WEBVTT 00:00:00.040 --> 00:00:02.460 The following content is provided under a Creative 00:00:02.460 --> 00:00:03.870 Commons license. 00:00:03.870 --> 00:00:06.910 Your support will help MIT OpenCourseWare continue to 00:00:06.910 --> 00:00:10.560 offer high quality educational resources for free. 00:00:10.560 --> 00:00:13.460 To make a donation or view additional materials from 00:00:13.460 --> 00:00:18.910 hundreds of MIT courses, visit MIT OpenCourseWare at MIT.edu. 00:00:21.636 --> 00:00:24.780 PROFESSOR: We've been talking so far about basically 00:00:24.780 --> 00:00:27.700 overviews of supply and demand relationships and 00:00:27.700 --> 00:00:30.670 understanding how markets work. 00:00:30.670 --> 00:00:34.950 Now we're going to step back and get behind the supply and 00:00:34.950 --> 00:00:38.400 demand curves and understand where those curves 00:00:38.400 --> 00:00:39.520 themselves come from. 00:00:39.520 --> 00:00:41.490 So we talked about, given that we have supply and demand 00:00:41.490 --> 00:00:43.730 curves, how they interact. 00:00:43.730 --> 00:00:45.650 Now we're going to get behind that and see where these 00:00:45.650 --> 00:00:47.400 curves actually come from. 00:00:47.400 --> 00:00:48.550 Thank you, by the way for coming down. 00:00:48.550 --> 00:00:49.800 I appreciate it. 00:00:51.730 --> 00:00:53.490 So what we're going to do is, we're going to start with the 00:00:53.490 --> 00:00:56.410 demand curve, and we're going to spend the next few lectures 00:00:56.410 --> 00:00:59.830 talking about consumers and how consumer preferences are 00:00:59.830 --> 00:01:01.555 ultimately what leads to the construction 00:01:01.555 --> 00:01:03.380 of the demand curve. 00:01:03.380 --> 00:01:08.200 Then after that and after the first exam-- that will cover 00:01:08.200 --> 00:01:11.250 what's on the first exam-- 00:01:11.250 --> 00:01:13.740 after the first exam, we'll start talking about firms and 00:01:13.740 --> 00:01:16.380 what determines the firm supply curve. 00:01:16.380 --> 00:01:19.210 So today we'll talk about consumers and we're going to 00:01:19.210 --> 00:01:21.580 talk about where the demand curve comes from. 00:01:21.580 --> 00:01:24.810 And where it comes from, and where all consumer behavior 00:01:24.810 --> 00:01:27.665 coming from in economics is from utility maximization. 00:01:33.490 --> 00:01:35.980 That's where everything with consumers starts is with 00:01:35.980 --> 00:01:37.790 utility maximization. 00:01:37.790 --> 00:01:44.030 That's the basic building block of consumer behavior. 00:01:44.030 --> 00:01:48.050 And basically, utility maximization-- 00:01:48.050 --> 00:01:50.330 that's what this lecture will be about, describing it. 00:01:50.330 --> 00:01:55.410 But basically, an overview is, we posit some type of 00:01:55.410 --> 00:01:56.870 preferences. 00:01:56.870 --> 00:02:03.070 We posit consumer preferences, what consumers would like. 00:02:03.070 --> 00:02:10.370 We posit some budget constraint, what resources 00:02:10.370 --> 00:02:12.980 consumers have to get what they'd like. 00:02:12.980 --> 00:02:16.360 And then we do a constrained maximization problem that 00:02:16.360 --> 00:02:20.500 says, given your preferences, given what you'd like, subject 00:02:20.500 --> 00:02:22.840 to the resources you have available, what 00:02:22.840 --> 00:02:25.870 choices will you make? 00:02:25.870 --> 00:02:27.710 And in particular, we're going to ask, the term we'll use is 00:02:27.710 --> 00:02:32.860 we'll ask what bundle of goods makes you the best off? 00:02:32.860 --> 00:02:34.020 Given your preference, given your constraints, 00:02:34.020 --> 00:02:35.510 what bundle of goods? 00:02:35.510 --> 00:02:37.050 So think about consumers choosing 00:02:37.050 --> 00:02:38.160 across a set of goods. 00:02:38.160 --> 00:02:41.390 Typically, we'll think about two goods because graphs are 00:02:41.390 --> 00:02:43.760 easier to think about two dimensions than more. 00:02:43.760 --> 00:02:46.230 So we'll typically think about trading off two goods. 00:02:46.230 --> 00:02:49.140 So think about consumers with preferences across two goods, 00:02:49.140 --> 00:02:51.880 some budget they can allocate, and how 00:02:51.880 --> 00:02:53.080 they make those choices. 00:02:53.080 --> 00:02:56.170 But this basic framework applies to the multiplicity of 00:02:56.170 --> 00:02:59.790 choices we all make along many, many dimensions. 00:02:59.790 --> 00:03:03.380 So doing two dimensions as one of the simplifying assumptions 00:03:03.380 --> 00:03:04.560 I'll talk about. 00:03:04.560 --> 00:03:07.590 But that's just a simplifying assumption. 00:03:07.590 --> 00:03:08.930 So basically what we we're going to do is we're going to 00:03:08.930 --> 00:03:13.180 go through this in three steps, not just in this 00:03:13.180 --> 00:03:15.740 lecture, but over the next few lectures. 00:03:15.740 --> 00:03:19.600 Step one, is we're going to talk about what assumptions we 00:03:19.600 --> 00:03:21.300 make about preferences. 00:03:21.300 --> 00:03:23.235 So I'll talk today about preference assumptions. 00:03:27.540 --> 00:03:32.320 So the axioms that underlie how economists model consumer 00:03:32.320 --> 00:03:34.600 preferences. 00:03:34.600 --> 00:03:38.840 We'll then talk about how we translate these preferences 00:03:38.840 --> 00:03:42.770 assumptions into mathematical tractability through the use 00:03:42.770 --> 00:03:48.570 of the utility function, which is basically a mathematical 00:03:48.570 --> 00:03:52.690 representation of underlying consumer preferences. 00:03:52.690 --> 00:03:54.660 So we'll talk about how we basically take these 00:03:54.660 --> 00:03:56.560 preferences and translate them into something that we can 00:03:56.560 --> 00:03:59.440 work with here at MIT by making it mathematical, by 00:03:59.440 --> 00:04:01.420 making a utility function. 00:04:01.420 --> 00:04:06.560 And then finally, we'll talk about budget constraints. 00:04:06.560 --> 00:04:09.360 And armed with these three things, we'll then be able to 00:04:09.360 --> 00:04:12.610 model how consumers make decisions. 00:04:12.610 --> 00:04:18.120 Now, importantly for today's lecture, we are not dealing 00:04:18.120 --> 00:04:19.420 with budget constraints. 00:04:19.420 --> 00:04:22.690 So this is not happening today. 00:04:22.690 --> 00:04:24.280 So today we're not going to worry about the budget 00:04:24.280 --> 00:04:24.530 constraints. 00:04:24.530 --> 00:04:26.325 Today we're in a world where we're just going to talk about 00:04:26.325 --> 00:04:28.590 what people want and we're going to put out of our mind 00:04:28.590 --> 00:04:31.140 whether or not they can afford it. 00:04:31.140 --> 00:04:32.690 So just talk about people want, and we'll put out of 00:04:32.690 --> 00:04:33.200 mind for today. 00:04:33.200 --> 00:04:35.440 We'll come back next time to whether they can afford it. 00:04:35.440 --> 00:04:36.910 We're just going to think about unconstrained 00:04:36.910 --> 00:04:39.810 preferences for today's lecture. 00:04:42.570 --> 00:04:47.310 So let's talk about our preference assumptions. 00:04:47.310 --> 00:04:53.180 So, to model consumers' preferences across goods, 00:04:53.180 --> 00:04:55.360 we're going to impose three preference assumptions. 00:05:02.340 --> 00:05:05.160 Three preference assumptions. 00:05:05.160 --> 00:05:06.260 Assumption one-- 00:05:06.260 --> 00:05:08.990 now once again, let me remind you from the first lecture, 00:05:08.990 --> 00:05:11.260 this is getting to some of the harder material. 00:05:11.260 --> 00:05:15.320 I'm going to write messily and talk quickly, so stop me if 00:05:15.320 --> 00:05:16.520 anything is unclear. 00:05:16.520 --> 00:05:18.450 And if you don't stop me, I'll just go faster and faster 00:05:18.450 --> 00:05:19.860 until I explode. 00:05:19.860 --> 00:05:22.190 So basically, feel free to interrupt and stop me with 00:05:22.190 --> 00:05:24.260 questions and such. 00:05:24.260 --> 00:05:26.400 Three assumptions on preferences. 00:05:26.400 --> 00:05:27.800 The first assumption is completeness. 00:05:32.000 --> 00:05:34.140 The first assumption is the assumption of completeness. 00:05:34.140 --> 00:05:38.910 When comparing two bundles of goods, you prefer one or the 00:05:38.910 --> 00:05:44.180 other, but you don't value them equally. 00:05:44.180 --> 00:05:46.720 OK when comparing two bundles of goods, you prefer one or 00:05:46.720 --> 00:05:48.870 you prefer the other, but you're not indifferent. 00:05:48.870 --> 00:05:51.860 Completeness is the same as no indifference. 00:05:51.860 --> 00:05:54.230 So what we're saying is whenever I offer you two 00:05:54.230 --> 00:05:56.170 bundles of goods, you could always tell me 00:05:56.170 --> 00:05:57.090 what you like better. 00:05:57.090 --> 00:05:59.490 Now it could be infinitesimally better. 00:05:59.490 --> 00:06:01.440 I'm not saying you have to have strong preferences. 00:06:01.440 --> 00:06:04.330 But you cannot say I'm indifferent. 00:06:04.330 --> 00:06:05.680 You can never be purely indifferent. 00:06:05.680 --> 00:06:09.390 There always at least some slight preference for one 00:06:09.390 --> 00:06:11.090 bundle of goods over another. 00:06:11.090 --> 00:06:13.340 That's the completeness assumption. 00:06:13.340 --> 00:06:14.800 This is an assumption we make. 00:06:14.800 --> 00:06:17.640 Now in reality, oftentimes we are indifferent. 00:06:17.640 --> 00:06:18.900 Well once again, this is one of these simplifying 00:06:18.900 --> 00:06:20.650 assumptions that will make the model work. 00:06:20.650 --> 00:06:23.200 And in fact, in reality if forced, you can always decide 00:06:23.200 --> 00:06:24.910 whether you like one thing better than another, we just 00:06:24.910 --> 00:06:27.440 often follow heuristic rules which say we're roughly 00:06:27.440 --> 00:06:28.250 indifferent. 