WEBVTT 00:01.740 --> 00:03.550 Prof: All right, so we spent a long time 00:03.554 --> 00:06.954 reviewing general equilibrium and we've now switched to 00:06.946 --> 00:09.346 finance, and you're hopefully going to 00:09.353 --> 00:12.663 see that the principles of finance emerge very quickly from 00:12.661 --> 00:15.001 the principles of general equilibrium. 00:15.000 --> 00:18.150 So that although it seems it was a long interlude we've 00:18.149 --> 00:21.239 actually learned a lot about the financial economy. 00:21.240 --> 00:24.960 So I'm going to continue with the example that we started with 00:24.963 --> 00:25.943 the last time. 00:25.940 --> 00:28.200 So we have a financial economy. 00:28.200 --> 00:31.090 So in a financial economy--what is a financial economy? 00:31.090 --> 00:36.200 On this top board the financial economy is defined by lots of 00:36.201 --> 00:39.951 people in the economy and their utilities. 00:39.950 --> 00:44.080 So here we have for simplicity two kinds of people A and B with 00:44.075 --> 00:47.395 utilities given by the log X_1 1 half log 00:47.403 --> 00:49.203 X_2 etcetera. 00:49.200 --> 00:53.060 It's also people know today what their endowments are and 00:53.061 --> 00:57.131 they have some idea of what they're going to be tomorrow. 00:57.130 --> 01:00.120 They're labor powered today and they're going to be able to work 01:00.115 --> 01:00.965 again next year. 01:00.969 --> 01:06.449 So the labor endowments are given by (1,1) for A, 01:06.453 --> 01:08.513 and (1,0) for B. 01:08.510 --> 01:11.190 And then they also know that there are two stocks in the 01:11.186 --> 01:13.766 economy and they have to anticipate what the dividends 01:13.766 --> 01:14.736 are going to be. 01:14.739 --> 01:17.339 And as Fisher said, the main value of assets is 01:17.340 --> 01:20.450 that they give you something, they produce something. 01:20.450 --> 01:22.820 In this case they're going to be dividends and beta's 01:22.822 --> 01:25.352 producing dividends of 2, and alpha is producing a 01:25.349 --> 01:29.329 dividend of 1 next period, and then the ownership of 01:29.331 --> 01:30.141 shares. 01:30.140 --> 01:33.970 So that's the beginning of the economy and we want to define 01:33.971 --> 01:37.151 from that equilibrium which involves: what are the 01:37.152 --> 01:39.752 contemporaneous prices going to be, 01:39.750 --> 01:42.360 that's Q for contemporaneous, what are the prices of the 01:42.364 --> 01:45.544 stocks going to be, and who's going to hold which 01:45.535 --> 01:50.115 portfolio of assets of stocks, and who's going to consume what. 01:50.120 --> 01:53.590 And so Fisher said that's a very complicated problem. 01:53.590 --> 01:58.010 You can simplify it by looking at a general equilibrium problem 01:58.012 --> 02:00.582 which is much shorter to describe. 02:00.578 --> 02:03.408 And so the general equilibrium economy is going to be a much 02:03.408 --> 02:04.078 simpler one. 02:04.078 --> 02:08.588 It's going to consist of U^(A) and U^(B) the same as before, 02:08.590 --> 02:12.770 and E-hat^(A)_1, the endowments, 02:12.770 --> 02:18.150 E-hat^(A)_2 and (E-hat^(B)_1 02:18.147 --> 02:21.007 E-hat^(B)_2). 02:21.008 --> 02:27.308 So we've left out half the variables up there and we define 02:27.307 --> 02:32.517 E-hat^(A)_1 = E^(A)_1 = 1 and 02:32.520 --> 02:38.060 E-hat^(B)_1 = E^(B)_1 = 1, 02:38.060 --> 02:44.360 but E-hat^(A)_2 (this is the Fisher insight) = 02:44.355 --> 02:50.875 E^(A)_2 what A owns of the payoffs of the future 02:50.882 --> 02:54.392 dividends, [theta-bar^(A)_alpha 02:54.391 --> 02:57.981 times D^(alpha)_2 plus theta-bar^(A)_beta 02:57.977 --> 02:59.827 times] D^(beta)_2. 02:59.830 --> 03:02.840 Since A owns half of the alpha stock, 03:02.840 --> 03:06.260 sorry, all of the alpha stock and half of the beta stock, 03:06.258 --> 03:09.928 his endowment is 1, his original thing, 03:09.930 --> 03:11.450 plus what the stock is going to produce, 03:11.449 --> 03:12.879 and after all he's the owner. 03:12.878 --> 03:23.408 So he's going to get all of 1 a half of 2 which is = 3. 03:23.408 --> 03:25.708 I took more space than I thought. 03:25.710 --> 03:30.860 And so similarly E-hat^(B)_2 is going 03:30.864 --> 03:34.454 to be 1 a half of 2 which = 2. 03:34.449 --> 03:44.479 So here endowments are this and also let's just write it here, 03:44.483 --> 03:50.573 E-hat^(A)_2 = 3, so this. 03:50.568 --> 03:53.598 So Fisher said we start with a financial equilibrium, 03:53.598 --> 03:57.278 we can switch to the economic equilibrium and solve this 03:57.282 --> 03:59.152 problem, and having solved that one go 03:59.146 --> 04:00.816 back and figure out how to solve this one. 04:00.818 --> 04:02.988 And you remember what the prices were. 04:02.990 --> 04:06.780 They turned out to be q_1--I might as well 04:06.777 --> 04:09.747 write it up there what the prices we had, 04:09.750 --> 04:10.790 we solved. 04:10.788 --> 04:13.168 We said first of all Fisher has no theory for the 04:13.169 --> 04:14.409 contemporaneous prices. 04:14.409 --> 04:16.159 It's all relative prices. 04:16.160 --> 04:17.350 I'm going to write that. 04:17.350 --> 04:21.220 Relative prices, is all we can ever figure out. 04:21.220 --> 04:24.140 Someone might always come along and change dollars to cents. 04:24.139 --> 04:25.519 When I was a little boy in France, 04:25.519 --> 04:27.799 on vacation, they suddenly announced that 04:27.795 --> 04:29.895 the franc was going to be divided-- 04:29.899 --> 04:33.689 everything that was a hundred francs would now be one franc. 04:33.690 --> 04:36.230 They just redefined the currency, so that might always 04:36.228 --> 04:36.658 happen. 04:36.660 --> 04:39.000 So you have to have some theory of money and whether the 04:38.997 --> 04:41.757 government's going to do that to figure out the nominal prices. 04:41.759 --> 04:47.109 So contemporaneous prices he says are 1,1. 04:47.110 --> 04:50.190 All right, but having realized that if there are many goods at 04:50.187 --> 04:52.707 time 1 he could figure out the relative prices, 04:52.709 --> 04:55.639 but with only 1 good at time one who's to say whether we're 04:55.644 --> 04:57.674 measuring dollars or francs or cents, 04:57.670 --> 04:59.550 we'll just call it 1, and the same thing's going to 04:59.553 --> 05:00.273 happen next year. 05:00.269 --> 05:02.539 Who knows whether it's dollars or cents or francs so we're 05:02.536 --> 05:03.606 going to call it 1 again. 05:03.610 --> 05:06.470 But after that he figured everything out. 05:06.470 --> 05:10.110 This turned out to be a price of a third, 05:10.110 --> 05:14.150 this turned out to be a price of 2 thirds and we figured out 05:14.153 --> 05:17.763 all the consumptions, which I've forgotten, of course. 05:17.759 --> 05:24.389 But anyway they were--who knows what they were, 05:24.392 --> 05:28.722 not that it's too important. 05:28.720 --> 05:29.740 All right, well I forgot what they were. 05:29.740 --> 05:31.340 Anyway, he figured out all the consumptions. 05:31.339 --> 05:38.769 I think they were--actually I sort of remember them. 05:38.769 --> 05:39.439 Well, let's say I don't. 05:39.440 --> 05:40.860 Anyway, he figured out all the consumptions. 05:40.860 --> 05:46.840 Does anyone remember what they were? 05:46.839 --> 05:58.109 All right, I will look them up, 4 thirds 2,2 thirds 2, 05:58.113 --> 06:08.753 so they were 4 thirds and 2, and 2 thirds and 2. 06:08.750 --> 06:11.420 He figured out in equilibrium, and how did he do it--because 06:11.420 --> 06:12.690 he solved over here first. 06:12.689 --> 06:14.369 We would have solved--he didn't do this exact problem, 06:14.370 --> 06:17.130 but he would have solved over here and we would have found 06:17.129 --> 06:20.289 with P_1 = 1, P_2 = a third, 06:20.288 --> 06:24.008 and sure enough X^(A)_1 = 4 thirds, 06:24.009 --> 06:28.919 X^(A)_2 = 2, and X^(B)_1 = 2 06:28.915 --> 06:32.635 thirds, and X^(B)_2 = 2. 06:32.639 --> 06:35.239 So Fisher said start with the financial economy, 06:35.240 --> 06:39.330 figure out what the reduced general equilibrium is, 06:39.329 --> 06:42.939 solve for this equilibrium, and go back and figure out what 06:42.935 --> 06:45.295 the financial equilibrium should be. 06:45.300 --> 06:47.420 All right, so I want to now examine what we've done. 06:47.420 --> 06:48.740 And we did that the end of last class. 06:48.740 --> 06:50.680 You had to do it in a problem set. 06:50.680 --> 06:53.580 And you notice that the only difference between this and that 06:53.579 --> 06:55.419 is, the general equilibrium throws 06:55.422 --> 06:58.272 away a lot of irrelevant information because Fisher said 06:58.269 --> 06:59.459 people are rational. 06:59.459 --> 07:02.479 They look through the veil of all the gibberish of who owns 07:02.483 --> 07:05.453 the company and stuff like that, and they're just anticipating 07:05.447 --> 07:06.937 what the company is going to produce. 07:06.939 --> 07:09.849 They don't really care about whether there's a man running 07:09.845 --> 07:12.025 the company, or a woman running the company, 07:12.029 --> 07:14.549 or whether she's got an MBA from Harvard or from Yale. 07:14.550 --> 07:17.730 None of this is relevant, what the business plan is. 07:17.730 --> 07:20.510 All they care about is what's going to actually happen in the 07:20.511 --> 07:20.791 end. 07:20.790 --> 07:23.080 So if you think they're going to anticipate that correctly you 07:23.084 --> 07:24.894 don't need to worry about all the other stuff. 07:24.889 --> 07:29.079 So looking through the veil you can always reduce the financial 07:29.081 --> 07:31.721 equilibrium to a general equilibrium. 07:31.720 --> 07:36.440 Now, I want to go back and reexamine all that logic. 07:36.440 --> 07:44.040 So what's the first step in what Fisher did? 07:44.040 --> 07:50.950 And this is the idea of no arbitrage. 07:50.949 --> 07:54.979 So Fisher said people look through the veil of things. 07:54.980 --> 07:58.440 They understand stuff and you can count on their understanding 07:58.437 --> 08:00.987 to guide your understanding of the economy. 08:00.990 --> 08:05.180 So if you know that pi_alpha-- 08:05.180 --> 08:10.190 (this is a big pi)--pi_alpha = a 08:10.189 --> 08:12.499 third, so Fisher says well, 08:12.497 --> 08:16.237 you don't have to solve for the whole equilibrium to figure out 08:16.238 --> 08:17.988 what pi_beta is. 08:17.990 --> 08:19.770 What would pi_beta be? 08:19.769 --> 08:23.929 Well, Fisher would have said stock beta always pays off 08:23.934 --> 08:26.714 exactly what stock alpha pays off. 08:26.709 --> 08:29.979 So if these people are rational they're not going to allow for 08:29.983 --> 08:30.793 an arbitrage. 08:30.790 --> 08:35.170 So arbitrage means if there are two assets or two things that 08:35.167 --> 08:38.377 are identical, they have to sell for the same 08:38.378 --> 08:40.638 price--that's no arbitrage. 08:40.639 --> 08:43.759 If they sold for a different price there'd be an arbitrage. 08:43.759 --> 08:46.769 You'd sell the more expensive one and buy the cheaper one, 08:46.769 --> 08:49.629 and so you'd have accomplished a perfect tradeoff, 08:49.629 --> 08:51.749 but you'd have gotten the difference of money. 08:51.750 --> 08:56.080 So since pi_alpha is 1 third, pi_beta has 08:56.077 --> 08:57.517 to equal 2 thirds. 