRUBER: Because of? 642 00:27:05,130 --> 00:27:05,970 AUDIENCE: Diminishing marginal utility. 643 00:27:05,970 --> 00:27:07,050 JONATHAN GRUBER: Exactly. 644 00:27:07,050 --> 00:27:09,810 Diminishing margin utility has caused 645 00:27:09,810 --> 00:27:11,730 the marginal rate of substitution 646 00:27:11,730 --> 00:27:12,883 itself to diminish. 647 00:27:12,883 --> 00:27:15,300 For those who are really kind of better at math than I am, 648 00:27:15,300 --> 00:27:17,790 it turns out technically, mathematically, 649 00:27:17,790 --> 00:27:19,820 marginal utility isn't always diminishing. 650 00:27:19,820 --> 00:27:21,030 You can draw up cases. 651 00:27:21,030 --> 00:27:23,075 MRS is always diminishing. 652 00:27:23,075 --> 00:27:25,200 So you can think of marginal as always diminishing. 653 00:27:25,200 --> 00:27:26,140 It's fine for this class. 654 00:27:26,140 --> 00:27:27,690 When you get to higher level math and economics, 655 00:27:27,690 --> 00:27:29,898 you'll see marginal utility doesn't have to diminish. 656 00:27:29,898 --> 00:27:32,650 MRS has to diminish, OK? 657 00:27:32,650 --> 00:27:35,015 MRS is always diminishing. 658 00:27:35,015 --> 00:27:36,640 As you go along the indifference curve, 659 00:27:36,640 --> 00:27:41,740 that slope is always falling, OK? 660 00:27:41,740 --> 00:27:45,400 So basically, what we can right now 661 00:27:45,400 --> 00:27:48,690 is how the MRS relates to utility function. 662 00:27:48,690 --> 00:27:50,680 Our first sort of mind-blowing result 663 00:27:50,680 --> 00:27:53,830 is that the MRS is equal to the negative 664 00:27:53,830 --> 00:27:56,470 of the marginal utility of cookies 665 00:27:56,470 --> 00:27:59,730 over the marginal utility of pizza. 666 00:27:59,730 --> 00:28:02,240 That's our first key definition. 667 00:28:02,240 --> 00:28:05,130 It's equal to the negative of the marginal utility 668 00:28:05,130 --> 00:28:07,730 of the good on the x-axis over the marginal utility 669 00:28:07,730 --> 00:28:11,390 of the good on the y-axis, OK? 670 00:28:11,390 --> 00:28:13,730 Essentially, the marginal rate of substitution 671 00:28:13,730 --> 00:28:17,690 tells you how your relative marginal utilities 672 00:28:17,690 --> 00:28:22,150 evolve as you move down the indifference curve. 673 00:28:22,150 --> 00:28:28,150 When you start at point A, you have lots of pizza 674 00:28:28,150 --> 00:28:30,890 and not a lot of cookies. 675 00:28:30,890 --> 00:28:37,040 When you have lots of pizza, your marginal utility is small. 676 00:28:37,040 --> 00:28:38,488 Here's the key insight. 677 00:28:38,488 --> 00:28:41,030 This is the thing which, once again, it's a light bulb thing. 678 00:28:41,030 --> 00:28:43,240 If you get this, it'll make your life so much easier. 679 00:28:43,240 --> 00:28:47,860 Marginal utilities are negative functions of quantity. 680 00:28:47,860 --> 00:28:50,380 The more you have of a thing, the less 681 00:28:50,380 --> 00:28:53,170 you want the next unit of it. 682 00:28:53,170 --> 00:28:55,540 That's why, for example, cookies is now in the numerator 683 00:28:55,540 --> 00:28:59,110 and pizza is in the denominator, flipping from this side, OK? 684 00:28:59,110 --> 00:29:02,200 The more you have a good, the less you want it. 685 00:29:02,200 --> 00:29:05,680 So start at point A. You have lots of pizza 686 00:29:05,680 --> 00:29:07,290 and not a lot of cookies. 