WEBVTT 00:00:00.000 --> 00:00:02.480 align:middle line:90% [SQUEAKING] 00:00:02.480 --> 00:00:03.968 align:middle line:90% [RUSTLING] 00:00:03.968 --> 00:00:06.448 align:middle line:90% [CLICKING] 00:00:06.448 --> 00:00:16.540 align:middle line:90% 00:00:16.540 --> 00:00:18.760 align:middle line:84% GLENN ELLISON: OK, as I said, so, 00:00:18.760 --> 00:00:24.545 align:middle line:84% classic example here, American Repertory Theater in Cambridge, 00:00:24.545 --> 00:00:26.170 align:middle line:84% plays that are going to go to Broadway, 00:00:26.170 --> 00:00:29.650 align:middle line:84% they try them out there, also sort of avant garde stuff. 00:00:29.650 --> 00:00:32.619 align:middle line:84% If I buy a ticket there, it's like $72 00:00:32.619 --> 00:00:35.580 align:middle line:84% to sit in the back corner of the theater. 00:00:35.580 --> 00:00:38.080 align:middle line:84% You, as students, they actually, if you go on their website, 00:00:38.080 --> 00:00:40.247 align:middle line:84% they have a tremendous number of students, basically 00:00:40.247 --> 00:00:42.670 align:middle line:90% everyone except me. 00:00:42.670 --> 00:00:46.300 align:middle line:84% And the student discount there, you 00:00:46.300 --> 00:00:49.850 align:middle line:84% can go see plays that cost me $72 and you pay, like, $10. 00:00:49.850 --> 00:00:51.725 align:middle line:90% It's less than going to a movie. 00:00:51.725 --> 00:00:53.350 align:middle line:84% I would say, it's a great thing to see, 00:00:53.350 --> 00:00:55.900 align:middle line:84% that it is typical, though, that you might buy a ticket 00:00:55.900 --> 00:01:00.160 align:middle line:84% to see Hamlet and find that you've got guys standing 00:01:00.160 --> 00:01:03.430 align:middle line:84% in kiddie bathtubs, wearing shorts, playing guitars, 00:01:03.430 --> 00:01:04.069 align:middle line:90% or whatever. 00:01:04.069 --> 00:01:07.035 align:middle line:84% So it is-- you have to be aware that you may not 00:01:07.035 --> 00:01:08.410 align:middle line:84% get what you think you're getting 00:01:08.410 --> 00:01:10.910 align:middle line:84% when you see the title of the play, but a great thing to go. 00:01:10.910 --> 00:01:13.600 align:middle line:84% But anyway, example of this, they're 00:01:13.600 --> 00:01:15.680 align:middle line:84% selling the same ticket to you for $10 00:01:15.680 --> 00:01:18.650 align:middle line:90% they would charge me $72 for. 00:01:18.650 --> 00:01:20.190 align:middle line:84% People often also think about this 00:01:20.190 --> 00:01:21.522 align:middle line:90% when you have nonlinear prices. 00:01:21.522 --> 00:01:22.730 align:middle line:90% You'll go to the supermarket. 00:01:22.730 --> 00:01:25.620 align:middle line:84% And it's, like, buy one, get one half off. 00:01:25.620 --> 00:01:27.200 align:middle line:84% It's like, the first good is being 00:01:27.200 --> 00:01:29.490 align:middle line:84% sold at a different price from the second good. 00:01:29.490 --> 00:01:31.700 align:middle line:84% And again, the first thing of strawberries 00:01:31.700 --> 00:01:33.050 align:middle line:84% you buy and the second thing of strawberries you 00:01:33.050 --> 00:01:35.210 align:middle line:84% buy, they're identical, except they're selling them 00:01:35.210 --> 00:01:38.660 align:middle line:90% to you at different prices. 00:01:38.660 --> 00:01:41.270 align:middle line:84% We also talk about price discrimination 00:01:41.270 --> 00:01:46.950 align:middle line:84% when firms are selling similar goods at very different prices. 00:01:46.950 --> 00:01:50.000 align:middle line:84% So, for instance, I put the iPhone 14 down there. 00:01:50.000 --> 00:01:57.630 align:middle line:84% The iPhone 14, 128-gigabyte version is $799. 00:01:57.630 --> 00:02:01.140 align:middle line:84% The 512-gigabyte version is $1,099. 00:02:01.140 --> 00:02:04.603 align:middle line:84% So it's $300 extra for the more expensive iPhone. 00:02:04.603 --> 00:02:06.020 align:middle line:84% You might think to yourself, wait, 00:02:06.020 --> 00:02:10.520 align:middle line:84% I can buy a 512-gigabyte flash drive for $50. 00:02:10.520 --> 00:02:13.107 align:middle line:84% Why does it cost $300 more to put it in the phone? 00:02:13.107 --> 00:02:13.940 align:middle line:90% Is it better memory? 