WEBVTT 00:01.610 --> 00:06.350 Prof: So for those of you who weren't here yesterday-- 00:06.350 --> 00:07.850 or, last class, first class, 00:07.845 --> 00:10.445 I'll say a couple words about what happened, 00:10.450 --> 00:12.700 basically four words. 00:12.700 --> 00:16.820 The course is really made of up four different elements. 00:16.820 --> 00:20.970 The first part is the standard financial theory course that 00:20.970 --> 00:25.550 grew up in the last ten years at a lot of major universities, 00:25.550 --> 00:29.800 pioneered by a bunch of guys who won Nobel Prizes in business 00:29.801 --> 00:30.511 schools. 00:30.510 --> 00:33.560 And it's the method, some of them quite clever and I 00:33.562 --> 00:36.972 think fun, methods for pricing financial assets and making 00:36.974 --> 00:38.894 optimal financial decisions. 00:38.890 --> 00:42.360 So you're going to learn all these tricks and how the 00:42.363 --> 00:45.213 financial system works, and you'll learn it both from a 00:45.208 --> 00:47.988 theoretical point of view, the way they thought of it in 00:47.993 --> 00:51.693 these finance schools, and also from a practical point 00:51.693 --> 00:56.073 of view since many of these very same problems come up all the 00:56.069 --> 00:59.009 time in the hedge fund I helped start. 00:59.010 --> 01:02.100 So that'll be the main part of the course, but there are three 01:02.100 --> 01:05.090 other things that I want to concentrate on in the course. 01:05.090 --> 01:07.820 So the second point is reexamining the logic of 01:07.819 --> 01:09.659 laissez-faire and regulation. 01:09.659 --> 01:13.769 This is a dramatic moment in our history now where there's 01:13.772 --> 01:17.552 tremendous pressure on-- temporarily anyway--on the 01:17.548 --> 01:21.488 government to establish all sorts of new regulations. 01:21.489 --> 01:23.749 There's also tremendous resistance to establishing the 01:23.754 --> 01:24.914 new sorts of regulations. 01:24.909 --> 01:28.529 So there's a debate going on now in Congress and in the halls 01:28.528 --> 01:32.028 of academia about what kind of regulations should we put in 01:32.025 --> 01:34.185 place, what regulations would have 01:34.185 --> 01:36.785 prevented the crisis we've just lived through. 01:36.790 --> 01:39.370 The crisis, by the way, which I don't think we're done 01:39.373 --> 01:39.913 with yet. 01:39.910 --> 01:42.160 So there's a very powerful argument in economics. 01:42.160 --> 01:44.100 The most famous argument in economics, 01:44.099 --> 01:48.139 the invisible hand argument that basically says markets work 01:48.138 --> 01:52.448 best when they're not encumbered by government interventions. 01:52.450 --> 01:55.330 So we're going to reexamine that argument in the context of 01:55.334 --> 01:56.334 financial markets. 01:56.330 --> 01:59.600 Then the third thing I'm going to discuss in this course at 01:59.596 --> 02:02.916 some length is the mortgage market and the recent crisis. 02:02.920 --> 02:06.240 After all, my hedge fund is a mortgage hedge fund. 02:06.239 --> 02:12.109 We founded it in 1994, by the way, which was-- 02:12.110 --> 02:15.170 the five years before that I was running the Fixed Income 02:15.169 --> 02:17.409 Research Department at Kidder Peabody, 02:17.408 --> 02:20.238 which was the biggest player in the mortgage market then on the 02:20.241 --> 02:20.791 sell side. 02:20.788 --> 02:24.158 The hedge funds buy mortgages, investment banks create and 02:24.163 --> 02:26.003 sell the mortgage securities. 02:26.000 --> 02:30.290 So I was running the research department at the firm that did 02:30.294 --> 02:34.164 twenty percent of the market in what's called CMOs, 02:34.160 --> 02:38.270 and then I changed to the buy side and was at a hedge fund 02:38.272 --> 02:42.472 that bought those kinds of CMOs, and bought sub-prime mortgage, 02:42.470 --> 02:43.750 CDOs, everything. 02:43.750 --> 02:47.880 So it seems I suffered greatly through the last two years of 02:47.875 --> 02:52.205 the mortgage crisis and it would just be foolish not to explain 02:52.210 --> 02:56.260 what was going on and what it felt like to be in a mortgage 02:56.264 --> 03:01.164 hedge fund while the rest of the world was collapsing around us. 03:01.158 --> 03:03.928 And for quite a while it's given me some great 03:03.925 --> 03:06.625 embarrassment to have been part of it all. 03:06.628 --> 03:09.728 On the other hand, now I feel like one of those 03:09.730 --> 03:10.540 survivors. 03:10.538 --> 03:16.258 Hundreds of our counter-parties and much bigger mortgage players 03:16.258 --> 03:19.708 went out of business and we didn't, 03:19.710 --> 03:22.370 so I don't feel quite as bad about it as I did before. 03:22.370 --> 03:24.840 And I don't know every detail of what went on in my hedge 03:24.836 --> 03:26.486 fund, because after all I'm only part 03:26.492 --> 03:28.852 time there, but there's a lot I do know 03:28.848 --> 03:32.128 about and so I'll try and tell you some of that. 03:32.128 --> 03:35.108 And then the fourth thing is Social Security. 03:35.110 --> 03:40.440 This is the biggest government program and it's a financial 03:40.443 --> 03:44.033 problem what to do about retirement, 03:44.030 --> 03:46.960 and Social Security is the biggest government program of 03:46.960 --> 03:47.280 all. 03:47.280 --> 03:51.490 The only thing close is the military budget in terms of 03:51.485 --> 03:53.195 annual expenditures. 03:53.199 --> 03:56.049 And so I'm going to explain how that works, and what the problem 03:56.050 --> 03:58.310 is, and how it arose, and what I think the solution 03:58.312 --> 03:58.632 is. 03:58.628 --> 04:00.668 So those are the four things the course is going to 04:00.674 --> 04:01.374 concentrate on. 04:01.370 --> 04:03.380 The mechanics of the course, again, 04:03.378 --> 04:06.628 are homeworks, every week there's going to be 04:06.633 --> 04:11.223 a homework with little problems illustrating what we're talking 04:11.219 --> 04:11.959 about. 04:11.960 --> 04:13.660 So there's one already on the web, Tuesday, 04:13.662 --> 04:15.772 today, every Tuesday there will be one on the web. 04:15.770 --> 04:17.540 It'll be due the next Tuesday. 04:17.540 --> 04:21.610 The sections will always meet between Thursday and Monday, 04:21.613 --> 04:24.403 so the problem set will come Tuesday. 04:24.399 --> 04:27.349 You'll have two days of classes on the material that the problem 04:27.348 --> 04:30.058 set will cover and then you can talk to the TAs about stuff 04:30.064 --> 04:32.694 between Thursday and Tuesday when I presume you'll do the 04:32.687 --> 04:33.527 problem set. 04:33.529 --> 04:35.169 And that's twenty percent of the grade. 04:35.170 --> 04:36.660 Twenty percent is the first midterm. 04:36.660 --> 04:40.320 Twenty percent is the second midterm and forty percent is the 04:40.321 --> 04:40.811 final. 04:40.810 --> 04:44.180 Two midterms takes a lot of class time, on the other hand, 04:44.180 --> 04:47.790 and it also takes a tremendous amount of effort by the TAs. 04:47.790 --> 04:51.130 And so I appreciate their willingness to grade two 04:51.130 --> 04:53.430 midterms, but I think you'll find it's 04:53.428 --> 04:56.538 helpful to study the course in two pieces than try to do the 04:56.543 --> 05:00.993 whole thing-- It'll be much better for you I 05:00.985 --> 05:05.775 found in the past to have two midterms. 05:05.779 --> 05:07.149 Oh, and one warning. 05:07.149 --> 05:09.799 The course doesn't require difficult mathematics, 05:09.800 --> 05:12.740 but for me, as I said in the first class, 05:12.740 --> 05:17.240 it's very interesting that there are so many subtle things 05:17.238 --> 05:20.078 that affect a financial decision, 05:20.079 --> 05:22.239 and you have to think about what you know and all the 05:22.238 --> 05:23.398 different things you know. 05:23.399 --> 05:25.519 You have to think about what the other guy knows who's taking 05:25.516 --> 05:26.606 the other side of the market. 05:26.610 --> 05:29.960 You have to think about what he knows about what you know, 05:29.959 --> 05:31.889 and you have to think about what he knows about what you 05:31.887 --> 05:34.177 know about what he knows, and all that thing in the end 05:34.175 --> 05:36.265 boils down to one number, the price. 05:36.269 --> 05:40.329 So it's a philosophically interesting problem, 05:40.331 --> 05:42.771 interactive epistemology. 05:42.769 --> 05:45.459 Some people have described economics as interactive 05:45.461 --> 05:46.271 epistemology. 05:46.269 --> 05:48.919 It's more complicated than standard epistemology and 05:48.923 --> 05:52.153 philosophy because there they go in circles thinking about what 05:52.148 --> 05:55.478 one person knows and whether you can know that you know and stuff 05:55.476 --> 05:56.306 like that. 05:56.310 --> 05:58.110 In economics you have to worry about what you know, 05:58.110 --> 05:59.980 what the other guy knows, what you know about what he 05:59.983 --> 06:01.393 knows about what you know etcetera. 06:01.389 --> 06:04.459 So it's a more complex problem, and yet at the end there's just 06:04.464 --> 06:06.504 one number which can be right or wrong. 06:06.500 --> 06:10.520 And so when I was a freshman here at Yale my roommate who was 06:10.516 --> 06:14.396 a classics major said that his subject was much harder than 06:14.399 --> 06:16.929 mine-- that was math--because all I 06:16.927 --> 06:18.517 had to do was be right. 06:18.519 --> 06:21.939 And so I'm going to take advantage of that simplicity and 06:21.937 --> 06:25.717 every problem is going to have a number that you're supposed to 06:25.720 --> 06:26.270 find. 06:26.269 --> 06:30.529 And so it's not complicated mathematics, but it involves 06:30.526 --> 06:31.916 lots of numbers. 06:31.920 --> 06:34.410 And so if you hate numbers you shouldn't take this course. 06:34.410 --> 06:37.040 And as I said before, there have always been people 06:37.043 --> 06:39.103 who, you know, you can be very smart. 06:39.100 --> 06:43.630 You can also have a great future in finance and not like 06:43.625 --> 06:44.445 numbers. 06:44.449 --> 06:47.289 You can like making deals and things like that not thinking in 06:47.293 --> 06:48.183 terms of numbers. 06:48.180 --> 06:50.890 So just because you don't like numbers and maybe shouldn't take 06:50.894 --> 06:53.304 this course doesn't mean you should be discouraged about 06:53.303 --> 06:53.833 finance. 06:53.829 --> 06:56.539 It's just how I happen to teach the course because that's what's 06:56.536 --> 06:57.436 comfortable for me. 06:57.440 --> 06:58.850 So I'm just warning you about it. 06:58.850 --> 07:05.090 It won't be hard, but it'll be relentless. 07:05.088 --> 07:07.748 I want to talk today about that second problem, 07:07.749 --> 07:11.099 about the logic of the free market and to do that I'm going 07:11.101 --> 07:13.011 to have to introduce a model. 07:13.009 --> 07:15.639 So it raises the question of what is a model in economics. 07:15.639 --> 07:17.709 Many of you have taken economics before. 07:17.709 --> 07:20.639 You sort of know what this idea is, but I think it's worth 07:20.637 --> 07:23.767 spending a minute on it because it represented a revolution in 07:23.773 --> 07:24.393 thought. 07:24.389 --> 07:28.109 So for an economist a model means you distinguish exogenous 07:28.110 --> 07:30.550 variables from endogenous variables. 07:30.550 --> 07:32.950 The exogenous things people can't control. 07:32.949 --> 07:34.879 They're just the weather and things like that. 07:34.879 --> 07:37.889 The endogenous variables are things they can control and 07:37.889 --> 07:41.009 you're trying to predict what the endogenous variables are 07:41.009 --> 07:43.989 going to turn out to be like, what will the prices be, 07:43.992 --> 07:46.392 what will the consumptions be, things like that. 07:46.389 --> 07:47.589 How much income will people have? 07:47.589 --> 07:49.379 Those are the endogenous variables. 07:49.379 --> 07:51.009 So you have a theory. 07:51.009 --> 07:54.889 So the theory is couched in terms of equilibrium. 07:54.889 --> 07:59.079 There's a bunch of equations which have to be satisfied, 07:59.077 --> 08:00.217 F of E and X. 08:00.220 --> 08:02.860 So given the endogenous variables and the exogenous 08:02.862 --> 08:04.632 variables, exogenous and endogenous, 08:04.632 --> 08:07.352 I wrote them in that order, there's a set of simultaneous 08:07.346 --> 08:10.026 equations, F, that have to be satisfied. 08:10.028 --> 08:13.398 And so you find equilibrium when given the exogenous 08:13.396 --> 08:17.086 variables E you find the endogenous variables X of E that 08:17.091 --> 08:20.261 solve that system of simultaneous equations. 