687 00:29:07,290 --> 00:29:09,070 You don't really want more pizza. 688 00:29:09,070 --> 00:29:10,750 You want more cookies. 689 00:29:10,750 --> 00:29:13,570 That means the denominator is small. 690 00:29:13,570 --> 00:29:16,900 The marginal utility of pizza is small. 691 00:29:16,900 --> 00:29:18,340 You don't really want it. 692 00:29:18,340 --> 00:29:20,600 But the marginal utility of cookies is high. 693 00:29:20,600 --> 00:29:21,590 You want many of them. 694 00:29:21,590 --> 00:29:24,490 So this is a big number. 695 00:29:24,490 --> 00:29:28,650 Now let's move to point B. Think about your next decision. 696 00:29:28,650 --> 00:29:32,618 Well, now, your marginal utility of pizza, 697 00:29:32,618 --> 00:29:34,910 if you were going to go from two to one slice of pizza, 698 00:29:34,910 --> 00:29:37,100 now pizza is worth a lot more than cookies. 699 00:29:37,100 --> 00:29:39,080 So now it gets smaller. 700 00:29:39,080 --> 00:29:42,147 So essentially, as you move along that indifference curve, 701 00:29:42,147 --> 00:29:44,230 because of this, you want-- because of diminishing 702 00:29:44,230 --> 00:29:46,720 marginal utility, it leads this issue 703 00:29:46,720 --> 00:29:50,630 of a diminishing marginal rate substitution, OK? 704 00:29:50,630 --> 00:29:53,060 So basically, as you move along the indifference curve, 705 00:29:53,060 --> 00:29:57,050 you're more and more willing to give up the good on the x-axis 706 00:29:57,050 --> 00:29:58,457 to get the good on the y-axis. 707 00:29:58,457 --> 00:30:00,290 As you move from the upper left to the lower 708 00:30:00,290 --> 00:30:03,660 right on that indifference map, figure 2-6, 709 00:30:03,660 --> 00:30:06,260 you're more you're more willing to give up 710 00:30:06,260 --> 00:30:11,220 the good on the x-axis to get the good on the y-axis. 711 00:30:11,220 --> 00:30:16,040 And what this implies is that indifference curves are-- 712 00:30:16,040 --> 00:30:21,230 indifference curves are convex to the origin. 713 00:30:21,230 --> 00:30:24,060 Indifference curves are convex to the origin. 714 00:30:24,060 --> 00:30:25,430 That's very important. 715 00:30:25,430 --> 00:30:28,873 OK, let's see, they are not concave. 716 00:30:28,873 --> 00:30:30,290 They're either convex or straight. 717 00:30:30,290 --> 00:30:34,723 Let's say they're not concave to the origin, to be technical. 718 00:30:34,723 --> 00:30:36,140 Indifference curves can be linear. 719 00:30:36,140 --> 00:30:37,563 We'll come to that. 720 00:30:37,563 --> 00:30:39,230 But they can't be concave to the origin. 721 00:30:39,230 --> 00:30:39,872 Why? 722 00:30:39,872 --> 00:30:42,080 Well, let's look at the next figure, the last figure, 723 00:30:42,080 --> 00:30:43,145 figure 2-7. 724 00:30:43,145 --> 00:30:45,020 What would happen if indifference curves were 725 00:30:45,020 --> 00:30:47,820 concave to the origin? 726 00:30:47,820 --> 00:30:52,820 Then that would say, moving from one pizza-- 727 00:30:52,820 --> 00:30:55,352 so now I've drawn a concave indifference curve. 728 00:30:55,352 --> 00:30:57,560 And with this indifference curve, moving from point A 729 00:30:57,560 --> 00:31:00,290 to point B leaves you indifferent. 