00:02:13.940 --> 00:02:18.110 align:middle line:84% No, it's exactly the same memory that's in the $50 flash drive 00:02:18.110 --> 00:02:19.530 align:middle line:84% that someone's making a profit on. 00:02:19.530 --> 00:02:22.460 align:middle line:84% But somehow, two similar goods are just 00:02:22.460 --> 00:02:24.010 align:middle line:84% being sold at very different markups. 00:02:24.010 --> 00:02:29.330 align:middle line:90% 00:02:29.330 --> 00:02:32.720 align:middle line:84% Again, whether we think of something 00:02:32.720 --> 00:02:37.430 align:middle line:84% as price discrimination when the goods differ, 00:02:37.430 --> 00:02:39.590 align:middle line:84% do you talk about discrimination if it's, like, 00:02:39.590 --> 00:02:41.870 align:middle line:84% the ratio of the prices to costs are different, 00:02:41.870 --> 00:02:44.780 align:middle line:84% or if the dollar value of price to cost is different? 00:02:44.780 --> 00:02:46.790 align:middle line:84% But it is-- often in these examples, 00:02:46.790 --> 00:02:48.980 align:middle line:84% it's very, very clear that, however you 00:02:48.980 --> 00:02:51.000 align:middle line:84% think about adjusting for the cost, 00:02:51.000 --> 00:02:53.250 align:middle line:84% something is just much more expensive than the others. 00:02:53.250 --> 00:02:54.792 align:middle line:84% We'll call that price discrimination. 00:02:54.792 --> 00:02:58.550 align:middle line:84% The business class seat is $12,000 when the coach seat is 00:02:58.550 --> 00:02:59.900 align:middle line:90% $600 or whatever. 00:02:59.900 --> 00:03:02.390 align:middle line:84% It's like, I don't know whether I'm counting cubic inches 00:03:02.390 --> 00:03:02.930 align:middle line:90% or whatever. 00:03:02.930 --> 00:03:06.620 align:middle line:84% But one is just much more expensive. 00:03:06.620 --> 00:03:08.930 align:middle line:84% Also, sometimes, you can think about it 00:03:08.930 --> 00:03:13.400 align:middle line:84% as being price discrimination when costs differ, 00:03:13.400 --> 00:03:15.540 align:middle line:84% and you don't discriminate in prices. 00:03:15.540 --> 00:03:18.200 align:middle line:84% So for instance, there are places that offer free delivery. 00:03:18.200 --> 00:03:20.090 align:middle line:84% And the free delivery doesn't depend 00:03:20.090 --> 00:03:22.152 align:middle line:90% on how far it is to get to you. 00:03:22.152 --> 00:03:24.110 align:middle line:84% So you might think that they're, in some sense, 00:03:24.110 --> 00:03:27.045 align:middle line:84% when the firm is incurring a large delivery cost to get it 00:03:27.045 --> 00:03:29.420 align:middle line:84% to you, they're giving you a discount, relative to people 00:03:29.420 --> 00:03:31.610 align:middle line:84% for whom they're spending a small amount of money 00:03:31.610 --> 00:03:32.730 align:middle line:90% to get it to you. 00:03:32.730 --> 00:03:35.990 align:middle line:84% And so, again, I would think of that as charging the same price 00:03:35.990 --> 00:03:38.240 align:middle line:84% can actually be price discrimination, 00:03:38.240 --> 00:03:40.190 align:middle line:84% if the costs are very different of serving 00:03:40.190 --> 00:03:42.020 align:middle line:90% the different consumers. 00:03:42.020 --> 00:03:45.170 align:middle line:84% OK, obviously, price discrimination 00:03:45.170 --> 00:03:46.470 align:middle line:90% requires market power. 00:03:46.470 --> 00:03:48.470 align:middle line:84% This was actually one of my favorite signs 00:03:48.470 --> 00:03:52.640 align:middle line:84% I found at the Whole Foods once, which was cranberries for sale, 00:03:52.640 --> 00:03:57.707 align:middle line:84% regularly $2, now 2 for $4, which, I didn't quite 00:03:57.707 --> 00:03:58.915 align:middle line:90% know what was going on there. 00:03:58.915 --> 00:04:01.520 align:middle line:90% 00:04:01.520 --> 00:04:05.150 align:middle line:84% OK, so, theory of price discrimination goes back 00:04:05.150 --> 00:04:07.490 align:middle line:90% to Pigou in the 1920s. 00:04:07.490 --> 00:04:10.310 align:middle line:84% Pigou made up three names for three different types 00:04:10.310 --> 00:04:11.850 align:middle line:90% of price discrimination. 