08:57.519 --> 09:01.149 That's the first, most important principle of 09:01.153 --> 09:05.683 finance that Fisher introduced; the idea of no arbitrage and 09:05.679 --> 09:08.059 making deductions for no arbitrage, 09:08.058 --> 09:11.698 so most of finance is actually being more and more clever about 09:11.701 --> 09:13.171 how to do no arbitrage. 09:13.168 --> 09:16.888 Over half of this course is going to be, let's look at 09:16.888 --> 09:21.098 situations where at first glance there doesn't seem to be any 09:21.096 --> 09:22.076 arbitrage. 09:22.080 --> 09:24.840 Then you realize if you're clever enough you'll recognize 09:24.837 --> 09:27.397 an arbitrage and be able to figure out all the prices 09:27.399 --> 09:30.649 without having to know all the utilities and everything else-- 09:30.649 --> 09:34.719 so one of the main goals of finance is to explain asset 09:34.721 --> 09:35.401 prices. 09:35.399 --> 09:38.529 You can see how no arbitrage is going to help do that, 09:38.529 --> 09:41.979 because if you knew what some of the asset prices were you 09:41.980 --> 09:44.280 could deduce what the rest might be. 09:44.279 --> 09:48.159 So that's the first thing Fisher did, and he's used this 09:48.158 --> 09:51.048 fact in connecting these two economies. 09:51.049 --> 09:53.109 So that's the first thing. 09:53.110 --> 10:01.080 Now, that principle can be used over and over again. 10:01.080 --> 10:12.220 Another application of it, let's suppose that we 10:12.216 --> 10:26.666 introduced a nominal bond with payoff 1 dollar in period 2. 10:26.668 --> 10:31.718 And suppose, as before, that q_1 = 10:31.715 --> 10:37.225 q_2 = 1, as we've already supposed. 10:37.230 --> 10:50.160 So then by definition the price of this bond is equal to 1 over 10:50.162 --> 10:59.342 1 i, where i is the nominal interest rate. 10:59.340 --> 11:00.130 Why is that? 11:00.129 --> 11:02.399 Because you're going to get a dollar next year. 11:02.399 --> 11:05.529 If the price is less than a dollar this year you're turning 11:05.532 --> 11:08.392 something less than a dollar into something equal to a 11:08.394 --> 11:08.994 dollar. 11:08.990 --> 11:11.970 You're multiplying today's price by 1 i to get tomorrows 11:11.971 --> 11:14.281 price, so the rate of return is 1 i, 11:14.278 --> 11:17.978 taking whatever you put in today and getting 1 i tomorrow. 11:17.980 --> 11:21.670 So what is 1 i? 11:21.668 --> 11:29.588 So by no arbitrage we can figure out what 1 i must be. 11:29.590 --> 11:40.040 So 1 dollar today can go into 3 units of stock alpha, 11:40.037 --> 11:50.677 which goes into 3 units of X_2 as dividends, 11:50.684 --> 11:56.114 which equals 3 dollars. 11:56.110 --> 12:00.790 So you take 1 dollar today by buying stock alpha you can get 3 12:00.788 --> 12:04.008 units of it since its price is a third, 12:04.009 --> 12:10.719 and since stock alpha pays one unit of output next period you 12:10.724 --> 12:17.554 know that 1 dollar today gives you 3 units of stock alpha, 12:17.548 --> 12:21.098 which gives you 3 units of good 2 as the output and at price 1 12:21.102 --> 12:24.252 dollar tomorrow you've anticipated that's 3 dollars. 12:24.250 --> 12:27.020 So by buying stock alpha you can put in a dollar and get out 12:27.024 --> 12:27.594 3 dollars. 12:27.590 --> 12:35.000 So it means that 1 i = 3, which means the interest rate 12:34.996 --> 12:37.326 is 200 percent. 12:37.330 --> 12:42.000 So that's a second thing you can deduce from that. 12:42.000 --> 12:45.270 So notice that by looking at part of the equilibrium here we 12:45.273 --> 12:48.273 can figure out a lot of the rest of the equilibrium. 12:48.269 --> 12:52.049 So what's another application? 12:52.048 --> 13:03.938 Well, Fisher said define the real interest rate as number of 13:03.942 --> 13:13.622 goods today goes into number of good tomorrow. 13:13.620 --> 13:19.950 So this will be, 1 r equals that. 13:19.950 --> 13:23.120 The number of goods today and how many good tomorrow do you 13:23.120 --> 13:23.450 get? 13:23.450 --> 13:24.850 So how can you do that? 13:24.850 --> 13:34.880 Well, 1 good today, 1 unit of X_1 is 1 13:34.883 --> 13:39.583 dollar today, right? 13:39.580 --> 13:43.330 If you had one apple today you could sell it for q_1 13:43.326 --> 13:45.616 times 1 apple, which is q_1 times 1, 13:45.615 --> 13:48.755 which is 1 times 1, which is 1 dollar today, 13:48.758 --> 13:55.298 which you can get 3 units, 3 shares, 3 units of stock 13:55.301 --> 14:02.581 alpha, which gives you 3 units of X_2. 14:02.580 --> 14:07.350 So 1 unit of X_1 today turns into 3 units of 14:07.354 --> 14:11.324 X_2, so therefore 1 r = 3 implies r 14:11.317 --> 14:12.937 = 200 percent. 14:12.940 --> 14:15.480 So that's the real rate of interest. 14:15.480 --> 14:18.030 So one of the tricks in going from here to here was to say 14:18.025 --> 14:20.745 that Fisher realized that people are going to look through all 14:20.750 --> 14:23.160 the gibberish of money and they're going to think about 14:23.163 --> 14:25.843 what apples are they giving up today and what apples are they 14:25.842 --> 14:26.962 getting tomorrow. 14:26.960 --> 14:32.160 They're not going to be confused by all the holding of 14:32.164 --> 14:34.134 assets in between. 14:34.129 --> 14:37.629 All right, so let's just make it a little bit more 14:37.629 --> 14:38.629 complicated. 14:38.629 --> 14:47.819 Suppose we started with q_1 = 1, 14:47.823 --> 14:52.313 q_2 = 2. 14:52.308 --> 14:56.958 Now, I told you that equilibrium--Fisher says there's 14:56.961 --> 14:59.201 always a normalization. 14:59.200 --> 15:02.010 Walras originally had the normalization in one period. 15:02.009 --> 15:04.229 There's a one period model in general equilibrium. 15:04.230 --> 15:07.680 In multi-period models there's a normalization every period. 15:07.678 --> 15:10.348 Every period there's a choice of whether you're dealing with 15:10.345 --> 15:11.745 dollars, or francs, or centimes, 15:11.745 --> 15:13.235 or how many, and so there's a free 15:13.235 --> 15:14.135 normalization. 15:14.139 --> 15:17.229 So let's take q_1 = 1 and q_2 = 2. 15:17.230 --> 15:18.780 Well, what does that mean? 15:18.778 --> 15:24.088 That means that inflation 1 (let's call it growth of money) 15:24.091 --> 15:29.221 g--i, I've already used for the nominal interest rate. 15:29.220 --> 15:33.320 So, 1 g is going to be 2 over 1 or just 2. 15:33.320 --> 15:44.480 So inflation = 100 percent. 15:44.480 --> 15:50.190 So what's pi_alpha going to be? 15:50.190 --> 15:51.020 I've done my work. 15:51.019 --> 15:53.079 Now the rest I'm going to just ask you for the rest of the 15:53.077 --> 15:53.437 numbers. 15:53.440 --> 15:57.350 What's pi_alpha? 15:57.350 --> 16:00.850 So if I re-solved equilibrium taking q_1 = 1 and 16:00.847 --> 16:04.467 q_2 = 2 all that's kind of money stuff so it's not 16:04.469 --> 16:07.169 going to change what happens over there. 16:07.168 --> 16:09.058 You're going to get the same equilibrium over there and 16:09.057 --> 16:10.417 you're going to go back to over here. 16:10.418 --> 16:21.048 So what's pi_alpha going to be? 16:21.049 --> 16:24.369 Ah-ha! 16:24.370 --> 16:27.180 Suppose we knew we were in the same real economy. 16:27.178 --> 16:30.038 There's nothing changed about utilities, endowments of goods, 16:30.044 --> 16:31.434 productivity of the stocks. 16:31.428 --> 16:34.438 All we know is that inflation's going to be higher now. 16:34.440 --> 16:36.460 So what do you think would happen in the new equilibrium? 16:36.460 --> 16:47.260 What's going to happen to the price of stocks today? 16:47.259 --> 16:48.549 Yes? 16:48.548 --> 16:51.258 Student: Is it just 2 dollars? 16:51.259 --> 16:53.379 Prof: Price of stock alpha. 16:53.379 --> 16:54.319 What was it before? 16:54.320 --> 16:56.800 Student: > 16:56.798 --> 16:58.138 Prof: So what was it before? 16:58.139 --> 16:59.289 Student: 1 third. 16:59.288 --> 17:06.368 Prof: Yeah, 1 third, so it's still 1 third. 17:06.368 --> 17:10.048 This is a big mystery in finance, a big question in 17:10.053 --> 17:10.793 finance. 17:10.789 --> 17:13.469 So you see why it's puzzling. 17:13.470 --> 17:15.900 You didn't get the answer right off, although she did. 17:15.900 --> 17:17.610 So you just have to think about it a second. 17:17.608 --> 17:21.168 If you really thought that people when they were buying and 17:21.165 --> 17:25.025 selling only bought a stock because they said to themselves, 17:25.028 --> 17:27.568 "How many apples am I going to get out of this stock? 17:27.568 --> 17:30.108 I don't care about dollars and centimes and francs. 17:30.109 --> 17:30.969 I'm not going to eat that. 17:30.970 --> 17:33.870 I'm going to eat the apples, and maybe I get the apples and 17:33.865 --> 17:36.955 sell them and eat pears instead, but I care about the goods I'm 17:36.961 --> 17:37.811 going to get. 17:37.808 --> 17:39.328 So I looked through all the veil." 17:39.328 --> 17:43.628 I should recognize that the stock, although it's now going 17:43.632 --> 17:47.032 to pay twice as many dollars as it did before, 17:47.028 --> 17:49.668 so it's going to pay 2 dollars. 17:49.670 --> 17:51.290 That's how someone guessed 2. 17:51.289 --> 17:52.399 Someone said 2. 17:52.400 --> 17:53.320 So how did he get 2? 17:53.318 --> 17:55.188 I didn't even realize how he came up with the number 2. 17:55.190 --> 17:56.980 He came up with the number 2 because he said, 17:56.980 --> 17:59.710 well the stock is paying 1 apple tomorrow, 17:59.710 --> 18:03.800 the price of apples is now 2, so it's paying 2 dollars 18:03.797 --> 18:07.497 tomorrow so maybe its price today should be 2. 18:07.500 --> 18:09.370 But no, that isn't how much the stock is worth. 18:09.368 --> 18:14.598 The stock is worth solving for this general equilibrium supply 18:14.604 --> 18:15.724 and demand. 18:15.720 --> 18:18.530 We already calculated before that the stock was a third, 18:18.528 --> 18:23.108 so the price of the stock is going to stay a third because 18:23.105 --> 18:26.715 the apples it pays tomorrow hasn't changed. 18:26.720 --> 18:28.470 It's still the same one apple. 18:28.470 --> 18:32.060 Now, how did we know the stock was priced at a third before? 18:32.059 --> 18:34.909 What was the stock in general? 18:34.910 --> 18:36.760 What's the price of the stock? 18:36.759 --> 18:39.789 The price of stock, remember, is how did we get it 18:39.787 --> 18:41.577 by going from here to here? 18:41.578 --> 18:46.438 We said it's going to equal the price of the stock divided by 18:46.442 --> 18:47.742 P_1. 18:47.740 --> 18:51.330 Now, the stock is only paying a certain number of goods. 18:51.328 --> 19:10.498 The price of the stock today is going to equal the present value 19:10.501 --> 19:20.851 1 over (1 r) times its dividend. 19:20.849 --> 19:23.479 I'll write it this way. 19:23.480 --> 19:26.000 The price of the stock is P_2 times this. 19:26.000 --> 19:28.170 Let's just write this. 19:28.170 --> 19:29.880 What would Fisher say? 19:29.880 --> 19:34.820 How did we get the price of the stock from going from here to 19:34.823 --> 19:35.403 here? 19:35.400 --> 19:47.400 We got the price of the stock by saying the stock pays off one 19:47.404 --> 19:53.374 good tomorrow, but one good tomorrow is only 19:53.373 --> 20:00.203 worth a third of one good today, so therefore the value of the 20:00.204 --> 20:06.684 stock is only equal to a third times 1 = 1 third. 