730 00:31:00,290 --> 00:31:03,320 So you're happy to give up one slice of pizza 731 00:31:03,320 --> 00:31:04,820 to get one cookie. 732 00:31:04,820 --> 00:31:07,780 Starting with four slices of pizza and one cookie, 733 00:31:07,780 --> 00:31:10,280 you were happy to give up one slice of pizza 734 00:31:10,280 --> 00:31:12,580 to get one cookie. 735 00:31:12,580 --> 00:31:15,248 Now, starting from two and three, 736 00:31:15,248 --> 00:31:17,290 you're now willing to give up two slices of pizza 737 00:31:17,290 --> 00:31:19,250 to get one cookie. 738 00:31:19,250 --> 00:31:20,390 What does that violate? 739 00:31:20,390 --> 00:31:22,070 Why does that not make sense? 740 00:31:22,070 --> 00:31:23,123 Yeah. 741 00:31:23,123 --> 00:31:25,040 AUDIENCE: Law of diminishing marginal returns? 742 00:31:25,040 --> 00:31:27,498 JONATHAN GRUBER: Yeah, law of diminishing marginal utility. 743 00:31:27,498 --> 00:31:30,860 Here, you were happy to have one slice of pizza 744 00:31:30,860 --> 00:31:31,790 to get one cookie. 745 00:31:31,790 --> 00:31:33,060 Now you are willing to have two slices of pizza 746 00:31:33,060 --> 00:31:33,980 to get one cookie, even though you have 747 00:31:33,980 --> 00:31:35,690 less pizza and more cookies. 748 00:31:35,690 --> 00:31:37,010 That can't be right. 749 00:31:37,010 --> 00:31:39,800 As you have less pizza and more cookies, cookies-- 750 00:31:39,800 --> 00:31:42,620 pizza should become more valuable, not less valuable, 751 00:31:42,620 --> 00:31:45,530 and cookies should become less valuable, not more valuable. 752 00:31:45,530 --> 00:31:47,660 So a concave to the origin indifference 753 00:31:47,660 --> 00:31:49,445 curve would violate the principle 754 00:31:49,445 --> 00:31:51,987 of diminishing marginal utility and diminishing marginal rate 755 00:31:51,987 --> 00:31:53,600 of substitution, OK? 756 00:31:53,600 --> 00:31:54,100 Yeah. 757 00:31:54,100 --> 00:31:56,524 AUDIENCE: What if it's like something like trading cards? 758 00:31:56,524 --> 00:31:57,357 JONATHAN GRUBER: OK. 759 00:31:57,357 --> 00:32:01,260 AUDIENCE: I mean, I mean, as you get more trading cards, 760 00:32:01,260 --> 00:32:04,482 you have-- you're already made a complete set. 761 00:32:04,482 --> 00:32:06,190 JONATHAN GRUBER: That's very interesting. 762 00:32:06,190 --> 00:32:09,400 So in some sense, what that is saying 763 00:32:09,400 --> 00:32:11,710 is that your utility function is really over sets. 764 00:32:11,710 --> 00:32:12,570 You're saying your utility functions 765 00:32:12,570 --> 00:32:13,950 isn't over trading cards. 766 00:32:13,950 --> 00:32:15,370 It's over sets. 767 00:32:15,370 --> 00:32:19,840 So basically, that's what's sort of a bit-- 768 00:32:19,840 --> 00:32:21,837 you know, our models are flexible. 769 00:32:21,837 --> 00:32:23,170 One way is to say they're loose. 770 00:32:23,170 --> 00:32:25,840 Another way is to say they're flexible. 771 00:32:25,840 --> 00:32:28,835 But one of the challenges you'll face on this course 772 00:32:28,835 --> 00:32:31,210 is thinking about what is the decision set over which I'm 773 00:32:31,210 --> 00:32:32,470 writing my utility function? 774 00:32:32,470 --> 00:32:34,510 You're saying it's sets, not trading cards. 775 00:32:34,510 --> 00:32:37,233 So that's why it happens. 776 00:32:37,233 --> 00:32:37,900 Other questions? 