00:04:11.850 --> 00:04:13.460 align:middle line:90% These names are terrible names. 00:04:13.460 --> 00:04:14.910 align:middle line:90% But they've survived. 00:04:14.910 --> 00:04:18.680 align:middle line:84% So, first one, he called first degree price discrimination, 00:04:18.680 --> 00:04:21.810 align:middle line:84% which some people also refer to as perfect price discrimination. 00:04:21.810 --> 00:04:27.260 align:middle line:84% This is the ideal of a theorist where the firm knows everything 00:04:27.260 --> 00:04:28.020 align:middle line:90% they need to know. 00:04:28.020 --> 00:04:29.370 align:middle line:84% They have all the power they would want. 00:04:29.370 --> 00:04:31.290 align:middle line:84% They can price separately to every consumer. 00:04:31.290 --> 00:04:33.753 align:middle line:84% It's really a theoretical ideal because firms are never 00:04:33.753 --> 00:04:36.170 align:middle line:84% in the situation of exactly knowing the consumer's utility 00:04:36.170 --> 00:04:38.360 align:middle line:90% function. 00:04:38.360 --> 00:04:41.990 align:middle line:84% Second degree price discrimination 00:04:41.990 --> 00:04:45.060 align:middle line:84% is price discrimination based on self-selection. 00:04:45.060 --> 00:04:47.450 align:middle line:84% So this would be offering an iPhone 00:04:47.450 --> 00:04:50.840 align:middle line:84% 14 in two different quality levels 00:04:50.840 --> 00:04:53.420 align:middle line:84% and relying on the consumers to sort themselves between, 00:04:53.420 --> 00:04:58.280 align:middle line:84% do they buy the cheap iPhone 14 or the expensive iPhone 14? 00:04:58.280 --> 00:05:02.690 align:middle line:84% And you see lots of other examples of this, cell phone 00:05:02.690 --> 00:05:04.970 align:middle line:84% plans, health insurance contracts, when you 00:05:04.970 --> 00:05:07.580 align:middle line:90% buy regular premium gasoline. 00:05:07.580 --> 00:05:10.430 align:middle line:84% Firms are setting these prices, relying entirely 00:05:10.430 --> 00:05:12.800 align:middle line:84% on the consumers to self-select among them. 00:05:12.800 --> 00:05:16.330 align:middle line:84% And then third degree price discrimination 00:05:16.330 --> 00:05:19.030 align:middle line:84% is the examples like the ART student tickets 00:05:19.030 --> 00:05:23.560 align:middle line:84% or military discount or senior citizen discount or whatever, 00:05:23.560 --> 00:05:27.910 align:middle line:84% where there are some observable characteristics 00:05:27.910 --> 00:05:29.110 align:middle line:90% of the consumers. 00:05:29.110 --> 00:05:31.067 align:middle line:84% And then the firms can set different prices 00:05:31.067 --> 00:05:32.650 align:middle line:84% based on the different characteristics 00:05:32.650 --> 00:05:34.030 align:middle line:90% of the consumers. 00:05:34.030 --> 00:05:36.070 align:middle line:84% Another one you'd see here, classic third degree 00:05:36.070 --> 00:05:38.740 align:middle line:84% discrimination, is geographic location. 00:05:38.740 --> 00:05:41.410 align:middle line:84% Firms will set different prices in different countries 00:05:41.410 --> 00:05:44.200 align:middle line:84% because they can observe in which country 00:05:44.200 --> 00:05:47.470 align:middle line:90% someone is buying the good. 00:05:47.470 --> 00:05:50.890 align:middle line:84% I would say, why is this a bad nomenclature? 00:05:50.890 --> 00:05:53.780 align:middle line:84% One is, names first, second, and third degree 00:05:53.780 --> 00:05:55.580 align:middle line:90% don't really have any meaning. 00:05:55.580 --> 00:05:57.580 align:middle line:84% And then, besides not really having any meaning, 00:05:57.580 --> 00:05:58.990 align:middle line:90% the order is wrong. 00:05:58.990 --> 00:06:02.020 align:middle line:84% In some sense, first degree is when you know 00:06:02.020 --> 00:06:03.310 align:middle line:90% everything about the consumer. 00:06:03.310 --> 00:06:05.810 align:middle line:84% Third degree is when you know something about the consumers. 00:06:05.810 --> 00:06:08.227 align:middle line:84% Second degree is when you know nothing about the consumer. 00:06:08.227 --> 00:06:10.220 align:middle line:84% So they really ought to be in this order. 