08:20.259 --> 08:23.339 All our equilibrium models are going to have that form, 08:23.339 --> 08:27.639 and one very important thing they allow you to do, 08:27.639 --> 08:30.729 which is the heart of economic analysis is comparative statics. 08:30.730 --> 08:36.130 If you change the exogenous variable E it'll require a 08:36.130 --> 08:39.800 different X to solve the equation. 08:39.798 --> 08:45.108 So E has an effect on X in order to restore equilibrium. 08:45.110 --> 08:49.030 And so the prediction that a change in E has a certain effect 08:49.030 --> 08:51.450 on X is called comparative statics. 08:51.450 --> 08:53.600 Now, how would a historian describe that? 08:53.600 --> 08:55.190 A historian would say, "Well, that's 08:55.187 --> 08:56.257 counterfactual reasoning. 08:56.259 --> 08:57.599 The environment is E. 08:57.600 --> 09:00.110 Why are you bothering to tell me about what would happen if 09:00.106 --> 09:02.266 the environment changed from E to E-prime?" 09:02.269 --> 09:04.649 Well, that's the heart of economic analysis. 09:04.649 --> 09:07.529 So in history you hardly ever get much. 09:07.528 --> 09:10.948 People talk about it a little just to raise the question. 09:10.950 --> 09:13.910 How would the Vietnam War have gone if Kennedy hadn't been 09:13.909 --> 09:14.689 assassinated? 09:14.690 --> 09:18.100 So they all bring that up, but you get two sentences. 09:18.100 --> 09:19.750 "Oh, he was really going to pull out," 09:19.749 --> 09:21.009 or "Oh, he had been sending more 09:21.013 --> 09:21.473 advisors. 09:21.470 --> 09:23.330 It would have gone the same way." 09:23.330 --> 09:24.530 That's about it. 09:24.528 --> 09:27.798 In economics the heart of the thing is to go off on a tangent 09:27.798 --> 09:31.118 and figure out what would have happened if the environment had 09:31.124 --> 09:32.164 been different. 09:32.159 --> 09:34.349 So why do a model? 09:34.350 --> 09:38.660 Well, because many different settings can be described by the 09:38.664 --> 09:39.604 same model. 09:39.600 --> 09:40.920 So it just saves time. 09:40.919 --> 09:45.399 It makes things much simpler. 09:45.399 --> 09:48.209 From the counterfactual reasoning you're making 09:48.206 --> 09:49.056 predictions. 09:49.059 --> 09:51.099 It helps your understanding. 09:51.100 --> 09:53.810 And then for the purposes of the next few lectures the most 09:53.812 --> 09:56.622 important thing is there's some properties of equilibrium. 09:56.620 --> 09:58.880 Like, for example, equilibrium is so good you 09:58.883 --> 10:01.923 wouldn't want to interfere with equilibrium because it makes 10:01.918 --> 10:04.748 everyone so well off and it would be a terrible thing to 10:04.748 --> 10:05.518 regulate. 10:05.519 --> 10:08.449 So those properties of equilibrium are what we have to 10:08.452 --> 10:09.562 test the logic of. 10:09.558 --> 10:14.128 So there's an obvious critique you can make of modeling. 10:14.129 --> 10:17.239 The first person to make a model was Ricardo, 10:17.243 --> 10:21.423 who you I'm sure have heard of, the principle of comparative 10:21.418 --> 10:22.408 advantage. 10:22.408 --> 10:24.998 He was the first guy who didn't write verbally. 10:25.000 --> 10:27.070 He said, "Okay, I'm talking about international 10:27.067 --> 10:28.767 trade and why free trade is a good idea. 10:28.769 --> 10:30.269 I could make a verbal argument. 10:30.269 --> 10:32.639 That's what everyone else has done, but I'm not going to do 10:32.635 --> 10:32.835 it. 10:32.840 --> 10:36.290 I'm going to say, 'Suppose that England produced 10:36.293 --> 10:40.633 with one hour of labor three bottles of wine' and so on, 10:40.629 --> 10:43.119 " and he had a little numerical example. 10:43.120 --> 10:46.240 And he solved it and he showed that in that numerical example 10:46.240 --> 10:49.410 it's better to have free trade as paradoxical as it might have 10:49.412 --> 10:50.662 sounded at the time. 10:50.658 --> 10:53.838 The Portuguese had such lower labor costs why shouldn't 10:53.844 --> 10:57.264 English workers be afraid of being thrown out of their jobs 10:57.264 --> 11:00.694 when trading with Portugal where the labor was so much less 11:00.686 --> 11:01.626 expensive. 11:01.629 --> 11:04.059 Well he explained why that turned out not to be the case, 11:04.061 --> 11:05.191 but in terms of a model. 11:05.190 --> 11:07.260 So Malthus, who you've also heard of, 11:07.259 --> 11:11.149 a contemporary of his and his rival but also his friend, 11:11.149 --> 11:14.639 said, "This model stuff is ridiculous because if you start 11:14.638 --> 11:18.068 making a model the point of a model is to make deductions from 11:18.068 --> 11:19.398 it, and to analyze it, 11:19.398 --> 11:21.508 and analyze it deeper, and deeper, and deeper, 11:21.514 --> 11:23.864 and of course the model to begin with is going to be wrong 11:23.856 --> 11:26.356 and as you go deeper and deeper into the analysis of the model 11:26.363 --> 11:28.623 the error that you made at the beginning is going to get 11:28.623 --> 11:29.613 compounded." 11:29.610 --> 11:31.840 Like he said, "The tailors of Laputa, 11:31.840 --> 11:34.960 who by a slight mistake at the outset"-- 11:34.960 --> 11:37.720 doing their stitches, go wrong--the stitch goes 11:37.720 --> 11:40.650 further and further wrong-- you "arrive at conclusions 11:40.647 --> 11:42.177 the most distance from the truth." 11:42.178 --> 11:44.378 Anyway, that's what you might think is wrong with models, 11:44.379 --> 11:48.099 and the very first model was critiqued by that reasoning, 11:48.100 --> 11:50.630 but it's turned out historically that modeling is 11:50.628 --> 11:53.518 the way to make progress in economics and everybody does 11:53.524 --> 11:54.424 modeling now. 11:54.418 --> 11:56.898 You'll find out as I talk more about it that the Cowles 11:56.897 --> 11:59.207 Foundation, which has been at Yale since 11:59.212 --> 12:02.022 1955, was founded by a Cowles [correction: Yale] 12:02.023 --> 12:03.043 undergraduate. 12:03.038 --> 12:04.138 You'll hear the whole history of it. 12:04.139 --> 12:06.009 I was the director of it for nine years. 12:06.009 --> 12:08.909 That was the one most important institution in the world 12:08.905 --> 12:11.535 promoting the uses of mathematics in economics, 12:11.538 --> 12:15.148 and the revolution succeeded and now all economists use 12:15.154 --> 12:16.834 models and mathematics. 12:16.830 --> 12:19.820 Anyway, let's take an example of the simplest model. 12:19.820 --> 12:25.000 There are so many different ways of organizing price and 12:24.995 --> 12:25.745 trade. 12:25.750 --> 12:28.280 At a supermarket the seller just sets the price and you 12:28.278 --> 12:29.168 decide to buy it. 12:29.168 --> 12:31.608 If you go to Jerusalem or something in the old city you 12:31.605 --> 12:33.585 know that you're haggling over everything. 12:33.590 --> 12:36.830 You offer this and the guy says no and you walk away, 12:36.830 --> 12:39.380 and you come back and it takes a half a day to argue the price, 12:39.379 --> 12:41.999 but that's another way of arguing the price. 12:42.000 --> 12:44.180 Then there's--the government could set the price. 12:44.178 --> 12:49.198 In the Paris Bourse the way it worked is there would be a 12:49.197 --> 12:53.677 temporary price set and then supply and demand-- 12:53.678 --> 12:55.358 people would announce how much they wanted to buy, 12:55.360 --> 12:57.660 and if the supply didn't equal demand the price would get 12:57.658 --> 12:58.068 changed. 13:00.009 --> 13:01.039 or groping to the price. 13:01.038 --> 13:03.538 There's the commodities futures just like the experiment we ran 13:03.538 --> 13:04.908 where people yell at each other. 13:04.908 --> 13:09.728 There's computer bid/ask prices where you do everything online. 13:09.730 --> 13:12.420 There's the specialist in the stock exchange. 13:12.418 --> 13:15.488 There's one guy everybody has to come to, and so he's 13:15.494 --> 13:17.804 responsible for clearing the markets. 13:17.798 --> 13:21.228 So I might, in fact, mention a little bit of the 13:21.226 --> 13:23.556 history of this sort of thing. 13:23.558 --> 13:25.018 I don't know if I can hit escape. 13:25.019 --> 13:30.529 It might be somewhat interesting. 13:30.528 --> 13:35.778 So the first people who had these well-developed markets and 13:35.783 --> 13:38.013 money were the Lydians. 13:38.009 --> 13:40.699 They invented money in 640 B.C. 13:40.700 --> 13:43.550 and they had gold coins, and with all this money and 13:43.546 --> 13:46.946 trading they got very quickly to gambling and prostitution for 13:46.951 --> 13:47.511 money. 13:47.509 --> 13:53.539 And Midas, the Midas touch was everything turned to gold was 13:53.539 --> 13:54.459 Lydian. 13:54.460 --> 13:58.710 They've discovered all these mints where their capital was so 13:58.711 --> 14:02.821 they know that they were making all this money and gold and 14:02.822 --> 14:04.242 stuff like that. 14:04.240 --> 14:05.650 So they had open-air markets. 14:05.649 --> 14:07.759 They invented the retail markets. 14:07.759 --> 14:10.699 Croesus was one of the most famous Lydian kings, 14:10.695 --> 14:14.375 and he's the guy--rich as Croesus is a famous expression. 14:14.379 --> 14:17.799 He's the one who went to the Delphic oracle and asked if he 14:17.796 --> 14:21.786 should fight the great Persian, Cyrus the Great and the Delphic 14:21.791 --> 14:25.391 oracle as usual mysteriously said a great kingdom will be 14:25.389 --> 14:27.829 destroyed, and since it was Cyrus the 14:27.827 --> 14:31.137 Great he figured it must be Cyrus' and it was his kingdom 14:31.139 --> 14:32.439 that was destroyed. 14:32.440 --> 14:33.990 So the Greeks copied a lot of that stuff. 14:33.990 --> 14:37.470 They had their agora which was the open market and they had 14:37.474 --> 14:40.124 lots of trade, and they understood supply and 14:40.118 --> 14:41.498 demand, by the way. 14:41.500 --> 14:44.470 This isn't the modern example. 14:44.470 --> 14:48.860 In the politics there's a story of Thales who predicts a bad 14:48.855 --> 14:49.595 harvest. 14:49.600 --> 14:52.040 He's a great mathematician and astronomer, 14:52.038 --> 14:55.018 and he predicts a bad harvest and he figures if he corners the 14:55.020 --> 14:56.830 wheat market he'll make a fortune, 14:56.830 --> 14:58.670 which he does. 14:58.668 --> 15:01.658 Aristotle was famous for saying, "Money is just a 15:01.664 --> 15:02.404 convention. 15:02.399 --> 15:03.869 It's not really worth anything. 15:03.870 --> 15:06.630 People just agree it's worth something even if it's just 15:06.629 --> 15:09.589 pieces of paper or coins that worth much more than the coins 15:09.591 --> 15:12.251 and how could that be," and anyway there's a long 15:12.251 --> 15:15.311 political connection to that, the difference between nature 15:15.307 --> 15:17.477 and convention, but anyhow he also said, 15:17.477 --> 15:20.947 "Loaning at interest was unnatural and terrible," 15:20.953 --> 15:24.313 but all the while he was saying it the Delphic oracle was 15:24.311 --> 15:25.811 lending at interest. 15:25.808 --> 15:28.468 Economics is a Greek word, household management, 15:28.471 --> 15:30.681 Xenophon wrote a whole book about it. 15:30.678 --> 15:34.448 And just one more little history or historical thing, 15:34.450 --> 15:38.750 Hermes, the messenger god, the god of information, 15:38.750 --> 15:42.120 so remember the modern financial view of information, 15:42.120 --> 15:44.370 markets and information, anyway he was the Greek god, 15:44.370 --> 15:46.100 messenger god, and god of information. 15:46.100 --> 15:48.080 The word commerce comes from Hermes. 15:48.080 --> 15:52.540 And the Romans who took over the same god and called him 15:52.543 --> 15:57.743 Mercury that's where we get the word merchant from and market. 15:57.740 --> 16:05.540 Anyway, all right I'm not going to bother with all this. 16:05.538 --> 16:07.698 I used to go on and on about this. 16:07.700 --> 16:11.070 So the point is that in ancient times the market was already 16:11.068 --> 16:14.318 established and this idea of supply and demand had already 16:14.323 --> 16:17.983 been created but there are many different kinds of markets, 16:17.980 --> 16:21.960 as I've just said, and they work in many different 16:21.960 --> 16:25.280 ways, but we're going to describe 16:25.279 --> 16:27.159 them in one model. 16:27.158 --> 16:29.698 So just to mention a couple of others, 16:29.700 --> 16:32.820 the model, the experiment we ran in the class last time is 16:32.821 --> 16:36.461 called the double auction, and the experiment I told you 16:36.458 --> 16:40.348 about and had you do was actually an experiment that has 16:40.346 --> 16:41.686 been run before. 