20:06.680 --> 20:30.850 So assuming P_1 = 1 that's what Fisher would say. 20:30.848 --> 20:37.958 Assuming P_1 is 1 you figure out how many units of 20:37.957 --> 20:41.207 today's good is it worth. 20:41.210 --> 20:43.960 Now, if P_1 isn't 1 then what do you do? 20:43.960 --> 20:47.030 Suppose P_1 were 5 and P_2 were--or 20:47.032 --> 20:49.882 P_1 is 6, let's say, and P_2 is 20:49.878 --> 20:51.528 2 then what would you do? 20:51.529 --> 20:59.059 You'd have to say P_1 times pi_alpha = 20:59.058 --> 21:02.228 D^(alpha)_2. 21:02.230 --> 21:08.070 So if you multiplied all the prices by--am I putting the 21:08.073 --> 21:12.963 P_1 down at the bottom or the top? 21:12.960 --> 21:17.520 If you multiply out all the prices by 3, just leave it like 21:17.519 --> 21:18.069 this. 21:18.068 --> 21:19.658 We'll say if pi_alpha = P_2 times 21:19.663 --> 21:20.403 D^(alpha)_2. 21:20.400 --> 21:25.860 If you measure it in terms of goods, that's how you do it. 21:25.858 --> 21:31.888 So if you take this, this is also equal to 1 over 21:31.891 --> 21:38.801 P_1 divided by P_2 (if P_1 21:38.803 --> 21:42.633 is 1, assuming P_1 is 1) 21:42.627 --> 21:48.517 times D^(alpha)_2, which is 1 over (1 r) times 21:48.517 --> 21:51.187 D^(alpha)_2. 21:51.190 --> 21:55.570 So Fisher said--so here's his famous equation. 21:55.568 --> 21:58.608 Fisher said the way to figure out the value of a stock, 21:58.608 --> 22:00.318 if you solve that problem over here, 22:00.318 --> 22:04.628 is to look at its dividends and discount them by the real rate 22:04.630 --> 22:07.170 of interest-- 1 unit of output tomorrow, 22:07.171 --> 22:10.471 since the value of an apple tomorrow is only a third of the 22:10.473 --> 22:12.073 value of an output today. 22:12.068 --> 22:20.118 Remember the interest rate 1 r, the real interest rate, 22:20.117 --> 22:26.227 is equal to the ratio of the two goods. 22:26.230 --> 22:29.450 So P_1 over P_2 is just 1 r, 22:29.445 --> 22:32.315 1 r is P_1 over P_2. 22:32.318 --> 22:36.048 I'm making some things simple seem more complicated, 22:36.045 --> 22:36.625 sorry. 22:36.630 --> 22:37.880 So let's just say it again. 22:37.880 --> 22:41.700 When we solved that equilibrium over there we figured out that 22:41.700 --> 22:44.770 P_2 is only a third of P_1. 22:44.769 --> 22:47.719 When people think today how much would I give up of apples 22:47.720 --> 22:50.770 today to get an apple next year they don't think apples next 22:50.773 --> 22:53.573 year are worth nearly as much as apples this year. 22:53.568 --> 22:57.268 So they'd only give up a third of an apple this year to get an 22:57.268 --> 22:58.358 apple next year. 22:58.358 --> 23:01.328 P_2 is the amount you give up today to get an apple 23:01.326 --> 23:02.756 next year, so it's a third. 23:02.759 --> 23:05.149 Another way of saying that, if P_1 is 1, 23:05.150 --> 23:08.440 is that the real interest rate, the tradeoff between apples 23:08.435 --> 23:11.375 tomorrow and apples today which is P_1 over 23:11.383 --> 23:14.753 P_2, because 1 apple today can give 23:14.750 --> 23:17.970 you three apples tomorrow, so P_1 over 23:17.973 --> 23:21.913 P_2 is 3, so 1 r is three. 23:21.910 --> 23:26.190 So the apple tomorrow is worth P_2 times the 23:26.191 --> 23:27.081 dividend. 23:27.078 --> 23:30.838 That's just 1 over (1 r) times the dividend. 23:30.838 --> 23:36.018 So the value of a stock is the real dividends it's paying in 23:36.018 --> 23:40.668 the future discounted by the real rate of interest. 23:40.670 --> 23:42.850 You're turning tomorrow's next year's goods, 23:42.848 --> 23:46.018 finding the equivalent in terms of this year's goods, 23:46.019 --> 23:48.759 and the ratio of those two prices is the real rate of 23:48.762 --> 23:51.192 interest and so that's how you would get it. 23:51.190 --> 23:56.430 So another way of saying the same thing is you could turn 23:56.428 --> 23:59.888 cash next year into cash this year. 23:59.890 --> 24:06.820 So assuming q_1 is 1, another way of saying that is 1 24:06.817 --> 24:11.397 over 1 i times D^(alpha)_2 times 24:11.397 --> 24:13.407 q_2. 24:13.410 --> 24:18.660 So you take the nominal rate of interest times the money that's 24:18.663 --> 24:21.653 being produced, because the nominal rate of 24:21.654 --> 24:24.974 interest says how do you trade off a dollar today for a dollar 24:24.967 --> 24:25.887 in the future? 24:25.890 --> 24:29.640 So a dollar in the future isn't worth, usually, 24:29.637 --> 24:34.117 as much as a dollar today so you have to discount it. 24:34.118 --> 24:37.008 So a certain number of dollars in the future are worth less 24:37.011 --> 24:37.811 dollars today. 24:37.808 --> 24:40.688 So you take the payoff of dollars in the future discounted 24:40.692 --> 24:43.782 by the nominal rate of interest and you get today's price, 24:43.779 --> 24:48.739 or you take the real dividends in the future discounted by the 24:48.736 --> 24:52.796 real rate of interest and you get today's price. 24:52.798 --> 24:56.608 So both those things are an application of the principle of 24:56.607 --> 24:59.297 no arbitrage, looking through the veil. 24:59.298 --> 25:01.658 So what would the nominal interest rate be in this case? 25:01.660 --> 25:03.860 In this case you see, how did I know that P^(alpha) 25:03.858 --> 25:04.738 was still a third? 25:04.740 --> 25:07.010 Because the real interest rate hasn't changed, 25:07.009 --> 25:08.269 it's still 200 percent. 25:08.269 --> 25:12.219 So D^(alpha)_2 is 1 and I'm still multiplying by 1 25:12.218 --> 25:16.298 third, so I'm still getting a third for the price of alpha. 25:16.298 --> 25:19.138 So that's how she knew that the answer should stay a third 25:19.140 --> 25:22.130 because she knew nothing real had changed in the economy, 25:22.130 --> 25:23.980 therefore the real interest rate couldn't have changed, 25:23.980 --> 25:27.990 therefore the price of the stock still had to be the same. 25:27.990 --> 25:29.720 So how could we have used this [clarification: 25:29.721 --> 25:30.761 another formula] formula? 25:30.759 --> 25:32.639 We have to know what the nominal interest rate is. 25:32.640 --> 25:35.980 So what is the nominal interest rate? 25:35.980 --> 25:39.870 If you put in a dollar today how many dollars can you get out 25:39.865 --> 25:43.105 in the future in this new economy where there's 100 25:43.105 --> 25:44.525 percent inflation? 25:44.529 --> 25:46.429 Yes? 25:46.430 --> 25:48.770 Student: 500 percent inflation. 25:48.769 --> 25:50.629 Prof: So that's right, now how did he do that? 25:50.630 --> 25:52.000 Because let's just do it. 25:52.000 --> 25:56.320 You take 1 dollar today at price q_1 = 1. 25:56.318 --> 26:00.918 You can buy 3 units of alpha still, because its price is 26:00.921 --> 26:04.691 still a third, and that tells you that you get 26:04.685 --> 26:08.865 3 units of X_2, that's the dividend. 26:08.868 --> 26:12.598 Of 3 units of alpha each share of alpha pays 1, 26:12.598 --> 26:16.048 right, 1 apple, so now you get 3 apples, 26:16.048 --> 26:20.558 but that's equal to 3 times 2 because the price is 2, 26:20.559 --> 26:25.159 = 6 dollars tomorrow. 26:25.160 --> 26:27.890 So you've turned 1 dollar into 6 dollars. 26:27.890 --> 26:35.050 So 1 i = 6 over 1 implies i = 500 percent, just exactly what 26:35.046 --> 26:36.256 he said. 26:36.259 --> 26:42.909 So to say that just more simply the real rate of interest 1 r, 26:42.906 --> 26:48.356 this is the most famous equation Fisher ever wrote, 26:48.355 --> 26:51.185 is 1 i divided by 1 g. 26:51.190 --> 26:53.850 So this is called the Fisher Equation. 26:53.848 --> 26:58.158 His two famous equations are this, this is called the Fisher 26:58.157 --> 27:00.857 Equation and this which is called-- 27:00.858 --> 27:09.768 these two things which are the same are called the Fundamental 27:09.773 --> 27:13.723 Theorem of Asset Pricing. 27:13.720 --> 27:15.570 So why is this theorem true? 27:15.568 --> 27:18.608 The real rate of interest trades off apples today for 27:18.608 --> 27:20.638 apples tomorrow, the real rate of interest, 27:20.644 --> 27:21.894 apples today for apples tomorrow, 27:21.890 --> 27:24.360 so we had 1 apple giving you 3 apples. 27:24.359 --> 27:26.069 That's why r was 200 percent. 27:26.068 --> 27:30.878 Well, if inflation is 100 percent, so this is 2, 27:30.880 --> 27:34.770 1 apple today gives you 3 apples in the future, 27:34.769 --> 27:37.849 but that means 1 apple today gives you 1 dollar, 27:37.848 --> 27:40.998 is one apple today gives you 3 apples or 6 dollars in the 27:41.002 --> 27:41.512 future. 27:41.509 --> 27:45.499 So 3 times 2, so if this is equal to 3 and 27:45.497 --> 27:51.327 inflation's 100 percent so this is equal to 2 then what's the 27:51.330 --> 27:53.860 fair rate of interest? 27:53.859 --> 27:55.079 What will the banks give you? 27:55.078 --> 27:57.938 Well, any banker can take a dollar, buy a stock, 27:57.936 --> 28:01.276 turn it into 3 units of dividends and then sell it for 2 28:01.279 --> 28:03.529 dollars apiece and get 6 dollars. 28:03.528 --> 28:06.278 And so a banker can take a dollar and turn it to 6, 28:06.278 --> 28:09.128 so competition will force the bankers to give you 6 dollars 28:09.134 --> 28:11.554 for every 1 dollar you give it, next period. 28:11.548 --> 28:17.368 So the interest rate has to be 1 i = 3 times 2, 28:17.365 --> 28:18.245 or 6. 28:18.250 --> 28:22.340 So the real rate of interest is the nominal rate of interest 28:22.344 --> 28:23.944 divided by inflation. 28:23.940 --> 28:29.800 So that's one subtle, but once you realize it, 28:29.798 --> 28:33.898 obvious implication of thinking people are rational and make 28:33.897 --> 28:37.507 sort of simple calculations looking at the future. 28:37.509 --> 28:40.479 And a consequence of that is the price of assets, 28:40.480 --> 28:42.860 or you look at the cash that comes out in the future 28:42.861 --> 28:44.871 discounted by the nominal interest rate, 28:44.868 --> 28:47.628 or you look at the real goods that come out in the future and 28:47.625 --> 28:49.505 discount it by the real interest rate, 28:49.509 --> 28:53.339 and it's all the same thing. 28:53.338 --> 28:57.408 So does anybody know what the inflation is today, 28:57.412 --> 29:01.402 or what the nominal interest rates are today? 29:01.400 --> 29:05.070 So i is the nominal interest rate, the amount of interest you 29:05.067 --> 29:08.977 put in the bank and what they'll pay you at the end of a year. 29:08.980 --> 29:11.960 So we're going to--next class we're going to find out the 29:11.962 --> 29:14.152 exact numbers, but what do you think it is 29:14.146 --> 29:14.676 about? 29:14.680 --> 29:19.610 Does anyone have any idea? 29:19.609 --> 29:20.579 Take a wild guess. 29:20.579 --> 29:22.629 Is it 10 percent, 5 percent? 29:22.630 --> 29:24.210 Yep? 29:24.210 --> 29:26.030 Student: I think the inflation is usually around 3 29:26.034 --> 29:26.364 percent. 29:26.358 --> 29:28.788 Prof: Usually, and do you think it's higher or 29:28.788 --> 29:30.188 lower than usual now-a-days? 29:30.190 --> 29:31.050 Student: It's probably lower. 29:31.049 --> 29:32.289 Prof: That's good. 29:32.288 --> 29:34.768 So let's say it's around 2 percent. 