00:06:28.250 --> 00:06:29.640 We're just going to say, more precisely, you are never 00:06:29.640 --> 00:06:32.300 purely indifferent. 00:06:32.300 --> 00:06:35.100 So, I'm not sure is not an option. 00:06:35.100 --> 00:06:36.900 You can never say I don't know, I don't know which I 00:06:36.900 --> 00:06:39.470 prefer, I'm indifferent. 00:06:39.470 --> 00:06:40.450 I'm sorry, let me back up. 00:06:40.450 --> 00:06:41.780 I'm using the wrong word. 00:06:41.780 --> 00:06:43.416 Forget I said indifferent, because we'll want to use that 00:06:43.416 --> 00:06:44.690 word in a different context later. 00:06:44.690 --> 00:06:47.470 You can't say, I'm not sure. 00:06:47.470 --> 00:06:49.010 You can't say, I'm not sure. 00:06:52.620 --> 00:06:54.580 You can't say, I'm not sure, can't say I don't know, I 00:06:54.580 --> 00:06:55.830 don't know how I feel about that. 00:07:03.710 --> 00:07:05.250 Scratch what I said a few minutes ago, because I want to 00:07:05.250 --> 00:07:06.460 use indifference differently. 00:07:06.460 --> 00:07:08.810 Completeness is not about not being different, we're going 00:07:08.810 --> 00:07:09.490 to use that. 00:07:09.490 --> 00:07:11.510 What I'm saying is it's about not being sure. 00:07:11.510 --> 00:07:14.480 You've got to value every bundle of goods. 00:07:14.480 --> 00:07:16.720 You've got to be willing to value every bundle of goods 00:07:16.720 --> 00:07:18.610 that's given you. 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 00:07:20.500 --> 00:07:21.110 about that. 00:07:21.110 --> 00:07:22.570 You've got to have some feeling about stuff. 00:07:22.570 --> 00:07:23.880 You can't say I'm not sure. 00:07:23.880 --> 00:07:25.810 You've got to have a complete set of preferences over all 00:07:25.810 --> 00:07:28.680 bundles of goods that are given you. 00:07:28.680 --> 00:07:31.910 OK, that's completeness. 00:07:31.910 --> 00:07:33.640 The second is transitivity. 00:07:37.950 --> 00:07:39.930 Which is something we've been learning since kindergarten 00:07:39.930 --> 00:07:41.000 about transitivity, right? 00:07:41.000 --> 00:07:42.570 And also, it's a different context. 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 00:07:45.020 --> 00:07:46.140 prefer x to z. 00:07:46.140 --> 00:07:47.650 OK, you guys should do transitivity in 00:07:47.650 --> 00:07:49.010 your sleep by now. 00:07:49.010 --> 00:07:50.970 OK, so the standard transitivity we always assume 00:07:50.970 --> 00:07:53.870 in math class, we're going to assume here as well. 00:07:53.870 --> 00:07:56.800 OK, that should be pretty noncontroversial. 00:07:56.800 --> 00:08:01.400 OK, and then finally, and probably most controversial, 00:08:01.400 --> 00:08:02.990 is we're going to assume non-satiation. 00:08:07.730 --> 00:08:09.520 Or the famous economic assumption that 00:08:09.520 --> 00:08:12.120 more is always better. 00:08:12.120 --> 00:08:13.260 OK. 00:08:13.260 --> 00:08:17.400 More is always better, that is, you never would turn down 00:08:17.400 --> 00:08:19.000 having more. 00:08:19.000 --> 00:08:21.950 Now we're going to talk later today and tomorrow about why 00:08:21.950 --> 00:08:24.490 you might not like the next unit as much as you like the 00:08:24.490 --> 00:08:25.530 current unit. 00:08:25.530 --> 00:08:28.270 But you'll always like it greater than zero. 00:08:28.270 --> 00:08:30.640 You're always happy to have more. 00:08:30.640 --> 00:08:32.799 You never say, I've had enough, I literally value at 00:08:32.799 --> 00:08:34.230 zero the next unit. 00:08:34.230 --> 00:08:37.070 You may value it as epsilon, but you'll always value it as 00:08:37.070 --> 00:08:38.289 greater than zero. 00:08:38.289 --> 00:08:40.130 That's the non-satiation assumption, 00:08:40.130 --> 00:08:41.230 more is always better. 00:08:41.230 --> 00:08:42.259 Now, this is the most controversial. 00:08:42.259 --> 00:08:43.840 And obviously we can think of many contexts in 00:08:43.840 --> 00:08:45.750 which that's not true. 00:08:45.750 --> 00:08:49.170 But if we don't allow for this assumption, the modeling gets 00:08:49.170 --> 00:08:50.120 a lot trickier. 00:08:50.120 --> 00:08:51.350 So once again, let's put it out of our mind. 00:08:51.350 --> 00:08:54.910 Realistically, we know once we've eaten a certain amount, 00:08:54.910 --> 00:08:57.060 we literally do not want any more. 00:08:57.060 --> 00:08:58.680 OK, so we're going to put that aside. 00:08:58.680 --> 00:09:00.480 Assume we're always in a space where we can always eat a 00:09:00.480 --> 00:09:02.240 little bit more. 00:09:02.240 --> 00:09:04.540 OK, we'll call it the Jewish mother space. 00:09:04.540 --> 00:09:06.670 OK, you can always eat a little bit more. 00:09:06.670 --> 00:09:08.430 OK, you can always eat a little bit more. 00:09:08.430 --> 00:09:10.620 We're just going to assume we're in that space for now. 00:09:10.620 --> 00:09:11.220 OK. 00:09:11.220 --> 00:09:13.360 And so, for large ranges, we can see it is not an 00:09:13.360 --> 00:09:14.170 unreasonable assumption. 00:09:14.170 --> 00:09:15.800 Although, I think in extremes, you could see this becomes 00:09:15.800 --> 00:09:17.320 unreasonable. 00:09:17.320 --> 00:09:19.090 OK, so those are assumptions. 00:09:19.090 --> 00:09:20.520 Completeness, which once again, I screwed up in 00:09:20.520 --> 00:09:21.360 describing. 00:09:21.360 --> 00:09:22.900 Come back to the second way I described it, which means you 00:09:22.900 --> 00:09:23.740 can't say you're not sure. 00:09:23.740 --> 00:09:25.970 You always have preferences over things. 00:09:25.970 --> 00:09:27.390 That doesn't seem unreasonable. 00:09:27.390 --> 00:09:29.360 Transitivity which we've been living with since we were 00:09:29.360 --> 00:09:30.070 kindergartners. 00:09:30.070 --> 00:09:32.410 And non-satiation, which could be a little controversial, but 00:09:32.410 --> 00:09:33.820 we'll live with it for now. 00:09:33.820 --> 00:09:37.570 Now given these, we're going to talk about the properties 00:09:37.570 --> 00:09:39.820 of what we call indifference curves. 00:09:39.820 --> 00:09:41.450 This is why I screwed up before. 00:09:41.450 --> 00:09:43.080 Of course you can be indifferent between things. 00:09:43.080 --> 00:09:43.990 That's the whole point of economics. 00:09:43.990 --> 00:09:47.706 I don't know why I got that wrong. 00:09:47.706 --> 00:09:50.160 I haven't taught this course about six years, so I lost 00:09:50.160 --> 00:09:52.130 track of things. 00:09:52.130 --> 00:09:54.170 Properties of indifference curves. 00:09:54.170 --> 00:09:59.080 So indifference curves are our name for what you could also 00:09:59.080 --> 00:10:02.325 think of as preference maps. 00:10:02.325 --> 00:10:05.160 In economics, we like to be able to describe everything, 00:10:05.160 --> 00:10:07.600 as I said, three ways, intuitively, graphically, and 00:10:07.600 --> 00:10:08.590 mathematically. 00:10:08.590 --> 00:10:12.320 Preference maps are the graphical representation of 00:10:12.320 --> 00:10:14.950 people's preferences which we do through graphics that we 00:10:14.950 --> 00:10:17.130 call indifference curves. 00:10:17.130 --> 00:10:19.421 So now let's go to the example I'm going to use that I'm 00:10:19.421 --> 00:10:21.680 going to use throughout these next couple lectures of a 00:10:21.680 --> 00:10:23.470 decision you have to make. 00:10:23.470 --> 00:10:26.330 Now I tried to think of a cool way to make this example cool, 00:10:26.330 --> 00:10:26.920 and I just couldn't. 00:10:26.920 --> 00:10:28.630 So its going to be a boring example. 00:10:28.630 --> 00:10:31.400 It's going to be, imagine your parents gave you some money 00:10:31.400 --> 00:10:34.760 and you had to decide whether to buy pizza or see movies. 00:10:34.760 --> 00:10:36.340 I tried to make it at least a little bit relevant even if I 00:10:36.340 --> 00:10:37.760 couldn't make it cool. 00:10:37.760 --> 00:10:39.950 You've got to decide whether to buy pizza or see movies. 00:10:39.950 --> 00:10:41.110 That's your decision. 00:10:41.110 --> 00:10:42.570 That's the trade-off you're making. 00:10:42.570 --> 00:10:47.150 We're in a world with only two goods, pizza and movies. 00:10:47.150 --> 00:10:49.930 And you're deciding how to allocate the money your 00:10:49.930 --> 00:10:52.210 parents gave you over pizza and movies. 00:10:56.450 --> 00:10:59.410 Now let's say we're going to consider three choices of 00:10:59.410 --> 00:11:00.490 pizza and movies. 00:11:00.490 --> 00:11:01.740 So go to figure 4-1a. 00:11:05.290 --> 00:11:10.140 We're going to consider, you could have two pizzas and one 00:11:10.140 --> 00:11:15.530 movie, that's point A. You could have one pizza and two 00:11:15.530 --> 00:11:18.030 movies, that's point B. Or you can have two of both, that's 00:11:18.030 --> 00:11:21.500 point C. That's just three choices you're facing. 00:11:21.500 --> 00:11:23.140 Once again, we're ignoring paying for them. 00:11:23.140 --> 00:11:24.860 Budget constraints is next time. 00:11:24.860 --> 00:11:26.950 Now we're just saying I'm giving these three choices. 00:11:26.950 --> 00:11:29.210 Well how do you feel about them? 00:11:29.210 --> 00:11:32.010 Well let's assume that you're indifferent-- 00:11:32.010 --> 00:11:32.970 and this is why you can be indifferent. 00:11:32.970 --> 00:11:35.070 What I said before, just strike. 00:11:35.070 --> 00:11:37.000 Let's say you're indifferent between two pizzas and one 00:11:37.000 --> 00:11:39.150 movie, and one pizza and two movies. 00:11:39.150 --> 00:11:43.730 Let's say, if you had two pizzas and one movie, or one 00:11:43.730 --> 00:11:45.350 pizza and two movies, you pretty much feel the same 00:11:45.350 --> 00:11:46.360 about them. 00:11:46.360 --> 00:11:50.880 But clearly you like two pizzas and two movies better 00:11:50.880 --> 00:11:54.200 than either of the first two combinations. 00:11:54.200 --> 00:11:57.000 Then what we can do is we can draw what we call 00:11:57.000 --> 00:11:58.510 indifference curves. 