16:41.690 --> 16:44.300 And for the last ten or twenty years many economists have run 16:44.304 --> 16:45.574 these sorts of experiments. 16:45.570 --> 16:48.210 It's amazing that before that, before twenty or thirty years 16:48.207 --> 16:49.637 ago no one thought to do that. 16:49.639 --> 16:52.469 You didn't think that students with no training and no 16:52.467 --> 16:55.987 experience could ever be led to do something that was sensible, 16:55.990 --> 16:58.100 but actually you did quite brilliantly. 16:58.100 --> 17:00.400 And by the way, I've been told that those of 17:00.397 --> 17:02.837 you who performed, maybe you're still in the first 17:02.841 --> 17:04.431 two rows, you have to sign, 17:04.434 --> 17:08.474 even those of you who were left at the end unable to trade you 17:08.474 --> 17:12.254 have to sign a release form so you can't sue Yale for your 17:12.250 --> 17:16.290 disappointed faces appearing on the internet afterwards. 17:16.288 --> 17:18.868 So anyway, the fact is we're going to see that the people who 17:18.873 --> 17:21.073 were left at the end were actually very rational. 17:21.069 --> 17:23.669 In fact nobody made a mistake. 17:23.670 --> 17:26.830 I've done this experiment now ten or twenty times and I would 17:26.834 --> 17:29.954 say that half the time somebody buys something for more than 17:29.945 --> 17:31.155 it's worth to them. 17:31.160 --> 17:33.810 Nobody made a mistake and it almost came out exactly as it 17:33.814 --> 17:35.914 should, but we'll come to that in a second. 17:35.910 --> 17:40.130 Anyway, that double auction is the most complicated kind of 17:40.125 --> 17:44.045 auction, but auctions have been run for a long time. 17:44.048 --> 17:47.178 The first recorded auction you may have heard about 17:47.180 --> 17:51.000 was--Herodotus describes the Babylonian auction in 500 B.C. 17:51.000 --> 17:52.900 These are all going to be very politically incorrect, 17:52.901 --> 17:54.731 but a lot of economics is politically incorrect. 17:54.730 --> 17:57.350 Anyway, the first auction in 500 B.C. 17:57.348 --> 18:01.508 was the Babylonians auctioned off all the 18-year-old women as 18:01.509 --> 18:05.879 wives and they auctioned them in order of most beautiful to least 18:05.875 --> 18:06.825 beautiful. 18:06.828 --> 18:10.008 And so they got a very high price and the price went down 18:10.009 --> 18:13.409 and down and down until it hit zero and then it started going 18:13.414 --> 18:16.384 negative, but they used the revenue from 18:16.384 --> 18:20.814 the first wives to subsidize the husbands who would accept the 18:20.807 --> 18:23.487 other wives as it kept going down. 18:23.490 --> 18:27.810 The next most awful auction was the Roman Empire itself was 18:27.807 --> 18:28.997 auctioned off. 18:29.000 --> 18:31.860 So if you saw the movie Gladiator you may 18:31.858 --> 18:35.008 remember that Marcus Aurelius is the great emperor, 18:35.009 --> 18:38.019 and he dies, and then the evil Commodus 18:38.019 --> 18:42.329 takes over, and he dies as a gladiator 18:42.327 --> 18:43.187 there. 18:43.190 --> 18:46.550 And then there's the senator who you sort of hardly ever see, 18:46.548 --> 18:49.518 but you know he's the good senator who somehow-- 18:49.519 --> 18:52.279 he appears a few times--you know that he's a good guy and 18:52.279 --> 18:53.559 he's going to take over. 18:53.558 --> 18:56.098 So his name is Pertinax, and he does take over. 18:56.098 --> 18:59.158 But he's a good guy and he gets killed almost immediately by the 18:59.160 --> 19:01.730 Praetorian Guard and the Praetorian Guard then doesn't 19:01.733 --> 19:04.943 know who to make emperor so they auction the whole empire off. 19:04.940 --> 19:09.170 And so it's bought by Didius Julianus, and he doesn't last 19:09.169 --> 19:11.839 very long, and he gets killed too. 19:11.838 --> 19:13.808 The Roman legions come back and kill him. 19:13.808 --> 19:18.158 So anyway, I grew up in Urbana, Illinois and I used to go to 19:18.156 --> 19:22.206 these livestock auctions where they'd sell something. 19:22.210 --> 19:24.810 They'd talk incredibly fast < 19:26.289 fast like an auctioneer>> 19:26.288 --> 19:28.248 They talk like that and I don't know how anybody can understand 19:28.247 --> 19:29.997 them, and then there's the famous 19:30.000 --> 19:31.890 slave auction, so--where they'd actually 19:31.890 --> 19:33.920 auction slaves, and you've seen it in the 19:33.922 --> 19:34.682 movies maybe. 19:34.680 --> 19:36.200 And that's where the expression, "Going once, 19:36.200 --> 19:38.090 going twice, third and last call, 19:38.087 --> 19:39.647 going, going, gone," 19:39.646 --> 19:42.556 that's what they used to say at the slave auction. 19:42.558 --> 19:46.878 So the double auction that we saw was kind of what happened at 19:46.880 --> 19:50.280 the beginnings of the New York Stock Exchange. 19:50.279 --> 19:52.879 The first traded securities--there were only five 19:52.881 --> 19:54.671 of them, so how did they start? 19:54.670 --> 19:56.670 There was the Revolutionary War. 19:56.670 --> 19:59.830 A lot of states had borrowed money and issued their bonds, 19:59.834 --> 20:02.504 and there are two banks, Bank of New York and the 20:02.499 --> 20:04.109 National Bank of the U.S. 20:04.109 --> 20:05.269 that had issued bonds. 20:05.269 --> 20:08.299 Those were the only tradable securities. 20:08.298 --> 20:10.898 And so a bunch of states had issued bonds. 20:10.900 --> 20:15.830 So what happened was after the Revolutionary War most people 20:15.834 --> 20:19.434 expected the bonds wouldn't be paid back. 20:19.430 --> 20:21.250 After all, there was a huge expense fighting the 20:21.252 --> 20:22.032 Revolutionary War. 20:22.028 --> 20:24.328 The government didn't have very much money. 20:24.328 --> 20:29.058 The price of the bonds had already collapsed, 20:29.057 --> 20:32.387 and Jefferson wanted the U.S. 20:32.390 --> 20:34.750 to just, you know, wanted to leave the states and 20:34.747 --> 20:35.677 let them default. 20:35.680 --> 20:38.750 And Hamilton said that that would be terrible, 20:38.750 --> 20:41.800 that the reputation of the country was going to be made at 20:41.798 --> 20:44.738 what happened at the very founding of the country and it 20:44.740 --> 20:46.400 was important that the U.S. 20:46.400 --> 20:48.050 never break a debt. 20:48.048 --> 20:51.838 So he persuaded Washington to have the federal government buy 20:51.836 --> 20:55.556 all the debt of the states and basically pay it all off, 20:55.558 --> 20:57.848 so none of the debts were broken. 20:57.848 --> 20:59.758 Jefferson argued, "That's crazy. 20:59.759 --> 21:01.329 The people who originally bought the bonds, 21:01.332 --> 21:03.432 who lent the money to the government, the farmers who did 21:03.428 --> 21:04.998 it they didn't own the bonds any more. 21:05.000 --> 21:06.830 They probably all sold it for twenty dollars. 21:06.828 --> 21:09.878 It was all this despicable speculators who held the bonds. 21:09.880 --> 21:12.200 You're only going to enrich them by paying them off." 21:12.200 --> 21:14.610 So he just wouldn't budge. 21:14.608 --> 21:17.188 And finally Hamilton, supposedly--this is a famous 21:17.185 --> 21:19.495 story, I assume it's true--Hamilton 21:19.503 --> 21:22.463 went to Washington and said, "All right, 21:22.460 --> 21:25.280 move the capitol from New York to Washington. 21:25.278 --> 21:27.818 That'll make Jefferson happy because it's near his dear 21:27.824 --> 21:30.754 Virginia and in exchange get him to concede that we have to pay 21:30.746 --> 21:31.826 off the debt." 21:31.828 --> 21:35.668 So Washington brokered that deal and the debt was paid, 21:35.673 --> 21:36.673 and the U.S. 21:36.670 --> 21:40.360 since then has never defaulted on its debt and virtually no 21:40.355 --> 21:42.195 other country can say that. 21:42.200 --> 21:44.760 For example, Russia has never paid a 21:44.759 --> 21:46.149 thirty-year debt. 21:46.150 --> 21:51.150 It always has defaulted, and we'll come back to that a 21:51.147 --> 21:56.427 little later when we talk about the crisis of '97-'98. 21:56.430 --> 21:59.070 Anyway, so these five securities--three government 21:59.069 --> 22:01.929 bonds and these two from the Revolutionary War and two 22:01.926 --> 22:03.716 banks-- were the only securities sold 22:03.724 --> 22:06.264 and they used to be sold every day in a double auction exactly 22:06.259 --> 22:08.589 as the kind that we described where people would yell and 22:08.587 --> 22:10.997 scream at each other and the whole thing would be over in a 22:10.998 --> 22:12.838 few minutes, and that would be it for the 22:12.843 --> 22:15.123 day, and then the next day they would do the same thing over and 22:15.123 --> 22:15.633 over again. 22:15.630 --> 22:19.210 Well, they had to stop that when Alexander Duer, 22:19.210 --> 22:21.990 who was Hamilton's assistant, started using his inside 22:21.993 --> 22:25.093 information about whether the government was or wasn't going 22:25.093 --> 22:28.143 to make all its payments and whether they're going to issue 22:28.140 --> 22:31.870 new bonds and stuff like that to try and speculate on the market. 22:31.868 --> 22:33.718 And he would do it all by borrowing. 22:33.720 --> 22:36.390 He'd borrow a huge amount of money and with the borrowed 22:36.393 --> 22:39.053 money he'd buy bonds, and if the price went against 22:39.053 --> 22:41.683 him he'd lose a lot more because he was leveraged. 22:41.680 --> 22:47.270 And so it caused gigantic gyrations in the market and the 22:47.270 --> 22:53.260 whole thing had to be changed, and it was made a much smaller 22:53.261 --> 22:55.261 group of people. 22:55.259 --> 22:57.619 Anyway, so that was the beginnings of it. 22:57.618 --> 23:00.758 And we're going to come back to that because that view of the 23:00.760 --> 23:03.950 gyrations of the market being caused by too much borrowing and 23:03.953 --> 23:06.883 speculation is exactly the view that I'm going to take in 23:06.884 --> 23:08.984 explaining the most recent crisis. 23:08.980 --> 23:13.890 So anyway, you remember what we did in our experiment. 23:13.890 --> 23:18.160 We had eight buyers whose reservation prices are those 23:18.156 --> 23:20.166 eight numbers up there. 23:20.170 --> 23:22.710 That's what each person thought it was worth to him. 23:22.710 --> 23:25.480 Each person knew his own price, but not any of the others. 23:25.480 --> 23:28.630 I told you almost nothing about what was going on. 23:28.630 --> 23:29.880 There was some context. 23:29.880 --> 23:33.070 I gave an example of a person who thought it was worth 23:33.067 --> 23:34.757 fifteen, so you had some idea, 23:34.762 --> 23:37.472 probably, from that example that the numbers weren't ten 23:37.470 --> 23:39.970 thousand, plus you knew your own number. 23:39.970 --> 23:42.360 But other than that you knew absolutely nothing and each 23:42.358 --> 23:45.008 buyer knew her own number and not any of the other numbers. 23:45.009 --> 23:47.799 So here we have sixteen different pieces of information. 23:47.798 --> 23:52.078 Everybody has an incentive to keep her information secret. 23:52.078 --> 23:55.468 Why should anybody admit that she's willing to sell at six? 23:55.470 --> 23:57.520 She'll get a worse price. 23:57.519 --> 24:00.409 She's going to lie and say the thing is much more. 24:00.410 --> 24:02.800 She's going to make an argument that says, "Well, 24:02.801 --> 24:05.101 these are football," okay, I better try the guy 24:05.103 --> 24:05.513 here. 24:05.509 --> 24:07.919 The forty-four guy, he's going to say, 24:07.922 --> 24:10.532 "This is a football ticket." 24:10.529 --> 24:11.319 No, sorry. 24:11.319 --> 24:11.959 What am I going to do? 24:11.960 --> 24:14.510 Let's say she's a forty-four. 24:14.509 --> 24:16.149 She's going to say, "Football tickets, 24:16.152 --> 24:17.602 they're completely worthless." 24:17.599 --> 24:18.249 I'm doing a stereotype. 24:18.250 --> 24:19.260 "These are completely worthless. 24:19.259 --> 24:20.629 Who would want to go to a football game? 24:20.630 --> 24:21.870 I certainly don't want to go to a football game. 24:21.868 --> 24:25.088 They can't be worth any more than twelve or something." 24:25.088 --> 24:27.188 So all the buyers, the blue buyers, 24:27.190 --> 24:29.630 are going to be making arguments suggesting the price 24:29.631 --> 24:31.671 should be low, reasons why the stuff really 24:31.670 --> 24:32.690 isn't worth very much. 24:32.690 --> 24:35.380 All the sellers are going to be making arguments saying the 24:35.381 --> 24:37.471 stuff is intrinsically incredibly valuable. 