1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,870 Commons license. 3 00:00:03,870 --> 00:00:06,910 Your support will help MIT OpenCourseWare continue to 4 00:00:06,910 --> 00:00:10,560 offer high quality educational resources for free. 5 00:00:10,560 --> 00:00:13,460 To make a donation or view additional materials from 6 00:00:13,460 --> 00:00:18,910 hundreds of MIT courses, visit MIT OpenCourseWare at MIT.edu. 7 00:00:21,636 --> 00:00:24,780 PROFESSOR: We've been talking so far about basically 8 00:00:24,780 --> 00:00:27,700 overviews of supply and demand relationships and 9 00:00:27,700 --> 00:00:30,670 understanding how markets work. 10 00:00:30,670 --> 00:00:34,950 Now we're going to step back and get behind the supply and 11 00:00:34,950 --> 00:00:38,400 demand curves and understand where those curves 12 00:00:38,400 --> 00:00:39,520 themselves come from. 13 00:00:39,520 --> 00:00:41,490 So we talked about, given that we have supply and demand 14 00:00:41,490 --> 00:00:43,730 curves, how they interact. 15 00:00:43,730 --> 00:00:45,650 Now we're going to get behind that and see where these 16 00:00:45,650 --> 00:00:47,400 curves actually come from. 17 00:00:47,400 --> 00:00:48,550 Thank you, by the way for coming down. 18 00:00:48,550 --> 00:00:49,800 I appreciate it. 19 00:00:51,730 --> 00:00:53,490 So what we're going to do is, we're going to start with the 20 00:00:53,490 --> 00:00:56,410 demand curve, and we're going to spend the next few lectures 21 00:00:56,410 --> 00:00:59,830 talking about consumers and how consumer preferences are 22 00:00:59,830 --> 00:01:01,555 ultimately what leads to the construction 23 00:01:01,555 --> 00:01:03,380 of the demand curve. 24 00:01:03,380 --> 00:01:08,200 Then after that and after the first exam-- that will cover 25 00:01:08,200 --> 00:01:11,250 what's on the first exam-- 26 00:01:11,250 --> 00:01:13,740 after the first exam, we'll start talking about firms and 27 00:01:13,740 --> 00:01:16,380 what determines the firm supply curve. 28 00:01:16,380 --> 00:01:19,210 So today we'll talk about consumers and we're going to 29 00:01:19,210 --> 00:01:21,580 talk about where the demand curve comes from. 30 00:01:21,580 --> 00:01:24,810 And where it comes from, and where all consumer behavior 31 00:01:24,810 --> 00:01:27,665 coming from in economics is from utility maximization. 32 00:01:33,490 --> 00:01:35,980 That's where everything with consumers starts is with 33 00:01:35,980 --> 00:01:37,790 utility maximization. 34 00:01:37,790 --> 00:01:44,030 That's the basic building block of consumer behavior. 35 00:01:44,030 --> 00:01:48,050 And basically, utility maximization-- 36 00:01:48,050 --> 00:01:50,330 that's what this lecture will be about, describing it. 37 00:01:50,330 --> 00:01:55,410 But basically, an overview is, we posit some type of 38 00:01:55,410 --> 00:01:56,870 preferences. 39 00:01:56,870 --> 00:02:03,070 We posit consumer preferences, what consumers would like. 40 00:02:03,070 --> 00:02:10,370 We posit some budget constraint, what resources 41 00:02:10,370 --> 00:02:12,980 consumers have to get what they'd like. 42 00:02:12,980 --> 00:02:16,360 And then we do a constrained maximization problem that 43 00:02:16,360 --> 00:02:20,500 says, given your preferences, given what you'd like, subject 44 00:02:20,500 --> 00:02:22,840 to the resources you have available, what 45 00:02:22,840 --> 00:02:25,870 choices will you make? 46 00:02:25,870 --> 00:02:27,710 And in particular, we're going to ask, the term we'll use is 47 00:02:27,710 --> 00:02:32,860 we'll ask what bundle of goods makes you the best off? 48 00:02:32,860 --> 00:02:34,020 Given your preference, given your constraints, 49 00:02:34,020 --> 00:02:35,510 what bundle of goods? 50 00:02:35,510 --> 00:02:37,050 So think about consumers choosing 51 00:02:37,050 --> 00:02:38,160 across a set of goods. 52 00:02:38,160 --> 00:02:41,390 Typically, we'll think about two goods because graphs are 53 00:02:41,390 --> 00:02:43,760 easier to think about two dimensions than more. 54 00:02:43,760 --> 00:02:46,230 So we'll typically think about trading off two goods. 55 00:02:46,230 --> 00:02:49,140 So think about consumers with preferences across two goods, 56 00:02:49,140 --> 00:02:51,880 some budget they can allocate, and how 57 00:02:51,880 --> 00:02:53,080 they make those choices. 58 00:02:53,080 --> 00:02:56,170 But this basic framework applies to the multiplicity of 59 00:02:56,170 --> 00:02:59,790 choices we all make along many, many dimensions. 60 00:02:59,790 --> 00:03:03,380 So doing two dimensions as one of the simplifying assumptions 61 00:03:03,380 --> 00:03:04,560 I'll talk about. 62 00:03:04,560 --> 00:03:07,590 But that's just a simplifying assumption. 63 00:03:07,590 --> 00:03:08,930 So basically what we we're going to do is we're going to 64 00:03:08,930 --> 00:03:13,180 go through this in three steps, not just in this 65 00:03:13,180 --> 00:03:15,740 lecture, but over the next few lectures. 66 00:03:15,740 --> 00:03:19,600 Step one, is we're going to talk about what assumptions we 67 00:03:19,600 --> 00:03:21,300 make about preferences. 68 00:03:21,300 --> 00:03:23,235 So I'll talk today about preference assumptions. 69 00:03:27,540 --> 00:03:32,320 So the axioms that underlie how economists model consumer 70 00:03:32,320 --> 00:03:34,600 preferences. 71 00:03:34,600 --> 00:03:38,840 We'll then talk about how we translate these preferences 72 00:03:38,840 --> 00:03:42,770 assumptions into mathematical tractability through the use 73 00:03:42,770 --> 00:03:48,570 of the utility function, which is basically a mathematical 74 00:03:48,570 --> 00:03:52,690 representation of underlying consumer preferences. 75 00:03:52,690 --> 00:03:54,660 So we'll talk about how we basically take these 76 00:03:54,660 --> 00:03:56,560 preferences and translate them into something that we can 77 00:03:56,560 --> 00:03:59,440 work with here at MIT by making it mathematical, by 78 00:03:59,440 --> 00:04:01,420 making a utility function. 79 00:04:01,420 --> 00:04:06,560 And then finally, we'll talk about budget constraints. 80 00:04:06,560 --> 00:04:09,360 And armed with these three things, we'll then be able to 81 00:04:09,360 --> 00:04:12,610 model how consumers make decisions. 82 00:04:12,610 --> 00:04:18,120 Now, importantly for today's lecture, we are not dealing 83 00:04:18,120 --> 00:04:19,420 with budget constraints. 84 00:04:19,420 --> 00:04:22,690 So this is not happening today. 85 00:04:22,690 --> 00:04:24,280 So today we're not going to worry about the budget 86 00:04:24,280 --> 00:04:24,530 constraints. 87 00:04:24,530 --> 00:04:26,325 Today we're in a world where we're just going to talk about 88 00:04:26,325 --> 00:04:28,590 what people want and we're going to put out of our mind 89 00:04:28,590 --> 00:04:31,140 whether or not they can afford it. 90 00:04:31,140 --> 00:04:32,690 So just talk about people want, and we'll put out of 91 00:04:32,690 --> 00:04:33,200 mind for today. 92 00:04:33,200 --> 00:04:35,440 We'll come back next time to whether they can afford it. 93 00:04:35,440 --> 00:04:36,910 We're just going to think about unconstrained 94 00:04:36,910 --> 00:04:39,810 preferences for today's lecture. 95 00:04:42,570 --> 00:04:47,310 So let's talk about our preference assumptions. 96 00:04:47,310 --> 00:04:53,180 So, to model consumers' preferences across goods, 97 00:04:53,180 --> 00:04:55,360 we're going to impose three preference assumptions. 98 00:05:02,340 --> 00:05:05,160 Three preference assumptions. 99 00:05:05,160 --> 00:05:06,260 Assumption one-- 100 00:05:06,260 --> 00:05:08,990 now once again, let me remind you from the first lecture, 101 00:05:08,990 --> 00:05:11,260 this is getting to some of the harder material. 102 00:05:11,260 --> 00:05:15,320 I'm going to write messily and talk quickly, so stop me if 103 00:05:15,320 --> 00:05:16,520 anything is unclear. 104 00:05:16,520 --> 00:05:18,450 And if you don't stop me, I'll just go faster and faster 105 00:05:18,450 --> 00:05:19,860 until I explode. 106 00:05:19,860 --> 00:05:22,190 So basically, feel free to interrupt and stop me with 107 00:05:22,190 --> 00:05:24,260 questions and such. 108 00:05:24,260 --> 00:05:26,400 Three assumptions on preferences. 109 00:05:26,400 --> 00:05:27,800 The first assumption is completeness. 110 00:05:32,000 --> 00:05:34,140 The first assumption is the assumption of completeness. 111 00:05:34,140 --> 00:05:38,910 When comparing two bundles of goods, you prefer one or the 112 00:05:38,910 --> 00:05:44,180 other, but you don't value them equally. 113 00:05:44,180 --> 00:05:46,720 OK when comparing two bundles of goods, you prefer one or 114 00:05:46,720 --> 00:05:48,870 you prefer the other, but you're not indifferent. 115 00:05:48,870 --> 00:05:51,860 Completeness is the same as no indifference. 116 00:05:51,860 --> 00:05:54,230 So what we're saying is whenever I offer you two 117 00:05:54,230 --> 00:05:56,170 bundles of goods, you could always tell me 118 00:05:56,170 --> 00:05:57,090 what you like better. 119 00:05:57,090 --> 00:05:59,490 Now it could be infinitesimally better. 120 00:05:59,490 --> 00:06:01,440 I'm not saying you have to have strong preferences. 121 00:06:01,440 --> 00:06:04,330 But you cannot say I'm indifferent. 122 00:06:04,330 --> 00:06:05,680 You can never be purely indifferent. 123 00:06:05,680 --> 00:06:09,390 There always at least some slight preference for one 124 00:06:09,390 --> 00:06:11,090 bundle of goods over another. 125 00:06:11,090 --> 00:06:13,340 That's the completeness assumption. 126 00:06:13,340 --> 00:06:14,800 This is an assumption we make. 127 00:06:14,800 --> 00:06:17,640 Now in reality, oftentimes we are indifferent. 128 00:06:17,640 --> 00:06:18,900 Well once again, this is one of these simplifying 129 00:06:18,900 --> 00:06:20,650 assumptions that will make the model work. 130 00:06:20,650 --> 00:06:23,200 And in fact, in reality if forced, you can always decide 131 00:06:23,200 --> 00:06:24,910 whether you like one thing better than another, we just 132 00:06:24,910 --> 00:06:27,440 often follow heuristic rules which say we're roughly 133 00:06:27,440 --> 00:06:28,250 indifferent. 134 00:06:28,250 --> 00:06:29,640 We're just going to say, more precisely, you are never 135 00:06:29,640 --> 00:06:32,300 purely indifferent. 136 00:06:32,300 --> 00:06:35,100 So, I'm not sure is not an option. 