00:11:58.510 --> 00:12:01.820 And that's in figure 4-1b. 00:12:01.820 --> 00:12:04.330 These are maps of your preferences. 00:12:04.330 --> 00:12:09.060 An indifference curve is the curve showing all combinations 00:12:09.060 --> 00:12:13.050 of consumption along which the individual is indifferent. 00:12:13.050 --> 00:12:14.600 And I'll say that again, very important concept. 00:12:14.600 --> 00:12:17.970 An indifference curve is a curve showing all combinations 00:12:17.970 --> 00:12:22.490 of consumption along which an individual is indifferent. 00:12:22.490 --> 00:12:23.800 So you have an indifference curve. 00:12:23.800 --> 00:12:26.810 I said you were indifferent between A and B. So you have 00:12:26.810 --> 00:12:30.370 an indifference curve that runs between A and B. That 00:12:30.370 --> 00:12:33.400 means that all, and I'm assuming that all combinations 00:12:33.400 --> 00:12:35.670 along this curve, you're indifferent. 00:12:35.670 --> 00:12:37.850 So you're equally happy getting two pizzas and one 00:12:37.850 --> 00:12:39.820 movie or one pizza and two movies. 00:12:39.820 --> 00:12:44.566 But point C, which is two pizzas and two movies is on a 00:12:44.566 --> 00:12:45.530 different indifference curve. 00:12:45.530 --> 00:12:50.120 You're not indifferent between point C and points A and B. 00:12:50.120 --> 00:12:51.340 You're indifferent between A and B-- 00:12:51.340 --> 00:12:53.210 I'm just assuming this, I'm not saying you are. 00:12:53.210 --> 00:12:56.050 But I'm just assuming, let's imagine you are. 00:12:56.050 --> 00:13:01.010 But you clearly like two pizzas and two movies better 00:13:01.010 --> 00:13:03.430 than one of one and two of the other. 00:13:03.430 --> 00:13:03.927 Yeah? 00:13:03.927 --> 00:13:07.406 AUDIENCE: Does that break the completeness rule for the-- 00:13:07.406 --> 00:13:09.160 PROFESSOR: Does that break it? 00:13:09.160 --> 00:13:10.120 Why would that break it? 00:13:10.120 --> 00:13:11.411 AUDIENCE: Do you prefer pizza over movies 00:13:11.411 --> 00:13:12.470 or movies over pizza? 00:13:12.470 --> 00:13:13.460 PROFESSOR: No. 00:13:13.460 --> 00:13:14.740 Because this is my screw up before. 00:13:14.740 --> 00:13:16.600 Completeness just means you know how you feel about 00:13:16.600 --> 00:13:18.090 everything. 00:13:18.090 --> 00:13:22.110 So strike from the record my initial description. 00:13:22.110 --> 00:13:24.030 Completeness means you just know how you feel about 00:13:24.030 --> 00:13:24.620 everything. 00:13:24.620 --> 00:13:25.960 You're allowed to be indifferent. 00:13:25.960 --> 00:13:27.416 Completeness just means you can't say, I don't know, I 00:13:27.416 --> 00:13:28.690 don't know how I feel about pizza. 00:13:28.690 --> 00:13:30.740 You've got to have feelings for pizza. 00:13:30.740 --> 00:13:31.260 OK. 00:13:31.260 --> 00:13:32.490 You've got to know how you feel about stuff. 00:13:32.490 --> 00:13:35.750 That's what completeness is. 00:13:35.750 --> 00:13:40.780 So armed with those assumptions, there are four 00:13:40.780 --> 00:13:43.530 key properties of indifference curves that we have 00:13:43.530 --> 00:13:44.700 to keep track of. 00:13:44.700 --> 00:13:48.010 Four key properties of indifference curves. 00:13:48.010 --> 00:13:51.770 The first is that consumers prefer higher 00:13:51.770 --> 00:13:53.440 indifference curves. 00:13:53.440 --> 00:13:58.410 So you prefer higher indifference curves. 00:14:02.140 --> 00:14:03.620 Prefer higher indifference curves. 00:14:03.620 --> 00:14:05.290 What I mean by that is, the further out the indifference 00:14:05.290 --> 00:14:06.920 curve, the more you prefer it. 00:14:06.920 --> 00:14:11.060 And this comes naturally from the non-satiation assumption. 00:14:11.060 --> 00:14:14.340 Given that we've assumed non-satiation, you must always 00:14:14.340 --> 00:14:16.690 prefer an indifference curve that's further from the origin 00:14:16.690 --> 00:14:19.770 because it's more, and more is better. 00:14:19.770 --> 00:14:22.960 OK so given non-satiation, you will always prefer an 00:14:22.960 --> 00:14:26.100 indifference curves that are further from the origin. 00:14:26.100 --> 00:14:29.000 That follows directly from non-satiation. 00:14:31.610 --> 00:14:39.750 The second point is that indifference curves are always 00:14:39.750 --> 00:14:41.000 downward sloping. 00:14:45.640 --> 00:14:47.705 Indifference curves are always downward sloping. 00:14:51.994 --> 00:14:54.050 Indifference curves are always downward sloping. 00:14:54.050 --> 00:14:56.160 And that, once again, comes from non-satiation. 00:14:56.160 --> 00:14:59.040 To see this, let's look at the next figure, an upward sloping 00:14:59.040 --> 00:15:02.020 indifference curve. 00:15:02.020 --> 00:15:04.320 Why does an upward sloping indifference curve, someone 00:15:04.320 --> 00:15:07.529 tell me, violate non-satiation. 00:15:07.529 --> 00:15:08.002 Yeah? 00:15:08.002 --> 00:15:10.367 AUDIENCE: Because you're indifferent to getting more. 00:15:10.367 --> 00:15:10.681 PROFESSOR: Yeah. 00:15:10.681 --> 00:15:11.850 Because this would say you're indifferent 00:15:11.850 --> 00:15:13.480 between (1,1) and (2,2). 00:15:13.480 --> 00:15:14.770 It's not quite drawn right. 00:15:14.770 --> 00:15:18.010 We ought to just have this go through to point (2,2). 00:15:18.010 --> 00:15:20.710 But basically, this would say you're indifferent between 00:15:20.710 --> 00:15:22.610 getting one pizza and one movie or two 00:15:22.610 --> 00:15:23.870 pizzas and two movies. 00:15:23.870 --> 00:15:26.880 You can't be because that violates more is better. 00:15:26.880 --> 00:15:29.710 So indifference curves can't be upward sloping, they've got 00:15:29.710 --> 00:15:33.510 to be downward sloping by the non-satiation assumption. 00:15:33.510 --> 00:15:37.890 OK, that's the second property of indifference curves. 00:15:37.890 --> 00:15:40.730 The third property of indifference curves is 00:15:40.730 --> 00:15:42.530 indifference curves cannot cross. 00:15:46.150 --> 00:15:50.080 Indifference curves cannot cross. 00:15:50.080 --> 00:15:51.910 Why can't indifference curves cross? 00:15:51.910 --> 00:15:54.405 Well here I forgot to have Jessica do a pretty diagram, 00:15:54.405 --> 00:15:57.840 so you'll have to deal with my ugly handwriting here. 00:15:57.840 --> 00:16:00.720 So why can't indifferent curves cross? 00:16:00.720 --> 00:16:03.820 Well imagine a situation where you have your 00:16:03.820 --> 00:16:06.230 pizza and your movies. 00:16:06.230 --> 00:16:11.690 And imagine a situation where you have one indifference 00:16:11.690 --> 00:16:14.150 curve that looks like this, and one indifference curve 00:16:14.150 --> 00:16:15.840 that looks like this. 00:16:15.840 --> 00:16:17.480 OK, two indifference curves. 00:16:17.480 --> 00:16:25.570 And you've got, let's label these points A, B, and C. 00:16:25.570 --> 00:16:28.810 Now could someone give me, based on the properties of 00:16:28.810 --> 00:16:31.405 indifference curves that we talked about over here, given 00:16:31.405 --> 00:16:33.030 these three properties, can someone tell me 00:16:33.030 --> 00:16:35.440 why this is a violation? 00:16:35.440 --> 00:16:35.845 Yeah? 00:16:35.845 --> 00:16:38.628 AUDIENCE: Because A and B are on the same curve, meaning 00:16:38.628 --> 00:16:41.405 you're indifferent between A and B. A and C are also on the 00:16:41.405 --> 00:16:43.990 same curve because you're indifferent between the two. 00:16:43.990 --> 00:16:46.693 But that means you're also indifferent between B and C 00:16:46.693 --> 00:16:48.426 which can't be true because more is better. 00:16:48.426 --> 00:16:49.490 PROFESSOR: Exactly. 00:16:49.490 --> 00:16:52.050 So transitivity says I must then be indifferent between B 00:16:52.050 --> 00:16:54.200 and C through the logic you just laid out. 00:16:54.200 --> 00:16:56.090 But I can't be indifferent between B and C because B 00:16:56.090 --> 00:17:00.390 dominates C. B has a basically the same number of movies, but 00:17:00.390 --> 00:17:03.040 more pizza, so I must like B better. 00:17:03.040 --> 00:17:06.810 So by the combination of transitivity and non-satiation 00:17:06.810 --> 00:17:09.930 indifference curves can't cross. 00:17:09.930 --> 00:17:13.269 And finally, completeness, which is the most awkward of 00:17:13.269 --> 00:17:15.770 these assumptions, it simply means you can't have more than 00:17:15.770 --> 00:17:18.930 one indifference curve through a point. 00:17:18.930 --> 00:17:24.790 So basically, the idea of every possible bundle has one 00:17:24.790 --> 00:17:25.730 indifference curve. 00:17:25.730 --> 00:17:27.399 You can't have two indifference curves through it 00:17:27.399 --> 00:17:29.250 sayin, I'm not sure which indifference curve I'm on. 00:17:29.250 --> 00:17:30.650 I'm not sure how I feel about this. 00:17:30.650 --> 00:17:31.560 You know how you feel. 00:17:31.560 --> 00:17:34.120 There's one indifference curve through every bundle. 00:17:34.120 --> 00:17:37.150 There's not two indifference curves through a bundle. 00:17:37.150 --> 00:17:40.800 So this is the way we think about preference maps which is 00:17:40.800 --> 00:17:44.350 the sort of core building block of utility theory. 00:17:44.350 --> 00:17:48.960 Now I was an undergrad here, took this course, but I never 00:17:48.960 --> 00:17:51.820 really understood indifference curves until I had a year off 00:17:51.820 --> 00:17:54.900 with a grad student who was trying to decide where to take 00:17:54.900 --> 00:17:57.672 a job and he did it through just showing me an 00:17:57.672 --> 00:17:58.900 indifference map. 00:17:58.900 --> 00:18:00.680 He said look, I'm trying to decide where to take a job, 00:18:00.680 --> 00:18:01.600 and I care about two things. 