29:34.769 --> 29:38.529 So that means this is 1.02 and what do you think the nominal 29:38.525 --> 29:39.985 interest rate is now? 29:39.990 --> 29:42.050 Student: 1 percent. 29:42.049 --> 29:42.579 Prof: Who said that? 29:42.578 --> 29:46.418 That's a good--1 percent, that's about right. 29:46.420 --> 29:49.470 So what is the real rate of interest now? 29:49.470 --> 29:51.150 Student: > 29:51.150 --> 29:51.710 Prof: What? 29:51.710 --> 29:53.710 Student: > 29:53.710 --> 29:56.520 Prof: Well, 1 r is less than 1. 29:56.519 --> 30:02.359 So 1 r is around .99. 30:02.358 --> 30:04.908 So the real rate of interest is actually like negative 1 30:04.914 --> 30:05.384 percent. 30:05.380 --> 30:06.300 How did that happen? 30:06.298 --> 30:09.918 Do you think it's standard to have the real interest rate be 30:09.915 --> 30:10.525 under 0? 30:10.529 --> 30:13.139 So why is it under 0? 30:13.140 --> 30:15.350 What's going on now that would make that happen? 30:15.349 --> 30:16.449 Yep? 30:16.450 --> 30:18.070 Student: The Federal Reserve wants to stimulate 30:18.071 --> 30:18.471 investment. 30:18.470 --> 30:18.900 Prof: Ah ha! 30:18.900 --> 30:21.820 The Federal Reserve has cut the interest rate, 30:21.818 --> 30:25.978 the nominal interest rate that it lends at to close to 0, 30:25.980 --> 30:30.230 let's say to 1 percent on the 1 year bond to 0 on the 3 month 30:30.231 --> 30:30.801 thing. 30:30.798 --> 30:33.388 So the reason they're saying they're doing that is to 30:33.385 --> 30:34.525 stimulate investment. 30:34.529 --> 30:36.919 That's what they teach you in macro, Keynesian, 30:36.923 --> 30:38.123 stimulate investment. 30:38.118 --> 30:40.328 We're going to find out that that's not the reason they're 30:40.330 --> 30:41.030 doing it at all. 30:41.029 --> 30:43.929 The reason the Federal Reserve is cutting the interest rate to 30:43.932 --> 30:46.362 almost zero is to just give money away to the banks, 30:46.357 --> 30:47.307 and why it that? 30:47.308 --> 30:49.648 Well, when you put your money and deposit it in the bank 30:49.646 --> 30:51.216 you're getting almost no interest, 30:51.220 --> 30:53.380 so the banks, the big banks have got all 30:53.378 --> 30:56.368 these deposits and people don't change what they do. 30:56.368 --> 30:58.968 They just leave their money in the banks getting no interest. 30:58.970 --> 31:02.540 So the banks have the money for free and they can make money 31:02.535 --> 31:03.135 with it. 31:03.140 --> 31:05.960 So normally they'd have to pay 3 percent interest or something 31:05.960 --> 31:07.810 and that would be expensive for them, 31:07.808 --> 31:10.568 and that expense is a big part of their expenses, 31:10.569 --> 31:12.309 they don't have it anymore. 31:12.308 --> 31:14.168 So we're going to come back to that what's really going on 31:14.166 --> 31:15.336 today, but that's what's going on. 31:15.338 --> 31:18.848 But anyway, the point is the nominal interest rate is somehow 31:18.846 --> 31:20.246 controlled by the Fed. 31:20.250 --> 31:21.730 That's why we don't have a theory of it. 31:21.730 --> 31:23.510 We're not going to do macro in this course. 31:23.509 --> 31:26.619 So Fisher doesn't have a theory of the nominal interest rate, 31:26.618 --> 31:28.788 of inflation, but he does tell you, 31:28.788 --> 31:32.258 given inflation and the nominal interest rate, 31:32.259 --> 31:34.439 that's determining a real interest rate, 31:34.440 --> 31:36.770 and people should look through that. 31:36.769 --> 31:39.059 So now they should say, this is sort of the Keynesian 31:39.057 --> 31:41.157 part, they should realize that 31:41.155 --> 31:45.595 actually an apple today if you just sort of put it in the bank 31:45.595 --> 31:49.885 you get less than an apple in the future so you should spend 31:49.887 --> 31:52.287 it and do something with it. 31:52.288 --> 31:54.698 That's the Keynesian idea, so people--why fritter away 31:54.702 --> 31:56.662 part of your apple, do something with it. 31:56.660 --> 31:59.850 That's why it's supposed to stimulate demand and activity 31:59.845 --> 32:00.295 today. 32:00.298 --> 32:03.238 So the point is, that's how you calculate the 32:03.239 --> 32:06.779 real rate of interest and shockingly it's negative and 32:06.778 --> 32:10.008 it's hardly ever negative, but it can be negative. 32:10.009 --> 32:17.289 Are there any questions about this no arbitrage business? 32:17.288 --> 32:45.068 All right, so let's do one more trick here, a Fisher thing. 32:45.068 --> 32:52.248 So let's go back to the equilibrium with q_1 = 32:52.252 --> 32:55.652 1 and q_2 = 1. 32:55.650 --> 33:05.730 Suppose China offered to lend money, lend us dollars at a 0 33:05.734 --> 33:09.044 percent interest? 33:09.039 --> 33:14.729 Would that be a great deal? 33:14.730 --> 33:24.760 Would people rush to do that? 33:24.759 --> 33:31.239 This is the equilibrium we solved over here already. 33:31.240 --> 33:32.230 So is that a great deal? 33:32.230 --> 33:33.490 Would that upset the equilibrium? 33:33.490 --> 33:36.430 Would anyone bother to take the Chinese deal if they lent at 0 33:36.430 --> 33:38.840 percent interest, they were offering to do that? 33:38.839 --> 33:48.539 33:48.539 --> 33:49.879 What? 33:49.880 --> 33:50.650 Student: No. 33:50.650 --> 33:54.790 Professor John Geanakoplos: They wouldn't take it? 33:54.789 --> 33:56.139 We're back here. 33:56.140 --> 33:59.120 What's the nominal interest rate in this economy?. 33:59.115 --> 34:00.995 Student: 200 percent. 34:01.000 --> 34:02.810 Professor John Geanakoplos: 200 percent interest, 34:02.808 --> 34:05.388 so if you want to borrow in this economy from another 34:05.390 --> 34:08.220 American you have to give the guy 200 percent interest. 34:08.219 --> 34:10.449 Here the Chinese are offering to lend you at 0 percent 34:10.447 --> 34:10.907 interest. 34:10.909 --> 34:14.479 So, yes, everyone would rush to take the thing and that would 34:14.480 --> 34:17.990 have a big effect on what the equilibrium was if the Chinese 34:17.989 --> 34:21.679 were willing to lend money at such a low rate of interest. 34:21.679 --> 34:23.899 Let's try another question. 34:23.900 --> 34:33.550 Suppose you invented a technology, new technology, 34:33.554 --> 34:41.834 new technology turns 1 unit, 1 apple today, 34:41.829 --> 34:47.149 into 2 apples tomorrow. 34:47.150 --> 34:50.160 Is this something people would rush to do or not? 34:50.159 --> 34:53.259 Suppose some inventor figured out how to do that, 34:53.262 --> 34:54.882 would he rush to do it? 34:54.880 --> 34:57.270 Could it be used to help the economy? 34:57.269 --> 34:58.789 So let's put it this way. 34:58.789 --> 35:12.309 Could this new technology be used to make a Pareto 35:12.313 --> 35:22.253 improvement, everybody better off? 35:22.250 --> 35:23.430 Yep? 35:23.429 --> 35:27.709 Student: That's no, because an apple tomorrow is 35:27.710 --> 35:30.960 worth less than half of an apple today. 35:30.960 --> 35:36.680 It's worth a third of an apple today, so no one would want to 35:36.684 --> 35:37.644 do that. 35:37.639 --> 35:40.229 Professor John Geanakoplos: So that's exactly the right 35:40.228 --> 35:40.658 answer. 35:40.659 --> 35:41.809 Actually you're answering two questions. 35:41.809 --> 35:43.009 I asked two questions. 35:43.010 --> 35:46.510 One is could it be used to help the economy, make everybody 35:46.514 --> 35:47.304 better off? 35:47.300 --> 35:50.740 If a social planner was in charge of things and the Chinese 35:50.740 --> 35:54.270 invented this new technology, or some American in Alaska 35:54.268 --> 35:57.838 invented this new technology should the government use the 35:57.838 --> 36:01.528 technology and could it use the technology to make everybody 36:01.534 --> 36:04.314 better off, and the answer to that is no. 36:04.309 --> 36:07.079 And then the answer to a second question is--suppose the guy in 36:07.083 --> 36:08.473 Alaska discovered it himself. 36:08.469 --> 36:11.759 He couldn't care less about the Pareto improvement and helping 36:11.759 --> 36:14.509 other guys or the American planners or anything, 36:14.510 --> 36:17.670 he just wanted to make a profit for himself. 36:17.670 --> 36:18.820 Would he make a profit? 36:18.820 --> 36:22.790 The answer is no, because the real prices, 36:22.789 --> 36:26.239 Fisher would say, are 1 and a third and no matter 36:26.235 --> 36:29.605 how you look at it the interest rate is 200-- 36:29.610 --> 36:32.460 he's losing money, because he's giving something 36:32.460 --> 36:35.800 up that's worth 1 and he's getting something that's only 36:35.797 --> 36:36.947 worth 2 thirds. 36:36.949 --> 36:38.429 So he'd be losing money to do it. 36:38.429 --> 36:39.479 He'd lose money. 36:39.480 --> 36:43.510 So we could prove that even. 36:43.510 --> 36:48.260 So the answer is no. 36:48.260 --> 36:51.700 That's the first question, and nobody would do it anyway. 36:51.699 --> 37:04.069 And fortunately nobody would choose to do it--choose to use 37:04.072 --> 37:10.262 it--because it loses money. 37:10.260 --> 37:12.000 So those are two separate questions. 37:12.000 --> 37:16.290 Could it be used and would any individual choose to do it? 37:16.289 --> 37:18.509 Would it be good for the society and would any individual 37:18.507 --> 37:19.217 choose to do it? 37:19.219 --> 37:21.059 The answers happen to agree here. 37:21.059 --> 37:23.769 So why can't it be used as a Pareto improvement? 37:23.768 --> 37:27.848 What's the proof of this that it can't be? 37:27.849 --> 37:28.809 The answer's no. 37:28.809 --> 37:31.749 What's the proof? 37:31.750 --> 37:35.760 Well, the proof is that if it did, 37:35.760 --> 37:43.410 if in the end it led to an allocation 37:43.414 --> 37:49.694 X-hat^(A)_1, let's call it X-tilde 37:49.690 --> 37:52.790 ^(A)_1, X-tilde^(A)_2, 37:52.791 --> 38:00.931 and Xtilde^(B)_1, Xtilde^(B)_2 that 38:00.934 --> 38:06.184 made everyone better off. 38:06.179 --> 38:08.789 Then, well, we give their old proof. 38:08.789 --> 38:09.559 Then what? 38:09.559 --> 38:12.939 It means that P_1 Xtilde^(A)_1 38:12.940 --> 38:16.040 P_2 Xtilde^(A)_2 is bigger 38:16.043 --> 38:17.013 than what? 38:17.010 --> 38:20.040 P_1^( )E-hat^(A)_1-- 38:20.039 --> 38:25.199 (all right, that's what you have in the Fisher economy) 38:25.202 --> 38:30.082 P_2 E-hat^(A)2 and similarly P_1 38:30.079 --> 38:33.519 X-tilde^(B)_1 P_2 38:33.521 --> 38:38.401 X-tilde^(B)_2 is bigger than P_1 38:38.398 --> 38:41.648 E-hat^(B)_1 P_2 38:41.650 --> 38:44.710 E-hat^(B)_2. 38:44.710 --> 38:47.320 So why is that? 38:47.320 --> 38:50.600 Because in this Fisher economy, the general equilibrium-- 38:50.599 --> 38:53.689 if this allocation really made A better off than what he's 38:53.688 --> 38:55.788 gotten, than 4 third and 2, 38:55.788 --> 38:57.838 he would have chosen it. 38:57.840 --> 39:01.420 And B, she would have chosen her thing if it was better than 39:01.418 --> 39:02.448 2 thirds and 2. 39:02.449 --> 39:04.839 So clearly they must have been too expensive for those two to 39:04.838 --> 39:06.948 choose because they were rationally choosing the right 39:06.947 --> 39:08.497 thing given what they could afford. 39:08.500 --> 39:11.980 So then you just add the stuff up. 39:11.980 --> 39:22.120 You add and you find that total consumption value is bigger than 39:22.117 --> 39:25.977 total endowment value. 