00:06:10.220 --> 00:06:13.730 align:middle line:84% But anyway, that's the order Pigou described them in. 00:06:13.730 --> 00:06:16.800 align:middle line:84% People still talk about second degree price discrimination. 00:06:16.800 --> 00:06:19.430 align:middle line:84% So, anyway, I'm going to continue 00:06:19.430 --> 00:06:23.270 align:middle line:84% to use those names because that's what everyone else uses. 00:06:23.270 --> 00:06:26.900 align:middle line:84% So let me start with first degree price discrimination. 00:06:26.900 --> 00:06:29.370 align:middle line:84% So, first degree is the simplest. 00:06:29.370 --> 00:06:34.460 align:middle line:84% So suppose this is the omniscient monopolist, 00:06:34.460 --> 00:06:37.440 align:middle line:84% the monopolist, powerful, whatever. 00:06:37.440 --> 00:06:40.460 align:middle line:84% So, a monopolist, every different consumer 00:06:40.460 --> 00:06:45.200 align:middle line:84% who walks into the store, the monopolist knows, this 00:06:45.200 --> 00:06:48.860 align:middle line:90% is p1 of x, this is p2 of x. 00:06:48.860 --> 00:06:53.870 align:middle line:84% So if customer 1 walks into the store, 00:06:53.870 --> 00:06:56.090 align:middle line:84% the monopolist knows, OK, I'm facing customer 1. 00:06:56.090 --> 00:06:58.940 align:middle line:84% This is customer 1's willingness to pay for x units, 00:06:58.940 --> 00:07:00.380 align:middle line:90% for any number, x. 00:07:00.380 --> 00:07:04.395 align:middle line:84% And then, customer 2 walks in the store. 00:07:04.395 --> 00:07:06.020 align:middle line:84% This is customer 2's willingness to pay 00:07:06.020 --> 00:07:07.490 align:middle line:90% for any number of units, x. 00:07:07.490 --> 00:07:10.010 align:middle line:90% 00:07:10.010 --> 00:07:13.110 align:middle line:84% So I'm going to suppose that this monopolist is powerful. 00:07:13.110 --> 00:07:16.310 align:middle line:84% It can set customer-specific nonlinear prices. 00:07:16.310 --> 00:07:20.600 align:middle line:84% And it can prevent resale across the consumers. 00:07:20.600 --> 00:07:22.530 align:middle line:90% So what's going to happen? 00:07:22.530 --> 00:07:26.180 align:middle line:84% You can imagine some very complicated menu 00:07:26.180 --> 00:07:27.762 align:middle line:90% of prices you set to consumers. 00:07:27.762 --> 00:07:28.970 align:middle line:90% You have them play some game. 00:07:28.970 --> 00:07:30.690 align:middle line:84% You have them do something or other. 00:07:30.690 --> 00:07:33.830 align:middle line:84% But at the end of the day, suppose, in equilibrium, 00:07:33.830 --> 00:07:39.440 align:middle line:84% this consumer buys x1 units and ends up paying x2-- 00:07:39.440 --> 00:07:40.730 align:middle line:90% sorry, ends up paying t1. 00:07:40.730 --> 00:07:45.240 align:middle line:84% And this consumer buys x2 units and ends up paying t2. 00:07:45.240 --> 00:07:47.480 align:middle line:84% If this is what's going to happen in equilibrium 00:07:47.480 --> 00:07:49.502 align:middle line:84% under some very complicated scheme, 00:07:49.502 --> 00:07:51.710 align:middle line:84% you might as well just make a direct take it or leave 00:07:51.710 --> 00:07:53.070 align:middle line:90% it offer to each consumer. 00:07:53.070 --> 00:07:57.410 align:middle line:84% So just offer consumer 1, either you buy x1 units at a price t1 00:07:57.410 --> 00:07:58.980 align:middle line:90% or you get nothing at all. 00:07:58.980 --> 00:07:59.960 align:middle line:90% You go to consumer 2. 00:07:59.960 --> 00:08:02.780 align:middle line:84% Either you get x2 units at a price of t2 00:08:02.780 --> 00:08:04.200 align:middle line:90% or you get nothing at all. 00:08:04.200 --> 00:08:07.160 align:middle line:84% And so, anything you can achieve with a more complicated scheme, 00:08:07.160 --> 00:08:08.600 align:middle line:84% you can achieve with these simple 00:08:08.600 --> 00:08:10.850 align:middle line:84% take it or leave it, customer by customer take it 00:08:10.850 --> 00:08:12.720 align:middle line:90% or leave it schemes, OK? 00:08:12.720 --> 00:08:14.720 align:middle line:84% So that's what we're going to think about doing, 00:08:14.720 --> 00:08:16.610 align:middle line:84% is just offering these customer-specific 00:08:16.610 --> 00:08:19.160 align:middle line:90% take it or leave it schemes. 