00:18:01.600 --> 00:18:04.730 I care about how good the place is and where it is. 00:18:04.730 --> 00:18:09.230 So he said here, he had location and he 00:18:09.230 --> 00:18:10.870 had academic rank. 00:18:13.690 --> 00:18:21.060 And he said look, I'm indifferent between Princeton 00:18:21.060 --> 00:18:26.130 which has a shitty location but a wonderful academic rank. 00:18:26.130 --> 00:18:28.680 I'm from New Jersey, but it's still a shitty location. 00:18:28.680 --> 00:18:32.240 OK, and Santa Cruz. 00:18:32.240 --> 00:18:37.130 And Santa Cruz which has not such a good academic 00:18:37.130 --> 00:18:39.250 reputation, but a pretty awesome location. 00:18:39.250 --> 00:18:42.680 And he said here's my indifference map. 00:18:42.680 --> 00:18:43.810 And where did he end up going? 00:18:43.810 --> 00:18:47.730 He ended up going to the IMF, the international monetary 00:18:47.730 --> 00:18:51.970 fund in DC which had a better location than Princeton-- 00:18:51.970 --> 00:18:54.075 worse than Santa Cruz, but a better reputation than Santa 00:18:54.075 --> 00:18:55.640 Cruz and worse than Princeton. 00:18:55.640 --> 00:18:57.710 So he decided he was indifferent along this map, 00:18:57.710 --> 00:19:00.180 and he ended up choosing a point in the middle. 00:19:00.180 --> 00:19:02.700 But indifference curves are just a way of representing two 00:19:02.700 --> 00:19:05.090 dimensional choices. 00:19:05.090 --> 00:19:07.110 Now very few choice in life are really two dimensional, 00:19:07.110 --> 00:19:08.100 but that's a nice example. 00:19:08.100 --> 00:19:08.865 Question in the back? 00:19:08.865 --> 00:19:12.590 AUDIENCE: I was wondering if IMF, the point would be 00:19:12.590 --> 00:19:14.825 actually not on the curve, but further out? 00:19:14.825 --> 00:19:15.719 PROFESSOR: If it were further out. 00:19:15.719 --> 00:19:17.225 A great question. 00:19:17.225 --> 00:19:18.740 So imagine if IMF were here. 00:19:21.490 --> 00:19:24.054 What should he have done? 00:19:24.054 --> 00:19:25.380 Definitely go to IMF. 00:19:25.380 --> 00:19:26.700 Here he was indifferent. 00:19:26.700 --> 00:19:29.560 He could flip a coin and be equally happy at all three. 00:19:29.560 --> 00:19:31.610 But if IMF were out here, and maybe it was because that's 00:19:31.610 --> 00:19:32.520 what he chose. 00:19:32.520 --> 00:19:33.120 That's a good point. 00:19:33.120 --> 00:19:36.440 I don't know if IMF was here or here. 00:19:36.440 --> 00:19:39.380 The fact that he chose IMF, it can reveal it 00:19:39.380 --> 00:19:40.390 wasn't anywhere in here. 00:19:40.390 --> 00:19:41.760 It's a very good point actually. 00:19:41.760 --> 00:19:44.510 It can reveal it wasn't anywhere in here. 00:19:44.510 --> 00:19:45.510 That we know. 00:19:45.510 --> 00:19:47.420 But I can't tell if it was on the curve 00:19:47.420 --> 00:19:49.030 or outside the curve. 00:19:49.030 --> 00:19:49.890 It could have been on the curve because he's 00:19:49.890 --> 00:19:51.720 indifferent, so who knows, he could have flipped the coin. 00:19:51.720 --> 00:19:53.470 Or it could have been outside the curve because it's better. 00:19:53.470 --> 00:19:54.360 We can't tell that. 00:19:54.360 --> 00:19:56.220 That's a good point. 00:19:56.220 --> 00:19:57.110 All right. 00:19:57.110 --> 00:19:58.590 So that's a preference map. 00:19:58.590 --> 00:20:00.950 That's indifference curves. 00:20:00.950 --> 00:20:03.890 Now let's step from indifference curves, which is 00:20:03.890 --> 00:20:07.935 a building block of preferences, to utility. 00:20:12.710 --> 00:20:15.180 Now everything you need to know about preferences is 00:20:15.180 --> 00:20:17.920 represented in those indifference maps. 00:20:17.920 --> 00:20:21.630 The problem is they're pretty awkward to work with when we 00:20:21.630 --> 00:20:25.990 need to actually prove theorems and solve and 00:20:25.990 --> 00:20:27.880 understand how people make decisions. 00:20:27.880 --> 00:20:31.060 That's a lot easier if we have a mathematical representation 00:20:31.060 --> 00:20:32.540 of those preference maps. 00:20:32.540 --> 00:20:35.280 And that's the utility function 00:20:35.280 --> 00:20:40.200 So the utility function is a mathematical representation of 00:20:40.200 --> 00:20:40.770 preferences. 00:20:40.770 --> 00:20:41.950 That's all it is. 00:20:41.950 --> 00:20:45.415 You're going to be hearing this term in your nightmares 00:20:45.415 --> 00:20:46.910 for the next semester. 00:20:46.910 --> 00:20:48.060 Utility functions. 00:20:48.060 --> 00:20:51.520 But remember, it's just a mathematical representation of 00:20:51.520 --> 00:20:52.950 people's underlying preferences. 00:20:52.950 --> 00:20:55.890 Don't be scared of it. 00:20:55.890 --> 00:20:58.450 And the key thing is that we assume individuals have these 00:20:58.450 --> 00:21:01.820 well-defined utility functions, and by maximizing 00:21:01.820 --> 00:21:03.840 those utility functions we can tell what choices they're 00:21:03.840 --> 00:21:05.060 going to make. 00:21:05.060 --> 00:21:09.120 So for example, suppose that I said that your utility 00:21:09.120 --> 00:21:13.660 function over pizza and movies was the square root of pizza 00:21:13.660 --> 00:21:16.390 times movies. 00:21:16.390 --> 00:21:17.360 That's a utility function. 00:21:17.360 --> 00:21:18.270 I'm going to say, what the hell does that mean? 00:21:18.270 --> 00:21:19.570 Well, it doesn't mean anything, 00:21:19.570 --> 00:21:20.820 it's a utility function. 00:21:20.820 --> 00:21:21.900 It's your preferences. 00:21:21.900 --> 00:21:23.280 It's a mathematical representation of your 00:21:23.280 --> 00:21:24.530 preferences. 00:21:26.590 --> 00:21:27.730 What does that mean? 00:21:27.730 --> 00:21:29.440 What it means is-- 00:21:29.440 --> 00:21:32.290 it doesn't mean anything inherently, but it tells us 00:21:32.290 --> 00:21:33.960 about your preferences. 00:21:33.960 --> 00:21:36.880 What it tells us is that your preferences can be 00:21:36.880 --> 00:21:38.450 represented. 00:21:38.450 --> 00:21:43.030 If you flip back to figure 4-1b, it tells us those are 00:21:43.030 --> 00:21:47.350 your preferences because you're indifferent between two 00:21:47.350 --> 00:21:50.390 pizzas and one movie and one pizza and two movies. 00:21:50.390 --> 00:21:50.890 Of course you're indifferent. 00:21:50.890 --> 00:21:53.860 They both give a utility square root two. 00:21:53.860 --> 00:21:56.265 But you prefer two pizzas and two movies because that gives 00:21:56.265 --> 00:21:58.140 a utility of two. 00:21:58.140 --> 00:22:00.650 So this is a mathematical representation consistent with 00:22:00.650 --> 00:22:02.110 those utility indifference curves. 00:22:02.110 --> 00:22:03.540 Not the only one. 00:22:03.540 --> 00:22:04.910 There's other mathematical representations that could be 00:22:04.910 --> 00:22:06.750 consistent with those indifference curves. 00:22:06.750 --> 00:22:09.760 But let's posit that this is your utility function. 00:22:09.760 --> 00:22:13.260 This is a mathematical representation of your tastes. 00:22:13.260 --> 00:22:15.120 Now what does utility mean? 00:22:15.120 --> 00:22:20.040 Utility means nothing in the sense that it is not a 00:22:20.040 --> 00:22:21.035 cardinal concept. 00:22:21.035 --> 00:22:23.690 It's only an ordinal concept. 00:22:23.690 --> 00:22:30.110 So if I say to you that you get two utils from two pizzas 00:22:30.110 --> 00:22:32.290 and two movies, that doesn't mean anything. 00:22:32.290 --> 00:22:35.450 It just means that you get more than from one 00:22:35.450 --> 00:22:36.420 pizza and one movie. 00:22:36.420 --> 00:22:39.080 And we can even get the ratio that you get square root of 00:22:39.080 --> 00:22:43.320 two more, than you get from one pizza and two movies. 00:22:43.320 --> 00:22:46.340 We can do ranking and ordinality, but we can't 00:22:46.340 --> 00:22:47.560 assign cardinality. 00:22:47.560 --> 00:22:52.260 I can't say how happy you are in some abstract absolute 00:22:52.260 --> 00:22:54.120 sense from two pizzas and one movie. 00:22:54.120 --> 00:22:56.270 I can't give a cardinal form preference. 00:22:56.270 --> 00:22:58.150 But this is an ordinal ranking of preferences. 00:22:58.150 --> 00:23:01.130 I can tell what you like better than what else. 00:23:01.130 --> 00:23:03.192 That's why utility function is a representation of 00:23:03.192 --> 00:23:04.400 indifference maps. 00:23:04.400 --> 00:23:07.340 They're just a mathematical tool for comparing bundles, 00:23:07.340 --> 00:23:09.710 they're not some inner answer to the value of your soul or 00:23:09.710 --> 00:23:11.250 something like that. 00:23:11.250 --> 00:23:12.660 Don't imbue these with too much magic. 00:23:12.660 --> 00:23:15.050 They're just mathematical ways of representing preferences. 00:23:18.110 --> 00:23:22.530 The key concept, the single most important concept, for 00:23:22.530 --> 00:23:25.170 consumer theory for understanding how consumers 00:23:25.170 --> 00:23:28.245 make decisions is the concept of marginal utility. 00:23:32.690 --> 00:23:35.150 We'll talk a lot this semester about marginal this and 00:23:35.150 --> 00:23:36.560 marginal that. 00:23:36.560 --> 00:23:38.220 And this is our first example. 00:23:38.220 --> 00:23:40.840 Marginal utility. 00:23:40.840 --> 00:23:45.740 That is how your utility changes with each additional 00:23:45.740 --> 00:23:47.390 unit of the good, or the derivative 00:23:47.390 --> 00:23:49.150 of the utility function. 00:23:49.150 --> 00:23:51.025 If you want to do it in calculus terms, marginal 00:23:51.025 --> 00:23:52.790 utility is the derivative of your utility function with 00:23:52.790 --> 00:23:55.080 respect to one of the inputs. 00:23:55.080 --> 00:23:57.490 But if you don't want to put it in calculus terms, it's as 00:23:57.490 --> 00:24:01.040 you add each unit of one of the elements of the utility 00:24:01.040 --> 00:24:05.130 function, how does utility change 00:24:05.130 --> 00:24:08.380 So to see this, let's do an example of marginal utility. 