777 00:32:37,900 --> 00:32:38,350 Good question. 778 00:32:38,350 --> 00:32:39,120 Yeah, at the back. 779 00:32:39,120 --> 00:32:41,412 AUDIENCE: What about like addictive things, where like, 780 00:32:41,412 --> 00:32:43,433 the more you have it, the more you want to buy? 781 00:32:43,433 --> 00:32:45,850 JONATHAN GRUBER: Yeah, that's a really relishing question. 782 00:32:45,850 --> 00:32:48,160 I spent a lot of my research life, actually-- 783 00:32:48,160 --> 00:32:50,290 I did a lot of research for a number of years 784 00:32:50,290 --> 00:32:51,970 on thinking about how you properly 785 00:32:51,970 --> 00:32:54,910 model addictive decisions like smoking. 786 00:32:54,910 --> 00:32:56,700 Addictive decisions like smoking, 787 00:32:56,700 --> 00:33:00,730 essentially, it really is that your utility 788 00:33:00,730 --> 00:33:04,030 function itself shifts as you get more addictive. 789 00:33:04,030 --> 00:33:06,315 It's not that your marginal utility-- 790 00:33:06,315 --> 00:33:07,690 the next cigarette is still worth 791 00:33:07,690 --> 00:33:09,310 less than the first cigarette. 792 00:33:09,310 --> 00:33:10,977 It's just that as you get more addicted, 793 00:33:10,977 --> 00:33:13,450 that first cigarette gets worth more and more to you. 794 00:33:13,450 --> 00:33:15,667 So when you wake up in the morning feeling crappy, 795 00:33:15,667 --> 00:33:17,500 that first cigarette still does more for you 796 00:33:17,500 --> 00:33:18,910 than the second cigarette. 797 00:33:18,910 --> 00:33:22,163 It's just, the next day you wake up feeling crappier, OK? 798 00:33:22,163 --> 00:33:23,580 So we model addiction as something 799 00:33:23,580 --> 00:33:27,090 where essentially, each day, cigarettes 800 00:33:27,090 --> 00:33:28,140 do less and less for you. 801 00:33:28,140 --> 00:33:30,390 You get essentially adjusted to new-- you habituate 802 00:33:30,390 --> 00:33:32,042 to higher levels. 803 00:33:32,042 --> 00:33:34,500 And this is why I do a lot of work-- you know, this is why, 804 00:33:34,500 --> 00:33:36,747 unfortunately, we saw last year, the number-- 805 00:33:36,747 --> 00:33:38,580 the highest number of deaths from accidental 806 00:33:38,580 --> 00:33:39,540 overdose in US history. 807 00:33:39,540 --> 00:33:42,870 72,000 people died from drug overdoses last year, more than 808 00:33:42,870 --> 00:33:46,770 ever died in traffic accidents in our nation's history, OK? 809 00:33:46,770 --> 00:33:47,880 Why? 810 00:33:47,880 --> 00:33:49,940 Because people get habituated to certain levels, 811 00:33:49,940 --> 00:33:51,690 and they get habituated to certain levels. 812 00:33:51,690 --> 00:33:53,965 So people get hooked on Oxycontin. 813 00:33:53,965 --> 00:33:55,590 They get habituated to a certain level. 814 00:33:55,590 --> 00:33:57,140 They maybe switch to heroin, and they 815 00:33:57,140 --> 00:33:58,260 habituate to a certain level. 816 00:33:58,260 --> 00:34:00,060 And now there's this thing called fentanyl, 817 00:34:00,060 --> 00:34:02,800 which is a synthetic opioid brought over from China, 818 00:34:02,800 --> 00:34:04,470 which is incredibly powerful. 819 00:34:04,470 --> 00:34:07,920 And dealers are mixing the fentanyl in with the heroin. 