137 00:06:35,100 --> 00:06:36,900 You can never say I don't know, I don't know which I 138 00:06:36,900 --> 00:06:39,470 prefer, I'm indifferent. 139 00:06:39,470 --> 00:06:40,450 I'm sorry, let me back up. 140 00:06:40,450 --> 00:06:41,780 I'm using the wrong word. 141 00:06:41,780 --> 00:06:43,416 Forget I said indifferent, because we'll want to use that 142 00:06:43,416 --> 00:06:44,690 word in a different context later. 143 00:06:44,690 --> 00:06:47,470 You can't say, I'm not sure. 144 00:06:47,470 --> 00:06:49,010 You can't say, I'm not sure. 145 00:06:52,620 --> 00:06:54,580 You can't say, I'm not sure, can't say I don't know, I 146 00:06:54,580 --> 00:06:55,830 don't know how I feel about that. 147 00:07:03,710 --> 00:07:05,250 Scratch what I said a few minutes ago, because I want to 148 00:07:05,250 --> 00:07:06,460 use indifference differently. 149 00:07:06,460 --> 00:07:08,810 Completeness is not about not being different, we're going 150 00:07:08,810 --> 00:07:09,490 to use that. 151 00:07:09,490 --> 00:07:11,510 What I'm saying is it's about not being sure. 152 00:07:11,510 --> 00:07:14,480 You've got to value every bundle of goods. 153 00:07:14,480 --> 00:07:16,720 You've got to be willing to value every bundle of goods 154 00:07:16,720 --> 00:07:18,610 that's given you. 155 00:07:18,610 --> 00:07:20,500 So you can't say that I don't know, I don't know how I feel 156 00:07:20,500 --> 00:07:21,110 about that. 157 00:07:21,110 --> 00:07:22,570 You've got to have some feeling about stuff. 158 00:07:22,570 --> 00:07:23,880 You can't say I'm not sure. 159 00:07:23,880 --> 00:07:25,810 You've got to have a complete set of preferences over all 160 00:07:25,810 --> 00:07:28,680 bundles of goods that are given you. 161 00:07:28,680 --> 00:07:31,910 OK, that's completeness. 162 00:07:31,910 --> 00:07:33,640 The second is transitivity. 163 00:07:37,950 --> 00:07:39,930 Which is something we've been learning since kindergarten 164 00:07:39,930 --> 00:07:41,000 about transitivity, right? 165 00:07:41,000 --> 00:07:42,570 And also, it's a different context. 166 00:07:42,570 --> 00:07:45,020 That's just if you prefer x to y, and y to z, you've got to 167 00:07:45,020 --> 00:07:46,140 prefer x to z. 168 00:07:46,140 --> 00:07:47,650 OK, you guys should do transitivity in 169 00:07:47,650 --> 00:07:49,010 your sleep by now. 170 00:07:49,010 --> 00:07:50,970 OK, so the standard transitivity we always assume 171 00:07:50,970 --> 00:07:53,870 in math class, we're going to assume here as well. 172 00:07:53,870 --> 00:07:56,800 OK, that should be pretty noncontroversial. 173 00:07:56,800 --> 00:08:01,400 OK, and then finally, and probably most controversial, 174 00:08:01,400 --> 00:08:02,990 is we're going to assume non-satiation. 175 00:08:07,730 --> 00:08:09,520 Or the famous economic assumption that 176 00:08:09,520 --> 00:08:12,120 more is always better. 177 00:08:12,120 --> 00:08:13,260 OK. 178 00:08:13,260 --> 00:08:17,400 More is always better, that is, you never would turn down 179 00:08:17,400 --> 00:08:19,000 having more. 180 00:08:19,000 --> 00:08:21,950 Now we're going to talk later today and tomorrow about why 181 00:08:21,950 --> 00:08:24,490 you might not like the next unit as much as you like the 182 00:08:24,490 --> 00:08:25,530 current unit. 183 00:08:25,530 --> 00:08:28,270 But you'll always like it greater than zero. 184 00:08:28,270 --> 00:08:30,640 You're always happy to have more. 185 00:08:30,640 --> 00:08:32,799 You never say, I've had enough, I literally value at 186 00:08:32,799 --> 00:08:34,230 zero the next unit. 187 00:08:34,230 --> 00:08:37,070 You may value it as epsilon, but you'll always value it as 188 00:08:37,070 --> 00:08:38,289 greater than zero. 189 00:08:38,289 --> 00:08:40,130 That's the non-satiation assumption, 190 00:08:40,130 --> 00:08:41,230 more is always better. 191 00:08:41,230 --> 00:08:42,259 Now, this is the most controversial. 192 00:08:42,259 --> 00:08:43,840 And obviously we can think of many contexts in 193 00:08:43,840 --> 00:08:45,750 which that's not true. 194 00:08:45,750 --> 00:08:49,170 But if we don't allow for this assumption, the modeling gets 195 00:08:49,170 --> 00:08:50,120 a lot trickier. 196 00:08:50,120 --> 00:08:51,350 So once again, let's put it out of our mind. 197 00:08:51,350 --> 00:08:54,910 Realistically, we know once we've eaten a certain amount, 198 00:08:54,910 --> 00:08:57,060 we literally do not want any more. 199 00:08:57,060 --> 00:08:58,680 OK, so we're going to put that aside. 200 00:08:58,680 --> 00:09:00,480 Assume we're always in a space where we can always eat a 201 00:09:00,480 --> 00:09:02,240 little bit more. 202 00:09:02,240 --> 00:09:04,540 OK, we'll call it the Jewish mother space. 203 00:09:04,540 --> 00:09:06,670 OK, you can always eat a little bit more. 204 00:09:06,670 --> 00:09:08,430 OK, you can always eat a little bit more. 205 00:09:08,430 --> 00:09:10,620 We're just going to assume we're in that space for now. 206 00:09:10,620 --> 00:09:11,220 OK. 207 00:09:11,220 --> 00:09:13,360 And so, for large ranges, we can see it is not an 208 00:09:13,360 --> 00:09:14,170 unreasonable assumption. 209 00:09:14,170 --> 00:09:15,800 Although, I think in extremes, you could see this becomes 210 00:09:15,800 --> 00:09:17,320 unreasonable. 211 00:09:17,320 --> 00:09:19,090 OK, so those are assumptions. 212 00:09:19,090 --> 00:09:20,520 Completeness, which once again, I screwed up in 213 00:09:20,520 --> 00:09:21,360 describing. 214 00:09:21,360 --> 00:09:22,900 Come back to the second way I described it, which means you 215 00:09:22,900 --> 00:09:23,740 can't say you're not sure. 216 00:09:23,740 --> 00:09:25,970 You always have preferences over things. 217 00:09:25,970 --> 00:09:27,390 That doesn't seem unreasonable. 218 00:09:27,390 --> 00:09:29,360 Transitivity which we've been living with since we were 219 00:09:29,360 --> 00:09:30,070 kindergartners. 220 00:09:30,070 --> 00:09:32,410 And non-satiation, which could be a little controversial, but 221 00:09:32,410 --> 00:09:33,820 we'll live with it for now. 222 00:09:33,820 --> 00:09:37,570 Now given these, we're going to talk about the properties 223 00:09:37,570 --> 00:09:39,820 of what we call indifference curves. 224 00:09:39,820 --> 00:09:41,450 This is why I screwed up before. 225 00:09:41,450 --> 00:09:43,080 Of course you can be indifferent between things. 226 00:09:43,080 --> 00:09:43,990 That's the whole point of economics. 227 00:09:43,990 --> 00:09:47,706 I don't know why I got that wrong. 228 00:09:47,706 --> 00:09:50,160 I haven't taught this course about six years, so I lost 229 00:09:50,160 --> 00:09:52,130 track of things. 230 00:09:52,130 --> 00:09:54,170 Properties of indifference curves. 231 00:09:54,170 --> 00:09:59,080 So indifference curves are our name for what you could also 232 00:09:59,080 --> 00:10:02,325 think of as preference maps. 233 00:10:02,325 --> 00:10:05,160 In economics, we like to be able to describe everything, 234 00:10:05,160 --> 00:10:07,600 as I said, three ways, intuitively, graphically, and 235 00:10:07,600 --> 00:10:08,590 mathematically. 236 00:10:08,590 --> 00:10:12,320 Preference maps are the graphical representation of 237 00:10:12,320 --> 00:10:14,950 people's preferences which we do through graphics that we 238 00:10:14,950 --> 00:10:17,130 call indifference curves. 239 00:10:17,130 --> 00:10:19,421 So now let's go to the example I'm going to use that I'm 240 00:10:19,421 --> 00:10:21,680 going to use throughout these next couple lectures of a 241 00:10:21,680 --> 00:10:23,470 decision you have to make. 242 00:10:23,470 --> 00:10:26,330 Now I tried to think of a cool way to make this example cool, 243 00:10:26,330 --> 00:10:26,920 and I just couldn't. 244 00:10:26,920 --> 00:10:28,630 So its going to be a boring example. 245 00:10:28,630 --> 00:10:31,400 It's going to be, imagine your parents gave you some money 246 00:10:31,400 --> 00:10:34,760 and you had to decide whether to buy pizza or see movies. 247 00:10:34,760 --> 00:10:36,340 I tried to make it at least a little bit relevant even if I 248 00:10:36,340 --> 00:10:37,760 couldn't make it cool. 249 00:10:37,760 --> 00:10:39,950 You've got to decide whether to buy pizza or see movies. 250 00:10:39,950 --> 00:10:41,110 That's your decision. 251 00:10:41,110 --> 00:10:42,570 That's the trade-off you're making. 252 00:10:42,570 --> 00:10:47,150 We're in a world with only two goods, pizza and movies. 253 00:10:47,150 --> 00:10:49,930 And you're deciding how to allocate the money your 254 00:10:49,930 --> 00:10:52,210 parents gave you over pizza and movies. 255 00:10:56,450 --> 00:10:59,410 Now let's say we're going to consider three choices of 256 00:10:59,410 --> 00:11:00,490 pizza and movies. 257 00:11:00,490 --> 00:11:01,740 So go to figure 4-1a. 258 00:11:05,290 --> 00:11:10,140 We're going to consider, you could have two pizzas and one 259 00:11:10,140 --> 00:11:15,530 movie, that's point A. You could have one pizza and two 260 00:11:15,530 --> 00:11:18,030 movies, that's point B. Or you can have two of both, that's 261 00:11:18,030 --> 00:11:21,500 point C. That's just three choices you're facing. 262 00:11:21,500 --> 00:11:23,140 Once again, we're ignoring paying for them. 263 00:11:23,140 --> 00:11:24,860 Budget constraints is next time. 264 00:11:24,860 --> 00:11:26,950 Now we're just saying I'm giving these three choices. 265 00:11:26,950 --> 00:11:29,210 Well how do you feel about them? 266 00:11:29,210 --> 00:11:32,010 Well let's assume that you're indifferent-- 267 00:11:32,010 --> 00:11:32,970 and this is why you can be indifferent. 268 00:11:32,970 --> 00:11:35,070 What I said before, just strike. 269 00:11:35,070 --> 00:11:37,000 Let's say you're indifferent between two pizzas and one 270 00:11:37,000 --> 00:11:39,150 movie, and one pizza and two movies. 271 00:11:39,150 --> 00:11:43,730 Let's say, if you had two pizzas and one movie, or one 272 00:11:43,730 --> 00:11:45,350 pizza and two movies, you pretty much feel the same 273 00:11:45,350 --> 00:11:46,360 about them. 274 00:11:46,360 --> 00:11:50,880 But clearly you like two pizzas and two movies better 275 00:11:50,880 --> 00:11:54,200 than either of the first two combinations. 276 00:11:54,200 --> 00:11:57,000 Then what we can do is we can draw what we call 277 00:11:57,000 --> 00:11:58,510 indifference curves. 278 00:11:58,510 --> 00:12:01,820 And that's in figure 4-1b. 279 00:12:01,820 --> 00:12:04,330 These are maps of your preferences. 