00:24:08.380 --> 00:24:13.330 Imagine for a moment that you have two pizzas, p equals two. 00:24:13.330 --> 00:24:14.730 You've got two pizzas, they're there. 00:24:14.730 --> 00:24:16.660 Your roommate's got them or something. 00:24:16.660 --> 00:24:20.910 OK, now I want to ask, how does your utility change as 00:24:20.910 --> 00:24:23.060 you see additional movies? 00:24:23.060 --> 00:24:25.060 And to show that, let's look at figure 00:24:25.060 --> 00:24:28.310 4-3 which isn't here. 00:24:28.310 --> 00:24:29.410 Whoops. 00:24:29.410 --> 00:24:30.982 There's no figure 4-3. 00:24:30.982 --> 00:24:32.100 Do you got that figure 4-3? 00:24:32.100 --> 00:24:33.865 AUDIENCE: There was never any figure 4-3. 00:24:33.865 --> 00:24:37.310 PROFESSOR: There was never any figure 4-3. 00:24:37.310 --> 00:24:39.620 So let's go to 4-5. 00:24:43.370 --> 00:24:43.933 So basically-- 00:24:43.933 --> 00:24:46.588 AUDIENCE: Figure 4-4? 00:24:46.588 --> 00:24:47.838 PROFESSOR: No but-- 00:24:52.200 --> 00:24:53.110 actually fine. 00:24:53.110 --> 00:24:53.620 4-4. 00:24:53.620 --> 00:24:56.460 So basically what this is showing, what figure 4-4 is 00:24:56.460 --> 00:25:00.010 showing, is it showing how-- 00:25:00.010 --> 00:25:01.970 no actually, let's go to 4-5. 00:25:01.970 --> 00:25:02.910 They're out of order. 00:25:02.910 --> 00:25:04.120 Let's go to 4-5. 00:25:04.120 --> 00:25:06.420 What 4-5 is showing-- 00:25:06.420 --> 00:25:07.780 no, that's not going to work. 00:25:07.780 --> 00:25:09.540 OK, back to 4-4. 00:25:09.540 --> 00:25:14.600 What figure 4-4 is showing, is it's showing how your marginal 00:25:14.600 --> 00:25:18.650 utility for movies evolves, how your utility evolves as 00:25:18.650 --> 00:25:20.590 you get more movies. 00:25:20.590 --> 00:25:24.370 Given that you have two pizzas, this is the evolution 00:25:24.370 --> 00:25:28.440 of your utility as you get more movies. 00:25:28.440 --> 00:25:31.900 So each additional movie increases your utility. 00:25:31.900 --> 00:25:33.390 The slope is positive. 00:25:33.390 --> 00:25:35.610 By more is better, we know that. 00:25:35.610 --> 00:25:40.420 Even if it's some date movie, it still 00:25:40.420 --> 00:25:42.510 improves your utility. 00:25:42.510 --> 00:25:46.590 So it still improves your utility, but at 00:25:46.590 --> 00:25:48.010 a diminishing rate. 00:25:48.010 --> 00:25:50.910 And that's the key is that we assume 00:25:50.910 --> 00:25:58.020 diminishing marginal utility. 00:25:58.020 --> 00:26:00.550 The key assumption underlies everything we'll do for 00:26:00.550 --> 00:26:05.110 consumers is diminishing marginal utility. 00:26:05.110 --> 00:26:09.190 We assume that additional movie increases your utility, 00:26:09.190 --> 00:26:13.430 but at an ever diminishing rate. 00:26:13.430 --> 00:26:19.670 So basically, we can actually graph your margins. 00:26:19.670 --> 00:26:22.970 And that's what figure 4-5 is, is a graph of 00:26:22.970 --> 00:26:24.220 your marginal utility. 00:26:28.980 --> 00:26:38.080 So basically, when you have two pizzas and one movie, 00:26:38.080 --> 00:26:40.720 utility is square root of 2, right? 00:26:40.720 --> 00:26:45.860 Now what I'm saying is if you get one more movie, your 00:26:45.860 --> 00:26:49.120 utility is going to rise from square root of 2 to 2. 00:26:49.120 --> 00:26:53.262 So the marginal utility of that next movie -- 00:26:53.262 --> 00:26:54.711 is that right? 00:26:54.711 --> 00:26:56.160 Two movies. 00:26:56.160 --> 00:26:58.740 1.4. 00:26:58.740 --> 00:27:00.840 Yeah, it's going to rise by the square root of 2. 00:27:00.840 --> 00:27:03.746 You're going to multiply your utility by the square root of 00:27:03.746 --> 00:27:05.110 two, so your marginal utility-- 00:27:05.110 --> 00:27:08.140 you're going to go from the utility of square root of 2 to 00:27:08.140 --> 00:27:09.580 utility of two. 00:27:09.580 --> 00:27:11.730 So utility is going to increase by the 00:27:11.730 --> 00:27:14.170 square root of 2. 00:27:14.170 --> 00:27:15.400 Utility is going to increase-- 00:27:15.400 --> 00:27:16.681 I'm doing this wrong, hold on. 00:27:20.120 --> 00:27:21.370 One second. 00:27:24.000 --> 00:27:25.030 From one movie. 00:27:25.030 --> 00:27:25.520 I see. 00:27:25.520 --> 00:27:25.850 I see. 00:27:25.850 --> 00:27:26.650 So, I'm sorry. 00:27:26.650 --> 00:27:28.710 This isn't the delta, this is the level of marginal utility. 00:27:28.710 --> 00:27:30.010 So I'm graphing the actual level of marginal utility. 00:27:30.010 --> 00:27:30.700 Back up. 00:27:30.700 --> 00:27:33.115 OK, so I'm graphing the actual level of marginal utility. 00:27:36.960 --> 00:27:41.880 So when you have two pizzas and one movie, your marginal 00:27:41.880 --> 00:27:44.730 utility, your actual utility-- 00:27:44.730 --> 00:27:46.020 I see, that's what this is. 00:27:46.020 --> 00:27:47.480 This is the actual utility I'm graphing. 00:27:47.480 --> 00:27:49.270 So I told you a minute ago, we can't measure utility as a 00:27:49.270 --> 00:27:52.290 cardinal concept, but actually here I'm doing it anyway 00:27:52.290 --> 00:27:54.190 because it's to illustrate marginal utility. 00:27:54.190 --> 00:27:56.120 So your utility, OK. 00:27:56.120 --> 00:28:01.250 When you have one movie is 1.4, square root of 2. 00:28:01.250 --> 00:28:02.990 That's your utility. 00:28:02.990 --> 00:28:10.720 Now when you move from one movie to a second movie, your 00:28:10.720 --> 00:28:13.320 utility goes up from square root of 2 to 2. 00:28:13.320 --> 00:28:15.700 Your utility goes up by 0.6. 00:28:15.700 --> 00:28:19.560 So the marginal utility of that second movie is 0.6. 00:28:19.560 --> 00:28:23.680 Utility was 1.4, was a square root of 2. 00:28:23.680 --> 00:28:25.930 Now it's increased to 2. 00:28:25.930 --> 00:28:28.480 So the marginal utility of the first movie is 0.6. 00:28:28.480 --> 00:28:31.390 Now let's say you add another movie, you go to three movies. 00:28:31.390 --> 00:28:32.190 What's your utility now? 00:28:32.190 --> 00:28:34.280 It's the square root of 6. 00:28:34.280 --> 00:28:37.020 So it's gone from 4, to the square root 00:28:37.020 --> 00:28:40.070 of 6, which is 2.45. 00:28:40.070 --> 00:28:44.380 So your marginal utility of the third movie is 0.45. 00:28:44.380 --> 00:28:46.850 This graph is messed up because the first one is an 00:28:46.850 --> 00:28:48.450 actual utility level. 00:28:48.450 --> 00:28:49.873 So the first one I say, for one movie, you 00:28:49.873 --> 00:28:51.630 have a utility 1.4. 00:28:51.630 --> 00:28:54.260 And then for the second movie, I give the marginal utility, 00:28:54.260 --> 00:28:55.800 the third movie marginal utility. 00:28:55.800 --> 00:28:56.950 So, this graph sort of-- yeah? 00:28:56.950 --> 00:28:59.720 AUDIENCE: It shows the marginal utility of the very 00:28:59.720 --> 00:29:00.499 first movie. 00:29:00.499 --> 00:29:04.500 PROFESSOR: Yeah, I guess that's right 00:29:04.500 --> 00:29:05.200 because you're zero. 00:29:05.200 --> 00:29:06.390 You're zero movies. 00:29:06.390 --> 00:29:07.100 OK, right. 00:29:07.100 --> 00:29:07.410 You're right. 00:29:07.410 --> 00:29:08.820 OK, so the first one is the marginal utility of the very 00:29:08.820 --> 00:29:09.980 first movie, you're right. 00:29:09.980 --> 00:29:12.380 So the very first movie gives you marginal utility of 1.4 00:29:12.380 --> 00:29:13.840 because you go from 0 to square root of 2. 00:29:13.840 --> 00:29:14.420 That's right. 00:29:14.420 --> 00:29:15.490 My bad. 00:29:15.490 --> 00:29:17.610 So you go from 0 to square root of 2 to get a marginal 00:29:17.610 --> 00:29:20.473 utility of 1.4 for the first movie From square root of 2 to 00:29:20.473 --> 00:29:23.550 2, you get 0.6 the next movie. 00:29:23.550 --> 00:29:25.436 From 2 to square root of 6, you get 0.45 00:29:25.436 --> 00:29:26.950 for the third movie. 00:29:26.950 --> 00:29:29.950 For square root of 6 to square root of 8, you only get 0.38 00:29:29.950 --> 00:29:31.930 from the fourth movie, and so on. 00:29:31.930 --> 00:29:35.270 So the key point is that these marginal utilities are ever 00:29:35.270 --> 00:29:36.990 decreasing. 00:29:36.990 --> 00:29:42.790 Each additional movie gives you less incremental utility. 00:29:42.790 --> 00:29:44.385 And if you stop and think about it, 00:29:44.385 --> 00:29:45.720 it's kind of intuitive. 00:29:45.720 --> 00:29:47.620 Just stop and think, think about the movies you want to 00:29:47.620 --> 00:29:49.230 see right now. 00:29:49.230 --> 00:29:50.530 The four movies you want to see. 00:29:50.530 --> 00:29:53.970 Presumably whichever you ranked first would give you 00:29:53.970 --> 00:29:57.320 more utility to see than whichever you ranked second. 00:29:57.320 --> 00:29:58.860 And if you think the movies that are out right now are 00:29:58.860 --> 00:30:00.930 pretty crappy like I do, by the time you get to the fourth 00:30:00.930 --> 00:30:04.740 movie, you're not getting much utility from it at all. 00:30:04.740 --> 00:30:06.620 Thinking about movies that are out now, you're getting a lot 00:30:06.620 --> 00:30:08.650 of utility from that first movie you see. 00:30:08.650 --> 00:30:11.040 Marginal, extra utility from the first movie you see. 00:30:11.040 --> 00:30:13.200 But each additional one is giving you less and less. 00:30:13.200 --> 00:30:14.920 And that's the idea of diminishing marginal utility. 00:30:14.920 --> 00:30:18.370 Likewise with pizzas, if you haven't eaten all day, that 00:30:18.370 --> 00:30:21.050 first pizza can give you a very high marginal utility. 00:30:21.050 --> 00:30:23.950 The enjoyment you get from eating that first pizza can be 00:30:23.950 --> 00:30:25.890 very large. 00:30:25.890 --> 00:30:27.990 But the second pizza, not so much. 00:30:27.990 --> 00:30:29.240 You're already pretty full. 00:30:29.240 --> 00:30:29.840 Third pizza, even less. 00:30:29.840 --> 00:30:31.660 And then fourth pizza would probably violate 00:30:31.660 --> 00:30:34.030 non-satiation. 