24:37.470 --> 24:39.270 Football tickets are incredibly important. 24:39.269 --> 24:42.609 So that's the facts. 24:42.608 --> 24:45.518 Now you need a model and a theory that fits the facts, 24:45.519 --> 24:48.129 and I'm belaboring the obvious, but the obvious is always 24:48.125 --> 24:51.475 central to everything, the obvious theory would go 24:51.480 --> 24:54.420 something like, well, somehow these people are 24:54.419 --> 24:57.429 going to get matched up and maybe thirty-eight will sell to 24:57.433 --> 24:59.933 forty-four and all eight things will be sold. 24:59.930 --> 25:02.470 And the more transactions you have the better. 25:02.470 --> 25:05.930 And what else might a theory say, a wrong theory? 25:05.930 --> 25:09.010 It might say the more people in red, or the more people making 25:09.012 --> 25:12.052 arguments that the price should be higher the more compelling 25:12.046 --> 25:13.306 the argument will be. 25:13.308 --> 25:15.618 You'll be overwhelmed by numbers and you'll think that 25:15.618 --> 25:17.928 the price should be higher because more people will be 25:17.929 --> 25:19.279 arguing for a higher price. 25:19.278 --> 25:21.708 But the theory, the economic theory is the 25:21.710 --> 25:23.430 exact opposite of all that. 25:23.430 --> 25:28.410 So the economic theory is quite a shocking theory, 25:28.413 --> 25:29.433 I think. 25:29.430 --> 25:32.360 It starts with a situation where people are arguing and 25:32.358 --> 25:33.768 talking about the price. 25:33.769 --> 25:36.739 They're not doing anything else but making arguments about the 25:36.742 --> 25:38.792 price and making offers about the price. 25:38.788 --> 25:40.548 They're haggling about the price. 25:40.548 --> 25:44.138 The whole of the activity is about the price and how to 25:44.138 --> 25:46.398 change it and what it should be. 25:46.400 --> 25:48.340 The economic theory, the first theory, 25:48.338 --> 25:49.858 the most important theory of economics, 25:49.858 --> 25:54.928 supply and demand, is that--so that describes what 25:54.928 --> 25:57.608 happened, is the exact opposite. 25:57.608 --> 26:02.318 The theory says let's suppose that a price appeared out of 26:02.319 --> 26:03.229 thin air. 26:03.230 --> 26:05.380 There was no arguing about the price. 26:05.380 --> 26:08.380 Nobody even thinks they have any chance of changing the 26:08.384 --> 26:08.834 price. 26:08.828 --> 26:11.738 Somehow a price gets into everybody's head, 26:11.740 --> 26:15.160 the price of twenty-five and at that price of twenty-five 26:15.164 --> 26:18.534 everybody who wants to buy buys as much as they want. 26:18.528 --> 26:22.438 So mister forty-four he thinks the ticket is worth forty-four. 26:22.440 --> 26:25.150 If he can buy it for twenty-five he'll want to buy. 26:25.150 --> 26:27.650 Forty thinks it's worth forty and the price is only 26:27.653 --> 26:29.813 twenty-five so, again, he's going to gain by 26:29.807 --> 26:31.307 buying, he'll want to buy. 26:31.308 --> 26:33.278 Twelve thinks it's only worth twelve. 26:33.279 --> 26:35.479 He's not going to pay twenty-five for it. 26:35.480 --> 26:37.480 And similarly the sellers, seller number ten, 26:37.478 --> 26:39.298 she's going to say, "Okay, I can get 26:39.295 --> 26:40.335 twenty-five for it. 26:40.339 --> 26:42.349 It was worth ten. 26:42.348 --> 26:43.948 It's a good deal for me to do." 26:43.950 --> 26:47.380 So the theory says somehow miraculously the price comes out 26:47.381 --> 26:48.211 of thin air. 26:48.210 --> 26:49.140 It's given. 26:49.140 --> 26:53.130 Everybody taking that price as given, figuring they have no 26:53.133 --> 26:56.513 power to change it, buys or sells all they want at 26:56.507 --> 26:57.537 that price. 26:57.539 --> 26:59.129 And so that's the theory. 26:59.130 --> 27:02.070 So it's price taking, out of thin air. 27:02.069 --> 27:03.289 The price comes from somewhere. 27:03.288 --> 27:08.578 Everybody acts by maximizing, doing the best for them given 27:08.584 --> 27:09.684 the price. 27:09.680 --> 27:13.670 They all understand what the price is, and the price has 27:13.673 --> 27:17.743 miraculously been imagined at exactly the level that will 27:17.740 --> 27:19.630 clear all the markets. 27:19.630 --> 27:21.630 So everyone who wants to buy is able to, and everyone who wants 27:21.631 --> 27:22.311 to sell is able to. 27:22.309 --> 27:23.689 That's the theory. 27:23.690 --> 27:26.750 The theory's completely the opposite of what common sense 27:26.747 --> 27:29.237 suggests since, as I said, the whole thing was 27:29.243 --> 27:32.323 this grappling and groping and pushing and shoving and yelling 27:32.321 --> 27:35.401 and arguing about what the price should be and the theory says 27:35.401 --> 27:37.421 nobody says a word about the price. 27:37.420 --> 27:40.780 They just take it as given and then they act after that. 27:40.779 --> 27:44.499 So the most basic economic model is a paradox, 27:44.496 --> 27:48.456 and good economics is almost always a paradox. 27:48.460 --> 27:51.270 If you want to make a convincing economic argument you 27:51.272 --> 27:53.612 almost always say it in a paradoxical way. 27:53.608 --> 27:57.398 And so going back to the very beginning where we said what a 27:57.398 --> 27:59.828 model is, the standard economic model is 27:59.834 --> 28:03.034 you take the exogenous things, which in this case are the 28:03.026 --> 28:05.146 reservation prices of all the people, 28:05.150 --> 28:07.820 you have to solve equations which are here, 28:07.818 --> 28:10.388 supply equals demand, which determines the endogenous 28:10.386 --> 28:12.766 variables, which are the price and who 28:12.769 --> 28:14.059 buys and who sells. 28:14.058 --> 28:17.688 And the reason the theory is always often paradoxical is if 28:17.690 --> 28:20.940 you change some exogenous variable it looks like it's 28:20.943 --> 28:24.453 going to move things in a commonsensical direction, 28:24.450 --> 28:27.190 but then when people react to the changed environment-- 28:27.190 --> 28:31.230 X is a reaction to the change in E-- 28:31.230 --> 28:34.120 and the change in X might be so big and so important that it 28:34.116 --> 28:35.876 reverses the apparent change in E. 28:35.880 --> 28:38.880 So you get these surprising conclusions. 28:38.880 --> 28:40.860 "If everybody tries to save more," 28:40.858 --> 28:43.508 Keynes said, "It may be that everyone 28:43.505 --> 28:46.805 will end up saving less," things like that. 28:46.808 --> 28:51.048 So economics at its best takes advantage of its paradoxical 28:51.053 --> 28:55.373 nature at its heart and uses that as a rhetorical device. 28:55.369 --> 28:56.989 So it's a non-obvious theory. 28:56.990 --> 28:58.320 Now, why do we believe the theory? 28:58.318 --> 29:02.328 Well, all those different examples I gave you of markets 29:02.325 --> 29:03.995 they all seem to fit. 29:04.000 --> 29:07.680 I forgot where they were and I don't even remember what they 29:07.682 --> 29:08.122 were. 29:08.119 --> 29:12.229 I don't remember what they were. 29:12.230 --> 29:15.040 The shopping center thing, the haggling, 29:18.675 --> 29:21.995 all that, if you look after the fact at what people wanted to do 29:22.001 --> 29:24.801 and what price emerged it seems to fit the theory. 29:24.798 --> 29:27.218 So there's overwhelming evidence that this theory seems 29:27.221 --> 29:27.671 to work. 29:27.670 --> 29:31.830 And you saw that in our own example, in our experiment where 29:31.832 --> 29:35.432 you had no training at all, it came pretty close. 29:35.430 --> 29:41.080 So all these five red sellers they all sold, 29:41.078 --> 29:44.158 I think, and the five buyers the only difference was that 29:44.164 --> 29:46.704 instead of twenty-six buying twenty bought, 29:46.700 --> 29:49.330 and the prices were all between twenty and twenty-five, 29:49.328 --> 29:51.028 so they weren't exactly twenty-five, 29:51.029 --> 29:52.809 but they were very close to twenty-five. 29:52.808 --> 29:55.698 And the ten people who were supposed to have bought and 29:55.701 --> 29:58.861 sold, well nine out of the ten actually did buy and sell. 29:58.858 --> 30:02.698 So it's pretty hard to match a theory like that with so little 30:02.696 --> 30:03.386 practice. 30:03.390 --> 30:12.440 I mean, I've always found it quite astonishing. 30:12.440 --> 30:15.860 Why is this happening? 30:15.858 --> 30:22.028 Does anyone want to make a comment or ask a question about 30:22.025 --> 30:23.535 this theory? 30:23.538 --> 30:25.788 All right, well what are the properties of equilibrium you 30:25.788 --> 30:26.498 get out of this? 30:26.500 --> 30:28.920 Well, everyone trades at one price. 30:28.920 --> 30:31.390 So this is going to be very important for finance, 30:31.390 --> 30:33.860 the idea that there's one price for everything. 30:33.858 --> 30:42.808 Then you can also define the--so you know what the theory 30:42.809 --> 30:43.609 is. 30:43.608 --> 30:48.058 I already told you the exogenous variables are the 30:48.060 --> 30:49.970 reservation values. 30:49.970 --> 30:53.070 The endogenous variable is the price that emerges and who buys 30:53.067 --> 30:53.877 and who sells. 30:53.880 --> 30:56.700 So why is this such a good outcome? 30:56.700 --> 30:58.110 It seems like a terrible outcome. 30:58.108 --> 31:01.028 There are those six people standing there at the end unable 31:01.034 --> 31:02.584 to trade, facing the camera, 31:02.576 --> 31:05.596 looking slightly embarrassed that all their friends managed 31:05.596 --> 31:08.346 to buy and sell and they couldn't do it and what's the 31:08.354 --> 31:09.504 matter with them. 31:09.500 --> 31:10.450 So they feel bad. 31:10.450 --> 31:12.140 They feel discriminated against. 31:12.140 --> 31:14.390 It doesn't look like it's such a great thing. 31:14.390 --> 31:17.580 We know that there's another way of making all eight buyers 31:17.578 --> 31:20.988 purchase from all eight sellers just by doing the corresponding 31:20.990 --> 31:21.760 one above. 31:21.759 --> 31:23.919 What's so good about the market outcome? 31:23.920 --> 31:25.340 It actually doesn't sound so great. 31:25.338 --> 31:30.088 Well, the answer is it is great and what's great about is that 31:30.092 --> 31:34.612 within two minutes the market figured out enough about what 31:34.611 --> 31:39.211 everybody valued the football tickets at to put the football 31:39.207 --> 31:43.957 tickets in the ten peoples' hands who valued them most. 31:43.960 --> 31:48.330 All right, so in the end those five blue guys-- 31:48.328 --> 31:55.078 almost without that one exception--and the one, 31:55.078 --> 32:00.708 two, three red sellers, those three sellers and those 32:00.705 --> 32:03.665 five buyers, the top eight people ended up 32:03.671 --> 32:06.541 with the eight football tickets and the bottom eight didn't end 32:06.538 --> 32:08.018 up with any football tickets. 32:08.019 --> 32:10.739 So the football tickets got put into the hands of the people who 32:10.737 --> 32:11.727 valued them the most. 32:11.730 --> 32:14.250 And so, as I said, if you just simply sat there 32:14.250 --> 32:17.590 and went through sixteen tickets and sorted them into most and 32:17.594 --> 32:20.774 least and then tried to arrange all the football tickets it 32:20.771 --> 32:24.351 would have taken almost as long, and that would have been with 32:24.352 --> 32:26.592 benefit of knowing what all the numbers are. 32:26.588 --> 32:29.708 Here the market does it not knowing what the numbers are and 32:29.713 --> 32:33.103 the only accessed information is through people who don't want to 32:33.103 --> 32:36.403 reveal their numbers, and still the market figured it 32:36.400 --> 32:36.710 out. 32:36.710 --> 32:41.150 All right, so that's the message. 32:41.150 --> 32:43.980 So we have a model which is surprising, 32:43.980 --> 32:48.750 which seems to describe the facts, and which gives us a 32:48.751 --> 32:54.321 surprising conclusion and an incredibly important conclusion. 32:54.318 --> 32:57.958 The market is an extremely useful mechanism of eliciting 32:57.955 --> 33:01.785 information and turning the information into something that 33:01.790 --> 33:05.560 allocates things efficiently, and you couldn't do better than 33:05.564 --> 33:05.864 that. 33:05.858 --> 33:10.888 No other arrangement would have put football tickets in the 33:10.894 --> 33:14.284 hands of people who like them better. 33:14.278 --> 33:21.668 So Hayek described the market as a great calculating machine, 33:21.666 --> 33:24.126 and well so it is. 33:24.130 --> 33:26.800 Now, there are a couple other things that you can get out of 33:26.800 --> 33:27.390 this model. 