39:25.980 --> 39:29.270 That's in the Fisher economy, but we've changed the Fisher 39:29.273 --> 39:32.863 economy because now we've added this technology which took away 39:32.855 --> 39:36.375 some of the first good and made it into the second good, 39:36.380 --> 39:38.590 but that technology just lost money, 39:38.590 --> 39:50.520 which is bigger than total value in new technology economy, 39:50.519 --> 39:50.919 right? 39:50.920 --> 39:55.690 And so that's a contradiction because the consumption of this, 39:55.690 --> 39:58.290 however the new technology got used in the end the total 39:58.286 --> 40:01.206 consumption of the people had to be the total of what there was 40:01.213 --> 40:03.153 and what was produced in the economy. 40:03.150 --> 40:06.600 The value after the new technology is introduced in that 40:06.596 --> 40:10.666 new economy has only gone down compared to the Fisher economy, 40:10.670 --> 40:14.050 and the Fisher economy value of endowments must have been less 40:14.045 --> 40:16.145 than this brilliant new allocation, 40:16.150 --> 40:19.300 and that's a contradiction because this new allocation has 40:19.300 --> 40:22.400 to add up to the stuff that's there in the new technology 40:22.396 --> 40:23.056 economy. 40:23.059 --> 40:26.849 So that's how we know that no new technology could possibly 40:26.853 --> 40:31.513 make everybody better off, and we know trivially it makes 40:31.507 --> 40:36.467 everyone better off if and only if it makes a profit. 40:36.469 --> 40:39.949 So if and only if it makes a profit can it be used to make 40:39.945 --> 40:42.425 everybody better off, and amazingly, 40:42.427 --> 40:45.677 in a free market economy, people are going to use it if 40:45.679 --> 40:47.059 and only if it makes a profit. 40:47.059 --> 40:49.539 So they're going to use it if and only if it's a good thing 40:49.539 --> 40:50.309 for the economy. 40:50.309 --> 40:53.249 So that's the basic laissez-faire argument--that 40:53.246 --> 40:55.806 there are new discoveries all the time. 40:55.809 --> 40:58.529 Every other day somebody's thinking of something new. 40:58.530 --> 41:00.000 Are we going to use it? 41:00.000 --> 41:00.620 Should we use it? 41:00.619 --> 41:03.279 Is it something we need to read about in the papers and use? 41:03.280 --> 41:06.130 Well, there are a whole bunch of people, 41:06.130 --> 41:08.510 the discoverers themselves they're going to talk to their 41:08.510 --> 41:10.370 business friends, and they're going to say, 41:10.373 --> 41:12.603 "Do you want to lend me the money to get this thing 41:12.601 --> 41:14.831 going," and all of them are going to do this profit 41:14.831 --> 41:15.521 calculation. 41:15.518 --> 41:18.338 If they decide it loses money they're not going to do it, 41:18.335 --> 41:20.995 and thank god for that because it couldn't have helped 41:21.000 --> 41:22.660 everybody if they did use it. 41:22.659 --> 41:25.689 So that's the main lesson of laissez-faire. 41:25.690 --> 41:30.440 So let me just put this in perspective a little bit. 41:30.440 --> 41:35.720 In the old Russian economy of the 1930s and '40s there was no 41:35.715 --> 41:39.065 profit system, so the central planner had to 41:39.074 --> 41:41.534 figure out, should a new invention be used 41:41.527 --> 41:41.957 or not. 41:41.960 --> 41:44.330 So every time there's a new invention a committee had to get 41:44.333 --> 41:46.753 together, of central planners and decide whether to use it or 41:46.748 --> 41:47.068 not. 41:47.070 --> 41:50.480 And there's a famous guy named Kantorovich who was in charge of 41:50.480 --> 41:51.360 a lot of that. 41:51.360 --> 41:54.420 He won the Nobel Prize in economics. 41:54.420 --> 41:57.830 He shared it with a Yale economist named Koopmans and so 41:57.826 --> 42:00.486 Kantorovich told this very amusing story. 42:00.489 --> 42:02.929 He said that there were two central planning bureaus. 42:02.929 --> 42:05.429 One was in charge of allocations and one was in 42:05.427 --> 42:06.457 charge of prices. 42:06.460 --> 42:07.520 One had to set the prices. 42:07.518 --> 42:09.068 The other had to set the allocations. 42:09.070 --> 42:12.190 And of course the whole message here is that you have to combine 42:12.193 --> 42:12.593 these. 42:12.590 --> 42:14.990 You don't know whether it's worthwhile to change the 42:14.992 --> 42:17.492 allocation until you know whether the new technology's 42:17.489 --> 42:20.299 going to make a profit or not, and here they had the two 42:20.295 --> 42:21.125 things separated. 42:21.130 --> 42:23.700 They were telling people what to do before knowing whether 42:23.697 --> 42:26.217 they made a profit or not because they didn't have prices 42:26.222 --> 42:27.982 because there weren't free markets. 42:27.980 --> 42:32.550 So the bottom line of the Fisher story is that you take 42:32.545 --> 42:35.755 this complicated financial economy, 42:35.760 --> 42:38.480 you reduce it to something very simple that you learned how to 42:38.476 --> 42:40.746 do in your freshman year or your sophomore year, 42:40.750 --> 42:43.990 solve that, and you go back to this and you can understand a 42:43.987 --> 42:45.357 lot about this economy. 42:45.360 --> 42:48.330 That's something that most people didn't realize at the 42:48.326 --> 42:50.246 time and still don't realize now. 42:50.250 --> 42:52.410 So you ask a typical person if there's inflation, 42:52.409 --> 42:56.619 that means the dividends next year is going to be higher, 42:56.619 --> 42:59.119 is that going to raise the value of the stock today? 42:59.119 --> 43:01.329 Just like he said, "Yes of course because it 43:01.331 --> 43:03.961 makes the price of the dividends higher tomorrow." 43:03.960 --> 43:06.620 Fisher would say no, it doesn't change anything real 43:06.621 --> 43:07.511 in the economy. 43:07.510 --> 43:10.500 If there's more inflation there will be a higher nominal 43:10.496 --> 43:13.206 interest rate, so discounted by the higher 43:13.210 --> 43:16.920 interest rate payoffs of the stock will give you the same 43:16.922 --> 43:18.582 stock price as before. 43:18.579 --> 43:22.429 So we're going to do a thousand examples of this, 43:22.429 --> 43:25.719 but are there any questions about this? 43:25.719 --> 43:27.219 Yes? 43:27.219 --> 43:28.919 Student: Can you just review your arguments at the 43:28.916 --> 43:29.036 end? 43:29.036 --> 43:30.366 I'm just having a very hard time reading. 43:30.369 --> 43:31.999 Prof: Yeah, sorry. 43:32.000 --> 43:36.060 I don't know if this is in the way, by the way. 43:36.059 --> 43:39.049 So this is the argument we gave a few classes ago. 43:39.050 --> 43:40.180 I forgot when. 43:40.179 --> 43:44.149 We said, how do you know that a final allocation that emerges as 43:44.146 --> 43:47.166 a competitive equilibrium is Pareto efficient? 43:47.170 --> 43:50.110 And the argument was if you can do better-- 43:50.110 --> 43:52.010 that means, make everybody better off-- 43:52.010 --> 43:54.270 then each person, if you look at the value of 43:54.268 --> 43:57.398 what they're getting under the new regime it must be more than 43:57.402 --> 44:00.532 the value of their endowments otherwise they would have chosen 44:00.534 --> 44:02.644 the new regime and nobody chose it. 44:02.639 --> 44:06.779 That means everybody would have had to pay more for this new 44:06.775 --> 44:10.625 regime allocation than the value of their endowments. 44:10.630 --> 44:13.310 So this is more than that for person A, 44:13.309 --> 44:16.169 and person B's consumption is more than the value of this 44:16.172 --> 44:18.682 endowments, his extended endowments in the 44:18.675 --> 44:20.875 Fisher thing under this new regime, 44:20.880 --> 44:22.590 than the value of his endowments. 44:22.590 --> 44:23.370 You're following that? 44:23.369 --> 44:24.039 Student: Yeah. 44:24.039 --> 44:27.619 Prof: Then the next step was to add all this up. 44:27.619 --> 44:31.419 Now notice, however the new technology affects the world, 44:31.422 --> 44:35.092 obviously people can only eat what's being produced. 44:35.090 --> 44:37.950 Everything that's being produced is part of somebody's 44:37.952 --> 44:38.602 endowment. 44:38.599 --> 44:41.119 So if the new technology, if Mr. A invents the new 44:41.117 --> 44:43.877 technology, he gives up some of his good at 44:43.882 --> 44:46.582 time 1 to get more of the good at time 2, 44:46.579 --> 44:48.739 so his endowment has changed--but he's got a new 44:48.742 --> 44:50.882 endowment, but it's still his endowment. 44:50.880 --> 44:54.200 So whatever the new allocation is it has to add up to the new 44:54.195 --> 44:54.855 endowment. 44:54.860 --> 44:58.110 Now, I haven't even bothered to write down the new endowment, 44:58.105 --> 45:00.535 but I know the value of that new endowment. 45:00.539 --> 45:03.539 Whatever it is, it's going to be less than the 45:03.543 --> 45:07.083 value of the old endowment, because the new technology 45:07.081 --> 45:08.151 loses money. 45:08.150 --> 45:13.380 So the contradiction is the value of the new endowment after 45:13.382 --> 45:17.502 the technology is used, at the old equilibrium prices, 45:17.501 --> 45:20.761 is lower than the value of the old endowment at the old 45:20.760 --> 45:22.090 equilibrium prices. 45:22.090 --> 45:26.160 But that, since it's true for every person in the aggregate, 45:26.164 --> 45:30.314 that's less than the value of this new regime consumption. 45:30.309 --> 45:33.069 And that's a contradiction because the new regime 45:33.074 --> 45:35.314 consumption, that's all this stuff, 45:35.306 --> 45:38.906 has to equal exactly the total endowments in the economy to 45:38.907 --> 45:41.577 begin with, and that's the contradiction. 45:41.579 --> 45:43.559 So you can't make everybody better off. 45:43.559 --> 45:47.329 That simple argument, which as I said, 45:47.329 --> 45:49.879 my advisor Ken Arrow, another guy at Yale named 45:49.878 --> 45:51.898 Gerard Debreu-- both of them were working at 45:51.902 --> 45:53.682 the Cowles Foundation which is part of Yale-- 45:53.679 --> 45:57.729 that proof that they gave is the simplest and most important 45:57.731 --> 45:59.861 argument in all of economics. 45:59.860 --> 46:05.490 So we get as a conclusion that, putting it another way, 46:05.489 --> 46:19.019 that owners of firms should maximize the value of their 46:19.023 --> 46:32.453 firms, the stock market value of their 46:32.454 --> 46:36.774 firms, and thank God they do because 46:36.766 --> 46:39.616 if they find some new way of producing that's going to lose 46:39.617 --> 46:42.517 money it's going to make the stock market value go down. 46:42.518 --> 46:45.418 Remember the stock market value is just the same calculation, 46:45.420 --> 46:47.740 the value of all the output they're producing. 46:47.739 --> 46:50.539 If they find some way of losing money and they try to use it 46:50.538 --> 46:52.718 it'll make their stock market value go down. 46:52.719 --> 46:56.569 That's why they're not going to do it, and thank God for that 46:56.565 --> 47:00.405 because it'd be a bad thing for society if they did do it. 47:00.409 --> 47:01.489 Yes? 47:01.489 --> 47:03.659 Student: Well, it seems to me this proof is 47:03.659 --> 47:06.049 logically flawed because you're assuming that after the 47:06.048 --> 47:08.748 inception of a technology the prices are left unchanged, 47:08.750 --> 47:10.050 but that might not be true. 47:10.050 --> 47:14.120 Shouldn't you have some argument for the prices not 47:14.119 --> 47:18.109 changing after the inception of the technology? 