820 00:34:07,920 --> 00:34:09,889 And the people shoot up, not realizing-- 821 00:34:09,889 --> 00:34:11,280 at their habituated level-- not realizing 822 00:34:11,280 --> 00:34:12,738 they have this dangerous substance, 823 00:34:12,738 --> 00:34:14,260 and they overdose and die. 824 00:34:14,260 --> 00:34:16,120 And that's because they've got habituated to high levels. 825 00:34:16,120 --> 00:34:17,750 They don't realize they're getting a different product. 826 00:34:17,750 --> 00:34:19,875 So it's not about not diminishing marginal utility. 827 00:34:19,875 --> 00:34:22,550 It's about different-- underlying different products. 828 00:34:22,550 --> 00:34:23,690 All right? 829 00:34:23,690 --> 00:34:25,703 Other questions? 830 00:34:25,703 --> 00:34:27,370 Sorry for that depressing note, but it's 831 00:34:27,370 --> 00:34:28,239 important to be thinking about that. 832 00:34:28,239 --> 00:34:30,010 That's why, once again, we're the dismal science. 833 00:34:30,010 --> 00:34:31,510 We have to think about these things. 834 00:34:31,510 --> 00:34:35,020 OK, now, let's come to a great example 835 00:34:35,020 --> 00:34:36,489 that I hope you've wondered about, 836 00:34:36,489 --> 00:34:38,650 and maybe you've already figured out in your life, 837 00:34:38,650 --> 00:34:40,067 but I hope you've at least stopped 838 00:34:40,067 --> 00:34:43,780 and wondered about, which is the prices 839 00:34:43,780 --> 00:34:48,639 of different sizes of goods, in a convenience store, say. 840 00:34:48,639 --> 00:34:51,610 OK, take Starbucks. 841 00:34:51,610 --> 00:34:55,510 You can get a tall iced coffee for 2.25, 842 00:34:55,510 --> 00:34:58,990 or the next size, whatever the hell they call it, bigger, OK? 843 00:34:58,990 --> 00:35:01,750 You can get, for 70 more cents-- 844 00:35:01,750 --> 00:35:05,050 so 2.25, and you can double it for 70 more cents. 845 00:35:05,050 --> 00:35:06,640 Or take McDonald's. 846 00:35:06,640 --> 00:35:11,500 A small drink is $1.22 at the local McDonald's, but for 50 847 00:35:11,500 --> 00:35:14,760 more cents, you can double the size, OK? 848 00:35:14,760 --> 00:35:16,930 What's going on here? 849 00:35:16,930 --> 00:35:19,390 Why did they give you twice as much liquid, 850 00:35:19,390 --> 00:35:21,780 or if you go for ice cream, it's the same thing. 851 00:35:21,780 --> 00:35:24,900 Why do they give you twice as much for much less than twice 852 00:35:24,900 --> 00:35:26,243 as much money? 853 00:35:26,243 --> 00:35:26,910 What's going on? 854 00:35:26,910 --> 00:35:28,230 Yeah. 855 00:35:28,230 --> 00:35:31,110 AUDIENCE: Since your marginal utility is diminishing 856 00:35:31,110 --> 00:35:34,290 as you have more coffee available to you, 857 00:35:34,290 --> 00:35:36,060 you're willing to pay less for it, 858 00:35:36,060 --> 00:35:39,278 so they make the additional coffee cheaper. 859 00:35:39,278 --> 00:35:40,320 JONATHAN GRUBER: Exactly. 860 00:35:40,320 --> 00:35:41,820 That's a great way to explain it. 861 00:35:41,820 --> 00:35:45,120 The point is it's all about diminishing marginal utility. 862 00:35:45,120 --> 00:35:47,970 OK, when you come in to McDonald's on a hot day, 863 00:35:47,970 --> 00:35:50,738 you are desperate for that soda, but you're not 864 00:35:50,738 --> 00:35:52,280 as desperate have twice as much soda. 865 00:35:52,280 --> 00:35:53,090 You'd like it. 866 00:35:53,090 --> 00:35:54,830 You probably want to pay more for it, 867 00:35:54,830 --> 00:35:58,540 but you don't like it nearly as much as that first bit of soda. 868 00:35:58,540 --> 00:36:01,980 So those prices simply reflects the market's reaction 869 00:36:01,980 --> 00:36:04,407 to understanding diminishing marginal utility. 