280 00:12:04,330 --> 00:12:09,060 An indifference curve is the curve showing all combinations 281 00:12:09,060 --> 00:12:13,050 of consumption along which the individual is indifferent. 282 00:12:13,050 --> 00:12:14,600 And I'll say that again, very important concept. 283 00:12:14,600 --> 00:12:17,970 An indifference curve is a curve showing all combinations 284 00:12:17,970 --> 00:12:22,490 of consumption along which an individual is indifferent. 285 00:12:22,490 --> 00:12:23,800 So you have an indifference curve. 286 00:12:23,800 --> 00:12:26,810 I said you were indifferent between A and B. So you have 287 00:12:26,810 --> 00:12:30,370 an indifference curve that runs between A and B. That 288 00:12:30,370 --> 00:12:33,400 means that all, and I'm assuming that all combinations 289 00:12:33,400 --> 00:12:35,670 along this curve, you're indifferent. 290 00:12:35,670 --> 00:12:37,850 So you're equally happy getting two pizzas and one 291 00:12:37,850 --> 00:12:39,820 movie or one pizza and two movies. 292 00:12:39,820 --> 00:12:44,566 But point C, which is two pizzas and two movies is on a 293 00:12:44,566 --> 00:12:45,530 different indifference curve. 294 00:12:45,530 --> 00:12:50,120 You're not indifferent between point C and points A and B. 295 00:12:50,120 --> 00:12:51,340 You're indifferent between A and B-- 296 00:12:51,340 --> 00:12:53,210 I'm just assuming this, I'm not saying you are. 297 00:12:53,210 --> 00:12:56,050 But I'm just assuming, let's imagine you are. 298 00:12:56,050 --> 00:13:01,010 But you clearly like two pizzas and two movies better 299 00:13:01,010 --> 00:13:03,430 than one of one and two of the other. 300 00:13:03,430 --> 00:13:03,927 Yeah? 301 00:13:03,927 --> 00:13:07,406 AUDIENCE: Does that break the completeness rule for the-- 302 00:13:07,406 --> 00:13:09,160 PROFESSOR: Does that break it? 303 00:13:09,160 --> 00:13:10,120 Why would that break it? 304 00:13:10,120 --> 00:13:11,411 AUDIENCE: Do you prefer pizza over movies 305 00:13:11,411 --> 00:13:12,470 or movies over pizza? 306 00:13:12,470 --> 00:13:13,460 PROFESSOR: No. 307 00:13:13,460 --> 00:13:14,740 Because this is my screw up before. 308 00:13:14,740 --> 00:13:16,600 Completeness just means you know how you feel about 309 00:13:16,600 --> 00:13:18,090 everything. 310 00:13:18,090 --> 00:13:22,110 So strike from the record my initial description. 311 00:13:22,110 --> 00:13:24,030 Completeness means you just know how you feel about 312 00:13:24,030 --> 00:13:24,620 everything. 313 00:13:24,620 --> 00:13:25,960 You're allowed to be indifferent. 314 00:13:25,960 --> 00:13:27,416 Completeness just means you can't say, I don't know, I 315 00:13:27,416 --> 00:13:28,690 don't know how I feel about pizza. 316 00:13:28,690 --> 00:13:30,740 You've got to have feelings for pizza. 317 00:13:30,740 --> 00:13:31,260 OK. 318 00:13:31,260 --> 00:13:32,490 You've got to know how you feel about stuff. 319 00:13:32,490 --> 00:13:35,750 That's what completeness is. 320 00:13:35,750 --> 00:13:40,780 So armed with those assumptions, there are four 321 00:13:40,780 --> 00:13:43,530 key properties of indifference curves that we have 322 00:13:43,530 --> 00:13:44,700 to keep track of. 323 00:13:44,700 --> 00:13:48,010 Four key properties of indifference curves. 324 00:13:48,010 --> 00:13:51,770 The first is that consumers prefer higher 325 00:13:51,770 --> 00:13:53,440 indifference curves. 326 00:13:53,440 --> 00:13:58,410 So you prefer higher indifference curves. 327 00:14:02,140 --> 00:14:03,620 Prefer higher indifference curves. 328 00:14:03,620 --> 00:14:05,290 What I mean by that is, the further out the indifference 329 00:14:05,290 --> 00:14:06,920 curve, the more you prefer it. 330 00:14:06,920 --> 00:14:11,060 And this comes naturally from the non-satiation assumption. 331 00:14:11,060 --> 00:14:14,340 Given that we've assumed non-satiation, you must always 332 00:14:14,340 --> 00:14:16,690 prefer an indifference curve that's further from the origin 333 00:14:16,690 --> 00:14:19,770 because it's more, and more is better. 334 00:14:19,770 --> 00:14:22,960 OK so given non-satiation, you will always prefer an 335 00:14:22,960 --> 00:14:26,100 indifference curves that are further from the origin. 336 00:14:26,100 --> 00:14:29,000 That follows directly from non-satiation. 337 00:14:31,610 --> 00:14:39,750 The second point is that indifference curves are always 338 00:14:39,750 --> 00:14:41,000 downward sloping. 339 00:14:45,640 --> 00:14:47,705 Indifference curves are always downward sloping. 340 00:14:51,994 --> 00:14:54,050 Indifference curves are always downward sloping. 341 00:14:54,050 --> 00:14:56,160 And that, once again, comes from non-satiation. 342 00:14:56,160 --> 00:14:59,040 To see this, let's look at the next figure, an upward sloping 343 00:14:59,040 --> 00:15:02,020 indifference curve. 344 00:15:02,020 --> 00:15:04,320 Why does an upward sloping indifference curve, someone 345 00:15:04,320 --> 00:15:07,529 tell me, violate non-satiation. 346 00:15:07,529 --> 00:15:08,002 Yeah? 347 00:15:08,002 --> 00:15:10,367 AUDIENCE: Because you're indifferent to getting more. 348 00:15:10,367 --> 00:15:10,681 PROFESSOR: Yeah. 349 00:15:10,681 --> 00:15:11,850 Because this would say you're indifferent 350 00:15:11,850 --> 00:15:13,480 between (1,1) and (2,2). 351 00:15:13,480 --> 00:15:14,770 It's not quite drawn right. 352 00:15:14,770 --> 00:15:18,010 We ought to just have this go through to point (2,2). 353 00:15:18,010 --> 00:15:20,710 But basically, this would say you're indifferent between 354 00:15:20,710 --> 00:15:22,610 getting one pizza and one movie or two 355 00:15:22,610 --> 00:15:23,870 pizzas and two movies. 356 00:15:23,870 --> 00:15:26,880 You can't be because that violates more is better. 357 00:15:26,880 --> 00:15:29,710 So indifference curves can't be upward sloping, they've got 358 00:15:29,710 --> 00:15:33,510 to be downward sloping by the non-satiation assumption. 359 00:15:33,510 --> 00:15:37,890 OK, that's the second property of indifference curves. 360 00:15:37,890 --> 00:15:40,730 The third property of indifference curves is 361 00:15:40,730 --> 00:15:42,530 indifference curves cannot cross. 362 00:15:46,150 --> 00:15:50,080 Indifference curves cannot cross. 363 00:15:50,080 --> 00:15:51,910 Why can't indifference curves cross? 364 00:15:51,910 --> 00:15:54,405 Well here I forgot to have Jessica do a pretty diagram, 365 00:15:54,405 --> 00:15:57,840 so you'll have to deal with my ugly handwriting here. 366 00:15:57,840 --> 00:16:00,720 So why can't indifferent curves cross? 367 00:16:00,720 --> 00:16:03,820 Well imagine a situation where you have your 368 00:16:03,820 --> 00:16:06,230 pizza and your movies. 369 00:16:06,230 --> 00:16:11,690 And imagine a situation where you have one indifference 370 00:16:11,690 --> 00:16:14,150 curve that looks like this, and one indifference curve 371 00:16:14,150 --> 00:16:15,840 that looks like this. 372 00:16:15,840 --> 00:16:17,480 OK, two indifference curves. 373 00:16:17,480 --> 00:16:25,570 And you've got, let's label these points A, B, and C. 374 00:16:25,570 --> 00:16:28,810 Now could someone give me, based on the properties of 375 00:16:28,810 --> 00:16:31,405 indifference curves that we talked about over here, given 376 00:16:31,405 --> 00:16:33,030 these three properties, can someone tell me 377 00:16:33,030 --> 00:16:35,440 why this is a violation? 378 00:16:35,440 --> 00:16:35,845 Yeah? 379 00:16:35,845 --> 00:16:38,628 AUDIENCE: Because A and B are on the same curve, meaning 380 00:16:38,628 --> 00:16:41,405 you're indifferent between A and B. A and C are also on the 381 00:16:41,405 --> 00:16:43,990 same curve because you're indifferent between the two. 382 00:16:43,990 --> 00:16:46,693 But that means you're also indifferent between B and C 383 00:16:46,693 --> 00:16:48,426 which can't be true because more is better. 384 00:16:48,426 --> 00:16:49,490 PROFESSOR: Exactly. 385 00:16:49,490 --> 00:16:52,050 So transitivity says I must then be indifferent between B 386 00:16:52,050 --> 00:16:54,200 and C through the logic you just laid out. 387 00:16:54,200 --> 00:16:56,090 But I can't be indifferent between B and C because B 388 00:16:56,090 --> 00:17:00,390 dominates C. B has a basically the same number of movies, but 389 00:17:00,390 --> 00:17:03,040 more pizza, so I must like B better. 390 00:17:03,040 --> 00:17:06,810 So by the combination of transitivity and non-satiation 391 00:17:06,810 --> 00:17:09,930 indifference curves can't cross. 392 00:17:09,930 --> 00:17:13,269 And finally, completeness, which is the most awkward of 393 00:17:13,269 --> 00:17:15,770 these assumptions, it simply means you can't have more than 394 00:17:15,770 --> 00:17:18,930 one indifference curve through a point. 395 00:17:18,930 --> 00:17:24,790 So basically, the idea of every possible bundle has one 396 00:17:24,790 --> 00:17:25,730 indifference curve. 397 00:17:25,730 --> 00:17:27,399 You can't have two indifference curves through it 398 00:17:27,399 --> 00:17:29,250 sayin, I'm not sure which indifference curve I'm on. 399 00:17:29,250 --> 00:17:30,650 I'm not sure how I feel about this. 400 00:17:30,650 --> 00:17:31,560 You know how you feel. 401 00:17:31,560 --> 00:17:34,120 There's one indifference curve through every bundle. 402 00:17:34,120 --> 00:17:37,150 There's not two indifference curves through a bundle. 403 00:17:37,150 --> 00:17:40,800 So this is the way we think about preference maps which is 404 00:17:40,800 --> 00:17:44,350 the sort of core building block of utility theory. 405 00:17:44,350 --> 00:17:48,960 Now I was an undergrad here, took this course, but I never 406 00:17:48,960 --> 00:17:51,820 really understood indifference curves until I had a year off 407 00:17:51,820 --> 00:17:54,900 with a grad student who was trying to decide where to take 408 00:17:54,900 --> 00:17:57,672 a job and he did it through just showing me an 409 00:17:57,672 --> 00:17:58,900 indifference map. 410 00:17:58,900 --> 00:18:00,680 He said look, I'm trying to decide where to take a job, 411 00:18:00,680 --> 00:18:01,600 and I care about two things. 412 00:18:01,600 --> 00:18:04,730 I care about how good the place is and where it is. 413 00:18:04,730 --> 00:18:09,230 So he said here, he had location and he 414 00:18:09,230 --> 00:18:10,870 had academic rank. 415 00:18:13,690 --> 00:18:21,060 And he said look, I'm indifferent between Princeton 416 00:18:21,060 --> 00:18:26,130 which has a shitty location but a wonderful academic rank. 417 00:18:26,130 --> 00:18:28,680 I'm from New Jersey, but it's still a shitty location. 