00:08:19.160 --> 00:08:24.830 align:middle line:84% When is customer 1 going to accept an offer that involves 00:08:24.830 --> 00:08:29.270 align:middle line:90% x1 units at a price of t1? 00:08:29.270 --> 00:08:35.000 align:middle line:84% Well, if that's my offer, this is the maximum amount 00:08:35.000 --> 00:08:37.440 align:middle line:84% that the customer is willing to pay for x1 units. 00:08:37.440 --> 00:08:39.398 align:middle line:84% They're willing to pay this for the first unit, 00:08:39.398 --> 00:08:42.080 align:middle line:84% this for the second unit, this for the third unit, and so on. 00:08:42.080 --> 00:08:45.080 align:middle line:84% So the maximum they'll pay for x1 units 00:08:45.080 --> 00:08:48.790 align:middle line:84% is just the integral from 0 to x of Pi of s(ds). 00:08:48.790 --> 00:08:53.660 align:middle line:84% Given that the customer is going to accept that offer, if 00:08:53.660 --> 00:08:56.100 align:middle line:84% and only if Ti is less than this, 00:08:56.100 --> 00:08:58.340 align:middle line:84% clearly, the best thing to do is to set the price 00:08:58.340 --> 00:09:00.300 align:middle line:84% as high as the consumer's willingness to pay. 00:09:00.300 --> 00:09:02.420 align:middle line:84% So you set Ti equals the integral from 0 00:09:02.420 --> 00:09:04.940 align:middle line:90% to x, Pi of s(ds). 00:09:04.940 --> 00:09:09.230 align:middle line:84% And so, thinking about the monopoly problem, 00:09:09.230 --> 00:09:13.100 align:middle line:84% you're just trying to maximize the total amount. 00:09:13.100 --> 00:09:16.470 align:middle line:84% You pick the number of units, xi, to sell that consumer. 00:09:16.470 --> 00:09:19.470 align:middle line:84% This is the price you're going to charge when you sell x units. 00:09:19.470 --> 00:09:23.030 align:middle line:84% And then this is the cost of producing the units. 00:09:23.030 --> 00:09:28.010 align:middle line:84% So, clearly, I differentiate that with respect to xi. 00:09:28.010 --> 00:09:32.550 align:middle line:84% The derivative of this with respect to xi is just Pi of xi. 00:09:32.550 --> 00:09:35.160 align:middle line:84% The derivative of this with respect to xi is c. 00:09:35.160 --> 00:09:37.850 align:middle line:84% So the first order condition is just, set 00:09:37.850 --> 00:09:43.010 align:middle line:84% xi-star, such that Pi of xi-star equals c. 00:09:43.010 --> 00:09:47.990 align:middle line:84% So in some sense, it becomes, the optimal solution is, 00:09:47.990 --> 00:09:51.180 align:middle line:84% do exactly what would happen with perfect competition. 00:09:51.180 --> 00:09:54.080 align:middle line:84% So if this is my constant marginal cost, 00:09:54.080 --> 00:09:59.990 align:middle line:84% for every consumer, I just figure out, how many units 00:09:59.990 --> 00:10:05.570 align:middle line:84% would they buy if I was setting the price then equal to c. 00:10:05.570 --> 00:10:09.110 align:middle line:90% And I do this as x1-star. 00:10:09.110 --> 00:10:11.810 align:middle line:90% I do this as x2-star. 00:10:11.810 --> 00:10:15.590 align:middle line:84% And then the total amount that I charge 00:10:15.590 --> 00:10:19.830 align:middle line:84% them is just their total utility they 00:10:19.830 --> 00:10:22.160 align:middle line:84% get from buying the number of units that I sell them. 00:10:22.160 --> 00:10:25.810 align:middle line:90% 00:10:25.810 --> 00:10:30.400 align:middle line:84% So, comments, quantities are exactly the same as with perfect 00:10:30.400 --> 00:10:31.930 align:middle line:90% competition. 00:10:31.930 --> 00:10:35.120 align:middle line:84% First degree discrimination is socially optimal. 00:10:35.120 --> 00:10:37.390 align:middle line:84% Again, I'm ignoring distributional effects. 00:10:37.390 --> 00:10:40.180 align:middle line:84% But it's just, there's no failure 00:10:40.180 --> 00:10:41.360 align:middle line:90% to realize gains from trade. 00:10:41.360 --> 00:10:45.100 align:middle line:84% Every unit that is worth c gets sold to somebody. 