33:27.390 --> 33:34.260 Another lesson of this model is that the equilibrium price is 33:34.256 --> 33:40.546 equal not to the average of the price of the buyers, 33:40.548 --> 33:42.128 or the average of the price of the sellers, 33:42.130 --> 33:44.480 or the average of all the prices or something like that. 33:44.480 --> 33:49.040 It's equal to what the marginal buyer thinks it's worth. 33:49.038 --> 33:51.938 So there's a critical marginal buyer and marginal seller. 33:51.940 --> 33:54.670 They're almost indifferent to buying or selling. 33:54.670 --> 33:55.670 They could go either way. 33:55.670 --> 33:57.170 They're pretty close to buying or selling. 33:57.170 --> 34:02.460 The price is going to turn out to be very close to that 34:02.464 --> 34:05.804 valuation of the marginal buyer. 34:05.798 --> 34:09.748 So somehow the margin is going to play a big--so the word 34:09.746 --> 34:14.046 marginal, this is an invention in 1871, is going to play a big 34:14.045 --> 34:16.225 role in economic reasoning. 34:16.230 --> 34:18.530 So it gives us a completely different understanding. 34:18.530 --> 34:21.210 You might think that the price of tickets has something to do 34:21.208 --> 34:23.708 with their total value or average value or something like 34:23.708 --> 34:24.108 that. 34:24.110 --> 34:27.220 It's got to do with the value of a marginal person, 34:27.215 --> 34:29.075 the person just on the edge. 34:29.079 --> 34:31.759 So then the comparative statics are that the, 34:31.760 --> 34:34.330 as I said, the surprising thing that if you change a 34:34.329 --> 34:36.539 non-marginal person, you take mister forty-four, 34:36.543 --> 34:39.113 the buyer at the top, you change him to fifty. 34:39.110 --> 34:41.570 Looks like the buyers are now more desperate to buy, 34:41.567 --> 34:43.347 won't have any effect on the price. 34:43.349 --> 34:46.529 You change that seller, miss six, you change her to two 34:46.534 --> 34:48.854 or to eight, again, it'll have no effect on 34:48.847 --> 34:51.087 the price, because those two people, 34:51.090 --> 34:54.030 the guy at forty-four and the lady at six, 34:54.030 --> 34:57.820 they're not marginal so they don't affect the price. 34:57.820 --> 35:00.950 You add some more buyers you might think that they're arguing 35:00.954 --> 35:04.814 for the price to be lower, as I said you're going to end 35:04.811 --> 35:09.091 up raising the price or else having no effect on it if 35:09.090 --> 35:11.030 they're not marginal. 35:11.030 --> 35:13.260 Now one more thing, one last thing, 35:13.260 --> 35:15.680 one last message of this model, if you didn't know-- 35:15.679 --> 35:19.419 we knew the reservation prices ourselves because I set up the 35:19.416 --> 35:22.326 experiment, but if you didn't know it you 35:22.327 --> 35:24.997 could infer something from the price. 35:25.000 --> 35:27.260 So part of finance is going in the backwards direction. 35:27.260 --> 35:29.710 The theory says take the exogenous variables. 35:29.710 --> 35:32.430 Predict what the equilibrium's going to be. 35:32.429 --> 35:34.839 Financial theory does that, but often it goes in the 35:34.835 --> 35:35.775 reverse direction. 35:35.780 --> 35:37.490 We can see what the prices are. 35:37.489 --> 35:42.659 That must tell us something about the exogenous valuations. 35:42.659 --> 35:45.469 So financial theory says, "Well if the price is such 35:45.465 --> 35:48.515 and such it must mean that at least the marginal person values 35:48.523 --> 35:51.533 it at such and such and so that's why the price is that. 35:51.530 --> 35:54.400 It's the value of some special persons." 35:54.400 --> 35:57.220 So we'll come back to that argument. 35:57.219 --> 36:03.199 So that lesson of economics, that's the first economic 36:03.202 --> 36:05.522 model, the most important economic 36:05.523 --> 36:08.513 model, we're going to now have to generalize it in all kinds of 36:08.514 --> 36:10.224 ways, but it's always going to come 36:10.222 --> 36:11.412 back to that same message. 36:11.409 --> 36:14.399 And so Adam Smith he was the one who first invented the 36:14.398 --> 36:15.338 invisible hand. 36:15.340 --> 36:17.520 There was nothing mathematical in what he said. 36:17.518 --> 36:21.318 Ricardo was the first one to make a model. 36:21.320 --> 36:23.490 Marx said, I don't have time to talk about Marx, 36:23.489 --> 36:25.779 but he had quite elaborate models, actually, 36:25.780 --> 36:31.900 and his verbal arguments conceal a huge mathematical 36:31.900 --> 36:33.340 apparatus. 36:33.340 --> 36:35.900 On his deathbed, by the way, he was trying to 36:35.902 --> 36:37.712 learn calculus, incidentally. 36:37.710 --> 36:41.670 So Jevons, Menger and Walras 1871 right after Marx's famous 36:41.670 --> 36:45.630 Kapital came out in 1867 they invented the idea of 36:45.632 --> 36:49.732 the margin and things like that and the critique therefore of 36:49.730 --> 36:51.790 Marx, and Marx was trying to figure 36:51.793 --> 36:53.083 out what they were all about. 36:53.079 --> 36:56.029 Anyway, Marshall was a great economist, Fisher, 36:56.034 --> 36:58.224 Samuelson, Hicks, Arrow, Debreu; 36:58.219 --> 37:01.669 these are the most famous people who extended this model 37:01.673 --> 37:05.573 and the logic of laissez faire and regulation which we're going 37:05.567 --> 37:06.507 to come to. 37:06.510 --> 37:08.690 Now what are the two ways we have to generalize, 37:08.693 --> 37:11.253 there are three ways we have to generalize the model. 37:11.250 --> 37:16.340 We have to think of many commodities, not just one. 37:16.340 --> 37:18.880 We have to think of people buying more than one unit of a 37:18.876 --> 37:19.416 commodity. 37:19.420 --> 37:21.900 That's called general equilibrium. 37:21.900 --> 37:24.410 And then we have to put in financial things. 37:24.409 --> 37:27.429 We have to put in stocks and bonds and things like that. 37:27.429 --> 37:30.569 It sounds like things are going to get so complicated, 37:30.572 --> 37:33.892 but in fact it turns out I'm going to spend another class 37:33.893 --> 37:35.913 after this talking about this. 37:35.909 --> 37:38.329 There's not that much complication to get all those 37:38.329 --> 37:38.909 things in. 37:38.909 --> 37:40.829 There'll be two more classes about this. 37:40.829 --> 37:43.379 So I'm recapitulating all that you have to know for the 37:43.376 --> 37:45.876 purposes of this class from introductory economics and 37:45.876 --> 37:47.146 intermediate economics. 37:47.150 --> 37:50.180 The only thing you have to know you'll hear now in these two 37:50.184 --> 37:53.224 classes and some of you will find it's incomprehensible, 37:53.219 --> 37:55.999 and so that's one good reason for doing it now. 37:56.000 --> 37:58.310 You find out right at the beginning whether it's too 37:58.313 --> 37:59.633 complicated to bother with. 37:59.630 --> 38:05.600 So anyway, I'm going to keep going now to extend the model. 38:05.599 --> 38:09.369 So the biggest advance, the next advance, 38:09.369 --> 38:14.089 sort of, which was related to this is Adam Smith said, 38:14.090 --> 38:18.110 "How could it be that water which is so valuable has 38:18.112 --> 38:21.082 such a low price, and diamonds which are so 38:21.077 --> 38:24.437 useless, basically, to everybody has such a high 38:24.440 --> 38:24.960 price? 38:24.960 --> 38:28.390 I mean, there's not some marginal buyer who thinks that 38:28.393 --> 38:32.023 diamonds are somehow more important to him than water, 38:32.018 --> 38:35.118 so how could it be that water's got a much lower price than 38:35.121 --> 38:38.601 diamonds and everybody would say that it's more valuable?" 38:38.599 --> 38:44.179 Well, to answer that question what we have to do is we have to 38:44.175 --> 38:50.205 imagine that people are capable of consuming more than one good. 38:50.210 --> 38:55.100 So for instance, let's imagine that there's good 38:55.101 --> 39:00.301 X here which is the football tickets we had before, 39:00.304 --> 39:03.744 and you remember our numbers. 39:03.739 --> 39:05.739 Let's just go back to the numbers for a second. 39:05.739 --> 39:07.469 I'll stay here for a while. 39:07.469 --> 39:10.609 The first buyer thought one ticket was worth forty-four. 39:10.610 --> 39:13.130 A second ticket was useless to that buyer. 39:13.130 --> 39:28.240 Well, suppose we write utility here. 39:28.239 --> 39:32.629 Now, this first buyer--let's put this forty-four here--this 39:32.630 --> 39:36.720 first buyer you might say got utility of forty-four for 39:36.717 --> 39:38.457 holding one ticket. 39:38.460 --> 39:41.340 If he held half a ticket maybe his utility would be twenty-two. 39:41.340 --> 39:44.260 Now, in fact we know that half a ticket doesn't get you into a 39:44.255 --> 39:46.305 game so his utility would really be zero. 39:46.309 --> 39:49.699 When we're talking about thousands of tickets to a 39:49.701 --> 39:53.301 football game a half or one it's not so important. 39:53.300 --> 39:58.950 Let's just say his utility went up linearly with the quantity of 39:58.954 --> 40:00.484 tickets he had. 40:00.480 --> 40:04.020 To make a discrete variable a continuous variable his utility 40:04.016 --> 40:07.196 goes up linear at the rate of forty-four per ticket. 40:07.199 --> 40:11.169 Well, after one ticket he gets no extra utility out of holding 40:11.173 --> 40:15.413 any more tickets so his utility might look something like that. 40:15.409 --> 40:19.199 But now let's imagine he wanted two tickets and that the first 40:19.197 --> 40:23.047 ticket was important to him and the second ticket he could take 40:23.047 --> 40:27.397 his girlfriend, let's say, but he's not quite 40:27.400 --> 40:30.940 as worried about her as himself. 40:30.940 --> 40:34.830 So let's say that he, for the second ticket, 40:34.833 --> 40:37.373 gets an extra forty utils. 40:37.369 --> 40:40.709 So after you get to ticket number two his utility is going 40:40.710 --> 40:44.050 to be up to eighty-four, which is forty-four and forty. 40:44.050 --> 40:48.750 Now you notice that the rate of increase of utility per unit of 40:48.751 --> 40:53.151 ticket is forty-four here and then it switches to forty. 40:53.150 --> 41:01.470 Okay, now, why do I--why do I--okay, and if he wanted one 41:01.469 --> 41:10.379 more ticket maybe he'd only get utility of one-twenty for the 41:10.382 --> 41:12.762 last ticket. 41:12.760 --> 41:16.360 So for a third ticket his utility would--three goes up 41:16.358 --> 41:19.278 like that, utility would go up like this. 41:19.280 --> 41:26.520 It's a little flatter again. 41:26.518 --> 41:29.888 So here we have a utility function which is increasing the 41:29.893 --> 41:31.613 number of tickets you hold. 41:31.610 --> 41:33.780 It's not restricted to just having one ticket, 41:33.780 --> 41:36.640 but the rate of increase goes down as you get more and more 41:36.637 --> 41:39.147 tickets from the rate of increase of forty-four, 41:39.150 --> 41:42.090 to the rate of increase of forty, to the rate of increase 41:42.090 --> 41:42.930 of thirty-six. 41:42.929 --> 41:45.909 Now, if you ask this person how many tickets does he want to 41:45.911 --> 41:47.681 buy, well what's he going to say? 41:47.679 --> 41:49.749 How's he going to figure out how much to buy? 41:49.750 --> 41:53.710 This is his utility, but now I claim this person 41:53.713 --> 41:58.943 buying multiple tickets is going to behave exactly like the top 41:58.943 --> 42:02.743 three people up there would have behaved. 42:02.739 --> 42:05.909 So his utility at the top for three tickets is one-twenty, 42:05.909 --> 42:08.579 for two is eighty-four, for one is forty-four. 42:08.579 --> 42:10.909 Those sound like important numbers, his total utility, 42:10.909 --> 42:12.889 but actually they're not important numbers. 42:12.889 --> 42:16.109 The important number is the marginal utility. 42:16.110 --> 42:19.510 So the marginal utility, so if you go one, 42:19.505 --> 42:23.395 two and three here, the marginal utility for the 42:23.398 --> 42:26.048 first ticket was forty-four. 42:26.050 --> 42:29.740 The marginal utility for the second ticket was forty, 42:29.744 --> 42:34.224 and the marginal utility for the third ticket was thirty-six. 42:34.219 --> 42:37.019 So those are the important numbers, the same numbers that 42:37.018 --> 42:37.768 are up there. 42:37.769 --> 42:38.649 Why is that? 42:38.650 --> 42:40.480 Well, let's ask the guy. 42:40.480 --> 42:43.190 This person who now likes three tickets, 42:43.190 --> 42:46.810 after here let's say he's flat so it goes down to zero, 42:46.809 --> 42:50.809 let's ask him how many tickets would he buy at the price of 42:50.811 --> 42:51.641 forty-two. 42:51.639 --> 42:55.989 Well, from this utility function you have to say if I 42:55.989 --> 43:01.009 bought one ticket I'd have a utility of forty-four minus-- 43:01.010 --> 43:06.100 let's say my utility function now is U of X and money is this 43:06.101 --> 43:07.461 function of X. 43:07.460 --> 43:08.930 I'll call this U of X. 43:08.929 --> 43:10.029 I don't want to write it out. 43:10.030 --> 43:14.150 This is U of X plus M for money. 