418 00:18:28,680 --> 00:18:32,240 OK, and Santa Cruz. 419 00:18:32,240 --> 00:18:37,130 And Santa Cruz which has not such a good academic 420 00:18:37,130 --> 00:18:39,250 reputation, but a pretty awesome location. 421 00:18:39,250 --> 00:18:42,680 And he said here's my indifference map. 422 00:18:42,680 --> 00:18:43,810 And where did he end up going? 423 00:18:43,810 --> 00:18:47,730 He ended up going to the IMF, the international monetary 424 00:18:47,730 --> 00:18:51,970 fund in DC which had a better location than Princeton-- 425 00:18:51,970 --> 00:18:54,075 worse than Santa Cruz, but a better reputation than Santa 426 00:18:54,075 --> 00:18:55,640 Cruz and worse than Princeton. 427 00:18:55,640 --> 00:18:57,710 So he decided he was indifferent along this map, 428 00:18:57,710 --> 00:19:00,180 and he ended up choosing a point in the middle. 429 00:19:00,180 --> 00:19:02,700 But indifference curves are just a way of representing two 430 00:19:02,700 --> 00:19:05,090 dimensional choices. 431 00:19:05,090 --> 00:19:07,110 Now very few choice in life are really two dimensional, 432 00:19:07,110 --> 00:19:08,100 but that's a nice example. 433 00:19:08,100 --> 00:19:08,865 Question in the back? 434 00:19:08,865 --> 00:19:12,590 AUDIENCE: I was wondering if IMF, the point would be 435 00:19:12,590 --> 00:19:14,825 actually not on the curve, but further out? 436 00:19:14,825 --> 00:19:15,719 PROFESSOR: If it were further out. 437 00:19:15,719 --> 00:19:17,225 A great question. 438 00:19:17,225 --> 00:19:18,740 So imagine if IMF were here. 439 00:19:21,490 --> 00:19:24,054 What should he have done? 440 00:19:24,054 --> 00:19:25,380 Definitely go to IMF. 441 00:19:25,380 --> 00:19:26,700 Here he was indifferent. 442 00:19:26,700 --> 00:19:29,560 He could flip a coin and be equally happy at all three. 443 00:19:29,560 --> 00:19:31,610 But if IMF were out here, and maybe it was because that's 444 00:19:31,610 --> 00:19:32,520 what he chose. 445 00:19:32,520 --> 00:19:33,120 That's a good point. 446 00:19:33,120 --> 00:19:36,440 I don't know if IMF was here or here. 447 00:19:36,440 --> 00:19:39,380 The fact that he chose IMF, it can reveal it 448 00:19:39,380 --> 00:19:40,390 wasn't anywhere in here. 449 00:19:40,390 --> 00:19:41,760 It's a very good point actually. 450 00:19:41,760 --> 00:19:44,510 It can reveal it wasn't anywhere in here. 451 00:19:44,510 --> 00:19:45,510 That we know. 452 00:19:45,510 --> 00:19:47,420 But I can't tell if it was on the curve 453 00:19:47,420 --> 00:19:49,030 or outside the curve. 454 00:19:49,030 --> 00:19:49,890 It could have been on the curve because he's 455 00:19:49,890 --> 00:19:51,720 indifferent, so who knows, he could have flipped the coin. 456 00:19:51,720 --> 00:19:53,470 Or it could have been outside the curve because it's better. 457 00:19:53,470 --> 00:19:54,360 We can't tell that. 458 00:19:54,360 --> 00:19:56,220 That's a good point. 459 00:19:56,220 --> 00:19:57,110 All right. 460 00:19:57,110 --> 00:19:58,590 So that's a preference map. 461 00:19:58,590 --> 00:20:00,950 That's indifference curves. 462 00:20:00,950 --> 00:20:03,890 Now let's step from indifference curves, which is 463 00:20:03,890 --> 00:20:07,935 a building block of preferences, to utility. 464 00:20:12,710 --> 00:20:15,180 Now everything you need to know about preferences is 465 00:20:15,180 --> 00:20:17,920 represented in those indifference maps. 466 00:20:17,920 --> 00:20:21,630 The problem is they're pretty awkward to work with when we 467 00:20:21,630 --> 00:20:25,990 need to actually prove theorems and solve and 468 00:20:25,990 --> 00:20:27,880 understand how people make decisions. 469 00:20:27,880 --> 00:20:31,060 That's a lot easier if we have a mathematical representation 470 00:20:31,060 --> 00:20:32,540 of those preference maps. 471 00:20:32,540 --> 00:20:35,280 And that's the utility function 472 00:20:35,280 --> 00:20:40,200 So the utility function is a mathematical representation of 473 00:20:40,200 --> 00:20:40,770 preferences. 474 00:20:40,770 --> 00:20:41,950 That's all it is. 475 00:20:41,950 --> 00:20:45,415 You're going to be hearing this term in your nightmares 476 00:20:45,415 --> 00:20:46,910 for the next semester. 477 00:20:46,910 --> 00:20:48,060 Utility functions. 478 00:20:48,060 --> 00:20:51,520 But remember, it's just a mathematical representation of 479 00:20:51,520 --> 00:20:52,950 people's underlying preferences. 480 00:20:52,950 --> 00:20:55,890 Don't be scared of it. 481 00:20:55,890 --> 00:20:58,450 And the key thing is that we assume individuals have these 482 00:20:58,450 --> 00:21:01,820 well-defined utility functions, and by maximizing 483 00:21:01,820 --> 00:21:03,840 those utility functions we can tell what choices they're 484 00:21:03,840 --> 00:21:05,060 going to make. 485 00:21:05,060 --> 00:21:09,120 So for example, suppose that I said that your utility 486 00:21:09,120 --> 00:21:13,660 function over pizza and movies was the square root of pizza 487 00:21:13,660 --> 00:21:16,390 times movies. 488 00:21:16,390 --> 00:21:17,360 That's a utility function. 489 00:21:17,360 --> 00:21:18,270 I'm going to say, what the hell does that mean? 490 00:21:18,270 --> 00:21:19,570 Well, it doesn't mean anything, 491 00:21:19,570 --> 00:21:20,820 it's a utility function. 492 00:21:20,820 --> 00:21:21,900 It's your preferences. 493 00:21:21,900 --> 00:21:23,280 It's a mathematical representation of your 494 00:21:23,280 --> 00:21:24,530 preferences. 495 00:21:26,590 --> 00:21:27,730 What does that mean? 496 00:21:27,730 --> 00:21:29,440 What it means is-- 497 00:21:29,440 --> 00:21:32,290 it doesn't mean anything inherently, but it tells us 498 00:21:32,290 --> 00:21:33,960 about your preferences. 499 00:21:33,960 --> 00:21:36,880 What it tells us is that your preferences can be 500 00:21:36,880 --> 00:21:38,450 represented. 501 00:21:38,450 --> 00:21:43,030 If you flip back to figure 4-1b, it tells us those are 502 00:21:43,030 --> 00:21:47,350 your preferences because you're indifferent between two 503 00:21:47,350 --> 00:21:50,390 pizzas and one movie and one pizza and two movies. 504 00:21:50,390 --> 00:21:50,890 Of course you're indifferent. 505 00:21:50,890 --> 00:21:53,860 They both give a utility square root two. 506 00:21:53,860 --> 00:21:56,265 But you prefer two pizzas and two movies because that gives 507 00:21:56,265 --> 00:21:58,140 a utility of two. 508 00:21:58,140 --> 00:22:00,650 So this is a mathematical representation consistent with 509 00:22:00,650 --> 00:22:02,110 those utility indifference curves. 510 00:22:02,110 --> 00:22:03,540 Not the only one. 511 00:22:03,540 --> 00:22:04,910 There's other mathematical representations that could be 512 00:22:04,910 --> 00:22:06,750 consistent with those indifference curves. 513 00:22:06,750 --> 00:22:09,760 But let's posit that this is your utility function. 514 00:22:09,760 --> 00:22:13,260 This is a mathematical representation of your tastes. 515 00:22:13,260 --> 00:22:15,120 Now what does utility mean? 516 00:22:15,120 --> 00:22:20,040 Utility means nothing in the sense that it is not a 517 00:22:20,040 --> 00:22:21,035 cardinal concept. 518 00:22:21,035 --> 00:22:23,690 It's only an ordinal concept. 519 00:22:23,690 --> 00:22:30,110 So if I say to you that you get two utils from two pizzas 520 00:22:30,110 --> 00:22:32,290 and two movies, that doesn't mean anything. 521 00:22:32,290 --> 00:22:35,450 It just means that you get more than from one 522 00:22:35,450 --> 00:22:36,420 pizza and one movie. 523 00:22:36,420 --> 00:22:39,080 And we can even get the ratio that you get square root of 524 00:22:39,080 --> 00:22:43,320 two more, than you get from one pizza and two movies. 525 00:22:43,320 --> 00:22:46,340 We can do ranking and ordinality, but we can't 526 00:22:46,340 --> 00:22:47,560 assign cardinality. 527 00:22:47,560 --> 00:22:52,260 I can't say how happy you are in some abstract absolute 528 00:22:52,260 --> 00:22:54,120 sense from two pizzas and one movie. 529 00:22:54,120 --> 00:22:56,270 I can't give a cardinal form preference. 530 00:22:56,270 --> 00:22:58,150 But this is an ordinal ranking of preferences. 531 00:22:58,150 --> 00:23:01,130 I can tell what you like better than what else. 532 00:23:01,130 --> 00:23:03,192 That's why utility function is a representation of 533 00:23:03,192 --> 00:23:04,400 indifference maps. 534 00:23:04,400 --> 00:23:07,340 They're just a mathematical tool for comparing bundles, 535 00:23:07,340 --> 00:23:09,710 they're not some inner answer to the value of your soul or 536 00:23:09,710 --> 00:23:11,250 something like that. 537 00:23:11,250 --> 00:23:12,660 Don't imbue these with too much magic. 538 00:23:12,660 --> 00:23:15,050 They're just mathematical ways of representing preferences. 539 00:23:18,110 --> 00:23:22,530 The key concept, the single most important concept, for 540 00:23:22,530 --> 00:23:25,170 consumer theory for understanding how consumers 541 00:23:25,170 --> 00:23:28,245 make decisions is the concept of marginal utility. 542 00:23:32,690 --> 00:23:35,150 We'll talk a lot this semester about marginal this and 543 00:23:35,150 --> 00:23:36,560 marginal that. 544 00:23:36,560 --> 00:23:38,220 And this is our first example. 545 00:23:38,220 --> 00:23:40,840 Marginal utility. 546 00:23:40,840 --> 00:23:45,740 That is how your utility changes with each additional 547 00:23:45,740 --> 00:23:47,390 unit of the good, or the derivative 548 00:23:47,390 --> 00:23:49,150 of the utility function. 549 00:23:49,150 --> 00:23:51,025 If you want to do it in calculus terms, marginal 550 00:23:51,025 --> 00:23:52,790 utility is the derivative of your utility function with 551 00:23:52,790 --> 00:23:55,080 respect to one of the inputs. 552 00:23:55,080 --> 00:23:57,490 But if you don't want to put it in calculus terms, it's as 553 00:23:57,490 --> 00:24:01,040 you add each unit of one of the elements of the utility 554 00:24:01,040 --> 00:24:05,130 function, how does utility change 555 00:24:05,130 --> 00:24:08,380 So to see this, let's do an example of marginal utility. 556 00:24:08,380 --> 00:24:13,330 Imagine for a moment that you have two pizzas, p equals two. 557 00:24:13,330 --> 00:24:14,730 You've got two pizzas, they're there. 