00:30:34.030 --> 00:30:35.000 So that's the basic idea. 00:30:35.000 --> 00:30:35.400 Yeah? 00:30:35.400 --> 00:30:37.276 AUDIENCE: I have a question. 00:30:37.276 --> 00:30:40.090 Do we assume that the goods are homogeneous. 00:30:40.090 --> 00:30:42.910 Is it the same movie watched four times? 00:30:42.910 --> 00:30:45.016 Or different movies? 00:30:45.016 --> 00:30:47.180 PROFESSOR: Actually, that's a great question. 00:30:47.180 --> 00:30:49.450 And you have to specify that as part of the problem. 00:30:49.450 --> 00:30:52.695 I haven't specified that here. 00:30:52.695 --> 00:30:54.710 Obviously it can't be the same pizza eaten four times. 00:30:54.710 --> 00:30:58.060 It could be the same kind of pizza eaten four times. 00:30:58.060 --> 00:31:03.340 But do you see the same movie? 00:31:03.340 --> 00:31:04.940 I haven't specified that here. 00:31:04.940 --> 00:31:06.615 So there's not a general assumption about that. 00:31:06.615 --> 00:31:08.775 It depends on how I define movies. 00:31:08.775 --> 00:31:12.870 Did I define movies as-- 00:31:12.870 --> 00:31:13.630 I don't know. 00:31:13.630 --> 00:31:14.170 God, I'm terrible. 00:31:14.170 --> 00:31:15.990 All I know that's out now is the Guardians of G'ahoole 00:31:15.990 --> 00:31:17.290 because I've got a little kid who is interested in it. 00:31:17.290 --> 00:31:18.330 Whatever movie's out. 00:31:18.330 --> 00:31:20.765 Do I define movies as Guardians of G'ahoole, or do I 00:31:20.765 --> 00:31:23.050 define movies as seeing a movie? 00:31:23.050 --> 00:31:24.340 And I didn't specify that. 00:31:24.340 --> 00:31:25.960 Implicit in my examples, I specify 00:31:25.960 --> 00:31:27.980 movies as seeing a movie. 00:31:27.980 --> 00:31:30.660 But you have to specify that to be more precise if you're 00:31:30.660 --> 00:31:32.510 actually trying to figure out-- 00:31:32.510 --> 00:31:34.330 it depends what you're maximizing over. 00:31:34.330 --> 00:31:36.270 If you're maximizing over seeing any movie or maximize 00:31:36.270 --> 00:31:37.970 over seeing the same movie. 00:31:37.970 --> 00:31:39.220 And I didn't specify here. 00:31:39.220 --> 00:31:40.080 AUDIENCE: It can work in both cases. 00:31:40.080 --> 00:31:41.830 PROFESSOR: It would work in both cases. 00:31:41.830 --> 00:31:43.590 Clearly you could imagine, actually it's a very good 00:31:43.590 --> 00:31:45.530 point, where do you think your marginal utility would 00:31:45.530 --> 00:31:47.590 diminish more? 00:31:47.590 --> 00:31:48.940 Seeing the same movie. 00:31:48.940 --> 00:31:52.530 So what your example points out is that different goods 00:31:52.530 --> 00:31:55.830 will have different rates of diminishing marginal utility. 00:31:55.830 --> 00:31:59.680 OK, so marginal utility will always be diminishing, but at 00:31:59.680 --> 00:32:02.500 very different rates for different goods. 00:32:02.500 --> 00:32:05.110 So the general principle is that they'll be generally 00:32:05.110 --> 00:32:07.370 diminishing marginal utility. 00:32:07.370 --> 00:32:09.530 But at different rates for different goods. 00:32:09.530 --> 00:32:13.390 So after all my mess ups, let me just review. 00:32:13.390 --> 00:32:15.430 Marginal utility is diminishing because each good 00:32:15.430 --> 00:32:16.380 is worth less to you. 00:32:16.380 --> 00:32:20.240 It's always positive because of non-satiation. 00:32:20.240 --> 00:32:24.140 And this graph represents the marginal utility you get from 00:32:24.140 --> 00:32:28.610 each movie you see conditional on having eaten two pizzas. 00:32:28.610 --> 00:32:30.450 Marginal utility is the increment from 00:32:30.450 --> 00:32:33.200 the next unit consumed. 00:32:33.200 --> 00:32:34.750 Now let's get back on track here. 00:32:34.750 --> 00:32:40.400 Now let's go to thinking about-- 00:32:40.400 --> 00:32:43.890 now that we have this concept of utility and marginal 00:32:43.890 --> 00:32:46.920 utility, let's now bring utility back 00:32:46.920 --> 00:32:48.570 to preference maps. 00:32:48.570 --> 00:32:52.500 Let's ask, given what we know about utility, what can this 00:32:52.500 --> 00:32:55.720 teach us about the shape of preference maps? 00:32:55.720 --> 00:32:59.910 What's the linkage between utility and preference maps? 00:32:59.910 --> 00:33:05.700 And that linkage comes through something we call the marginal 00:33:05.700 --> 00:33:06.950 rate of substitution. 00:33:09.520 --> 00:33:11.270 The marginal rate of substitution is the 00:33:11.270 --> 00:33:16.950 mathematical concept that links preference utility with 00:33:16.950 --> 00:33:19.290 preference maps. 00:33:19.290 --> 00:33:22.680 The marginal rate of substitution technically is 00:33:22.680 --> 00:33:24.710 the slope of the indifference curve. 00:33:24.710 --> 00:33:29.190 It's delta P over delta M. The slope of the indifference 00:33:29.190 --> 00:33:32.880 curve is the marginal rate of substitution. 00:33:32.880 --> 00:33:35.930 That's what it means graphically, but here's what 00:33:35.930 --> 00:33:39.120 you have to understand at a deeper level. 00:33:39.120 --> 00:33:42.590 What it really is, it's the rate which you are 00:33:42.590 --> 00:33:45.900 willing to trade off. 00:33:45.900 --> 00:33:50.010 The rate at which you are willing to trade off the 00:33:50.010 --> 00:33:52.180 y-axis for the x-axis. 00:33:52.180 --> 00:33:53.790 The rate at which you're willing to trade 00:33:53.790 --> 00:33:55.040 off pizza for movies. 00:33:57.510 --> 00:34:00.070 So that's what it means intuitively. 00:34:00.070 --> 00:34:04.720 The slope of the curve tells you that you're indifferent. 00:34:04.720 --> 00:34:06.630 Remember, you're indifferent between any points along with 00:34:06.630 --> 00:34:07.540 this indifference curve. 00:34:07.540 --> 00:34:12.260 You're indifferent between four pizzas and one movie, 00:34:12.260 --> 00:34:15.159 you're indifferent between two pizzas and two movies, and 00:34:15.159 --> 00:34:16.690 four movies and one pizza. 00:34:16.690 --> 00:34:17.679 You're indifferent along all those 00:34:17.679 --> 00:34:20.090 combinations of figure 4-6. 00:34:20.090 --> 00:34:23.739 The MRS is the slope of that curve telling you the rate at 00:34:23.739 --> 00:34:28.750 which you're willing to trade off pizza for movies. 00:34:28.750 --> 00:34:32.820 Now just a side note here, you're never, of course, 00:34:32.820 --> 00:34:34.179 actually trading. 00:34:34.179 --> 00:34:35.850 There's not some market where you bring a 00:34:35.850 --> 00:34:37.960 pizza and get a movie. 00:34:37.960 --> 00:34:40.659 So I didn't say trade, it's not like baseball cards. 00:34:40.659 --> 00:34:42.429 I said trade off. 00:34:42.429 --> 00:34:47.190 What I mean is ultimately you have some budget, and you have 00:34:47.190 --> 00:34:49.330 to allocate that budget. 00:34:49.330 --> 00:34:51.949 So if you decide to allocate it on pizzas, you can't 00:34:51.949 --> 00:34:53.190 allocate it on movies. 00:34:53.190 --> 00:34:55.215 Or the more you allocate on pizzas, the less you can 00:34:55.215 --> 00:34:56.239 allocate on movies. 00:34:56.239 --> 00:34:58.110 So there's always a trade-off. 00:34:58.110 --> 00:35:00.350 Remember, I said, economics is always about trade-offs. 00:35:00.350 --> 00:35:03.720 Given your limited budget, there's always a trade off. 00:35:03.720 --> 00:35:06.720 And the rate at which you're willing to trade off is your 00:35:06.720 --> 00:35:08.180 marginal rate of substitution. 00:35:08.180 --> 00:35:10.040 Given that you're going to have to trade off-- and we 00:35:10.040 --> 00:35:11.380 haven't got a bunch of constraints yet, we'll get to 00:35:11.380 --> 00:35:12.400 that next time-- 00:35:12.400 --> 00:35:13.713 the rate at which you're willing to is your marginal 00:35:13.713 --> 00:35:14.600 rate of substitution. 00:35:14.600 --> 00:35:14.865 Yeah? 00:35:14.865 --> 00:35:17.755 AUDIENCE: Is that rate usually related to the price? 00:35:17.755 --> 00:35:19.600 PROFESSOR: Ultimately no. 00:35:19.600 --> 00:35:20.090 I'm sorry. 00:35:20.090 --> 00:35:22.020 The marginal rate of substitution purely comes from 00:35:22.020 --> 00:35:23.310 your preferences. 00:35:23.310 --> 00:35:26.455 Ultimately to decide how much you actually consume, you'll 00:35:26.455 --> 00:35:28.250 need to bring in the price. 00:35:28.250 --> 00:35:30.850 So remember, I haven't talked about prices here, we haven't 00:35:30.850 --> 00:35:31.690 talked about that here. 00:35:31.690 --> 00:35:33.790 But this is a preference concept. 00:35:33.790 --> 00:35:34.970 This has nothing to do with prices. 00:35:34.970 --> 00:35:36.230 But you're getting ahead of us. 00:35:36.230 --> 00:35:39.990 We'll see next time, to decide how much you actually consume, 00:35:39.990 --> 00:35:41.570 you're going to relate the marginal rate of substitution 00:35:41.570 --> 00:35:43.190 to the prices you face in the market. 00:35:43.190 --> 00:35:46.010 And that will decide how much you consume. 00:35:46.010 --> 00:35:47.440 This is just a utility concept. 00:35:47.440 --> 00:35:47.720 Yeah? 00:35:47.720 --> 00:35:53.990 AUDIENCE: Did you say it was the y-axis or the x-axis? 00:35:53.990 --> 00:35:55.902 That would be negative? 00:35:55.902 --> 00:35:56.390 PROFESSOR: It's negative. 00:35:56.390 --> 00:35:57.110 Yes. 00:35:57.110 --> 00:35:58.740 Of course. 00:35:58.740 --> 00:36:00.080 Right, of course. 00:36:00.080 --> 00:36:03.620 The point is how many movies are you willing to give up to 00:36:03.620 --> 00:36:04.870 get another pizza? 00:36:07.870 --> 00:36:09.230 How many pizzas are you willing to give up to get 00:36:09.230 --> 00:36:10.010 another movie? 00:36:10.010 --> 00:36:13.010 MRS, it's very hard to remember what's on the top, 00:36:13.010 --> 00:36:13.490 what's on the bottom. 