43:14.150 --> 43:17.190 So he says, "If I buy one ticket at a price of forty-four 43:17.193 --> 43:20.153 I lose forty-two from here, but I gain forty-four from 43:20.152 --> 43:22.572 here, so I probably should buy one ticket. 43:22.570 --> 43:25.890 If I buy a second ticket this number goes up to eighty-four 43:25.887 --> 43:28.687 and now this one goes down by forty-two twice, 43:28.690 --> 43:30.990 so maybe it's not such a great idea." 43:30.989 --> 43:32.609 So what is he actually thinking? 43:32.610 --> 43:35.930 All he's doing is he's looking at the price in this axis and 43:35.925 --> 43:39.185 comparing it to his marginal utility, the extra utility out 43:39.186 --> 43:40.926 of getting an extra ticket. 43:40.929 --> 43:43.219 So if the price is forty-two here he's going to say, 43:43.219 --> 43:45.469 "Well, at a price of forty-two the first one's 43:45.465 --> 43:46.135 worthwhile. 43:46.139 --> 43:48.049 I'm getting more utility out of that. 43:48.050 --> 43:50.440 After that it's stupid to buy another ticket because I'm 43:50.436 --> 43:52.686 getting extra utility of forty compared to a price of 43:52.692 --> 43:53.562 forty-two." 43:53.559 --> 43:59.699 So he's going to do exactly the same thing as our single ticket 43:59.702 --> 44:02.082 buyers did over there. 44:02.079 --> 44:05.849 One guy whose utility goes from forty-four to eighty-four to 44:05.849 --> 44:08.469 one-twenty is going to behave exactly-- 44:08.469 --> 44:12.059 provided he's got enough money to afford to buy at these going 44:12.061 --> 44:14.621 prices-- his behavior will be exactly 44:14.619 --> 44:18.489 the same as the three separate individuals over there. 44:18.489 --> 44:22.809 So in fact the marginal revolution-- 44:22.809 --> 44:30.699 so Jevons, Menger, and Walras in 1871 all came up 44:30.695 --> 44:41.205 with the idea at the same time of diminishing margin utility, 44:41.210 --> 44:44.390 and they said if you have people who consume multiple 44:44.385 --> 44:48.045 amounts of every commodity but they have diminishing marginal 44:48.050 --> 44:51.780 utility they're going to behave very much the same way as this 44:51.777 --> 44:53.057 little example. 44:53.059 --> 44:56.089 So this little example, in fact, is going to be 44:56.088 --> 44:57.668 extremely instructive. 44:57.670 --> 45:00.610 In fact it contains all the kernels of truth of a more 45:00.614 --> 45:03.674 general model where people consume huge amounts of every 45:03.670 --> 45:04.170 good. 45:04.170 --> 45:08.750 Just that they have diminishing marginal utility. 45:08.750 --> 45:15.220 So I'm going to now describe a slightly more complicated--so 45:15.217 --> 45:20.917 I'm going to describe this more complicated model. 45:20.920 --> 45:25.090 So what's the way of building a much more general, 45:25.090 --> 45:29.330 but hopefully still very simple abstract model of general 45:29.327 --> 45:33.717 equilibrium that will capture and generalize the example we 45:33.717 --> 45:34.927 already had? 45:34.929 --> 45:41.109 Well, the idea is to start with the exogenous variables-- 45:41.110 --> 45:43.650 this isn't going to move so I don't want to do that-- 45:43.650 --> 45:56.510 do this--the exogenous variables are going to be the 45:56.507 --> 46:00.427 people, so I'll have individuals, 46:00.425 --> 46:02.655 i in I, so let's call them individuals. 46:02.659 --> 46:09.469 So you see why I use the word I. 46:09.469 --> 46:17.019 i in I, and what is it that characterizes every individual, 46:17.016 --> 46:19.746 a utility function. 46:19.750 --> 46:27.730 So each individual is characterized by a utility and 46:27.731 --> 46:30.081 an endowment. 46:30.079 --> 46:35.379 So to start with let's say--so the individuals and we'll call 46:35.382 --> 46:38.832 the individuals and the goods c in C. 46:38.829 --> 46:44.259 So let's just say there are two goods X and Y. 46:44.260 --> 46:48.460 So an individual's going to be characterized by utility 46:48.456 --> 46:53.456 function, it's a welfare function of X 46:53.458 --> 47:01.738 and Y equals u_i of X plus v_i of Y. 47:01.739 --> 47:05.079 And an endowment, E_i equals 47:05.076 --> 47:08.946 E_i of X and E_i of Y or 47:08.952 --> 47:12.292 (E_iX, E_iY). 47:12.289 --> 47:16.249 So for example you could have, I don't know, 47:16.248 --> 47:20.208 you could have, this could be--so let's just 47:20.206 --> 47:22.136 think about this. 47:22.139 --> 47:25.469 So this is exactly the kind of situation we had before. 47:25.469 --> 47:27.699 We had precisely this going on before. 47:27.699 --> 47:28.969 What was the endowment? 47:28.969 --> 47:31.819 Every person began with money. 47:31.820 --> 47:41.010 It could have been money before and with football tickets. 47:41.010 --> 47:44.910 And we said that the story that--so these original 47:44.905 --> 47:49.515 marginalists argued that it's part of human nature that the 47:49.516 --> 47:54.366 more you get of something the less and less extra advantage it 47:54.367 --> 47:55.717 brings you. 47:55.719 --> 47:57.279 There may be exceptions. 47:57.280 --> 47:59.180 Maybe you need two of something. 47:59.179 --> 48:02.489 You need both shoes in order for the shoes to help, 48:02.494 --> 48:06.344 but every pair of shoes after that was going to be less and 48:06.342 --> 48:08.002 less valuable to you. 48:08.000 --> 48:11.500 And so beside from these small blips that come from 48:11.500 --> 48:15.840 indivisibilities or things like that peoples' utility increases 48:15.840 --> 48:19.480 but at a smaller and smaller rate as they get more of 48:19.480 --> 48:20.670 everything. 48:20.670 --> 48:22.170 That's just human nature, they claim. 48:22.170 --> 48:26.260 They even tried to measure utility. 48:26.260 --> 48:28.970 So they would try and measure the temperature of the skin and 48:28.974 --> 48:31.744 things like that and see how it increased when you gave people 48:31.735 --> 48:34.315 more of something and whether the rate of increase and how 48:34.315 --> 48:37.165 much they smiled and stuff like that whether that would actually 48:37.166 --> 48:39.736 change in a lesser and lesser way as you add more and more 48:39.744 --> 48:40.564 utility. 48:40.559 --> 48:42.669 Well, they abandoned that sort of thing eventually. 48:42.670 --> 48:45.950 But anyway, they kept the idea of diminishing marginal utility. 48:45.949 --> 48:50.479 So we want to keep the idea that u_i of X and 48:50.483 --> 48:55.103 v_i of Y show diminishing marginal utility. 48:55.099 --> 48:58.149 So the way of saying that, I told you this is one of the-- 48:58.150 --> 49:01.810 so the first handout in the reading list was review of 49:01.809 --> 49:05.819 mathematics you should know, or if you don't know you have 49:05.820 --> 49:07.620 to learn, diminishing marginal utility 49:07.623 --> 49:09.113 means something that looks like that. 49:09.110 --> 49:10.450 It's a concave function. 49:10.449 --> 49:11.849 So here's X. 49:11.849 --> 49:15.109 Here's utility, and here's u_i of X, 49:15.114 --> 49:15.554 say. 49:15.550 --> 49:19.550 It goes up as you get more X, but at a rate that declines. 49:19.550 --> 49:21.620 So the slope is getting smaller and smaller. 49:21.619 --> 49:23.739 That's diminishing marginal utility. 49:23.739 --> 49:26.249 So this curve that's increasing, but a lesser and 49:26.251 --> 49:29.491 lesser rate we can approximate with a continuous differentiable 49:29.494 --> 49:32.824 curve that looks like that, so it doesn't have the kinks 49:32.820 --> 49:36.180 here, and that's exactly the kind of assumption that seems 49:36.181 --> 49:39.681 reasonable to fit the facts, and at least for consumption. 49:39.679 --> 49:41.689 Our main interest, of course, is at the bottom 49:41.692 --> 49:44.202 here in financial equilibrium, but we have to know what's 49:44.197 --> 49:45.447 going on in the economy. 49:45.449 --> 49:49.609 All these finance professors, as I said in business schools, 49:49.606 --> 49:51.716 they ignored the part above. 49:51.719 --> 49:54.109 They started right away with the assets and the bonds. 49:54.110 --> 49:57.140 Said they didn't need to pay any attention to what was going 49:57.141 --> 49:59.661 on in the economy, because everything was going to 49:59.661 --> 50:00.331 be great. 50:00.329 --> 50:02.729 But we're going to find that there's a big interaction 50:02.728 --> 50:05.218 between the financial sector and the economic sector. 50:05.219 --> 50:07.969 That's going to be the heart of what we're doing even though it 50:07.974 --> 50:09.844 was ignored in finance most of the time. 50:09.840 --> 50:16.470 So anyway, diminishing marginal utility for both of these, 50:16.465 --> 50:23.085 so for instance we could have a hundred X minus one half X 50:23.090 --> 50:25.300 squared plus Y. 50:25.300 --> 50:32.990 That's one example of a utility function. 50:32.989 --> 50:35.669 So that's going to be a standard kind of utility 50:35.672 --> 50:36.302 function. 50:36.300 --> 50:40.810 So the only two ones I'm ever going to use are things like 50:40.806 --> 50:44.676 this, or one-third log X plus two-thirds log Y. 50:44.679 --> 50:54.619 Whenever I write log I mean natural log. 50:54.619 --> 50:57.189 This is linear quadratic. 50:57.190 --> 51:02.900 So this is quadratic, in fact linear quadratic, 51:02.898 --> 51:08.228 so maybe both will be quadratic, and this is 51:08.233 --> 51:10.223 logarithmic. 51:10.219 --> 51:13.529 Now both of these have this property of diminishing marginal 51:13.530 --> 51:16.280 utility because I can take derivative of this, 51:16.280 --> 51:22.590 the derivative of one hundred X minus one half X squared so the 51:22.588 --> 51:28.388 marginal utility of X is equal to one hundred minus X, 51:28.389 --> 51:30.819 and that obviously declines. 51:30.820 --> 51:32.850 So it's diminishing marginal utility. 51:32.849 --> 51:37.089 And then the derivative here--the marginal utility with 51:37.090 --> 51:39.840 respect to X depends on X again-- 51:39.840 --> 51:43.670 is going to be one-third times one over X because the 51:43.668 --> 51:46.538 derivative of the log is one over X, 51:46.539 --> 51:49.539 and as X gets bigger that also declines. 51:49.539 --> 51:52.259 So these are the two functions that we're going to use over and 51:52.255 --> 51:54.875 over again because I want to make things concrete with actual 51:54.884 --> 51:55.414 numbers. 51:55.409 --> 51:58.199 So we'll always solve examples with quadratic stuff, 51:58.202 --> 52:00.612 maybe everything will be quadratic or linear, 52:00.612 --> 52:02.312 and with logarithmic stuff. 52:02.309 --> 52:04.679 Those are the only two functions you really have to be 52:04.681 --> 52:05.891 totally comfortable with. 52:05.889 --> 52:07.709 So you have to understand what a derivative is. 52:07.710 --> 52:09.460 This is a partial derivative. 52:09.460 --> 52:12.830 So how much extra utility do you get out of consuming more X? 52:12.829 --> 52:16.379 If you've already got a certain amount of X in your possession 52:16.382 --> 52:17.842 it's a hundred minus X. 52:17.840 --> 52:20.900 How much more utility do you get out of consuming more X? 52:20.900 --> 52:25.090 If this is your utility when you're consumption's already a 52:25.088 --> 52:28.988 certain amount of X it's one-third times one over X. 52:28.989 --> 52:33.069 So those are the two things you have to be comfortable with 52:33.067 --> 52:33.627 using. 52:33.630 --> 52:36.550 So that's utility. 52:36.550 --> 52:39.130 What else do we need to describe a person? 52:39.130 --> 52:42.270 It's his endowment. 52:42.268 --> 52:48.128 So with only two goods, so here's X and here's Y, 52:48.132 --> 52:53.512 so we could have an endowment E_iX, 52:53.507 --> 52:55.827 E_iY. 52:55.829 --> 53:01.939 That's the endowment of X and Y of a certain person, 53:01.938 --> 53:06.248 E_iX and E_iY. 53:06.250 --> 53:08.930 So this person, let's say it's this top guy-- 53:08.929 --> 53:10.999 a hundred X minus one over two X squared plus Y-- 53:11.000 --> 53:13.750 he has a certain utility function, he's got a certain 53:13.746 --> 53:14.376 endowment. 53:14.380 --> 53:17.570 Maybe there's somebody else over here who I can put in a 53:17.574 --> 53:18.624 different color. 53:18.619 --> 53:24.659 Aha, I think pink is a good color. 