870 00:36:04,407 --> 00:36:06,240 Now, we haven't even talked about the supply 871 00:36:06,240 --> 00:36:07,198 side of the market yet. 872 00:36:07,198 --> 00:36:09,198 I'm not getting to how providers make decisions. 873 00:36:09,198 --> 00:36:10,470 That's a much deeper issue. 874 00:36:10,470 --> 00:36:13,170 I'm just saying that this is diminishing marginal utility 875 00:36:13,170 --> 00:36:15,090 in action, how it works in the market, 876 00:36:15,090 --> 00:36:18,300 and that's why you see this, OK? 877 00:36:18,300 --> 00:36:23,430 So basically, what you see is that that first bite of ice 878 00:36:23,430 --> 00:36:25,090 cream, for example, is worth more, 879 00:36:25,090 --> 00:36:27,090 and that's why the ice cream that's twice as big 880 00:36:27,090 --> 00:36:30,540 doesn't cost twice as much. 881 00:36:30,540 --> 00:36:33,330 Now, so basically, what this means 882 00:36:33,330 --> 00:36:37,620 is, if you think about our demand and supply model, 883 00:36:37,620 --> 00:36:43,800 on a hot day, or any day, the demand for the first 16 ounces 884 00:36:43,800 --> 00:36:48,640 is higher than the demand for the second 16 ounces. 885 00:36:48,640 --> 00:36:51,520 But the cost of producing 16 ounces is the same. 886 00:36:51,520 --> 00:36:52,720 So let's think about this. 887 00:36:52,720 --> 00:36:55,137 It's always risky when I try to draw a graph on the board, 888 00:36:55,137 --> 00:36:56,500 but let's bear with me. 889 00:36:56,500 --> 00:36:59,860 OK, so let's say we've got a simple supply and demand model. 890 00:36:59,860 --> 00:37:03,610 You have this supply function for soda, 891 00:37:03,610 --> 00:37:05,560 and let's assume it's roughly flat. 892 00:37:05,560 --> 00:37:08,530 OK, let's assume sort of the cost the firm proceeds 893 00:37:08,530 --> 00:37:09,820 within some range. 894 00:37:09,820 --> 00:37:12,880 The firm-- basically, every incremental 16 ounces 895 00:37:12,880 --> 00:37:14,260 costs them the same. 896 00:37:14,260 --> 00:37:16,720 So that's sort of their supply curve. 897 00:37:16,720 --> 00:37:19,630 And then you have some demand curve, OK? 898 00:37:19,630 --> 00:37:22,900 You have some demand curve which is downward sloping, OK, 899 00:37:22,900 --> 00:37:24,130 and they set some price. 900 00:37:24,130 --> 00:37:27,490 And this is the demand for 16 ounces. 901 00:37:27,490 --> 00:37:33,000 Now, what's the demand for the next 16 ounces, OK? 902 00:37:33,000 --> 00:37:34,450 Yeah, this isn't going to work. 903 00:37:34,450 --> 00:37:35,710 We have to have an upward-sloping supply curve. 904 00:37:35,710 --> 00:37:36,630 Sorry about that. 905 00:37:36,630 --> 00:37:39,630 We have a slightly upward sloping supply curve, OK? 906 00:37:39,630 --> 00:37:41,590 Now we have the demand for the next-- 907 00:37:41,590 --> 00:37:43,450 so here's your price. 908 00:37:43,450 --> 00:37:47,460 Here's your $1.22, OK? 909 00:37:47,460 --> 00:37:52,205 Now, you say, "Well, what's my demand when I sell 32 ounces?" 