47:18.110 --> 47:19.880 Prof: This is a very bold question, 47:19.878 --> 47:21.518 telling me that it's a flawed proof. 47:21.518 --> 47:24.698 I want to commend you for your courage. 47:24.699 --> 47:28.199 As it happens, however, you've asked the same 47:28.197 --> 47:32.887 question that somebody asked a class or two--which is a very 47:32.887 --> 47:34.317 good question. 47:34.320 --> 47:36.880 So the answer is no, I shouldn't have changed the 47:36.875 --> 47:39.585 prices and that's exactly the point of the proof. 47:39.590 --> 47:44.090 So, yes it's true that after the new technology is introduced 47:44.090 --> 47:46.780 the prices changes, everything changes, 47:46.780 --> 47:49.850 but we don't have to worry about all that complication. 47:49.849 --> 47:52.919 After all the changes there's going to be some final 47:52.922 --> 47:55.942 allocation of goods that supposedly makes everybody 47:55.936 --> 47:56.836 better off. 47:56.840 --> 47:58.820 So I can ask the hypothetical question. 47:58.820 --> 48:03.180 Would this new allocation to A at the old prices be something 48:03.177 --> 48:07.097 he could have afforded, and the answer must be no... 48:07.099 --> 48:07.809 Student: All right, I've got it. 48:07.809 --> 48:08.419 Prof: Well, let me just finish. 48:08.420 --> 48:11.330 You see the answer to your question, but I'm going to say 48:11.333 --> 48:13.833 it out because it's a very important question. 48:13.829 --> 48:16.909 The proof is clever precisely because of what you're asking. 48:16.909 --> 48:19.579 You have to do something that you wouldn't have thought of. 48:19.579 --> 48:22.489 You have this new economy, and new allocation, 48:22.489 --> 48:25.539 and new prices, but the proof says let's do the 48:25.541 --> 48:29.591 hypothetical thing of looking at the new allocation at the old 48:29.590 --> 48:30.320 prices. 48:30.320 --> 48:33.330 At the old prices A couldn't have afforded this new 48:33.326 --> 48:36.876 allocation because if he could have, he would have bought it 48:36.875 --> 48:39.035 because it makes him better off. 48:39.039 --> 48:42.719 So at the old prices A couldn't have afforded this new regime 48:42.722 --> 48:43.522 allocation. 48:43.518 --> 48:45.508 Similarly B, at the old prices, 48:45.512 --> 48:48.502 couldn't afford this new regime allocation. 48:48.500 --> 48:52.090 So at the old prices everybody would have to be spending more 48:52.090 --> 48:55.140 on the new regime allocation than the value of their 48:55.141 --> 48:55.981 endowment. 48:55.980 --> 48:59.530 That means at the old prices, the total in the whole 48:59.532 --> 49:02.032 society-- by adding it up--of the 49:02.030 --> 49:06.700 expenditures on the new regime consumptions must be bigger than 49:06.695 --> 49:09.775 the total value of the old endowments. 49:09.780 --> 49:11.960 Now that was the contradiction why at the old endowments 49:11.960 --> 49:14.340 without production you couldn't make everybody better off. 49:14.340 --> 49:15.850 We'd already have a contradiction. 49:15.849 --> 49:17.389 Now we add one more step. 49:17.389 --> 49:23.079 We've got this new technology that changed the old endowments. 49:23.079 --> 49:25.449 It changed the old endowments, but however it changed it we 49:25.451 --> 49:27.251 don't have to keep track of how it did it. 49:27.250 --> 49:30.090 It makes the value of the total endowments even less than it was 49:30.090 --> 49:32.930 before, so we actually get a worse contradiction than before. 49:32.929 --> 49:37.119 So it was a good question, so I thank you for the 49:37.119 --> 49:38.079 question. 49:38.079 --> 49:40.769 Any other questions? 49:40.769 --> 49:41.789 Yes? 49:41.789 --> 49:42.909 Student: Can you raise the board a little bit? 49:42.909 --> 49:44.589 Prof: Yes, I can raise which board, 49:44.585 --> 49:45.195 not this one? 49:45.199 --> 49:46.589 Student: Yes, that one. 49:46.590 --> 49:49.210 Prof: Yeah. 49:49.210 --> 49:50.250 Well, sorry. 49:50.250 --> 49:52.800 Student: Oh. 49:52.800 --> 49:58.800 Prof: So the bottom line here is that--let me just 49:58.802 --> 50:00.092 summarize. 50:00.090 --> 50:04.920 We've spent four classes on reviewing standard intermediate 50:04.920 --> 50:06.420 micro and macro. 50:06.420 --> 50:09.580 People never talk about that stuff when they do 50:09.581 --> 50:12.951 financial--finance courses, in typical courses. 50:12.949 --> 50:15.699 However, Irving Fisher, the inventor of half of 50:15.697 --> 50:17.547 finance, that's how he began. 50:17.550 --> 50:20.190 And it's going to turn out now, especially in light of this 50:20.186 --> 50:22.456 last crisis, that the best way to understand 50:22.463 --> 50:25.863 what's going on is to go back to the original underlying economy. 50:25.860 --> 50:28.410 So Fisher said you can always take--we haven't introduced 50:28.413 --> 50:29.283 risk, by the way. 50:29.280 --> 50:31.340 When that happens things are going to get more complicated. 50:31.340 --> 50:32.720 Fisher couldn't deal with risk. 50:32.719 --> 50:35.469 So without risk, where everybody's anticipating 50:35.467 --> 50:39.017 the dividends in the future, that means that you can always 50:39.018 --> 50:42.588 reduce a financial economy up there to a general equilibrium, 50:42.590 --> 50:45.460 which you've been taught before you got to this course, 50:45.460 --> 50:47.310 most of you, how to solve. 50:47.309 --> 50:50.339 And now that solution to that problem with marginal utility 50:50.344 --> 50:53.644 and Pareto efficiency that tells us an enormous amount about how 50:53.641 --> 50:55.841 the stock market and everything works. 50:55.840 --> 50:59.110 It tells us that the value of every stock is just the 50:59.106 --> 51:02.246 discounted real dividends, discounted at the real rate of 51:02.246 --> 51:05.076 interest, or the discounted nominal 51:05.081 --> 51:08.701 payoffs, cash flows, discounted at the nominal rate 51:08.704 --> 51:09.384 of interest. 51:09.380 --> 51:13.660 And it tells us that the real rate of interest is the nominal 51:13.657 --> 51:16.507 rate divided by the rate of inflation. 51:16.510 --> 51:19.420 And it tells us that it's a good thing all these owners of 51:19.422 --> 51:22.032 companies are maximizing profits or share value, 51:22.030 --> 51:25.380 which is the same thing, and that's helping society. 51:25.380 --> 51:28.090 So that's the lesson. 51:28.090 --> 51:30.680 A lot of that stuff is going to change a little bit, 51:30.684 --> 51:32.114 but that's the basic idea. 51:32.110 --> 51:34.810 So finally let's get to the point. 51:34.809 --> 51:40.739 For 2,000 years the public was confused about interest. 51:40.739 --> 51:43.649 They said--Aristotle, one of the greatest geniuses of 51:43.652 --> 51:46.682 all times, he thought interest was an unnatural act. 51:46.679 --> 51:49.609 It was horrible even though, of course, lots of people in 51:49.606 --> 51:51.276 Greece were charging interest. 51:51.280 --> 51:57.180 Delos, the Delphic oracle was charging interest, 51:57.179 --> 51:59.569 would lend money at interest, and Aristotle and everybody was 51:59.568 --> 52:01.478 talking about the Delphic oracle all the time. 52:01.480 --> 52:02.510 They weren't even paying attention. 52:02.510 --> 52:04.830 The Delphic oracle was charging interest and they were saying 52:04.831 --> 52:05.801 it's totally unnatural. 52:05.800 --> 52:11.220 So three religions all thought interest was a terrible thing. 52:11.219 --> 52:14.269 They all thought the just price was--the nominal rate of 52:14.271 --> 52:16.931 interest should be 0, but what Fisher says is the 52:16.934 --> 52:19.324 nominal rate of interest is irrelevant. 52:19.320 --> 52:21.700 Nobody cares about the nominal rate of interest. 52:21.699 --> 52:24.719 They look at apples today and apples next year. 52:24.719 --> 52:26.599 The money and stuff just gets in the way. 52:26.599 --> 52:29.549 It's the real rate of interest that you care about, 52:29.554 --> 52:33.104 and the real rate of interest doesn't have to be positive. 52:33.099 --> 52:35.479 It could be negative like it is today. 52:35.480 --> 52:39.130 The real rate of interest, what are the determinants 52:39.132 --> 52:43.292 usually of the real rate of interest if the Federal Reserve 52:43.286 --> 52:46.006 isn't mucking around with things, 52:46.010 --> 52:48.840 the real rate of interest is obtained by solving for 52:48.838 --> 52:52.048 P_1 and P_2 in this general equilibrium 52:52.054 --> 52:52.614 model. 52:52.610 --> 52:56.910 So what would change the real rate of interest? 52:56.909 --> 52:59.349 All you have are the utilities and the endowments. 52:59.349 --> 53:01.379 So here's the economy. 53:01.380 --> 53:03.660 What would change the real rate of interest? 53:03.659 --> 53:08.399 So the first thing Fisher says is impatience. 53:08.400 --> 53:11.670 So in fact one of his most famous articles is called an 53:11.673 --> 53:14.833 Impatience Theory of Interest, so let's call it that, 53:14.827 --> 53:16.887 Impatience Theory of Interest. 53:16.889 --> 53:20.939 So Fisher said that in his view people are impatient. 53:20.940 --> 53:21.740 Why? 53:21.739 --> 53:24.079 That means an apple today they thought was more valuable that 53:24.079 --> 53:24.899 an apple next year. 53:24.900 --> 53:25.650 Why? 53:25.650 --> 53:30.320 Because of the poor imagination, it was easy to 53:30.315 --> 53:34.065 think about eating the apple today. 53:34.070 --> 53:36.570 You can just hold it in your hand and it's so close, 53:36.568 --> 53:39.068 but to think about eating it in a year requires some 53:39.065 --> 53:39.845 imagination. 53:39.849 --> 53:42.809 They had poor imagination, and secondly, 53:42.806 --> 53:45.686 the second main reason is mortality. 53:45.690 --> 53:51.350 They might die between today and next year. 53:51.349 --> 53:52.729 So those are the two main reasons. 53:52.730 --> 53:54.530 He gives a bunch of others, which I'm going to mention 53:54.527 --> 53:55.967 shortly, but these are the two most 53:55.967 --> 53:58.177 interesting ones, poverty of imagination and the 53:58.177 --> 54:00.127 fact that you just might die in between. 54:00.130 --> 54:00.930 So what does it mean? 54:00.929 --> 54:03.179 An apple next year is not a sure thing. 54:03.179 --> 54:05.509 There is the Impatience Theory of Interest. 54:05.510 --> 54:09.720 So he said that's why it makes sense to have this guy A as 54:09.719 --> 54:14.149 impatient because he values the apple today more than a value 54:14.150 --> 54:15.110 tomorrow. 54:15.110 --> 54:18.020 He's got this discount rate, a half here. 54:18.018 --> 54:22.478 B's not impatient because the discount factor is one. 54:22.480 --> 54:26.690 So he put a discount factor--actually Fisher didn't 54:26.693 --> 54:31.473 quite have a discount factor, he had a more general thing, 54:31.472 --> 54:36.012 so Samuelson was the one who introduced the discount factor. 54:36.010 --> 54:38.240 It doesn't matter, but anyway so a discount factor 54:38.240 --> 54:40.610 to capture Fisher's idea that the good next year, 54:40.610 --> 54:44.720 the same apple next year is not worth as much to A as an apple 54:44.721 --> 54:45.531 this year. 54:45.530 --> 54:51.460 So suppose I change a half to a third? 