53:24.659 --> 53:35.529 So another person might be over here and this is E_jY 53:35.527 --> 53:39.207 and E_iX. 53:39.210 --> 53:42.660 So J has a lot more of Y, and I has a lot more of X. 53:42.659 --> 53:45.099 They're two different people, but you could imagine not two 53:45.099 --> 53:47.619 people you could imagine 150 of you with different endowments 53:47.623 --> 53:50.543 and different utility functions, or 300 million of you with 53:50.538 --> 53:53.358 different endowments and different utility functions. 53:53.360 --> 53:56.820 And what general equilibrium is about is saying, 53:56.820 --> 53:59.770 well, if you've got all these people with well defined utility 53:59.771 --> 54:01.151 functions, those are the data, 54:01.148 --> 54:03.438 we may not know them but they know them themselves with all 54:03.438 --> 54:05.528 those utility functions and all those endowments, 54:05.530 --> 54:08.810 and you throw 300 million of them together, 54:08.809 --> 54:12.559 or 150 of you together, can you predict what's going to 54:12.556 --> 54:16.716 happen and is the thing that happens good for the society. 54:16.719 --> 54:19.139 So that's the problem of general equilibrium. 54:19.139 --> 54:23.559 And it turns out that with these simple utility functions 54:23.556 --> 54:26.946 it's very easy to solve for equilibrium, 54:26.949 --> 54:29.969 predict what'll happen, and things look great until you 54:29.974 --> 54:31.714 get to financial equilibrium. 54:31.710 --> 54:35.640 And we'll be able to solve them either by hand or on a computer, 54:35.639 --> 54:37.679 and we're going to take advantage of that because we 54:37.684 --> 54:39.534 want concrete answers to concrete problems, 54:39.530 --> 54:44.050 and we want to interact it with the financial world to see what 54:44.050 --> 54:44.780 happens. 54:44.780 --> 54:49.720 So remember, what's the next step? 54:49.719 --> 54:52.109 The first step is exogenous variables. 54:52.110 --> 54:54.250 So we define the exogenous variables. 54:54.250 --> 54:56.770 The next step is endogenous variables. 54:56.768 --> 55:03.968 So what are the endogenous variables going to be? 55:03.969 --> 55:11.149 And the endogenous variables are going to be the prices and 55:11.152 --> 55:15.612 the trades, or final consumptions. 55:15.610 --> 55:20.320 You can always deduce a trade from a final consumption because 55:20.315 --> 55:23.525 if you know your endowment, the exogenous thing, 55:23.532 --> 55:26.152 and you're consuming more of X than you're endowed with you 55:26.152 --> 55:28.232 must have bought that difference somewhere. 55:28.230 --> 55:32.360 And if you're consuming less Y than you started with you must 55:32.364 --> 55:36.574 have sold some of that Y in order to end up consuming less. 55:36.570 --> 55:39.840 So the endogenous variables are the prices and the trades. 55:39.840 --> 55:44.490 Now, how can we make a general theory that for an arbitrary 55:44.494 --> 55:47.804 number of people, an arbitrary number of goods, 55:47.800 --> 55:51.030 you can solve and figure out what's going to happen that 55:51.027 --> 55:54.607 looks very much like the example and has as a special case the 55:54.605 --> 55:56.595 example we did to begin with? 55:56.599 --> 55:59.249 That's what happened with general equilibrium, 55:59.251 --> 56:01.081 and I'm about to describe it. 56:01.079 --> 56:09.559 So the next step is always to write down the equilibrium as a 56:09.556 --> 56:14.356 bunch of simultaneous equations. 56:14.360 --> 56:17.050 So what are all the equilibrium equations going to be, 56:17.052 --> 56:20.152 and that's what's going to be our model of what happens in the 56:20.150 --> 56:20.660 world. 56:20.659 --> 56:23.019 Are there any questions? 56:23.019 --> 56:24.069 How are you all doing here? 56:24.070 --> 56:28.130 Is this painfully repetitive of what you know. 56:28.130 --> 56:29.930 I need some feedback here. 56:29.929 --> 56:33.279 How many of you haven't seen this before? 56:33.280 --> 56:35.340 Everybody's seen this before? 56:35.340 --> 56:38.610 What about all these people who e-mailed me and said they were 56:38.610 --> 56:41.990 scientists and philosophers and psychologists and they wanted to 56:41.989 --> 56:43.759 take economics the first day. 56:43.760 --> 56:45.060 So you're one of those people. 56:45.059 --> 56:45.859 Maybe you didn't e-mail me. 56:45.860 --> 56:49.270 So this is a first for you, but everybody else you've all 56:49.271 --> 56:50.431 seen this before. 56:50.429 --> 56:53.279 Well, that's good. 56:53.280 --> 56:54.240 I can move along here. 56:54.239 --> 57:00.149 So I'll keep looking at you as I proceed here. 57:00.150 --> 57:03.080 So don't feel bashful. 57:03.079 --> 57:05.499 Speak up if it's not making sense. 57:05.500 --> 57:09.980 So what was the great conceptual advance? 57:09.980 --> 57:13.880 It was--one conceptual advance was the budget set. 57:13.880 --> 57:17.630 Now, this will turn out to be, in economics-- 57:17.630 --> 57:21.430 the rest of the 140 of them have all got this down, 57:21.429 --> 57:24.119 but as soon as we turn it into a financial problem they're not 57:24.117 --> 57:26.887 going to be able to do it again even though it's going to be the 57:26.893 --> 57:27.513 same idea. 57:27.510 --> 57:31.260 So this budget set was an extremely clever idea which I'll 57:31.264 --> 57:34.894 now repeat for them and tell you for the first time, 57:34.889 --> 57:37.789 but I can almost guarantee that although they all think it's 57:37.789 --> 57:39.589 obvious, when we do the first financial 57:39.592 --> 57:42.162 problem they aren't going to be able to do it even though it's 57:42.161 --> 57:43.131 the exact same idea. 57:43.130 --> 57:44.330 So what's the idea? 57:44.329 --> 57:46.799 You begin with your endowment, E_iX and 57:46.795 --> 57:47.665 E_iy. 57:47.670 --> 57:51.310 So this person has to buy and sell X and Y. 57:51.309 --> 57:54.749 So the person says to himself, "I've started with this X 57:54.753 --> 57:57.743 and Y, I might like something that's better." 57:57.739 --> 58:02.169 Now how can you illustrate what's better for this person? 58:02.170 --> 58:06.610 Well, Edgeworth, as I mentioned, 58:06.612 --> 58:14.642 Edgeworth invented the idea of the indifference curve. 58:14.639 --> 58:18.639 So he says, "All the goods that are of the same utility can 58:18.637 --> 58:21.807 be described by this indifference curve X." 58:21.809 --> 58:25.529 This person, her utility is one-third log X 58:25.532 --> 58:30.162 plus two-thirds log Y, well if she consumes less of X, 58:30.164 --> 58:34.614 enough extra Y will make her just indifferent to where she 58:34.606 --> 58:39.046 was before because there's a tradeoff between X and Y. 58:39.050 --> 58:40.560 Economics is all about tradeoffs. 58:40.559 --> 58:42.159 So this is her indifference curve. 58:42.159 --> 58:45.469 Maybe his indifference curve looks like that, 58:45.469 --> 58:48.479 a different slope, entirely different. 58:48.480 --> 58:52.230 So he thinks a lot of Y. 58:52.230 --> 58:54.690 A little diminution in Y you better get a lot of X to 58:54.686 --> 58:55.486 compensate him. 58:55.489 --> 58:58.009 She's kind of more balanced in things, X and Y, 58:58.005 --> 59:01.065 unless she starts to get too much of X in which case Y is 59:01.068 --> 59:02.488 more important to her. 59:02.489 --> 59:04.409 She in general is more balanced than he is. 59:04.409 --> 59:06.059 But anyway, so they have different tastes, 59:06.061 --> 59:08.321 different utility functions, and different endowments. 59:08.320 --> 59:10.020 So what's going to happen in the end? 59:10.018 --> 59:12.728 Well, the budget set describes what she can do. 59:12.730 --> 59:14.720 We're going to assume, as we did before, 59:14.719 --> 59:18.189 that cornerstone of economic reasoning, 59:18.190 --> 59:20.100 somehow when these hundred million people, 59:20.099 --> 59:23.519 300 million people get together they're going to miraculously 59:23.521 --> 59:24.721 discover the price. 59:24.719 --> 59:26.109 They're going to be screaming at each other, 59:26.114 --> 59:27.124 but we don't care about that. 59:27.119 --> 59:30.269 We just say for the purpose of the big picture, 59:30.266 --> 59:33.206 some price of X and Y is going to emerge. 59:33.210 --> 59:36.850 So equilibrium is going to be a price of X and a price of Y. 59:36.849 --> 59:40.449 It's going to emerge and now what can she do? 59:40.449 --> 59:45.319 Well, she can say, "Given my X I can buy more 59:45.318 --> 59:50.588 X than I started with, and if I do that the price of X 59:50.585 --> 59:53.265 is P_X." 59:53.268 --> 59:56.418 So if I want to buy more--I have this already. 59:56.420 --> 59:58.810 So I want to end up consuming X_i, 59:58.809 --> 1:00:02.279 so final consumptions will be X_i and Y_i, 1:00:02.280 --> 1:00:06.730 this is the final consumption, so my trade, 1:00:06.730 --> 1:00:09.560 if I want to buy more, I can express the idea that I'm 1:00:09.556 --> 1:00:12.696 buying more by saying my final consumption is bigger than my 1:00:12.702 --> 1:00:13.452 endowment. 1:00:13.449 --> 1:00:16.289 So I've had to buy, I've had to trade to get this 1:00:16.286 --> 1:00:19.706 much more which means I had to pay P_X times this 1:00:19.713 --> 1:00:20.603 difference. 1:00:20.599 --> 1:00:23.729 Now, how did I get the money for that? 1:00:23.730 --> 1:00:28.330 Well, I got the money for that by selling some of Y. 1:00:28.329 --> 1:00:30.169 So I sold Y. 1:00:30.170 --> 1:00:35.100 I started with E_iY and I sold some of it because I 1:00:35.101 --> 1:00:38.061 ended up with less than I started. 1:00:38.059 --> 1:00:42.419 So the money I got by selling Y I can use to spend on buying X. 1:00:42.420 --> 1:00:43.930 That's the basic budget constraint. 1:00:43.929 --> 1:00:46.519 Now, the cleverness is in realizing that it doesn't matter 1:00:46.518 --> 1:00:49.468 which one--So here X_i is bigger than E_iX. 1:00:49.469 --> 1:00:50.839 You're buying X. 1:00:50.840 --> 1:00:52.350 Here Y_i is less than E_iY. 1:00:52.349 --> 1:00:54.079 You're selling Y. 1:00:54.079 --> 1:00:57.419 And so the revenue you get from selling Y equals the expenditure 1:00:57.420 --> 1:00:58.640 you make on buying X. 1:00:58.639 --> 1:01:01.349 So the cleverness is in realizing it doesn't matter what 1:01:01.351 --> 1:01:02.141 the signs are. 1:01:02.139 --> 1:01:05.629 If X_i is less than E_iX this equation 1:01:05.632 --> 1:01:09.252 still makes sense because then you get a negative number. 1:01:09.250 --> 1:01:11.800 You've gotten money by consuming less X than you 1:01:11.804 --> 1:01:14.634 started with so that's money you can use to buy Y. 1:01:14.630 --> 1:01:18.840 And then Y_i--you'll be able to buy more Y than you 1:01:18.842 --> 1:01:23.052 started with so this number will also be negative by the same 1:01:23.054 --> 1:01:24.394 amount as this. 1:01:24.389 --> 1:01:25.909 This is the extra value on Y. 1:01:25.909 --> 1:01:27.339 This is the extra value on X. 1:01:27.340 --> 1:01:31.020 So whether the X's and the Y's are bigger or smaller than the 1:01:31.021 --> 1:01:34.031 E_iX's or E_iY's this equation 1:01:34.030 --> 1:01:37.590 defines the budget trading opportunities of the agent. 1:01:37.590 --> 1:01:39.880 Did that go too fast? 1:01:39.880 --> 1:01:40.990 You got that. 1:01:40.989 --> 1:01:44.449 So you can write that a little bit more simply by saying, 1:01:44.445 --> 1:01:47.095 putting a plus here and reversing the order, 1:01:47.099 --> 1:01:48.889 making it more symmetric. 1:01:48.889 --> 1:01:53.299 So this is Y_i minus E_iY equals zero. 1:01:53.300 --> 1:02:01.180 So that's the budget set of agent i. 1:02:01.179 --> 1:02:06.019 And in the diagram the budget set--I'm out of colors that show 1:02:06.018 --> 1:02:09.868 up I think-- all the others got vetoed, 1:02:09.869 --> 1:02:14.089 I think orange was okay-- the budget set, 1:02:14.092 --> 1:02:18.642 then, will be something that looks like this. 1:02:18.639 --> 1:02:21.589 That looks terrible. 1:02:21.590 --> 1:02:25.110 How bad can you get? 1:02:25.110 --> 1:02:31.500 So that budget set might look something like--let's make it 1:02:31.498 --> 1:02:32.708 this way. 1:02:32.710 --> 1:02:33.840 It looks something like that. 1:02:33.840 --> 1:02:38.510 It's a linear line that goes up--just forget this guy's 1:02:38.505 --> 1:02:39.625 budget set. 1:02:39.630 --> 1:02:40.460 We'll do the other one. 1:02:40.460 --> 1:02:41.630 I can get it better in the picture. 1:02:41.630 --> 1:02:45.030 So this one's budget set, his budget set might look 1:02:45.032 --> 1:02:46.532 something like that. 1:02:46.530 --> 1:02:48.740 So his budget set, never mind hers, 1:02:48.744 --> 1:02:52.004 it goes off the page, his budget set he starts with 1:02:52.001 --> 1:02:53.241 this endowment. 