00:10:45.100 --> 00:10:47.800 align:middle line:84% Notice also that, rather than having 00:10:47.800 --> 00:10:52.090 align:middle line:84% this take it or leave it offer bundle, 00:10:52.090 --> 00:10:53.860 align:middle line:84% the monopolist could also do this 00:10:53.860 --> 00:10:58.450 align:middle line:84% by just offering the good at a price of c, 00:10:58.450 --> 00:11:01.960 align:middle line:84% and then having a fixed fee that they add on top of that. 00:11:01.960 --> 00:11:07.160 align:middle line:84% So in this case, for this consumer, what I can do is say, 00:11:07.160 --> 00:11:10.450 align:middle line:84% you have to pay me this fixed fee, which 00:11:10.450 --> 00:11:14.410 align:middle line:84% is equal to the area of this region. 00:11:14.410 --> 00:11:16.180 align:middle line:84% And then you can buy as many units 00:11:16.180 --> 00:11:18.430 align:middle line:90% as you want at a cost of c. 00:11:18.430 --> 00:11:22.840 align:middle line:84% And so, for this consumer, again, you 00:11:22.840 --> 00:11:24.760 align:middle line:90% have to pay me this fixed fee. 00:11:24.760 --> 00:11:26.290 align:middle line:84% And then you can buy as many units 00:11:26.290 --> 00:11:28.360 align:middle line:90% as you want at a cost of c. 00:11:28.360 --> 00:11:31.420 align:middle line:84% So for instance, suppose you're a cloud computing provider. 00:11:31.420 --> 00:11:33.910 align:middle line:84% And you have customers who are going 00:11:33.910 --> 00:11:36.850 align:middle line:84% to be doing a lot of calculations on your platform. 00:11:36.850 --> 00:11:38.680 align:middle line:84% What you just have to do is, you want 00:11:38.680 --> 00:11:42.970 align:middle line:84% to charge all the cores that they rent from you and all 00:11:42.970 --> 00:11:45.670 align:middle line:84% the memory they rent from you at your marginal cost 00:11:45.670 --> 00:11:48.485 align:middle line:84% of providing cores and rent to avoid distorting 00:11:48.485 --> 00:11:50.860 align:middle line:84% what they do and make the service as valuable as possible 00:11:50.860 --> 00:11:51.730 align:middle line:90% for them. 00:11:51.730 --> 00:11:53.980 align:middle line:84% And then you make the service as valuable as possible. 00:11:53.980 --> 00:11:56.605 align:middle line:84% And then you extract all of the surplus they would have gotten, 00:11:56.605 --> 00:11:58.670 align:middle line:84% using the service in a fixed fee up front. 00:11:58.670 --> 00:12:03.590 align:middle line:84% So it costs you $2,743,000 to join my platform. 00:12:03.590 --> 00:12:06.945 align:middle line:84% And then you can rent computing costs at a marginal cost. 00:12:06.945 --> 00:12:09.350 align:middle line:90% It costs you $4.7 million. 00:12:09.350 --> 00:12:11.870 align:middle line:84% You just have a different price for every consumer to join. 00:12:11.870 --> 00:12:14.328 align:middle line:84% And then, once they're there, you set the price equal to c. 00:12:14.328 --> 00:12:18.467 align:middle line:90% 00:12:18.467 --> 00:12:20.050 align:middle line:84% In some sense, you could think of that 00:12:20.050 --> 00:12:22.990 align:middle line:84% as maybe that's what happens at Disneyland. 00:12:22.990 --> 00:12:26.530 align:middle line:84% Disneyland, you pay $135 to get into the park. 00:12:26.530 --> 00:12:28.240 align:middle line:90% And then the rides are free. 00:12:28.240 --> 00:12:31.000 align:middle line:84% And the rides are free because the marginal cost of providing 00:12:31.000 --> 00:12:32.870 align:middle line:90% a ride is essentially 0. 00:12:32.870 --> 00:12:36.160 align:middle line:84% So what you want to do is make the rides free, 00:12:36.160 --> 00:12:38.650 align:middle line:84% make the park as valuable as possible, and then extract it 00:12:38.650 --> 00:12:40.900 align:middle line:90% all with these fixed fees, OK? 00:12:40.900 --> 00:12:44.620 align:middle line:84% The difference between Disneyland and this example 00:12:44.620 --> 00:12:48.310 align:middle line:84% is, Disneyland tends to charge everyone the same price. 00:12:48.310 --> 00:12:50.745 align:middle line:84% Here, you would have a customer-specific price. 00:12:50.745 --> 00:12:52.120 align:middle line:84% Every family that walks in, you'd 00:12:52.120 --> 00:12:55.660 align:middle line:84% be like, oh, for you, $833 to go to the park, 00:12:55.660 --> 00:12:58.410 align:middle line:84% for you, $445 to get into the park. 00:12:58.410 --> 00:13:00.410 align:middle line:84% And every customer would have a different price. 