910 00:37:52,205 --> 00:37:53,580 Well, it turns out demand doesn't 911 00:37:53,580 --> 00:37:54,690 shift out twice as much. 912 00:37:54,690 --> 00:37:56,350 It just shifts out a little bit more. 913 00:37:56,350 --> 00:37:59,443 So you can only charge $1.72 for the next 16 ounces. 914 00:37:59,443 --> 00:38:01,110 Probably, if you want to go to the big-- 915 00:38:01,110 --> 00:38:04,230 if you go to 7-Eleven, where you can get sizes up to, you know, 916 00:38:04,230 --> 00:38:06,450 as big as your house, OK-- 917 00:38:06,450 --> 00:38:08,940 they keep these curves keep getting closer and closer 918 00:38:08,940 --> 00:38:09,870 to each other. 919 00:38:09,870 --> 00:38:12,270 So those price increments get smaller and smaller. 920 00:38:12,270 --> 00:38:14,312 And that's why you can get the monster, you know, 921 00:38:14,312 --> 00:38:16,200 ginormous Gulp at 7-Eleven-- 922 00:38:16,200 --> 00:38:19,800 is really just not that different from the price 923 00:38:19,800 --> 00:38:22,470 of getting the small little mini size, OK, 924 00:38:22,470 --> 00:38:25,010 because of diminishing marginal utility. 925 00:38:25,010 --> 00:38:27,200 All right, and so that's how the market-- 926 00:38:27,200 --> 00:38:31,820 that's essentially how we can take this abstract concept, 927 00:38:31,820 --> 00:38:33,950 this sort of crazy math, and turn it 928 00:38:33,950 --> 00:38:36,980 into literally what you see in the store you walk into, OK? 929 00:38:36,980 --> 00:38:38,720 Questions about that? 930 00:38:38,720 --> 00:38:40,160 Yeah. 931 00:38:40,160 --> 00:38:45,810 AUDIENCE: So how does this [? place ?] [INAUDIBLE],, 932 00:38:45,810 --> 00:38:48,985 like if for example, you wanted to buy a snack that you were 933 00:38:48,985 --> 00:38:50,610 going to have for breakfast every day-- 934 00:38:50,610 --> 00:38:51,390 JONATHAN GRUBER: Awesome. 935 00:38:51,390 --> 00:38:52,098 Awesome question. 936 00:38:52,098 --> 00:38:53,598 AUDIENCE: And then every single day, 937 00:38:53,598 --> 00:38:55,740 it was going to be your first granola bar, right? 938 00:38:55,740 --> 00:39:01,720 So I think that it's going to diminish every single time, 939 00:39:01,720 --> 00:39:03,325 but it's still cheaper to buy in bulk 940 00:39:03,325 --> 00:39:05,950 than it would be to buy a single granola bar every single time. 941 00:39:05,950 --> 00:39:07,050 JONATHAN GRUBER: Great, great question. 942 00:39:07,050 --> 00:39:07,685 Yeah? 943 00:39:07,685 --> 00:39:10,060 AUDIENCE: I think that has more to do with packaging cost 944 00:39:10,060 --> 00:39:11,800 than marginal utility. 945 00:39:11,800 --> 00:39:13,780 JONATHAN GRUBER: Well, I mean, the risk 946 00:39:13,780 --> 00:39:16,168 of my going to this model is, once we get nonlinear, 947 00:39:16,168 --> 00:39:17,710 the order we do things in this class, 948 00:39:17,710 --> 00:39:18,700 we have to start talking about supply 949 00:39:18,700 --> 00:39:19,990 factors I want to talk to. 950 00:39:19,990 --> 00:39:21,290 But there's two answers. 951 00:39:21,290 --> 00:39:23,080 One is packaging efficiencies. 952 00:39:23,080 --> 00:39:27,250 But the other is, if you actually go to Costco 953 00:39:27,250 --> 00:39:29,230 and look at their prices, for many things, 954 00:39:29,230 --> 00:39:31,630 they're not actually better than the supermarket. 