1:02:53.239 --> 1:02:56.719 If the prices are given P_X and P_Y, 1:02:56.719 --> 1:03:00.069 P_X and P_Y define a linear tradeoff between 1:03:00.074 --> 1:03:02.894 X_i and Y_i, in this case j, 1:03:02.894 --> 1:03:06.724 because the more X you consume the less Y you have to consume 1:03:06.719 --> 1:03:10.669 and there's going to be a linear tradeoff between the two given 1:03:10.670 --> 1:03:12.710 by rearranging these terms. 1:03:12.710 --> 1:03:15.390 P_X and P_Y are fixed, 1:03:15.389 --> 1:03:17.299 so this is just a linear equation in X_i and 1:03:17.304 --> 1:03:19.814 Y_i, and so that tradeoff is given 1:03:19.806 --> 1:03:21.106 by that budget set. 1:03:21.110 --> 1:03:25.760 So mister pink is going to try, given his opportunities on this 1:03:25.757 --> 1:03:29.657 budget set, to pick the combination of X and Y that's 1:03:29.655 --> 1:03:30.925 best for him. 1:03:30.929 --> 1:03:34.799 And so that's going to turn out to be something that's right 1:03:34.797 --> 1:03:38.267 here because no other combination of X and Y will give 1:03:38.271 --> 1:03:40.371 him as much utility as that. 1:03:40.369 --> 1:03:42.609 Did that make sense? 1:03:42.610 --> 1:03:44.040 All right, so that's it. 1:03:44.039 --> 1:03:46.349 That's the main lesson. 1:03:46.349 --> 1:03:50.929 So how do you describe now the whole equilibrium conditions? 1:03:50.929 --> 1:03:56.399 Well, so equilibrium now, if you can see this, 1:03:56.398 --> 1:04:00.408 equilibrium is defined by what? 1:04:00.409 --> 1:04:06.359 It's defined by P_X, P_Y, 1:04:06.356 --> 1:04:13.516 and X_i and Y_i for all i in I. 1:04:13.518 --> 1:04:16.978 It's just the prices that emerge and final consumptions 1:04:16.981 --> 1:04:19.291 that everybody chooses of X and Y. 1:04:19.289 --> 1:04:21.009 There are only two goods here. 1:04:21.010 --> 1:04:23.840 So the price of X, the price of Y what every 1:04:23.844 --> 1:04:27.344 person i ends up with X_i and Y_i, 1:04:27.340 --> 1:04:29.450 and what has to be the case? 1:04:29.449 --> 1:04:30.259 What has to be the case? 1:04:30.260 --> 1:04:34.450 The first equation is going to be that the final consumptions 1:04:34.452 --> 1:04:38.232 of everybody have to equal the final endowments because 1:04:38.226 --> 1:04:41.996 everyone who buys has to be met by another seller. 1:04:42.000 --> 1:04:45.510 Remember equilibrium was price taking, agent optimization, 1:04:45.510 --> 1:04:48.220 rational expectations and market clearing. 1:04:48.219 --> 1:04:50.919 Price taking means everybody knows what the prices are, 1:04:50.923 --> 1:04:53.133 miraculously P_X and P_Y, 1:04:53.128 --> 1:04:54.128 before they act. 1:04:54.130 --> 1:04:56.490 Agent optimization we're going to come to. 1:04:56.489 --> 1:04:59.129 It means they do the best thing they can. 1:04:59.130 --> 1:05:01.720 Rational expectations means even though they're only buying 1:05:01.722 --> 1:05:04.492 one good and there are thousands in the economy they understand 1:05:04.494 --> 1:05:06.634 all the prices, and when they act they're 1:05:06.632 --> 1:05:09.522 taking into account all of the tradeoffs they could make. 1:05:09.518 --> 1:05:11.328 So they realize the whole vector of prices. 1:05:11.329 --> 1:05:14.749 And market clearing means for any buyer there's a seller, 1:05:14.750 --> 1:05:19.010 so market clearing means summation from i in I of 1:05:19.005 --> 1:05:23.345 X_i has to equal summation i in I of the 1:05:23.349 --> 1:05:26.449 endowment, E_iX of X. 1:05:26.449 --> 1:05:32.449 So in this picture if I added this to this, 1:05:32.449 --> 1:05:36.639 this is the endowment, so I add this vector to that 1:05:36.644 --> 1:05:39.754 vector I get this thing over here, 1:05:39.750 --> 1:05:50.620 and this is going to be the total endowment in the economy. 1:05:50.619 --> 1:05:52.839 So this total endowment E_iX, 1:05:52.842 --> 1:05:56.122 I add over every person i what the total endowment is. 1:05:56.119 --> 1:05:59.179 So I add his endowment of X to this guy's endowment of X and I 1:05:59.182 --> 1:06:00.742 get the total endowment of X. 1:06:00.739 --> 1:06:05.569 I add her endowment of Y to his endowment of Y and I get the 1:06:05.574 --> 1:06:07.464 total endowment of Y. 1:06:07.460 --> 1:06:13.100 So the first two equations are summation i in I. 1:06:13.099 --> 1:06:18.799 Y_i equals summation i in I of E_iY. 1:06:18.800 --> 1:06:23.190 The third equation is everybody is going to choose on their 1:06:23.186 --> 1:06:24.166 budget set. 1:06:24.170 --> 1:06:26.860 Everyone, this person--mister pink here-- 1:06:26.860 --> 1:06:30.360 he's going to choose not inside his budget set, 1:06:30.360 --> 1:06:33.860 he can't choose outside of it because there's no point in 1:06:33.860 --> 1:06:34.860 wasting money. 1:06:34.860 --> 1:06:37.580 He's going to buy the combination of X and Y that lies 1:06:37.581 --> 1:06:40.511 on his budget set that does as well as he possibly can. 1:06:40.510 --> 1:06:46.410 So the equation here is going to be that P_X times 1:06:46.405 --> 1:06:50.195 X_i minus E_iX plus 1:06:50.204 --> 1:06:54.004 P_Y times Y_i minus 1:06:54.001 --> 1:06:57.801 E_iY is equal to zero. 1:06:57.800 --> 1:07:01.120 I could do this for j too just since I've got a picture 1:07:01.117 --> 1:07:04.247 of--this is P_X, this is P_Y. 1:07:04.250 --> 1:07:07.080 P_X times X_j minus 1:07:07.079 --> 1:07:09.699 E_jX, so I'm doing a special case now 1:07:09.704 --> 1:07:14.164 with two people, Y_j minus 1:07:14.161 --> 1:07:19.631 E_jX equals zero. 1:07:19.630 --> 1:07:21.990 Everybody's on their budget set. 1:07:21.989 --> 1:07:27.469 So he's on his budget set, she's going to be on her budget 1:07:27.472 --> 1:07:28.052 set. 1:07:28.050 --> 1:07:30.740 Her budget set, by the way, is better than his 1:07:30.737 --> 1:07:33.657 because her budget set is going to look like this, 1:07:33.661 --> 1:07:34.261 right? 1:07:34.260 --> 1:07:37.450 It's got to be parallel to his because the prices she faces are 1:07:37.452 --> 1:07:40.132 the same and her endowment is worth more than his. 1:07:40.130 --> 1:07:43.850 So her budget set is further out. 1:07:43.849 --> 1:07:46.129 So that's what he does, that's what she does, 1:07:46.132 --> 1:07:48.572 or that's what she does, that's what he does. 1:07:48.570 --> 1:07:52.280 And now the fifth one--so now we have the two mysterious 1:07:52.277 --> 1:07:54.027 equations that are left. 1:07:54.030 --> 1:07:58.480 So how do we express the idea that the choices X_i 1:07:58.478 --> 1:08:04.038 and Y_i by i, that's her--and she's going to 1:08:04.039 --> 1:08:08.479 optimize by choosing here somewhere. 1:08:08.480 --> 1:08:10.560 This is her indifference curve, right, looked like that. 1:08:10.559 --> 1:08:12.239 So that's what she's going to do. 1:08:12.239 --> 1:08:15.649 And remember he's going to choose here. 1:08:15.650 --> 1:08:20.680 So how can you turn her choice and his choice into an equation? 1:08:20.680 --> 1:08:27.180 Well, this was invented by a German guy Gossen in 1851 and 1:08:27.182 --> 1:08:32.352 then rediscovered by Jevons, Menger and Walras, 1:08:32.345 --> 1:08:36.495 the same three I mentioned several times now. 1:08:36.500 --> 1:08:38.660 This is the marginal revolution in economics. 1:08:38.658 --> 1:08:43.428 What they said is you can turn the behavior of individuals, 1:08:43.430 --> 1:08:46.530 of humans as Gossen said, "I can do for the bodies 1:08:46.533 --> 1:08:49.813 on earth what Copernicus did for the bodies in heaven, 1:08:49.810 --> 1:08:52.690 find equations that describe their motion." 1:08:52.689 --> 1:08:54.519 What is it that people are going to do? 1:08:54.520 --> 1:08:57.620 To say that you're choosing the best possible thing means that 1:08:57.621 --> 1:09:00.471 the slope of the budget set is equal to the slope of your 1:09:00.469 --> 1:09:02.729 indifference curve, but what is the slope of your 1:09:02.730 --> 1:09:03.450 indifference curve? 1:09:03.448 --> 1:09:05.778 That's the tradeoff between X and Y. 1:09:05.779 --> 1:09:07.769 So what does it mean? 1:09:07.770 --> 1:09:13.160 If you get a little bit less X you're losing the marginal 1:09:13.157 --> 1:09:14.597 utility of X. 1:09:14.600 --> 1:09:17.860 If you get a little bit more of Y you're gaining the marginal 1:09:17.863 --> 1:09:18.683 utility of Y. 1:09:18.680 --> 1:09:22.230 If the price of X and Y are the same then it had better be that 1:09:22.230 --> 1:09:25.670 the marginal utility of X is equal to the marginal utility of 1:09:25.667 --> 1:09:29.217 Y because you can always give up one unit of X and get one unit 1:09:29.219 --> 1:09:29.849 of Y. 1:09:29.850 --> 1:09:32.880 If this is optimal, and you can give up one unit of 1:09:32.884 --> 1:09:35.824 X and get two units-- sorry, if the marginal utility 1:09:35.823 --> 1:09:38.913 of Y was double the marginal utility of X then you would give 1:09:38.909 --> 1:09:41.999 up that one unit of X and you'd get two extra utils by taking 1:09:41.997 --> 1:09:45.597 the one unit of Y which you can afford by selling one unit of X, 1:09:45.600 --> 1:09:48.330 and the utility would be much higher than it was here. 1:09:48.328 --> 1:09:52.168 And so you wouldn't be optimizing by doing that. 1:09:52.170 --> 1:09:58.670 So the final equation is you're optimizing if and only if the 1:09:58.667 --> 1:10:04.837 marginal utility of i of X divided by the marginal utility 1:10:04.841 --> 1:10:10.691 of i of Y equals P_X over P_Y. 1:10:10.689 --> 1:10:14.329 And the last equation is the same thing for j, 1:10:14.328 --> 1:10:21.138 the marginal utility of j of X divided by the marginal utility 1:10:21.140 --> 1:10:27.060 of Y has to equal P_X over P_Y. 1:10:27.060 --> 1:10:27.920 So why is that again? 1:10:27.920 --> 1:10:29.750 That's the trickiest equation. 1:10:29.750 --> 1:10:34.310 That's the one that Marx and Adam Smith and not even Ricardo, 1:10:34.310 --> 1:10:35.250 the most brilliant one of them all, 1:10:35.250 --> 1:10:37.390 not even Ricardo could figure that out, 1:10:37.390 --> 1:10:41.330 this equation marginal utility, wait until 1871. 1:10:41.328 --> 1:10:44.048 And again, to repeat it, it's of course very obvious now 1:10:44.046 --> 1:10:46.706 but wasn't at the time, how can you describe what these 1:10:46.712 --> 1:10:47.752 people are doing? 1:10:47.750 --> 1:10:49.660 You have to figure out the budget constraint, 1:10:49.658 --> 1:10:52.298 that's what they can afford, and then they're going to 1:10:52.301 --> 1:10:55.491 choose the point on their budget constraint which maximizes their 1:10:55.490 --> 1:10:56.090 utility. 1:10:56.090 --> 1:10:58.400 But that just means in the picture it makes the 1:10:58.404 --> 1:11:00.824 indifference curve tangent to the budget set, 1:11:00.819 --> 1:11:05.549 which means that you set--so and what is the slope of the 1:11:05.546 --> 1:11:07.316 indifference curve? 1:11:07.319 --> 1:11:10.309 Well, the tradeoff between X and Y that leaves you 1:11:10.309 --> 1:11:14.029 indifferent--how much X do you have to give up to get an extra 1:11:14.029 --> 1:11:16.409 unit of Y and still be indifferent? 1:11:16.408 --> 1:11:20.048 It's determined by the ratio of the marginal utility of X to the 1:11:20.051 --> 1:11:22.771 marginal utility of Y because those are the, 1:11:22.770 --> 1:11:24.840 you know, when you give up a unit of X you're losing the 1:11:24.837 --> 1:11:25.737 marginal utility of X. 1:11:25.738 --> 1:11:28.338 When you're getting a unit of Y you're getting the marginal 1:11:28.337 --> 1:11:29.007 utility of Y. 1:11:29.010 --> 1:11:33.520 If you can trade them off in the market at 3:1 you optimize 1:11:33.524 --> 1:11:37.964 when, in your own personal evaluation, you're trading them 1:11:37.962 --> 1:11:40.222 off on the margin at 3:1. 1:11:40.220 --> 1:11:41.770 You really follow that? 1:11:41.770 --> 1:11:45.370 That's an idea that took fifty years to figure out and you 1:11:45.369 --> 1:11:48.149 claim you figured it out now in five minutes, 1:11:48.149 --> 1:11:49.349 so that's good. 1:11:49.350 --> 1:11:54.480 So you'll have a chance in the problem set to get practice. 1:11:54.479 --> 1:11:56.229 So those are the equations. 1:11:56.229 --> 1:12:00.789 We now basically have described economic equilibrium. 1:12:00.788 --> 1:12:04.908 So we now have the ability to play with all kinds of models, 1:12:04.908 --> 1:12:06.848 as we'll start in the next class doing, 1:12:06.850 --> 1:12:09.790 solving for economic equilibrium, figuring out what 1:12:09.787 --> 1:12:12.047 will happen, and then complicating it by 1:12:12.045 --> 1:12:15.045 adding a financial sector and see how that affects what goes 1:12:15.050 --> 1:12:16.120 on in equilibrium. 1:12:16.119 --> 1:12:21.999