558 00:24:14,730 --> 00:24:16,660 Your roommate's got them or something. 559 00:24:16,660 --> 00:24:20,910 OK, now I want to ask, how does your utility change as 560 00:24:20,910 --> 00:24:23,060 you see additional movies? 561 00:24:23,060 --> 00:24:25,060 And to show that, let's look at figure 562 00:24:25,060 --> 00:24:28,310 4-3 which isn't here. 563 00:24:28,310 --> 00:24:29,410 Whoops. 564 00:24:29,410 --> 00:24:30,982 There's no figure 4-3. 565 00:24:30,982 --> 00:24:32,100 Do you got that figure 4-3? 566 00:24:32,100 --> 00:24:33,865 AUDIENCE: There was never any figure 4-3. 567 00:24:33,865 --> 00:24:37,310 PROFESSOR: There was never any figure 4-3. 568 00:24:37,310 --> 00:24:39,620 So let's go to 4-5. 569 00:24:43,370 --> 00:24:43,933 So basically-- 570 00:24:43,933 --> 00:24:46,588 AUDIENCE: Figure 4-4? 571 00:24:46,588 --> 00:24:47,838 PROFESSOR: No but-- 572 00:24:52,200 --> 00:24:53,110 actually fine. 573 00:24:53,110 --> 00:24:53,620 4-4. 574 00:24:53,620 --> 00:24:56,460 So basically what this is showing, what figure 4-4 is 575 00:24:56,460 --> 00:25:00,010 showing, is it showing how-- 576 00:25:00,010 --> 00:25:01,970 no actually, let's go to 4-5. 577 00:25:01,970 --> 00:25:02,910 They're out of order. 578 00:25:02,910 --> 00:25:04,120 Let's go to 4-5. 579 00:25:04,120 --> 00:25:06,420 What 4-5 is showing-- 580 00:25:06,420 --> 00:25:07,780 no, that's not going to work. 581 00:25:07,780 --> 00:25:09,540 OK, back to 4-4. 582 00:25:09,540 --> 00:25:14,600 What figure 4-4 is showing, is it's showing how your marginal 583 00:25:14,600 --> 00:25:18,650 utility for movies evolves, how your utility evolves as 584 00:25:18,650 --> 00:25:20,590 you get more movies. 585 00:25:20,590 --> 00:25:24,370 Given that you have two pizzas, this is the evolution 586 00:25:24,370 --> 00:25:28,440 of your utility as you get more movies. 587 00:25:28,440 --> 00:25:31,900 So each additional movie increases your utility. 588 00:25:31,900 --> 00:25:33,390 The slope is positive. 589 00:25:33,390 --> 00:25:35,610 By more is better, we know that. 590 00:25:35,610 --> 00:25:40,420 Even if it's some date movie, it still 591 00:25:40,420 --> 00:25:42,510 improves your utility. 592 00:25:42,510 --> 00:25:46,590 So it still improves your utility, but at 593 00:25:46,590 --> 00:25:48,010 a diminishing rate. 594 00:25:48,010 --> 00:25:50,910 And that's the key is that we assume 595 00:25:50,910 --> 00:25:58,020 diminishing marginal utility. 596 00:25:58,020 --> 00:26:00,550 The key assumption underlies everything we'll do for 597 00:26:00,550 --> 00:26:05,110 consumers is diminishing marginal utility. 598 00:26:05,110 --> 00:26:09,190 We assume that additional movie increases your utility, 599 00:26:09,190 --> 00:26:13,430 but at an ever diminishing rate. 600 00:26:13,430 --> 00:26:19,670 So basically, we can actually graph your margins. 601 00:26:19,670 --> 00:26:22,970 And that's what figure 4-5 is, is a graph of 602 00:26:22,970 --> 00:26:24,220 your marginal utility. 603 00:26:28,980 --> 00:26:38,080 So basically, when you have two pizzas and one movie, 604 00:26:38,080 --> 00:26:40,720 utility is square root of 2, right? 605 00:26:40,720 --> 00:26:45,860 Now what I'm saying is if you get one more movie, your 606 00:26:45,860 --> 00:26:49,120 utility is going to rise from square root of 2 to 2. 607 00:26:49,120 --> 00:26:53,262 So the marginal utility of that next movie -- 608 00:26:53,262 --> 00:26:54,711 is that right? 609 00:26:54,711 --> 00:26:56,160 Two movies. 610 00:26:56,160 --> 00:26:58,740 1.4. 611 00:26:58,740 --> 00:27:00,840 Yeah, it's going to rise by the square root of 2. 612 00:27:00,840 --> 00:27:03,746 You're going to multiply your utility by the square root of 613 00:27:03,746 --> 00:27:05,110 two, so your marginal utility-- 614 00:27:05,110 --> 00:27:08,140 you're going to go from the utility of square root of 2 to 615 00:27:08,140 --> 00:27:09,580 utility of two. 616 00:27:09,580 --> 00:27:11,730 So utility is going to increase by the 617 00:27:11,730 --> 00:27:14,170 square root of 2. 618 00:27:14,170 --> 00:27:15,400 Utility is going to increase-- 619 00:27:15,400 --> 00:27:16,681 I'm doing this wrong, hold on. 620 00:27:20,120 --> 00:27:21,370 One second. 621 00:27:24,000 --> 00:27:25,030 From one movie. 622 00:27:25,030 --> 00:27:25,520 I see. 623 00:27:25,520 --> 00:27:25,850 I see. 624 00:27:25,850 --> 00:27:26,650 So, I'm sorry. 625 00:27:26,650 --> 00:27:28,710 This isn't the delta, this is the level of marginal utility. 626 00:27:28,710 --> 00:27:30,010 So I'm graphing the actual level of marginal utility. 627 00:27:30,010 --> 00:27:30,700 Back up. 628 00:27:30,700 --> 00:27:33,115 OK, so I'm graphing the actual level of marginal utility. 629 00:27:36,960 --> 00:27:41,880 So when you have two pizzas and one movie, your marginal 630 00:27:41,880 --> 00:27:44,730 utility, your actual utility-- 631 00:27:44,730 --> 00:27:46,020 I see, that's what this is. 632 00:27:46,020 --> 00:27:47,480 This is the actual utility I'm graphing. 633 00:27:47,480 --> 00:27:49,270 So I told you a minute ago, we can't measure utility as a 634 00:27:49,270 --> 00:27:52,290 cardinal concept, but actually here I'm doing it anyway 635 00:27:52,290 --> 00:27:54,190 because it's to illustrate marginal utility. 636 00:27:54,190 --> 00:27:56,120 So your utility, OK. 637 00:27:56,120 --> 00:28:01,250 When you have one movie is 1.4, square root of 2. 638 00:28:01,250 --> 00:28:02,990 That's your utility. 639 00:28:02,990 --> 00:28:10,720 Now when you move from one movie to a second movie, your 640 00:28:10,720 --> 00:28:13,320 utility goes up from square root of 2 to 2. 641 00:28:13,320 --> 00:28:15,700 Your utility goes up by 0.6. 642 00:28:15,700 --> 00:28:19,560 So the marginal utility of that second movie is 0.6. 643 00:28:19,560 --> 00:28:23,680 Utility was 1.4, was a square root of 2. 644 00:28:23,680 --> 00:28:25,930 Now it's increased to 2. 645 00:28:25,930 --> 00:28:28,480 So the marginal utility of the first movie is 0.6. 646 00:28:28,480 --> 00:28:31,390 Now let's say you add another movie, you go to three movies. 647 00:28:31,390 --> 00:28:32,190 What's your utility now? 648 00:28:32,190 --> 00:28:34,280 It's the square root of 6. 649 00:28:34,280 --> 00:28:37,020 So it's gone from 4, to the square root 650 00:28:37,020 --> 00:28:40,070 of 6, which is 2.45. 651 00:28:40,070 --> 00:28:44,380 So your marginal utility of the third movie is 0.45. 652 00:28:44,380 --> 00:28:46,850 This graph is messed up because the first one is an 653 00:28:46,850 --> 00:28:48,450 actual utility level. 654 00:28:48,450 --> 00:28:49,873 So the first one I say, for one movie, you 655 00:28:49,873 --> 00:28:51,630 have a utility 1.4. 656 00:28:51,630 --> 00:28:54,260 And then for the second movie, I give the marginal utility, 657 00:28:54,260 --> 00:28:55,800 the third movie marginal utility. 658 00:28:55,800 --> 00:28:56,950 So, this graph sort of-- yeah? 659 00:28:56,950 --> 00:28:59,720 AUDIENCE: It shows the marginal utility of the very 660 00:28:59,720 --> 00:29:00,499 first movie. 661 00:29:00,499 --> 00:29:04,500 PROFESSOR: Yeah, I guess that's right 662 00:29:04,500 --> 00:29:05,200 because you're zero. 663 00:29:05,200 --> 00:29:06,390 You're zero movies. 664 00:29:06,390 --> 00:29:07,100 OK, right. 665 00:29:07,100 --> 00:29:07,410 You're right. 666 00:29:07,410 --> 00:29:08,820 OK, so the first one is the marginal utility of the very 667 00:29:08,820 --> 00:29:09,980 first movie, you're right. 668 00:29:09,980 --> 00:29:12,380 So the very first movie gives you marginal utility of 1.4 669 00:29:12,380 --> 00:29:13,840 because you go from 0 to square root of 2. 670 00:29:13,840 --> 00:29:14,420 That's right. 671 00:29:14,420 --> 00:29:15,490 My bad. 672 00:29:15,490 --> 00:29:17,610 So you go from 0 to square root of 2 to get a marginal 673 00:29:17,610 --> 00:29:20,473 utility of 1.4 for the first movie From square root of 2 to 674 00:29:20,473 --> 00:29:23,550 2, you get 0.6 the next movie. 675 00:29:23,550 --> 00:29:25,436 From 2 to square root of 6, you get 0.45 676 00:29:25,436 --> 00:29:26,950 for the third movie. 677 00:29:26,950 --> 00:29:29,950 For square root of 6 to square root of 8, you only get 0.38 678 00:29:29,950 --> 00:29:31,930 from the fourth movie, and so on. 679 00:29:31,930 --> 00:29:35,270 So the key point is that these marginal utilities are ever 680 00:29:35,270 --> 00:29:36,990 decreasing. 681 00:29:36,990 --> 00:29:42,790 Each additional movie gives you less incremental utility. 682 00:29:42,790 --> 00:29:44,385 And if you stop and think about it, 683 00:29:44,385 --> 00:29:45,720 it's kind of intuitive. 684 00:29:45,720 --> 00:29:47,620 Just stop and think, think about the movies you want to 685 00:29:47,620 --> 00:29:49,230 see right now. 686 00:29:49,230 --> 00:29:50,530 The four movies you want to see. 687 00:29:50,530 --> 00:29:53,970 Presumably whichever you ranked first would give you 688 00:29:53,970 --> 00:29:57,320 more utility to see than whichever you ranked second. 689 00:29:57,320 --> 00:29:58,860 And if you think the movies that are out right now are 690 00:29:58,860 --> 00:30:00,930 pretty crappy like I do, by the time you get to the fourth 691 00:30:00,930 --> 00:30:04,740 movie, you're not getting much utility from it at all. 692 00:30:04,740 --> 00:30:06,620 Thinking about movies that are out now, you're getting a lot 693 00:30:06,620 --> 00:30:08,650 of utility from that first movie you see. 694 00:30:08,650 --> 00:30:11,040 Marginal, extra utility from the first movie you see. 695 00:30:11,040 --> 00:30:13,200 But each additional one is giving you less and less. 696 00:30:13,200 --> 00:30:14,920 And that's the idea of diminishing marginal utility. 697 00:30:14,920 --> 00:30:18,370 Likewise with pizzas, if you haven't eaten all day, that 698 00:30:18,370 --> 00:30:21,050 first pizza can give you a very high marginal utility. 699 00:30:21,050 --> 00:30:23,950 The enjoyment you get from eating that first pizza can be 700 00:30:23,950 --> 00:30:25,890 very large. 701 00:30:25,890 --> 00:30:27,990 But the second pizza, not so much. 702 00:30:27,990 --> 00:30:29,240 You're already pretty full. 703 00:30:29,240 --> 00:30:29,840 Third pizza, even less. 704 00:30:29,840 --> 00:30:31,660 And then fourth pizza would probably violate 705 00:30:31,660 --> 00:30:34,030 non-satiation. 