54:51.460 --> 54:56.040 What will happen to the real rate of interest? 54:56.039 --> 55:03.019 So that makes people more impatient. 55:03.018 --> 55:06.918 Why does it make them more impatient, because now they care 55:06.920 --> 55:09.410 even less about the good next year. 55:09.409 --> 55:10.389 So when did this happen? 55:10.389 --> 55:13.189 In the Reagan years, the now generation, 55:13.190 --> 55:16.350 everybody talked about the now generation. 55:16.349 --> 55:17.789 People are getting more impatient. 55:17.789 --> 55:21.789 So what happens to the real rate of interest when people get 55:21.788 --> 55:22.938 more impatient? 55:22.940 --> 55:24.290 Does it go up or down? 55:24.289 --> 55:27.079 Student: It goes up. 55:27.079 --> 55:28.449 Prof: So why does it go up? 55:28.449 --> 55:31.099 That's correct. 55:31.099 --> 55:34.849 Student: Because there needs to be more of an incentive 55:34.853 --> 55:35.473 to save. 55:35.469 --> 55:39.949 Prof: Right, but now Fisher would say that a 55:39.949 --> 55:43.499 little bit more-- he would say it a little more 55:43.503 --> 55:45.643 formally, but that's exactly right. 55:45.639 --> 55:48.179 In order to get anybody to save, because they want the 55:48.184 --> 55:51.164 stuff now, you're going to have to give them a higher real rate 55:51.161 --> 55:51.931 of interest. 55:51.929 --> 55:53.389 That's exactly right. 55:53.389 --> 55:55.259 So how could you say it in this economy? 55:55.262 --> 55:57.392 [next slower] Remember in this economy, 55:57.393 --> 56:00.453 this Cobb-Douglas economy, you could prove it formally. 56:00.449 --> 56:04.949 You know that if P_2 (let's say) = 1 and we're 56:04.954 --> 56:08.804 solving for P_1 and here's the supply, 56:08.804 --> 56:12.494 this is X_1, and here's demand. 56:12.489 --> 56:21.669 So remember X^(A)_1 is going to be something like 56:21.673 --> 56:31.493 P_1 E^(A)_1 P_2 E^(A)_2 56:31.492 --> 56:37.512 times 1 over 1 delta where delta-- 56:37.510 --> 56:40.060 what's called delta, the discount. 56:40.059 --> 56:43.369 Let's call this delta, so the discount. 56:43.369 --> 56:47.729 So to get these to add up to 1 I take 1 delta. 56:47.730 --> 56:51.430 So the weight on this thing is 1 over 1 delta times this 56:51.431 --> 56:53.251 divided by P_1. 56:53.250 --> 57:01.370 So if P_2 is 1 then this is just equal to 1 over 1 57:01.367 --> 57:09.067 delta times (E^(A)_1 1 over P_1 times 57:09.074 --> 57:12.244 E^(A)_2). 57:12.239 --> 57:16.999 So clearly the demand goes down as P_1 goes-- 57:17.000 --> 57:19.840 as P_2--this is P_1, 57:19.840 --> 57:22.110 so P_2 = 1, so if I divide by 57:22.112 --> 57:23.852 P_1, P_1 over 57:23.853 --> 57:24.863 P_1 goes away. 57:24.860 --> 57:26.310 Then I have P_2 over P_1, 57:26.313 --> 57:27.743 and if P_2 is 1 that's just 1 over 57:27.735 --> 57:28.325 P_1. 57:28.329 --> 57:32.269 So obviously as P_1 goes up your demand goes down. 57:32.269 --> 57:33.339 That's just what you'd expect. 57:33.340 --> 57:36.450 So P_1 goes down the demand goes up, 57:36.451 --> 57:39.771 or P_1 goes up the demand goes down. 57:39.768 --> 57:43.928 So anyway, if you add up Cobb-Douglas people it always is 57:43.927 --> 57:44.817 like that. 57:44.820 --> 57:48.330 The demand for any good goes up as the price goes down, 57:48.333 --> 57:50.223 if its own price goes down. 57:50.219 --> 57:53.839 So if you change delta, if you make delta smaller, 57:53.835 --> 57:57.965 that's going to raise demand for A_1 at the old 57:57.967 --> 57:58.777 prices. 57:58.780 --> 58:01.530 Why? 58:01.530 --> 58:05.540 At old equilibrium prices, the same trick as before, 58:05.539 --> 58:09.549 at old equilibrium prices what's going to happen? 58:09.550 --> 58:19.800 Delta goes down like we just said, implies X^(A)_1 58:19.802 --> 58:21.542 goes up. 58:21.539 --> 58:31.049 So the guy's demanding more now, but if he's demanding more 58:31.048 --> 58:37.728 at the old equilibrium prices-- so at the old equilibrium 58:37.733 --> 58:40.843 prices he's demanding more so the only way to clear the market 58:40.842 --> 58:42.322 is to raise P_1. 58:42.320 --> 58:47.260 Implies P_1 must go up to clear the market. 58:47.260 --> 58:50.230 So this is a formal proof of what he just said. 58:50.230 --> 58:52.240 So the common sense maybe is enough for you. 58:52.239 --> 58:54.969 If you care less about the future to get anybody to save 58:54.969 --> 58:57.449 you're going to have to raise the interest rate. 58:57.449 --> 59:01.229 To say it formally if we solve for equilibrium with a lower 59:01.228 --> 59:03.768 delta at the old equilibrium prices, 59:03.768 --> 59:07.358 this guy at the old prices, A would now shift and try to 59:07.355 --> 59:08.915 demand more of good 1. 59:08.920 --> 59:12.040 But if he demanded more of good 1 that would mean too much 59:12.039 --> 59:14.489 demand for good 1, and the only way to clear the 59:14.487 --> 59:16.857 price of good 1 is to raise the price P_1. 59:16.860 --> 59:19.090 But if you raise P_1 holding P_2 fixed 59:19.090 --> 59:20.970 that's just P_1 over P_2, 59:20.969 --> 59:23.399 so the interest rate, so the interest rate has to go 59:23.400 --> 59:23.640 up. 59:23.639 --> 59:26.629 So that's your argument made formal. 59:26.630 --> 59:29.100 So that's his Impatience Theory. 59:29.099 --> 59:32.449 That's the main determinant of interest according to Fisher. 59:32.449 --> 59:34.729 What's the second one? 59:34.730 --> 59:44.380 He says suppose people are more optimistic about 59:44.375 --> 59:48.475 E^(i)_2? 59:48.480 --> 59:50.590 Everybody thinks the world's going to be much better next 59:50.585 --> 59:50.845 year. 59:50.849 --> 59:52.529 We're going to have more endowments. 59:52.530 --> 59:58.720 What do you think is going to happen to the interest rate, 59:58.722 --> 1:00:03.072 the real interest rate, somebody else? 1:00:03.070 --> 1:00:06.320 Student: It'll decrease. 1:00:06.320 --> 1:00:07.020 Prof: It'll what? 1:00:07.019 --> 1:00:07.789 Student: Decrease. 1:00:07.789 --> 1:00:10.849 Prof: Decrease, why? 1:00:10.849 --> 1:00:15.629 Student: Because you're expecting things to be better 1:00:15.628 --> 1:00:17.648 > 1:00:17.653 --> 1:00:20.493 signifies people will save less. 1:00:20.489 --> 1:00:27.019 Prof: To save less or to save more? 1:00:27.018 --> 1:00:29.078 So let's think of good X_1. 1:00:29.079 --> 1:00:32.759 If people thought they were going to be richer at the old 1:00:32.764 --> 1:00:36.914 prices what would they do today for X_1 demand more or 1:00:36.911 --> 1:00:37.901 less today? 1:00:37.900 --> 1:00:40.330 Student: The rate would go up, right? 1:00:40.329 --> 1:00:41.979 Prof: Yeah, the right answer is up. 1:00:41.980 --> 1:00:44.420 He said down, but let's just figure out why. 1:00:44.420 --> 1:00:47.770 Student: They demand more > 1:00:47.768 --> 1:00:50.848 Prof: So the reason I gave the formal argument is 1:00:50.851 --> 1:00:52.871 because you can get confused here. 1:00:52.869 --> 1:00:55.679 So let's just do the intuitive one. 1:00:55.679 --> 1:00:57.909 So you had the idea back there of the intuitive one, 1:00:57.907 --> 1:01:00.087 you just got it backward, but you were on the right 1:01:00.092 --> 1:01:00.532 track. 1:01:00.530 --> 1:01:03.990 The point is there's going to be so much stuff around for 1:01:03.985 --> 1:01:07.565 people to eat tomorrow, you've got to get them to want 1:01:07.565 --> 1:01:10.065 to eat all that extra stuff tomorrow. 1:01:10.070 --> 1:01:12.380 So you have to give them an incentive to want to eat all 1:01:12.382 --> 1:01:14.482 that extra stuff tomorrow, so you have to raise the 1:01:14.483 --> 1:01:15.833 interest rate, not lower it. 1:01:15.829 --> 1:01:17.489 So you had the right idea, the wrong conclusion. 1:01:17.489 --> 1:01:20.529 Now, how can you actually give a formal proof of that so you 1:01:20.528 --> 1:01:21.918 know you're not confused? 1:01:21.920 --> 1:01:25.880 Again, like his question, at the old prices what's going 1:01:25.880 --> 1:01:29.050 to happen to the demand for X_1? 1:01:29.050 --> 1:01:31.590 At the old prices, since you're going to be so 1:01:31.588 --> 1:01:33.698 rich in the future, you think you're just 1:01:33.699 --> 1:01:35.919 incredibly rich now, so of course you're going to 1:01:35.922 --> 1:01:36.862 consume more today. 1:01:36.860 --> 1:01:39.780 So there's going to be more demand today and the endowment 1:01:39.780 --> 1:01:40.960 today hasn't changed. 1:01:40.960 --> 1:01:43.330 So there's going to be more demand today with the same 1:01:43.329 --> 1:01:45.829 endowment today, so therefore in order to clear 1:01:45.827 --> 1:01:49.067 the market today you're going to have to raise P_1 1:01:49.068 --> 1:01:52.638 relative to P_2 so the interest rate's got to go up. 1:01:52.639 --> 1:01:55.349 So is that clear? 1:01:55.349 --> 1:02:00.399 It's a little surprising, so let me say that again. 1:02:00.400 --> 1:02:04.660 If you increase the endowments tomorrow the supply today of 1:02:04.659 --> 1:02:08.699 goods hasn't changed, but people are richer tomorrow. 1:02:08.699 --> 1:02:11.359 So clearly they're going to consume this fraction of their 1:02:11.360 --> 1:02:11.780 wealth. 1:02:11.780 --> 1:02:12.770 Their wealth is up. 1:02:12.768 --> 1:02:15.238 You tell anybody, "You're going to be rich 1:02:15.244 --> 1:02:15.894 next year. 1:02:15.889 --> 1:02:17.919 You're going to be worth a fortune," 1:02:17.916 --> 1:02:19.796 the normal person, Cobb-Douglas person, 1:02:19.795 --> 1:02:22.155 is going to consume more stuff today anticipating that he's 1:02:22.163 --> 1:02:23.473 going to be so rich tomorrow. 1:02:23.469 --> 1:02:25.939 He's going to borrow against tomorrow's wealth. 1:02:25.940 --> 1:02:27.990 And so therefore, in order to clear today's 1:02:27.985 --> 1:02:30.025 market where the supply hasn't changed, 1:02:30.030 --> 1:02:33.090 with all these people trying eat more today you have to raise 1:02:33.085 --> 1:02:34.965 today's price relative to tomorrow. 1:02:34.969 --> 1:02:37.649 That's, raise the real interest rate. 1:02:37.650 --> 1:02:42.380 So what's a third example? 1:02:42.380 --> 1:02:44.940 This is Fisher's most famous one. 1:02:44.940 --> 1:02:52.170 Suppose you transfer money, transfer wealth, 1:02:52.168 --> 1:02:55.528 from poor to rich. 1:02:55.530 --> 1:03:02.380 What would happen? 1:03:02.380 --> 1:03:05.870 We have to make an extra assumption here. 1:03:05.869 --> 1:03:08.509 Fisher felt that the people who were rich were rich because they 1:03:08.510 --> 1:03:09.140 were patient. 1:03:09.139 --> 1:03:12.229 They could charge interest and get lots of money. 1:03:12.230 --> 1:03:15.690 So if you change wealth you take away some money from the 1:03:15.686 --> 1:03:16.116 poor. 1:03:16.119 --> 1:03:20.239 That's what's happened in the American economy over the last 1:03:20.242 --> 1:03:21.432 15 or 20 years. 1:03:21.429 --> 1:03:23.819 The rich have gotten richer and the poor are pretty much back 1:03:23.822 --> 1:03:24.822 where they were before. 1:03:24.820 --> 1:03:27.890 So suppose the rich get rich at the expense of the poor? 1:03:27.889 --> 1:03:33.239 What's that going to do to the real rate of interest? 