00:13:00.410 --> 00:13:02.475 align:middle line:84% But other than that, the rides are free. 00:13:02.475 --> 00:13:06.360 align:middle line:90% 00:13:06.360 --> 00:13:09.610 align:middle line:84% OK, questions on first degree discrimination? 00:13:09.610 --> 00:13:14.020 align:middle line:90% 00:13:14.020 --> 00:13:18.070 align:middle line:84% In reality, there are a number of reasons why we don't do this. 00:13:18.070 --> 00:13:21.310 align:middle line:84% One is, at least before there were these omniscient internet 00:13:21.310 --> 00:13:24.980 align:middle line:84% firms, consumer preferences are typically not observable. 00:13:24.980 --> 00:13:27.320 align:middle line:84% We don't know what the goods are worth to the consumers. 00:13:27.320 --> 00:13:30.030 align:middle line:84% Therefore, we can't do these individual, personalized prices. 00:13:30.030 --> 00:13:32.620 align:middle line:90% 00:13:32.620 --> 00:13:37.600 align:middle line:84% Another constraint is arbitrage or resale across consumers. 00:13:37.600 --> 00:13:39.220 align:middle line:90% So, imagine you did-- 00:13:39.220 --> 00:13:43.420 align:middle line:90% 00:13:43.420 --> 00:13:45.700 align:middle line:90% Netflix is $12.95 a month. 00:13:45.700 --> 00:13:48.310 align:middle line:84% And you get to watch an unlimited number of movies. 00:13:48.310 --> 00:13:51.443 align:middle line:84% You have the problem that, instead of the one person 00:13:51.443 --> 00:13:53.860 align:middle line:84% watching an unlimited number of movies for $12.95 a month, 00:13:53.860 --> 00:13:55.600 align:middle line:84% all their friends and their relatives 00:13:55.600 --> 00:13:58.120 align:middle line:84% can all use the same password and all log in to Netflix 00:13:58.120 --> 00:14:00.600 align:middle line:84% and all watch an unlimited number of movies per month. 00:14:00.600 --> 00:14:03.580 align:middle line:84% So you need to be able to prevent people 00:14:03.580 --> 00:14:06.280 align:middle line:84% from reselling the good across consumers 00:14:06.280 --> 00:14:10.710 align:middle line:84% and having different people consuming off the same pattern. 00:14:10.710 --> 00:14:12.230 align:middle line:84% You could also imagine, you might 00:14:12.230 --> 00:14:13.940 align:middle line:84% want to have something like-- it seems 00:14:13.940 --> 00:14:17.360 align:middle line:84% like, with these statistical packages, 00:14:17.360 --> 00:14:20.330 align:middle line:84% I can get this much power for a very low price. 00:14:20.330 --> 00:14:25.280 align:middle line:84% And then, for a low price, you can get a low number of units. 00:14:25.280 --> 00:14:28.207 align:middle line:84% And then, for a high price, you can get many more units. 00:14:28.207 --> 00:14:30.290 align:middle line:84% You don't want someone just coming up to you twice 00:14:30.290 --> 00:14:31.970 align:middle line:84% and buying the good, and then showing 00:14:31.970 --> 00:14:33.845 align:middle line:84% up again half an hour later and say, OK, now, 00:14:33.845 --> 00:14:37.820 align:middle line:84% I'd like more units also at the low price. 00:14:37.820 --> 00:14:39.770 align:middle line:90% And then administrative costs. 00:14:39.770 --> 00:14:43.190 align:middle line:84% If you think about, where does price discrimination occur, 00:14:43.190 --> 00:14:46.670 align:middle line:84% in the United States, many, many goods 00:14:46.670 --> 00:14:49.287 align:middle line:84% are sold in stores that have prices printed on them. 00:14:49.287 --> 00:14:50.120 align:middle line:90% And you can walk in. 00:14:50.120 --> 00:14:51.140 align:middle line:90% And you buy the good. 00:14:51.140 --> 00:14:53.210 align:middle line:90% And you go home with it. 00:14:53.210 --> 00:14:55.440 align:middle line:84% You go to many developing countries, 00:14:55.440 --> 00:14:57.120 align:middle line:90% that's not the way stores work. 00:14:57.120 --> 00:15:00.320 align:middle line:84% You walk into a store, or a guy's shop. 00:15:00.320 --> 00:15:03.750 align:middle line:84% And you want to buy something, especially if you're a tourist, 00:15:03.750 --> 00:15:07.350 align:middle line:84% and they just start discussing what the price will be. 00:15:07.350 --> 00:15:08.780 align:middle line:84% And there is a long haggling time. 00:15:08.780 --> 00:15:10.155 align:middle line:84% And then, at the end of haggling, 00:15:10.155 --> 00:15:12.710 align:middle line:84% you eventually get to buy what you want to buy. 00:15:12.710 --> 00:15:14.840 align:middle line:90% Why does that happen? 