706 00:30:34,030 --> 00:30:35,000 So that's the basic idea. 707 00:30:35,000 --> 00:30:35,400 Yeah? 708 00:30:35,400 --> 00:30:37,276 AUDIENCE: I have a question. 709 00:30:37,276 --> 00:30:40,090 Do we assume that the goods are homogeneous. 710 00:30:40,090 --> 00:30:42,910 Is it the same movie watched four times? 711 00:30:42,910 --> 00:30:45,016 Or different movies? 712 00:30:45,016 --> 00:30:47,180 PROFESSOR: Actually, that's a great question. 713 00:30:47,180 --> 00:30:49,450 And you have to specify that as part of the problem. 714 00:30:49,450 --> 00:30:52,695 I haven't specified that here. 715 00:30:52,695 --> 00:30:54,710 Obviously it can't be the same pizza eaten four times. 716 00:30:54,710 --> 00:30:58,060 It could be the same kind of pizza eaten four times. 717 00:30:58,060 --> 00:31:03,340 But do you see the same movie? 718 00:31:03,340 --> 00:31:04,940 I haven't specified that here. 719 00:31:04,940 --> 00:31:06,615 So there's not a general assumption about that. 720 00:31:06,615 --> 00:31:08,775 It depends on how I define movies. 721 00:31:08,775 --> 00:31:12,870 Did I define movies as-- 722 00:31:12,870 --> 00:31:13,630 I don't know. 723 00:31:13,630 --> 00:31:14,170 God, I'm terrible. 724 00:31:14,170 --> 00:31:15,990 All I know that's out now is the Guardians of G'ahoole 725 00:31:15,990 --> 00:31:17,290 because I've got a little kid who is interested in it. 726 00:31:17,290 --> 00:31:18,330 Whatever movie's out. 727 00:31:18,330 --> 00:31:20,765 Do I define movies as Guardians of G'ahoole, or do I 728 00:31:20,765 --> 00:31:23,050 define movies as seeing a movie? 729 00:31:23,050 --> 00:31:24,340 And I didn't specify that. 730 00:31:24,340 --> 00:31:25,960 Implicit in my examples, I specify 731 00:31:25,960 --> 00:31:27,980 movies as seeing a movie. 732 00:31:27,980 --> 00:31:30,660 But you have to specify that to be more precise if you're 733 00:31:30,660 --> 00:31:32,510 actually trying to figure out-- 734 00:31:32,510 --> 00:31:34,330 it depends what you're maximizing over. 735 00:31:34,330 --> 00:31:36,270 If you're maximizing over seeing any movie or maximize 736 00:31:36,270 --> 00:31:37,970 over seeing the same movie. 737 00:31:37,970 --> 00:31:39,220 And I didn't specify here. 738 00:31:39,220 --> 00:31:40,080 AUDIENCE: It can work in both cases. 739 00:31:40,080 --> 00:31:41,830 PROFESSOR: It would work in both cases. 740 00:31:41,830 --> 00:31:43,590 Clearly you could imagine, actually it's a very good 741 00:31:43,590 --> 00:31:45,530 point, where do you think your marginal utility would 742 00:31:45,530 --> 00:31:47,590 diminish more? 743 00:31:47,590 --> 00:31:48,940 Seeing the same movie. 744 00:31:48,940 --> 00:31:52,530 So what your example points out is that different goods 745 00:31:52,530 --> 00:31:55,830 will have different rates of diminishing marginal utility. 746 00:31:55,830 --> 00:31:59,680 OK, so marginal utility will always be diminishing, but at 747 00:31:59,680 --> 00:32:02,500 very different rates for different goods. 748 00:32:02,500 --> 00:32:05,110 So the general principle is that they'll be generally 749 00:32:05,110 --> 00:32:07,370 diminishing marginal utility. 750 00:32:07,370 --> 00:32:09,530 But at different rates for different goods. 751 00:32:09,530 --> 00:32:13,390 So after all my mess ups, let me just review. 752 00:32:13,390 --> 00:32:15,430 Marginal utility is diminishing because each good 753 00:32:15,430 --> 00:32:16,380 is worth less to you. 754 00:32:16,380 --> 00:32:20,240 It's always positive because of non-satiation. 755 00:32:20,240 --> 00:32:24,140 And this graph represents the marginal utility you get from 756 00:32:24,140 --> 00:32:28,610 each movie you see conditional on having eaten two pizzas. 757 00:32:28,610 --> 00:32:30,450 Marginal utility is the increment from 758 00:32:30,450 --> 00:32:33,200 the next unit consumed. 759 00:32:33,200 --> 00:32:34,750 Now let's get back on track here. 760 00:32:34,750 --> 00:32:40,400 Now let's go to thinking about-- 761 00:32:40,400 --> 00:32:43,890 now that we have this concept of utility and marginal 762 00:32:43,890 --> 00:32:46,920 utility, let's now bring utility back 763 00:32:46,920 --> 00:32:48,570 to preference maps. 764 00:32:48,570 --> 00:32:52,500 Let's ask, given what we know about utility, what can this 765 00:32:52,500 --> 00:32:55,720 teach us about the shape of preference maps? 766 00:32:55,720 --> 00:32:59,910 What's the linkage between utility and preference maps? 767 00:32:59,910 --> 00:33:05,700 And that linkage comes through something we call the marginal 768 00:33:05,700 --> 00:33:06,950 rate of substitution. 769 00:33:09,520 --> 00:33:11,270 The marginal rate of substitution is the 770 00:33:11,270 --> 00:33:16,950 mathematical concept that links preference utility with 771 00:33:16,950 --> 00:33:19,290 preference maps. 772 00:33:19,290 --> 00:33:22,680 The marginal rate of substitution technically is 773 00:33:22,680 --> 00:33:24,710 the slope of the indifference curve. 774 00:33:24,710 --> 00:33:29,190 It's delta P over delta M. The slope of the indifference 775 00:33:29,190 --> 00:33:32,880 curve is the marginal rate of substitution. 776 00:33:32,880 --> 00:33:35,930 That's what it means graphically, but here's what 777 00:33:35,930 --> 00:33:39,120 you have to understand at a deeper level. 778 00:33:39,120 --> 00:33:42,590 What it really is, it's the rate which you are 779 00:33:42,590 --> 00:33:45,900 willing to trade off. 780 00:33:45,900 --> 00:33:50,010 The rate at which you are willing to trade off the 781 00:33:50,010 --> 00:33:52,180 y-axis for the x-axis. 782 00:33:52,180 --> 00:33:53,790 The rate at which you're willing to trade 783 00:33:53,790 --> 00:33:55,040 off pizza for movies. 784 00:33:57,510 --> 00:34:00,070 So that's what it means intuitively. 785 00:34:00,070 --> 00:34:04,720 The slope of the curve tells you that you're indifferent. 786 00:34:04,720 --> 00:34:06,630 Remember, you're indifferent between any points along with 787 00:34:06,630 --> 00:34:07,540 this indifference curve. 788 00:34:07,540 --> 00:34:12,260 You're indifferent between four pizzas and one movie, 789 00:34:12,260 --> 00:34:15,159 you're indifferent between two pizzas and two movies, and 790 00:34:15,159 --> 00:34:16,690 four movies and one pizza. 791 00:34:16,690 --> 00:34:17,679 You're indifferent along all those 792 00:34:17,679 --> 00:34:20,090 combinations of figure 4-6. 793 00:34:20,090 --> 00:34:23,739 The MRS is the slope of that curve telling you the rate at 794 00:34:23,739 --> 00:34:28,750 which you're willing to trade off pizza for movies. 795 00:34:28,750 --> 00:34:32,820 Now just a side note here, you're never, of course, 796 00:34:32,820 --> 00:34:34,179 actually trading. 797 00:34:34,179 --> 00:34:35,850 There's not some market where you bring a 798 00:34:35,850 --> 00:34:37,960 pizza and get a movie. 799 00:34:37,960 --> 00:34:40,659 So I didn't say trade, it's not like baseball cards. 800 00:34:40,659 --> 00:34:42,429 I said trade off. 801 00:34:42,429 --> 00:34:47,190 What I mean is ultimately you have some budget, and you have 802 00:34:47,190 --> 00:34:49,330 to allocate that budget. 803 00:34:49,330 --> 00:34:51,949 So if you decide to allocate it on pizzas, you can't 804 00:34:51,949 --> 00:34:53,190 allocate it on movies. 805 00:34:53,190 --> 00:34:55,215 Or the more you allocate on pizzas, the less you can 806 00:34:55,215 --> 00:34:56,239 allocate on movies. 807 00:34:56,239 --> 00:34:58,110 So there's always a trade-off. 808 00:34:58,110 --> 00:35:00,350 Remember, I said, economics is always about trade-offs. 809 00:35:00,350 --> 00:35:03,720 Given your limited budget, there's always a trade off. 810 00:35:03,720 --> 00:35:06,720 And the rate at which you're willing to trade off is your 811 00:35:06,720 --> 00:35:08,180 marginal rate of substitution. 812 00:35:08,180 --> 00:35:10,040 Given that you're going to have to trade off-- and we 813 00:35:10,040 --> 00:35:11,380 haven't got a bunch of constraints yet, we'll get to 814 00:35:11,380 --> 00:35:12,400 that next time-- 815 00:35:12,400 --> 00:35:13,713 the rate at which you're willing to is your marginal 816 00:35:13,713 --> 00:35:14,600 rate of substitution. 817 00:35:14,600 --> 00:35:14,865 Yeah? 818 00:35:14,865 --> 00:35:17,755 AUDIENCE: Is that rate usually related to the price? 819 00:35:17,755 --> 00:35:19,600 PROFESSOR: Ultimately no. 820 00:35:19,600 --> 00:35:20,090 I'm sorry. 821 00:35:20,090 --> 00:35:22,020 The marginal rate of substitution purely comes from 822 00:35:22,020 --> 00:35:23,310 your preferences. 823 00:35:23,310 --> 00:35:26,455 Ultimately to decide how much you actually consume, you'll 824 00:35:26,455 --> 00:35:28,250 need to bring in the price. 825 00:35:28,250 --> 00:35:30,850 So remember, I haven't talked about prices here, we haven't 826 00:35:30,850 --> 00:35:31,690 talked about that here. 827 00:35:31,690 --> 00:35:33,790 But this is a preference concept. 828 00:35:33,790 --> 00:35:34,970 This has nothing to do with prices. 829 00:35:34,970 --> 00:35:36,230 But you're getting ahead of us. 830 00:35:36,230 --> 00:35:39,990 We'll see next time, to decide how much you actually consume, 831 00:35:39,990 --> 00:35:41,570 you're going to relate the marginal rate of substitution 832 00:35:41,570 --> 00:35:43,190 to the prices you face in the market. 833 00:35:43,190 --> 00:35:46,010 And that will decide how much you consume. 834 00:35:46,010 --> 00:35:47,440 This is just a utility concept. 835 00:35:47,440 --> 00:35:47,720 Yeah? 836 00:35:47,720 --> 00:35:53,990 AUDIENCE: Did you say it was the y-axis or the x-axis? 837 00:35:53,990 --> 00:35:55,902 That would be negative? 838 00:35:55,902 --> 00:35:56,390 PROFESSOR: It's negative. 839 00:35:56,390 --> 00:35:57,110 Yes. 840 00:35:57,110 --> 00:35:58,740 Of course. 841 00:35:58,740 --> 00:36:00,080 Right, of course. 842 00:36:00,080 --> 00:36:03,620 The point is how many movies are you willing to give up to 843 00:36:03,620 --> 00:36:04,870 get another pizza? 844 00:36:07,870 --> 00:36:09,230 How many pizzas are you willing to give up to get 845 00:36:09,230 --> 00:36:10,010 another movie? 846 00:36:10,010 --> 00:36:13,010 MRS, it's very hard to remember what's on the top, 847 00:36:13,010 --> 00:36:13,490 what's on the bottom. 848 00:36:13,490 --> 00:36:14,620 Be very careful on this. 849 00:36:14,620 --> 00:36:17,080 But that's why I said remember it's the y-axis or the x-axis. 850 00:36:17,080 --> 00:36:19,870 It's how many pizzas you're willing to trade off to get 851 00:36:19,870 --> 00:36:21,120 another movie. 