00:36:13.490 --> 00:36:14.620 Be very careful on this. 00:36:14.620 --> 00:36:17.080 But that's why I said remember it's the y-axis or the x-axis. 00:36:17.080 --> 00:36:19.870 It's how many pizzas you're willing to trade off to get 00:36:19.870 --> 00:36:21.120 another movie. 00:36:23.530 --> 00:36:26.870 Basically remember when I say trade off, here, this is not 00:36:26.870 --> 00:36:30.310 that you're literally trading, it's that ultimately you're 00:36:30.310 --> 00:36:31.720 going to have to make that trade-off. 00:36:31.720 --> 00:36:33.400 Ultimately when we come to the next lecture and face a budget 00:36:33.400 --> 00:36:35.670 constraint, you're going to have to decide how do I want 00:36:35.670 --> 00:36:37.540 to allocate my budget across pizzas and movies? 00:36:37.540 --> 00:36:41.650 The way you're going to decide that is by the relationship of 00:36:41.650 --> 00:36:45.220 how you feel about trading off one for the other. 00:36:45.220 --> 00:36:47.790 Now here's the key feature of the MRS which 00:36:47.790 --> 00:36:50.050 is the MRS is yeah? 00:36:50.050 --> 00:36:51.254 Question? 00:36:51.254 --> 00:36:51.706 Yeah. 00:36:51.706 --> 00:36:53.559 AUDIENCE: That and exchange rates are always changing 00:36:53.559 --> 00:36:54.870 depending on how much you happen to be trading. 00:36:54.870 --> 00:36:55.690 PROFESSOR: Exactly. 00:36:55.690 --> 00:37:00.010 The MRS is diminishing. 00:37:00.010 --> 00:37:02.180 Technically when you go to grad school, you realize that 00:37:02.180 --> 00:37:04.020 marginal utility isn't actually technically always 00:37:04.020 --> 00:37:04.440 diminishing. 00:37:04.440 --> 00:37:05.010 I said it is. 00:37:05.010 --> 00:37:06.210 For this course it is. 00:37:06.210 --> 00:37:09.400 But if you want to get mathematically correct, really 00:37:09.400 --> 00:37:11.550 what's always diminishing that you prove is the marginal rate 00:37:11.550 --> 00:37:14.670 of substitution is always diminishing. 00:37:14.670 --> 00:37:16.230 So we have diminishing marginal utility for the 00:37:16.230 --> 00:37:19.490 purpose of this course, but the really important concept 00:37:19.490 --> 00:37:23.320 is you have diminishing marginal rate of substitution. 00:37:23.320 --> 00:37:26.140 The rate at which you're willing to trade off pizza for 00:37:26.140 --> 00:37:31.030 movies is going to fall as you have less 00:37:31.030 --> 00:37:34.700 pizza and more movies. 00:37:34.700 --> 00:37:37.940 So to see that, look at this graph, and let's compute the 00:37:37.940 --> 00:37:41.060 marginal rate of substitution along each segment. 00:37:41.060 --> 00:37:42.050 So let's localize. 00:37:42.050 --> 00:37:44.170 Imagine the segments were linear, imagine we had two 00:37:44.170 --> 00:37:45.170 linear segments between these points. 00:37:45.170 --> 00:37:46.000 We don't. 00:37:46.000 --> 00:37:48.210 But imagine for a second we did. 00:37:48.210 --> 00:37:50.970 So the marginal rate of substitution from the first 00:37:50.970 --> 00:37:55.140 point, four pizzas and one movie, to the second point, 00:37:55.140 --> 00:37:57.940 two pizzas and two movies, the marginal rate of 00:37:57.940 --> 00:38:00.570 substitution is -2. 00:38:00.570 --> 00:38:06.380 You are willing to give up two pizzas to get one movie. 00:38:06.380 --> 00:38:08.980 This is the same graph, figure 4-6. 00:38:08.980 --> 00:38:11.160 This isn't on the graph, you have to write it on. 00:38:11.160 --> 00:38:13.300 So going from that first point to that second point, you're 00:38:13.300 --> 00:38:18.310 willing to give up two pizzas to get one movie. 00:38:18.310 --> 00:38:21.330 So that rate of marginal substitution is -2. 00:38:21.330 --> 00:38:25.620 However, when you're at two movies and two pizzas, and I 00:38:25.620 --> 00:38:29.220 say OK, how about giving up one more pizza to see movies? 00:38:29.220 --> 00:38:30.580 Now you say, wait a second. 00:38:30.580 --> 00:38:34.420 To give up one more pizza, I need to see two movies. 00:38:34.420 --> 00:38:36.390 My marginal rate of substitution on that second 00:38:36.390 --> 00:38:39.340 segment is -1/2. 00:38:39.340 --> 00:38:40.680 The marginal rate of substitution on the first 00:38:40.680 --> 00:38:41.990 segment is -2. 00:38:41.990 --> 00:38:43.940 The marginal rate of substitution on the second 00:38:43.940 --> 00:38:44.690 segment is -1/2. 00:38:44.690 --> 00:38:46.860 Once again, assuming they're not linear, so it's actually 00:38:46.860 --> 00:38:48.587 changing everywhere, but if they were linear, that's what 00:38:48.587 --> 00:38:49.480 it would be. 00:38:49.480 --> 00:38:51.610 Can someone tell me why? 00:38:51.610 --> 00:38:55.230 Why is the marginal rate of substitution falling? 00:38:55.230 --> 00:38:58.060 Why is the marginal rate of substitution lower on that 00:38:58.060 --> 00:38:59.959 second segment than on the first? 00:38:59.959 --> 00:39:04.699 AUDIENCE: Because marginal utility increases the fewer of 00:39:04.699 --> 00:39:06.446 something you have. 00:39:06.446 --> 00:39:07.950 PROFESSOR: Exactly. 00:39:07.950 --> 00:39:11.180 So go ahead, flesh it out, the fewer of somthing you have, so 00:39:11.180 --> 00:39:13.100 tell me in terms of the trade you're willing to make. 00:39:13.100 --> 00:39:17.315 AUDIENCE: You value it more, so you want to trade more of 00:39:17.315 --> 00:39:18.205 something else for it. 00:39:18.205 --> 00:39:22.893 PROFESSOR: The point is when I have four pizzas my marginal 00:39:22.893 --> 00:39:26.600 utility of that last pizza is not very high. 00:39:26.600 --> 00:39:30.380 And I'm fine to give up two pizzas-- 00:39:30.380 --> 00:39:32.360 and plus I'm only seeing one movie, there's a second movie 00:39:32.360 --> 00:39:33.820 I really want to see. 00:39:33.820 --> 00:39:36.220 So you say to me, look, I've got four pizzas, 00:39:36.220 --> 00:39:37.700 I'm seeing one movie. 00:39:37.700 --> 00:39:39.420 You say hey, there's a second movie out I 00:39:39.420 --> 00:39:40.460 know you want to see. 00:39:40.460 --> 00:39:42.500 I know you don't really value four pizzas. 00:39:42.500 --> 00:39:43.850 At the end, you're totally full. 00:39:43.850 --> 00:39:45.350 Would you be willing to give up two pizzas to see the 00:39:45.350 --> 00:39:45.720 second movie? 00:39:45.720 --> 00:39:47.380 And you're like, sure why not? 00:39:47.380 --> 00:39:50.210 Well once you have two pizzas and you've seen two movies, 00:39:50.210 --> 00:39:51.930 you're not that interested in a third movie and you'll be 00:39:51.930 --> 00:39:54.610 hungry if you have less than two pizzas, so then you say, 00:39:54.610 --> 00:39:55.060 wait a second. 00:39:55.060 --> 00:39:56.970 If you want me to give up another pizza, you've got to 00:39:56.970 --> 00:39:59.800 give me two movies. 00:39:59.800 --> 00:40:04.220 Because my marginal utility of pizzas is rising, my marginal 00:40:04.220 --> 00:40:07.570 utility of movies is falling. 00:40:07.570 --> 00:40:09.600 And that's why the marginal rate of substitution 00:40:09.600 --> 00:40:15.490 diminishes along the indifference curve. 00:40:15.490 --> 00:40:18.160 So that allows us to write mathematically the definition 00:40:18.160 --> 00:40:23.470 of the marginal rate of substitution is the negative 00:40:23.470 --> 00:40:26.180 of the marginal utility of movies, or more generally 00:40:26.180 --> 00:40:32.030 what's on the x-axis, over the marginal utility of pizza, or 00:40:32.030 --> 00:40:33.280 more generally what's on the y-axis. 00:40:35.980 --> 00:40:37.670 The marginal rate of substitution, the first key 00:40:37.670 --> 00:40:39.992 formula you need to know for this course, the marginal rate 00:40:39.992 --> 00:40:41.060 of substitution is equal to the 00:40:41.060 --> 00:40:42.310 ratio of marginal utilities. 00:40:44.840 --> 00:40:46.720 Now this is tricky. 00:40:49.660 --> 00:40:51.060 Maybe you guys don't find it tricky, it's the kind of thing 00:40:51.060 --> 00:40:52.010 I find tricky. 00:40:52.010 --> 00:40:57.810 Which is I defined it as delta y-axis over delta x-axis. 00:40:57.810 --> 00:40:59.930 And yet, when I defined here the marginal utilities, I 00:40:59.930 --> 00:41:01.880 flipped it. 00:41:01.880 --> 00:41:03.700 I did the marginal utility of what's on the x-axis over the 00:41:03.700 --> 00:41:04.810 marginal utility of what's on the y-axis. 00:41:04.810 --> 00:41:05.300 Why is that? 00:41:05.300 --> 00:41:06.430 Can anyone tell me why that is? 00:41:06.430 --> 00:41:08.154 Why is it flipped when defined in 00:41:08.154 --> 00:41:09.595 terms of marginal utilities? 00:41:09.595 --> 00:41:09.910 Yeah? 00:41:09.910 --> 00:41:12.518 AUDIENCE: It's a denominator. 00:41:12.518 --> 00:41:14.506 So utility over movies-- 00:41:17.460 --> 00:41:20.510 PROFESSOR: Well, let me try for slightly more, how does 00:41:20.510 --> 00:41:21.320 marginal utility relate? 00:41:21.320 --> 00:41:21.575 Yeah. 00:41:21.575 --> 00:41:28.291 AUDIENCE: Marginal utility is delta P over 00:41:28.291 --> 00:41:30.279 P. So it gets flipped. 00:41:30.279 --> 00:41:30.780 Because of-- 00:41:30.780 --> 00:41:32.140 PROFESSOR: OK. 00:41:32.140 --> 00:41:34.620 Yeah, you're giving the same answer, which 00:41:34.620 --> 00:41:35.490 is technically right. 00:41:35.490 --> 00:41:38.470 What I was more looking for but it's the intuitive version 00:41:38.470 --> 00:41:42.380 of that, marginal utility is a negative function of quantity. 00:41:42.380 --> 00:41:44.810 Marginal utility is a negative function of quantity. 00:41:44.810 --> 00:41:47.700 So the fact that it's a ratio of the quantity of pizza over 00:41:47.700 --> 00:41:50.000 the quantity of movies is the same thing as the marginal 00:41:50.000 --> 00:41:52.340 utility of movies over the marginal utility of pizza. 00:41:52.340 --> 00:41:54.890 Because marginal utility is a negative function of quantity. 00:41:54.890 --> 00:41:56.300 The more quantity you have, the lower is 00:41:56.300 --> 00:41:58.440 your marginal utility. 00:41:58.440 --> 00:42:01.060 And that's the key to understand. 