1:03:33.239 --> 1:03:34.469 I'll--hang on a second. 1:03:34.469 --> 1:03:35.369 Yep? 1:03:35.369 --> 1:03:36.679 Student: That would make it lower. 1:03:36.679 --> 1:03:37.529 Prof: That's going to lower it. 1:03:37.530 --> 1:03:38.250 Why is that? 1:03:38.250 --> 1:03:45.100 Student: > 1:03:45.099 --> 1:03:48.879 Prof: So there's an intuitive way of saying it which 1:03:48.878 --> 1:03:52.338 is his which is that the rich, because they're patient, 1:03:52.344 --> 1:03:53.774 are probably the lenders. 1:03:53.768 --> 1:03:57.868 Now they're even more willing to lend and so the interest rate 1:03:57.873 --> 1:04:01.443 has to go down to get these other people to borrow. 1:04:01.440 --> 1:04:06.320 A formal way of saying it is that if you transfer money from 1:04:06.317 --> 1:04:08.467 the rich [correction: poor] 1:04:08.467 --> 1:04:10.857 to the poor [correction: rich] 1:04:10.864 --> 1:04:15.564 that means the poor guys-- the rich guys always consume a 1:04:15.563 --> 1:04:19.813 higher proportion in the future because they're more patient. 1:04:19.809 --> 1:04:22.449 So a more patient guy will consume more in the future. 1:04:22.449 --> 1:04:27.809 So if you take away wealth from an impatient guy and give it to 1:04:27.811 --> 1:04:31.791 a patient guy you're going to increase the-- 1:04:31.789 --> 1:04:39.769 the economy's going to be more in the hands of the patient 1:04:39.768 --> 1:04:42.898 people, and so the patient people--the 1:04:42.902 --> 1:04:44.292 mix is going to change. 1:04:44.289 --> 1:04:47.109 People on average are more patient than they were before so 1:04:47.106 --> 1:04:49.726 on average in the economy they're going to consume less 1:04:49.731 --> 1:04:52.701 than they were of today's good and so the shift is going to be 1:04:52.695 --> 1:04:54.215 in this direction, right? 1:04:54.219 --> 1:04:57.549 Because you've made people, a lot of them impatient, 1:04:57.550 --> 1:05:00.130 a lot of patient, you've increased the patient 1:05:00.128 --> 1:05:02.478 ones and decreased the impatient ones, 1:05:02.480 --> 1:05:05.480 so in balance you're going to decrease demand today because it 1:05:05.481 --> 1:05:08.091 was the impatient ones who wanted to eat today and the 1:05:08.088 --> 1:05:09.858 other guys were willing to wait. 1:05:09.860 --> 1:05:13.140 Now the guys who aren't willing to wait these guys don't have 1:05:13.135 --> 1:05:13.785 any money. 1:05:13.789 --> 1:05:16.389 They're the ones doing all the consuming today and now they 1:05:16.385 --> 1:05:18.705 can't afford to do much consuming, so you're going to 1:05:18.711 --> 1:05:20.011 reduce consumption today. 1:05:20.010 --> 1:05:22.470 So to get the market to clear again you have to lower the 1:05:22.467 --> 1:05:23.607 interest rate this time. 1:05:23.610 --> 1:05:27.070 So those are three famous conclusions of Fisher, 1:05:27.070 --> 1:05:29.950 more impatient people, higher interest rate, 1:05:29.949 --> 1:05:33.759 more optimistic about the future, higher interest rate, 1:05:33.760 --> 1:05:38.060 transfers from the poor to the rich lower interest rate. 1:05:38.059 --> 1:05:41.379 So what happens to the stock market in this case? 1:05:41.380 --> 1:05:43.370 Suppose people are more impatient. 1:05:43.369 --> 1:05:45.929 Does the stock market go up or down? 1:05:45.929 --> 1:05:51.529 Student: Down. 1:05:51.530 --> 1:05:55.610 Prof: Down, because the stock market price 1:05:55.606 --> 1:05:59.086 is just this, the real interest rate times 1:05:59.090 --> 1:06:00.620 the dividends. 1:06:00.619 --> 1:06:03.719 So I haven't told you the dividends changed, 1:06:03.722 --> 1:06:07.912 so if the dividends are the same and the real interest rate 1:06:07.907 --> 1:06:11.297 has gone up the stock market has gone down. 1:06:11.300 --> 1:06:14.630 Suppose people are more optimistic about the future, 1:06:14.630 --> 1:06:17.110 so not about the stocks producing more, 1:06:17.112 --> 1:06:20.642 but about whether there's more stuff in the world? 1:06:20.639 --> 1:06:23.759 Their own endowments will be bigger. 1:06:23.760 --> 1:06:25.570 The stock market is going to go down. 1:06:25.570 --> 1:06:28.930 That ones a little subtler because they could be optimistic 1:06:28.925 --> 1:06:32.105 about the stocks producing more, so that's ambiguous. 1:06:32.110 --> 1:06:33.050 So let's do the third. 1:06:33.050 --> 1:06:36.120 Suppose you transfer wealth from the poor to the rich, 1:06:36.115 --> 1:06:38.715 what's going to happen to the stock market? 1:06:38.719 --> 1:06:39.339 It's going to go up. 1:06:39.340 --> 1:06:41.030 So what happened in the last 20 years? 1:06:41.030 --> 1:06:43.170 The rich got richer, the poor got poorer, 1:06:43.170 --> 1:06:46.110 the interest rates got lower and lower and the stock market 1:06:46.110 --> 1:06:48.900 got higher and higher just as Fisher would have said. 1:06:48.900 --> 1:06:55.280 So I want to now end with just Fisher and Shakespeare, 1:06:55.275 --> 1:07:01.045 so I'm going to go over just a couple minutes. 1:07:01.050 --> 1:07:12.200 Maybe I'll have to start with Shakespeare. 1:07:12.199 --> 1:07:15.579 So Fisher's theory of interest, as I said, 1:07:15.579 --> 1:07:23.169 was making sense of thousands of years of confusion, 1:07:23.170 --> 1:07:27.050 so the idea is that interest is nothing other-- 1:07:27.050 --> 1:07:28.260 you shouldn't think of nominal interest. 1:07:28.260 --> 1:07:29.790 People look through all that. 1:07:29.789 --> 1:07:32.539 They look at the real rate of interest and the real rate of 1:07:32.539 --> 1:07:35.379 interest is just the ratio of two prices just like everything 1:07:35.384 --> 1:07:39.024 else in equilibrium, so therefore there is no such 1:07:39.019 --> 1:07:42.069 thing as-- it's an important price like 1:07:42.068 --> 1:07:44.908 anything else, but maybe I forgot to say it, 1:07:44.913 --> 1:07:47.113 there's no such thing as a just price. 1:07:47.110 --> 1:07:49.730 The price, in fact, that equilibrium finds is the 1:07:49.733 --> 1:07:52.963 best price because that's the price that's going to lead new 1:07:52.958 --> 1:07:55.798 firms and inventors to use technologies that help the 1:07:55.802 --> 1:07:58.642 economy as opposed to hurting the economy and wasting 1:07:58.644 --> 1:07:59.634 resources. 1:07:59.630 --> 1:08:02.380 So the price that the market finds is the just price and the 1:08:02.384 --> 1:08:04.954 real rate of interest is the right real rate of interest 1:08:04.952 --> 1:08:07.432 provided that people are rational and see through this 1:08:07.425 --> 1:08:07.935 veil. 1:08:07.940 --> 1:08:11.170 So, why is it that the real rate of interest is typically 1:08:11.173 --> 1:08:11.813 positive? 1:08:11.809 --> 1:08:15.899 Well, it's because, as I said, people are impatient 1:08:15.896 --> 1:08:18.346 and these different reasons. 1:08:18.350 --> 1:08:21.010 Now Fisher said one other reason that screws up the real 1:08:21.007 --> 1:08:23.467 rate of interest is people sometimes get confused by 1:08:23.472 --> 1:08:24.152 inflation. 1:08:24.149 --> 1:08:25.309 So this is an aside. 1:08:25.310 --> 1:08:29.780 He said that all contracts should be inflation indexed, 1:08:29.779 --> 1:08:34.129 and he forced his Yale secretary and his secretaries at 1:08:34.134 --> 1:08:37.444 his company to change their contracts-- 1:08:37.439 --> 1:08:38.719 I guess his Yale secretary is probably wrong, 1:08:38.720 --> 1:08:41.770 the secretaries at his business, Remington, 1:08:41.770 --> 1:08:46.760 he forced them to accept deals where their wage was indexed to 1:08:46.757 --> 1:08:47.737 inflation. 1:08:47.738 --> 1:08:49.958 And of course the Great Depression happened and all of 1:08:49.956 --> 1:08:53.456 the prices collapsed, and so all his secretaries got 1:08:53.457 --> 1:08:58.457 less money out of the deal so he wasn't too popular with them 1:08:58.457 --> 1:08:59.287 either. 1:08:59.288 --> 1:09:02.878 He says impatience is a fundamental attribute of human 1:09:02.880 --> 1:09:03.490 nature. 1:09:03.488 --> 1:09:05.488 As long as people like things today rather than tomorrow 1:09:05.490 --> 1:09:06.620 there's going to be interest. 1:09:06.618 --> 1:09:09.438 So interest is, as it were, impatience 1:09:09.440 --> 1:09:14.260 crystallized into a market rate, and the reasons for impatience 1:09:14.261 --> 1:09:16.851 are this foresight, lack of foresight, 1:09:16.854 --> 1:09:20.474 possibility of dying and then he talks about self control and 1:09:20.472 --> 1:09:23.262 stuff like that, the greater the foresight, 1:09:23.261 --> 1:09:23.871 etcetera. 1:09:23.868 --> 1:09:27.488 Now he has this racist view of the world, which I think is 1:09:27.492 --> 1:09:28.702 worth mentioning. 1:09:28.698 --> 1:09:33.198 So he compares the Scotch and the Irish, so the Scotch are 1:09:33.201 --> 1:09:37.941 patient, the Irish are totally impatient, no self-control and 1:09:37.938 --> 1:09:40.148 it gets worse and worse. 1:09:40.149 --> 1:09:41.279 I can't show you all of this. 1:09:41.279 --> 1:09:44.689 So Holland, Scotland, England, France these are all 1:09:44.693 --> 1:09:47.563 the places his family was probably from. 1:09:47.560 --> 1:09:48.590 They're incredibly patient. 1:09:48.590 --> 1:09:49.200 They're wonderful. 1:09:49.198 --> 1:09:51.778 They've got low rates of interest, incredibly thrifty 1:09:51.782 --> 1:09:52.232 people. 1:09:52.229 --> 1:09:54.719 Then you look at all these other dreadful people, 1:09:54.720 --> 1:09:59.500 Chinese, Indians, Blacks, Java Southerners, 1:09:59.500 --> 1:10:02.070 American Indians and then Greeks and Italians he mentions 1:10:02.067 --> 1:10:03.737 later, hopeless, high rates of 1:10:03.742 --> 1:10:05.502 interest, incredibly impatient. 1:10:05.500 --> 1:10:09.570 So anyway, the patient accumulate wealth and by waiting 1:10:09.573 --> 1:10:12.973 and lending they make production possible, 1:10:12.970 --> 1:10:15.300 because the people with all the good ideas where are they going 1:10:15.295 --> 1:10:16.415 to get the money to produce? 1:10:16.420 --> 1:10:19.230 They're going to get it out of the patient people who are 1:10:19.234 --> 1:10:20.144 willing to wait. 1:10:20.140 --> 1:10:23.530 If you can wait should I talk for five more minutes or do you 1:10:23.533 --> 1:10:24.273 need to go? 1:10:24.270 --> 1:10:26.700 I was going to do my--maybe I should let you go. 1:10:26.698 --> 1:10:28.358 Anyway, so what I was going to say last, 1:10:28.359 --> 1:10:31.069 I won't say it, is that Shakespeare anticipated 1:10:31.073 --> 1:10:34.323 all of Fisher's Impatience Theory of Interest and went a 1:10:34.317 --> 1:10:35.317 step further. 1:10:35.319 --> 1:10:37.309 He said, "Well, that's great but you should 1:10:37.305 --> 1:10:39.795 take into account that people won't keep their promises, 1:10:39.800 --> 1:10:42.310 and if they don't keep their promises you need collateral, 1:10:42.310 --> 1:10:44.860 and if you need collateral that's going to change a lot of 1:10:44.863 --> 1:10:47.243 stuff," and Shakespeare already had a lot of that 1:10:47.238 --> 1:10:48.868 figured out, and most of this course is 1:10:48.869 --> 1:10:50.459 going to be about, believe it or not, 1:10:50.457 --> 1:10:53.357 what Shakespeare had to say about the rate of interest and 1:10:53.364 --> 1:10:54.084 collateral. 1:10:54.079 --> 1:10:55.599 Okay, next time. 1:10:55.600 --> 1:11:01.000