852 00:36:23,530 --> 00:36:26,870 Basically remember when I say trade off, here, this is not 853 00:36:26,870 --> 00:36:30,310 that you're literally trading, it's that ultimately you're 854 00:36:30,310 --> 00:36:31,720 going to have to make that trade-off. 855 00:36:31,720 --> 00:36:33,400 Ultimately when we come to the next lecture and face a budget 856 00:36:33,400 --> 00:36:35,670 constraint, you're going to have to decide how do I want 857 00:36:35,670 --> 00:36:37,540 to allocate my budget across pizzas and movies? 858 00:36:37,540 --> 00:36:41,650 The way you're going to decide that is by the relationship of 859 00:36:41,650 --> 00:36:45,220 how you feel about trading off one for the other. 860 00:36:45,220 --> 00:36:47,790 Now here's the key feature of the MRS which 861 00:36:47,790 --> 00:36:50,050 is the MRS is yeah? 862 00:36:50,050 --> 00:36:51,254 Question? 863 00:36:51,254 --> 00:36:51,706 Yeah. 864 00:36:51,706 --> 00:36:53,559 AUDIENCE: That and exchange rates are always changing 865 00:36:53,559 --> 00:36:54,870 depending on how much you happen to be trading. 866 00:36:54,870 --> 00:36:55,690 PROFESSOR: Exactly. 867 00:36:55,690 --> 00:37:00,010 The MRS is diminishing. 868 00:37:00,010 --> 00:37:02,180 Technically when you go to grad school, you realize that 869 00:37:02,180 --> 00:37:04,020 marginal utility isn't actually technically always 870 00:37:04,020 --> 00:37:04,440 diminishing. 871 00:37:04,440 --> 00:37:05,010 I said it is. 872 00:37:05,010 --> 00:37:06,210 For this course it is. 873 00:37:06,210 --> 00:37:09,400 But if you want to get mathematically correct, really 874 00:37:09,400 --> 00:37:11,550 what's always diminishing that you prove is the marginal rate 875 00:37:11,550 --> 00:37:14,670 of substitution is always diminishing. 876 00:37:14,670 --> 00:37:16,230 So we have diminishing marginal utility for the 877 00:37:16,230 --> 00:37:19,490 purpose of this course, but the really important concept 878 00:37:19,490 --> 00:37:23,320 is you have diminishing marginal rate of substitution. 879 00:37:23,320 --> 00:37:26,140 The rate at which you're willing to trade off pizza for 880 00:37:26,140 --> 00:37:31,030 movies is going to fall as you have less 881 00:37:31,030 --> 00:37:34,700 pizza and more movies. 882 00:37:34,700 --> 00:37:37,940 So to see that, look at this graph, and let's compute the 883 00:37:37,940 --> 00:37:41,060 marginal rate of substitution along each segment. 884 00:37:41,060 --> 00:37:42,050 So let's localize. 885 00:37:42,050 --> 00:37:44,170 Imagine the segments were linear, imagine we had two 886 00:37:44,170 --> 00:37:45,170 linear segments between these points. 887 00:37:45,170 --> 00:37:46,000 We don't. 888 00:37:46,000 --> 00:37:48,210 But imagine for a second we did. 889 00:37:48,210 --> 00:37:50,970 So the marginal rate of substitution from the first 890 00:37:50,970 --> 00:37:55,140 point, four pizzas and one movie, to the second point, 891 00:37:55,140 --> 00:37:57,940 two pizzas and two movies, the marginal rate of 892 00:37:57,940 --> 00:38:00,570 substitution is -2. 893 00:38:00,570 --> 00:38:06,380 You are willing to give up two pizzas to get one movie. 894 00:38:06,380 --> 00:38:08,980 This is the same graph, figure 4-6. 895 00:38:08,980 --> 00:38:11,160 This isn't on the graph, you have to write it on. 896 00:38:11,160 --> 00:38:13,300 So going from that first point to that second point, you're 897 00:38:13,300 --> 00:38:18,310 willing to give up two pizzas to get one movie. 898 00:38:18,310 --> 00:38:21,330 So that rate of marginal substitution is -2. 899 00:38:21,330 --> 00:38:25,620 However, when you're at two movies and two pizzas, and I 900 00:38:25,620 --> 00:38:29,220 say OK, how about giving up one more pizza to see movies? 901 00:38:29,220 --> 00:38:30,580 Now you say, wait a second. 902 00:38:30,580 --> 00:38:34,420 To give up one more pizza, I need to see two movies. 903 00:38:34,420 --> 00:38:36,390 My marginal rate of substitution on that second 904 00:38:36,390 --> 00:38:39,340 segment is -1/2. 905 00:38:39,340 --> 00:38:40,680 The marginal rate of substitution on the first 906 00:38:40,680 --> 00:38:41,990 segment is -2. 907 00:38:41,990 --> 00:38:43,940 The marginal rate of substitution on the second 908 00:38:43,940 --> 00:38:44,690 segment is -1/2. 909 00:38:44,690 --> 00:38:46,860 Once again, assuming they're not linear, so it's actually 910 00:38:46,860 --> 00:38:48,587 changing everywhere, but if they were linear, that's what 911 00:38:48,587 --> 00:38:49,480 it would be. 912 00:38:49,480 --> 00:38:51,610 Can someone tell me why? 913 00:38:51,610 --> 00:38:55,230 Why is the marginal rate of substitution falling? 914 00:38:55,230 --> 00:38:58,060 Why is the marginal rate of substitution lower on that 915 00:38:58,060 --> 00:38:59,959 second segment than on the first? 916 00:38:59,959 --> 00:39:04,699 AUDIENCE: Because marginal utility increases the fewer of 917 00:39:04,699 --> 00:39:06,446 something you have. 918 00:39:06,446 --> 00:39:07,950 PROFESSOR: Exactly. 919 00:39:07,950 --> 00:39:11,180 So go ahead, flesh it out, the fewer of somthing you have, so 920 00:39:11,180 --> 00:39:13,100 tell me in terms of the trade you're willing to make. 921 00:39:13,100 --> 00:39:17,315 AUDIENCE: You value it more, so you want to trade more of 922 00:39:17,315 --> 00:39:18,205 something else for it. 923 00:39:18,205 --> 00:39:22,893 PROFESSOR: The point is when I have four pizzas my marginal 924 00:39:22,893 --> 00:39:26,600 utility of that last pizza is not very high. 925 00:39:26,600 --> 00:39:30,380 And I'm fine to give up two pizzas-- 926 00:39:30,380 --> 00:39:32,360 and plus I'm only seeing one movie, there's a second movie 927 00:39:32,360 --> 00:39:33,820 I really want to see. 928 00:39:33,820 --> 00:39:36,220 So you say to me, look, I've got four pizzas, 929 00:39:36,220 --> 00:39:37,700 I'm seeing one movie. 930 00:39:37,700 --> 00:39:39,420 You say hey, there's a second movie out I 931 00:39:39,420 --> 00:39:40,460 know you want to see. 932 00:39:40,460 --> 00:39:42,500 I know you don't really value four pizzas. 933 00:39:42,500 --> 00:39:43,850 At the end, you're totally full. 934 00:39:43,850 --> 00:39:45,350 Would you be willing to give up two pizzas to see the 935 00:39:45,350 --> 00:39:45,720 second movie? 936 00:39:45,720 --> 00:39:47,380 And you're like, sure why not? 937 00:39:47,380 --> 00:39:50,210 Well once you have two pizzas and you've seen two movies, 938 00:39:50,210 --> 00:39:51,930 you're not that interested in a third movie and you'll be 939 00:39:51,930 --> 00:39:54,610 hungry if you have less than two pizzas, so then you say, 940 00:39:54,610 --> 00:39:55,060 wait a second. 941 00:39:55,060 --> 00:39:56,970 If you want me to give up another pizza, you've got to 942 00:39:56,970 --> 00:39:59,800 give me two movies. 943 00:39:59,800 --> 00:40:04,220 Because my marginal utility of pizzas is rising, my marginal 944 00:40:04,220 --> 00:40:07,570 utility of movies is falling. 945 00:40:07,570 --> 00:40:09,600 And that's why the marginal rate of substitution 946 00:40:09,600 --> 00:40:15,490 diminishes along the indifference curve. 947 00:40:15,490 --> 00:40:18,160 So that allows us to write mathematically the definition 948 00:40:18,160 --> 00:40:23,470 of the marginal rate of substitution is the negative 949 00:40:23,470 --> 00:40:26,180 of the marginal utility of movies, or more generally 950 00:40:26,180 --> 00:40:32,030 what's on the x-axis, over the marginal utility of pizza, or 951 00:40:32,030 --> 00:40:33,280 more generally what's on the y-axis. 952 00:40:35,980 --> 00:40:37,670 The marginal rate of substitution, the first key 953 00:40:37,670 --> 00:40:39,992 formula you need to know for this course, the marginal rate 954 00:40:39,992 --> 00:40:41,060 of substitution is equal to the 955 00:40:41,060 --> 00:40:42,310 ratio of marginal utilities. 956 00:40:44,840 --> 00:40:46,720 Now this is tricky. 957 00:40:49,660 --> 00:40:51,060 Maybe you guys don't find it tricky, it's the kind of thing 958 00:40:51,060 --> 00:40:52,010 I find tricky. 959 00:40:52,010 --> 00:40:57,810 Which is I defined it as delta y-axis over delta x-axis. 960 00:40:57,810 --> 00:40:59,930 And yet, when I defined here the marginal utilities, I 961 00:40:59,930 --> 00:41:01,880 flipped it. 962 00:41:01,880 --> 00:41:03,700 I did the marginal utility of what's on the x-axis over the 963 00:41:03,700 --> 00:41:04,810 marginal utility of what's on the y-axis. 964 00:41:04,810 --> 00:41:05,300 Why is that? 965 00:41:05,300 --> 00:41:06,430 Can anyone tell me why that is? 966 00:41:06,430 --> 00:41:08,154 Why is it flipped when defined in 967 00:41:08,154 --> 00:41:09,595 terms of marginal utilities? 968 00:41:09,595 --> 00:41:09,910 Yeah? 969 00:41:09,910 --> 00:41:12,518 AUDIENCE: It's a denominator. 970 00:41:12,518 --> 00:41:14,506 So utility over movies-- 971 00:41:17,460 --> 00:41:20,510 PROFESSOR: Well, let me try for slightly more, how does 972 00:41:20,510 --> 00:41:21,320 marginal utility relate? 973 00:41:21,320 --> 00:41:21,575 Yeah. 974 00:41:21,575 --> 00:41:28,291 AUDIENCE: Marginal utility is delta P over 975 00:41:28,291 --> 00:41:30,279 P. So it gets flipped. 976 00:41:30,279 --> 00:41:30,780 Because of-- 977 00:41:30,780 --> 00:41:32,140 PROFESSOR: OK. 978 00:41:32,140 --> 00:41:34,620 Yeah, you're giving the same answer, which 979 00:41:34,620 --> 00:41:35,490 is technically right. 980 00:41:35,490 --> 00:41:38,470 What I was more looking for but it's the intuitive version 981 00:41:38,470 --> 00:41:42,380 of that, marginal utility is a negative function of quantity. 982 00:41:42,380 --> 00:41:44,810 Marginal utility is a negative function of quantity. 983 00:41:44,810 --> 00:41:47,700 So the fact that it's a ratio of the quantity of pizza over 984 00:41:47,700 --> 00:41:50,000 the quantity of movies is the same thing as the marginal 985 00:41:50,000 --> 00:41:52,340 utility of movies over the marginal utility of pizza. 986 00:41:52,340 --> 00:41:54,890 Because marginal utility is a negative function of quantity. 987 00:41:54,890 --> 00:41:56,300 The more quantity you have, the lower is 988 00:41:56,300 --> 00:41:58,440 your marginal utility. 989 00:41:58,440 --> 00:42:01,060 And that's the key to understand. 990 00:42:01,060 --> 00:42:05,460 So it's the slope of the indifference curve which is 991 00:42:05,460 --> 00:42:07,485 the ratio of the marginal utilities, but it's the 992 00:42:07,485 --> 00:42:10,700 marginal utility of movies over pizza. 