955 00:39:31,630 --> 00:39:34,400 So actually, the price of buying the giant like, 956 00:39:34,400 --> 00:39:40,540 8,000 bars of granola is actually not that much more-- 957 00:39:40,540 --> 00:39:45,040 not that much less than 1,000 time buying eight granola bars. 958 00:39:45,040 --> 00:39:48,340 It's less, but it's not nearly as much less of these examples 959 00:39:48,340 --> 00:39:51,520 as sodas in McDonald's, which is exactly your point. 960 00:39:51,520 --> 00:39:54,820 Utility diminishes less, so they don't 961 00:39:54,820 --> 00:39:58,000 want to charge as much less for multiple packages. 962 00:39:58,000 --> 00:39:59,890 So you can actually-- if you compare 963 00:39:59,890 --> 00:40:02,530 the gap in perishable product pricing by size, 964 00:40:02,530 --> 00:40:05,590 it's much larger than the gap in nonperishable pricing by size. 965 00:40:05,590 --> 00:40:06,370 Great point. 966 00:40:06,370 --> 00:40:07,006 Yeah. 967 00:40:07,006 --> 00:40:09,150 AUDIENCE: Is there also just like a different time 968 00:40:09,150 --> 00:40:10,720 frame to which the utility starts 969 00:40:10,720 --> 00:40:12,604 diminishing for every product? 970 00:40:12,604 --> 00:40:15,340 Because you gave the example of soda, but it's like, 971 00:40:15,340 --> 00:40:17,620 would that reset later in the day, if we wanted-- 972 00:40:17,620 --> 00:40:18,663 were thirsty again, or-- 973 00:40:18,663 --> 00:40:20,080 JONATHAN GRUBER: Awesome, and that 974 00:40:20,080 --> 00:40:22,413 is why they don't let you walk back in with the same cup 975 00:40:22,413 --> 00:40:23,875 and refill it, right? 976 00:40:23,875 --> 00:40:26,000 That's exactly right, and that comes to this point. 977 00:40:26,000 --> 00:40:27,970 It's sort of like it's nonperishable 978 00:40:27,970 --> 00:40:31,612 as you get longer apart. 979 00:40:31,612 --> 00:40:33,570 But you know, it's all just really interesting. 980 00:40:33,570 --> 00:40:36,520 So at Fenway, OK, you can get-- 981 00:40:36,520 --> 00:40:39,170 you get like a regular sized soda, it's like crazy. 982 00:40:39,170 --> 00:40:40,960 It's like $6. 983 00:40:40,960 --> 00:40:43,600 Then for like $8, you get a big soda. 984 00:40:43,600 --> 00:40:47,388 Then for $10, you get a refillable big soda, OK? 985 00:40:47,388 --> 00:40:49,930 Now, the question is, can you bring that refillable soda back 986 00:40:49,930 --> 00:40:51,700 to additional games? 987 00:40:51,700 --> 00:40:54,586 Technically not, but I do. 988 00:40:54,586 --> 00:40:55,440 [LAUGHING] 989 00:40:55,440 --> 00:40:58,570 And basically they sort of understand-- 990 00:40:58,570 --> 00:41:00,070 so this interesting question of sort 991 00:41:00,070 --> 00:41:02,780 of the perishability of things and how that's going 992 00:41:02,780 --> 00:41:04,630 to affect things going on. 993 00:41:04,630 --> 00:41:07,460 It's a really-- it's an interesting question. 994 00:41:07,460 --> 00:41:08,793 Other comments? 995 00:41:08,793 --> 00:41:09,960 OK, I'm going to stop there. 996 00:41:09,960 --> 00:41:11,020 Those are great comments. 997 00:41:11,020 --> 00:41:12,510 Thanks everyone for participating. 998 00:41:12,510 --> 00:41:14,910 And we will come back next time and talk about the sad reality 999 00:41:14,910 --> 00:41:16,535 that we haven't won the lottery, and we 1000 00:41:16,535 --> 00:41:18,650 have limited amounts of money.