00:42:01.060 --> 00:42:05.460 So it's the slope of the indifference curve which is 00:42:05.460 --> 00:42:07.485 the ratio of the marginal utilities, but it's the 00:42:07.485 --> 00:42:10.700 marginal utility of movies over pizza. 00:42:10.700 --> 00:42:14.290 Because what that's saying is that as you get more movies, 00:42:14.290 --> 00:42:17.730 you care less about each additional movie and ditto 00:42:17.730 --> 00:42:18.980 with pizzas. 00:42:20.870 --> 00:42:22.250 Let's just look at this for a minute, think about it 00:42:22.250 --> 00:42:23.270 intuitively for a minute. 00:42:23.270 --> 00:42:25.590 We've seen it graphically, we're seeing it 00:42:25.590 --> 00:42:27.510 mathematically, let's make sure we understand it 00:42:27.510 --> 00:42:29.120 intuitively. 00:42:29.120 --> 00:42:33.630 What this is saying is that as you get more movies-- 00:42:33.630 --> 00:42:36.470 so let's relate this to the graph. 00:42:36.470 --> 00:42:41.800 As you get more movies and less pizza, as you move down 00:42:41.800 --> 00:42:45.160 that curve, more movies, less pizza, what's happening? 00:42:45.160 --> 00:42:46.930 What's happening to the marginal utility of movies as 00:42:46.930 --> 00:42:48.650 you move down that curve? 00:42:48.650 --> 00:42:50.190 What direction is it heading? 00:42:50.190 --> 00:42:51.500 AUDIENCE: It's decreasing. 00:42:51.500 --> 00:42:51.870 PROFESSOR: What? 00:42:51.870 --> 00:42:52.240 AUDIENCE: It's decreasing. 00:42:52.240 --> 00:42:54.270 PROFESSOR: It's decreasing. 00:42:54.270 --> 00:42:56.540 Because you're getting more movies and marginal utility is 00:42:56.540 --> 00:42:58.260 a negative function of quantity. 00:42:58.260 --> 00:43:02.770 Likewise, the marginal utility of pizza is increasing because 00:43:02.770 --> 00:43:05.850 you're getting less pizza so you care 00:43:05.850 --> 00:43:07.720 about each pizza more. 00:43:07.720 --> 00:43:10.900 And that's why the marginal rate of substitution 00:43:10.900 --> 00:43:12.150 diminishes. 00:43:13.940 --> 00:43:16.470 That's why it diminishes because as you move down that 00:43:16.470 --> 00:43:19.830 curve, the numerator is falling, the denominator is 00:43:19.830 --> 00:43:20.690 increasing. 00:43:20.690 --> 00:43:23.220 And that's why we have everywhere diminishing 00:43:23.220 --> 00:43:24.470 marginal rates of substitution. 00:43:27.790 --> 00:43:35.140 So another way to think about this is imagine for a moment 00:43:35.140 --> 00:43:38.150 what life would be like if we didn't have diminishing 00:43:38.150 --> 00:43:39.990 marginal rates of substitution. 00:43:39.990 --> 00:43:42.460 And once again I'm going to try, once again Jessica, next 00:43:42.460 --> 00:43:43.700 year we'll let you make this pretty. 00:43:43.700 --> 00:43:46.450 But I'm going to try to draw it crudely here. 00:43:46.450 --> 00:43:48.990 Let's do pizzas and movies again. 00:43:52.570 --> 00:43:53.980 Let's do pizzas and movies again. 00:43:58.240 --> 00:43:59.570 Movies and pizza. 00:43:59.570 --> 00:44:01.639 And that's one, two, three, four. 00:44:07.062 --> 00:44:10.000 One, two, three, four. 00:44:10.000 --> 00:44:12.560 Now let's imagine that instead of diminishing marginal 00:44:12.560 --> 00:44:16.230 utility and instead of indifference curves being 00:44:16.230 --> 00:44:19.200 convex to the origin, imagine if indifference curves were 00:44:19.200 --> 00:44:22.270 concave to the origin, which is what increasing marginal 00:44:22.270 --> 00:44:24.355 rate substitution would imply. 00:44:24.355 --> 00:44:26.200 So that would be something where you'd be indifferent 00:44:26.200 --> 00:44:32.530 between four pizzas and one movie, between three pizzas 00:44:32.530 --> 00:44:36.740 and two movies, and between one pizza and three movies. 00:44:36.740 --> 00:44:38.680 So your indifference curve would look like that. 00:44:38.680 --> 00:44:40.495 Not quite to scale, but you get it. 00:44:40.495 --> 00:44:43.390 It would be concave to the origin instead of convex to 00:44:43.390 --> 00:44:44.320 the origin. 00:44:44.320 --> 00:44:47.930 In this case, marginal rates of substitution would be 00:44:47.930 --> 00:44:49.830 everywhere increasing. 00:44:49.830 --> 00:44:53.370 That is, basically I'd be willing to give up one pizza 00:44:53.370 --> 00:44:55.390 to get one movie. 00:44:55.390 --> 00:44:58.670 But to get that next movie, I'd give up two pizzas. 00:44:58.670 --> 00:45:02.050 But as you can see, that doesn't make sense. 00:45:02.050 --> 00:45:04.900 It doesn't make sense that given that as long as you're 00:45:04.900 --> 00:45:07.250 ranking movies, or even more in the example of seeing the 00:45:07.250 --> 00:45:08.590 same movie over and over again, it's maybe more 00:45:08.590 --> 00:45:11.050 compelling. 00:45:11.050 --> 00:45:15.810 That basically what you can see is that if you're willing 00:45:15.810 --> 00:45:19.310 to give up one pizza to see that movie a second time, why 00:45:19.310 --> 00:45:22.550 would you possibly give up two pizzas to see it a third time? 00:45:22.550 --> 00:45:24.340 That makes no sense at all. 00:45:24.340 --> 00:45:27.210 If you only like it so much you only give up one pizza to 00:45:27.210 --> 00:45:29.740 see it a second time, why would you possibly give up two 00:45:29.740 --> 00:45:30.870 pizzas to see it a third time? 00:45:30.870 --> 00:45:32.510 You wouldn't. 00:45:32.510 --> 00:45:33.650 It doesn't make sense. 00:45:33.650 --> 00:45:36.930 And that's why marginal rate of substitution has to be 00:45:36.930 --> 00:45:39.520 everywhere decreasing, it can't be increasing. 00:45:39.520 --> 00:45:39.795 Yeah? 00:45:39.795 --> 00:45:42.450 AUDIENCE: Could it remain constant? 00:45:42.450 --> 00:45:43.858 PROFESSOR: It could actually remain constant. 00:45:43.858 --> 00:45:45.070 Yes, that's right. 00:45:45.070 --> 00:45:46.230 You can be indifferent. 00:45:46.230 --> 00:45:48.640 My indifference curves-- 00:45:48.640 --> 00:45:51.210 how many of you guys have seen Toy Story 3? 00:45:51.210 --> 00:45:53.480 I think it's one of my 10 favorite movies of all time. 00:45:53.480 --> 00:45:55.970 The greatest children's movie ever made. 00:45:55.970 --> 00:45:56.900 I've seen it three times. 00:45:56.900 --> 00:45:58.050 My indifference curve is virtually-- 00:45:58.050 --> 00:45:59.625 I've enjoyed it the third times as much as the first-- 00:45:59.625 --> 00:46:02.840 it's virtually flat with respect to Toy Story 3. 00:46:02.840 --> 00:46:05.870 I could see it 10 more times and feel pretty much the same. 00:46:05.870 --> 00:46:08.340 So that's certainly possible that it would be constant, 00:46:08.340 --> 00:46:10.110 that I'd be willing to give up whatever I pay-- 00:46:10.110 --> 00:46:12.840 $10 a shot to see it. 00:46:12.840 --> 00:46:14.180 It's possible. 00:46:14.180 --> 00:46:18.900 So basically, almost always, inequalities will be greater 00:46:18.900 --> 00:46:21.020 than or equal to, or less than or equal to in this course. 00:46:21.020 --> 00:46:23.250 It's more fun to talk about the not equal to case, the 00:46:23.250 --> 00:46:24.180 non-linear case. 00:46:24.180 --> 00:46:26.290 But linear cases will exist as well. 00:46:26.290 --> 00:46:28.610 It's just a can't be can't be opposite sign. 00:46:28.610 --> 00:46:31.370 You can't have an increasing marginal rate of substitution. 00:46:31.370 --> 00:46:31.665 Another question over here? 00:46:31.665 --> 00:46:34.828 AUDIENCE: What about addictions? 00:46:34.828 --> 00:46:36.078 You could want it more the second time. 00:46:39.180 --> 00:46:40.210 PROFESSOR: That's interesting. 00:46:40.210 --> 00:46:41.885 So how would addiction work? so basically-- 00:46:41.885 --> 00:46:46.350 AUDIENCE: Well it's not really decreasing. 00:46:46.350 --> 00:46:48.670 You need more the second time, right? 00:46:48.670 --> 00:46:49.297 So it has to-- 00:46:49.297 --> 00:46:50.051 PROFESSOR: That's very interesting. 00:46:50.051 --> 00:46:53.010 I mean in some sense. 00:46:53.010 --> 00:46:58.160 So you give up one pizza for the first shot of heroin. 00:46:58.160 --> 00:47:03.326 And then, you're hooked, so then you'd be willing to give 00:47:03.326 --> 00:47:04.960 up two pizzas for the next shot of heroin. 00:47:09.433 --> 00:47:10.700 Yeah, I guess so. 00:47:10.700 --> 00:47:11.610 I guess that's right. 00:47:11.610 --> 00:47:14.860 I guess we're going to have to stay away from addiction in 00:47:14.860 --> 00:47:16.440 this course. 00:47:16.440 --> 00:47:19.470 I guess an addictive good could look like that. 00:47:19.470 --> 00:47:21.380 That's a very good point. 00:47:21.380 --> 00:47:24.490 Other questions, comments? 00:47:24.490 --> 00:47:27.440 So what we're doing is we're going to stop here, 00:47:27.440 --> 00:47:30.420 understanding that we're going to have-- 00:47:30.420 --> 00:47:31.670 leaving this example aside-- we're going to have 00:47:31.670 --> 00:47:32.710 diminishing marginal-- 00:47:32.710 --> 00:47:33.290 yes one more question? 00:47:33.290 --> 00:47:34.540 AUDIENCE: [UNINTELLIGIBLE] 00:47:42.817 --> 00:47:45.970 PROFESSOR: Basically, we're assuming by non-satiation that 00:47:45.970 --> 00:47:47.500 ever happens. 00:47:47.500 --> 00:47:49.360 So once again, that would violate the non-satiation. 00:47:49.360 --> 00:47:51.800 The problem with the addictiveness example is the 00:47:51.800 --> 00:47:54.580 reason it wouldn't work in this course is eventually 00:47:54.580 --> 00:47:56.630 you'd violate your budget constraint because you'd want 00:47:56.630 --> 00:47:58.340 more and more and more. 00:47:58.340 --> 00:47:59.810 Maybe not. 00:47:59.810 --> 00:48:01.830 But in any case, we're going to ignore that example, assume 00:48:01.830 --> 00:48:04.090 diminishing marginal rate of substitution, and we'll come 00:48:04.090 --> 00:48:05.930 back next time as I put this together with a budget 00:48:05.930 --> 00:48:07.360 constraint to actually dictate your choices.