993 00:42:10,700 --> 00:42:14,290 Because what that's saying is that as you get more movies, 994 00:42:14,290 --> 00:42:17,730 you care less about each additional movie and ditto 995 00:42:17,730 --> 00:42:18,980 with pizzas. 996 00:42:20,870 --> 00:42:22,250 Let's just look at this for a minute, think about it 997 00:42:22,250 --> 00:42:23,270 intuitively for a minute. 998 00:42:23,270 --> 00:42:25,590 We've seen it graphically, we're seeing it 999 00:42:25,590 --> 00:42:27,510 mathematically, let's make sure we understand it 1000 00:42:27,510 --> 00:42:29,120 intuitively. 1001 00:42:29,120 --> 00:42:33,630 What this is saying is that as you get more movies-- 1002 00:42:33,630 --> 00:42:36,470 so let's relate this to the graph. 1003 00:42:36,470 --> 00:42:41,800 As you get more movies and less pizza, as you move down 1004 00:42:41,800 --> 00:42:45,160 that curve, more movies, less pizza, what's happening? 1005 00:42:45,160 --> 00:42:46,930 What's happening to the marginal utility of movies as 1006 00:42:46,930 --> 00:42:48,650 you move down that curve? 1007 00:42:48,650 --> 00:42:50,190 What direction is it heading? 1008 00:42:50,190 --> 00:42:51,500 AUDIENCE: It's decreasing. 1009 00:42:51,500 --> 00:42:51,870 PROFESSOR: What? 1010 00:42:51,870 --> 00:42:52,240 AUDIENCE: It's decreasing. 1011 00:42:52,240 --> 00:42:54,270 PROFESSOR: It's decreasing. 1012 00:42:54,270 --> 00:42:56,540 Because you're getting more movies and marginal utility is 1013 00:42:56,540 --> 00:42:58,260 a negative function of quantity. 1014 00:42:58,260 --> 00:43:02,770 Likewise, the marginal utility of pizza is increasing because 1015 00:43:02,770 --> 00:43:05,850 you're getting less pizza so you care 1016 00:43:05,850 --> 00:43:07,720 about each pizza more. 1017 00:43:07,720 --> 00:43:10,900 And that's why the marginal rate of substitution 1018 00:43:10,900 --> 00:43:12,150 diminishes. 1019 00:43:13,940 --> 00:43:16,470 That's why it diminishes because as you move down that 1020 00:43:16,470 --> 00:43:19,830 curve, the numerator is falling, the denominator is 1021 00:43:19,830 --> 00:43:20,690 increasing. 1022 00:43:20,690 --> 00:43:23,220 And that's why we have everywhere diminishing 1023 00:43:23,220 --> 00:43:24,470 marginal rates of substitution. 1024 00:43:27,790 --> 00:43:35,140 So another way to think about this is imagine for a moment 1025 00:43:35,140 --> 00:43:38,150 what life would be like if we didn't have diminishing 1026 00:43:38,150 --> 00:43:39,990 marginal rates of substitution. 1027 00:43:39,990 --> 00:43:42,460 And once again I'm going to try, once again Jessica, next 1028 00:43:42,460 --> 00:43:43,700 year we'll let you make this pretty. 1029 00:43:43,700 --> 00:43:46,450 But I'm going to try to draw it crudely here. 1030 00:43:46,450 --> 00:43:48,990 Let's do pizzas and movies again. 1031 00:43:52,570 --> 00:43:53,980 Let's do pizzas and movies again. 1032 00:43:58,240 --> 00:43:59,570 Movies and pizza. 1033 00:43:59,570 --> 00:44:01,639 And that's one, two, three, four. 1034 00:44:07,062 --> 00:44:10,000 One, two, three, four. 1035 00:44:10,000 --> 00:44:12,560 Now let's imagine that instead of diminishing marginal 1036 00:44:12,560 --> 00:44:16,230 utility and instead of indifference curves being 1037 00:44:16,230 --> 00:44:19,200 convex to the origin, imagine if indifference curves were 1038 00:44:19,200 --> 00:44:22,270 concave to the origin, which is what increasing marginal 1039 00:44:22,270 --> 00:44:24,355 rate substitution would imply. 1040 00:44:24,355 --> 00:44:26,200 So that would be something where you'd be indifferent 1041 00:44:26,200 --> 00:44:32,530 between four pizzas and one movie, between three pizzas 1042 00:44:32,530 --> 00:44:36,740 and two movies, and between one pizza and three movies. 1043 00:44:36,740 --> 00:44:38,680 So your indifference curve would look like that. 1044 00:44:38,680 --> 00:44:40,495 Not quite to scale, but you get it. 1045 00:44:40,495 --> 00:44:43,390 It would be concave to the origin instead of convex to 1046 00:44:43,390 --> 00:44:44,320 the origin. 1047 00:44:44,320 --> 00:44:47,930 In this case, marginal rates of substitution would be 1048 00:44:47,930 --> 00:44:49,830 everywhere increasing. 1049 00:44:49,830 --> 00:44:53,370 That is, basically I'd be willing to give up one pizza 1050 00:44:53,370 --> 00:44:55,390 to get one movie. 1051 00:44:55,390 --> 00:44:58,670 But to get that next movie, I'd give up two pizzas. 1052 00:44:58,670 --> 00:45:02,050 But as you can see, that doesn't make sense. 1053 00:45:02,050 --> 00:45:04,900 It doesn't make sense that given that as long as you're 1054 00:45:04,900 --> 00:45:07,250 ranking movies, or even more in the example of seeing the 1055 00:45:07,250 --> 00:45:08,590 same movie over and over again, it's maybe more 1056 00:45:08,590 --> 00:45:11,050 compelling. 1057 00:45:11,050 --> 00:45:15,810 That basically what you can see is that if you're willing 1058 00:45:15,810 --> 00:45:19,310 to give up one pizza to see that movie a second time, why 1059 00:45:19,310 --> 00:45:22,550 would you possibly give up two pizzas to see it a third time? 1060 00:45:22,550 --> 00:45:24,340 That makes no sense at all. 1061 00:45:24,340 --> 00:45:27,210 If you only like it so much you only give up one pizza to 1062 00:45:27,210 --> 00:45:29,740 see it a second time, why would you possibly give up two 1063 00:45:29,740 --> 00:45:30,870 pizzas to see it a third time? 1064 00:45:30,870 --> 00:45:32,510 You wouldn't. 1065 00:45:32,510 --> 00:45:33,650 It doesn't make sense. 1066 00:45:33,650 --> 00:45:36,930 And that's why marginal rate of substitution has to be 1067 00:45:36,930 --> 00:45:39,520 everywhere decreasing, it can't be increasing. 1068 00:45:39,520 --> 00:45:39,795 Yeah? 1069 00:45:39,795 --> 00:45:42,450 AUDIENCE: Could it remain constant? 1070 00:45:42,450 --> 00:45:43,858 PROFESSOR: It could actually remain constant. 1071 00:45:43,858 --> 00:45:45,070 Yes, that's right. 1072 00:45:45,070 --> 00:45:46,230 You can be indifferent. 1073 00:45:46,230 --> 00:45:48,640 My indifference curves-- 1074 00:45:48,640 --> 00:45:51,210 how many of you guys have seen Toy Story 3? 1075 00:45:51,210 --> 00:45:53,480 I think it's one of my 10 favorite movies of all time. 1076 00:45:53,480 --> 00:45:55,970 The greatest children's movie ever made. 1077 00:45:55,970 --> 00:45:56,900 I've seen it three times. 1078 00:45:56,900 --> 00:45:58,050 My indifference curve is virtually-- 1079 00:45:58,050 --> 00:45:59,625 I've enjoyed it the third times as much as the first-- 1080 00:45:59,625 --> 00:46:02,840 it's virtually flat with respect to Toy Story 3. 1081 00:46:02,840 --> 00:46:05,870 I could see it 10 more times and feel pretty much the same. 1082 00:46:05,870 --> 00:46:08,340 So that's certainly possible that it would be constant, 1083 00:46:08,340 --> 00:46:10,110 that I'd be willing to give up whatever I pay-- 1084 00:46:10,110 --> 00:46:12,840 $10 a shot to see it. 1085 00:46:12,840 --> 00:46:14,180 It's possible. 1086 00:46:14,180 --> 00:46:18,900 So basically, almost always, inequalities will be greater 1087 00:46:18,900 --> 00:46:21,020 than or equal to, or less than or equal to in this course. 1088 00:46:21,020 --> 00:46:23,250 It's more fun to talk about the not equal to case, the 1089 00:46:23,250 --> 00:46:24,180 non-linear case. 1090 00:46:24,180 --> 00:46:26,290 But linear cases will exist as well. 1091 00:46:26,290 --> 00:46:28,610 It's just a can't be can't be opposite sign. 1092 00:46:28,610 --> 00:46:31,370 You can't have an increasing marginal rate of substitution. 1093 00:46:31,370 --> 00:46:31,665 Another question over here? 1094 00:46:31,665 --> 00:46:34,828 AUDIENCE: What about addictions? 1095 00:46:34,828 --> 00:46:36,078 You could want it more the second time. 1096 00:46:39,180 --> 00:46:40,210 PROFESSOR: That's interesting. 1097 00:46:40,210 --> 00:46:41,885 So how would addiction work? so basically-- 1098 00:46:41,885 --> 00:46:46,350 AUDIENCE: Well it's not really decreasing. 1099 00:46:46,350 --> 00:46:48,670 You need more the second time, right? 1100 00:46:48,670 --> 00:46:49,297 So it has to-- 1101 00:46:49,297 --> 00:46:50,051 PROFESSOR: That's very interesting. 1102 00:46:50,051 --> 00:46:53,010 I mean in some sense. 1103 00:46:53,010 --> 00:46:58,160 So you give up one pizza for the first shot of heroin. 1104 00:46:58,160 --> 00:47:03,326 And then, you're hooked, so then you'd be willing to give 1105 00:47:03,326 --> 00:47:04,960 up two pizzas for the next shot of heroin. 1106 00:47:09,433 --> 00:47:10,700 Yeah, I guess so. 1107 00:47:10,700 --> 00:47:11,610 I guess that's right. 1108 00:47:11,610 --> 00:47:14,860 I guess we're going to have to stay away from addiction in 1109 00:47:14,860 --> 00:47:16,440 this course. 1110 00:47:16,440 --> 00:47:19,470 I guess an addictive good could look like that. 1111 00:47:19,470 --> 00:47:21,380 That's a very good point. 1112 00:47:21,380 --> 00:47:24,490 Other questions, comments? 1113 00:47:24,490 --> 00:47:27,440 So what we're doing is we're going to stop here, 1114 00:47:27,440 --> 00:47:30,420 understanding that we're going to have-- 1115 00:47:30,420 --> 00:47:31,670 leaving this example aside-- we're going to have 1116 00:47:31,670 --> 00:47:32,710 diminishing marginal-- 1117 00:47:32,710 --> 00:47:33,290 yes one more question? 1118 00:47:33,290 --> 00:47:34,540 AUDIENCE: [UNINTELLIGIBLE] 1119 00:47:42,817 --> 00:47:45,970 PROFESSOR: Basically, we're assuming by non-satiation that 1120 00:47:45,970 --> 00:47:47,500 ever happens. 1121 00:47:47,500 --> 00:47:49,360 So once again, that would violate the non-satiation. 1122 00:47:49,360 --> 00:47:51,800 The problem with the addictiveness example is the 1123 00:47:51,800 --> 00:47:54,580 reason it wouldn't work in this course is eventually 1124 00:47:54,580 --> 00:47:56,630 you'd violate your budget constraint because you'd want 1125 00:47:56,630 --> 00:47:58,340 more and more and more. 1126 00:47:58,340 --> 00:47:59,810 Maybe not. 1127 00:47:59,810 --> 00:48:01,830 But in any case, we're going to ignore that example, assume 1128 00:48:01,830 --> 00:48:04,090 diminishing marginal rate of substitution, and we'll come 1129 00:48:04,090 --> 00:48:05,930 back next time as I put this together with a budget 1130 00:48:05,930 --> 00:48:07,360 constraint to actually dictate your choices.