00:15:14.840 --> 00:15:17.510 align:middle line:84% I would say, probably, it's the low cost 00:15:17.510 --> 00:15:19.950 align:middle line:84% of labor in developing country retail. 00:15:19.950 --> 00:15:23.390 align:middle line:84% There's just tremendous excess employees there. 00:15:23.390 --> 00:15:26.580 align:middle line:84% You have these excess employees whose time is worth almost 0. 00:15:26.580 --> 00:15:29.330 align:middle line:84% They can do the hard work of trying to price discriminate, 00:15:29.330 --> 00:15:33.020 align:middle line:84% figure out what it's worth to you, make some extra money. 00:15:33.020 --> 00:15:36.380 align:middle line:84% In the US, we actually we do this for-- 00:15:36.380 --> 00:15:40.820 align:middle line:84% we do haggle over cars and over houses and things, where 00:15:40.820 --> 00:15:42.440 align:middle line:90% it's like, it's a car. 00:15:42.440 --> 00:15:44.688 align:middle line:90% The car is $30,000. 00:15:44.688 --> 00:15:46.730 align:middle line:84% That's enough of a difference that it makes sense 00:15:46.730 --> 00:15:49.460 align:middle line:84% to have a salesperson who's trained in negotiating 00:15:49.460 --> 00:15:52.070 align:middle line:84% and figuring out how much the customer's willingness to pay 00:15:52.070 --> 00:15:53.870 align:middle line:84% and trying to get them to pay a little bit more, 00:15:53.870 --> 00:15:55.745 align:middle line:84% or pay them a little less, or get them to pay 00:15:55.745 --> 00:15:57.180 align:middle line:90% a little less if they need to. 00:15:57.180 --> 00:16:01.748 align:middle line:84% But normally, most goods, it's not worth it. 00:16:01.748 --> 00:16:04.040 align:middle line:84% I think there's a thought that price discrimination may 00:16:04.040 --> 00:16:08.480 align:middle line:84% have gone up with the rise of the internet because a bot 00:16:08.480 --> 00:16:10.520 align:middle line:84% that prices things in a discriminatory way 00:16:10.520 --> 00:16:12.800 align:middle line:84% doesn't charge by the hour for its work, 00:16:12.800 --> 00:16:17.570 align:middle line:84% trying to figure out how to price discriminate among people. 00:16:17.570 --> 00:16:20.630 align:middle line:84% Obviously, you can come up with several examples 00:16:20.630 --> 00:16:23.570 align:middle line:84% where, if these problems are severe, 00:16:23.570 --> 00:16:25.230 align:middle line:84% price discrimination is impossible. 00:16:25.230 --> 00:16:27.470 align:middle line:84% So, for instance, simplest example here, 00:16:27.470 --> 00:16:29.960 align:middle line:84% suppose customers have unit demands. 00:16:29.960 --> 00:16:33.200 align:middle line:84% And there's a competitive resale market. 00:16:33.200 --> 00:16:37.550 align:middle line:84% If there's a competitive resale market, then in that resale 00:16:37.550 --> 00:16:42.380 align:middle line:84% market, the price of the good is going to end up being capital P, 00:16:42.380 --> 00:16:48.030 align:middle line:84% where P is the inverse demand for aggregate demand. 00:16:48.030 --> 00:16:50.360 align:middle line:84% It's going to be P of the total number of units 00:16:50.360 --> 00:16:52.550 align:middle line:90% that got sold in equilibrium. 00:16:52.550 --> 00:16:56.840 align:middle line:84% And so, given that consumers can always buy this good at P* 00:16:56.840 --> 00:16:59.120 align:middle line:84% in the resale market, they're going to buy it from 00:16:59.120 --> 00:17:02.000 align:middle line:84% the monopolist, if and only if the number of units 00:17:02.000 --> 00:17:06.800 align:middle line:84% the monopolist is selling them is less than P* times the number 00:17:06.800 --> 00:17:08.630 align:middle line:84% of units they get, if that's the price. 00:17:08.630 --> 00:17:12.060 align:middle line:84% Therefore, you might as well just directly sell it for P*. 00:17:12.060 --> 00:17:13.360 align:middle line:90% And there's nothing you can do. 00:17:13.360 --> 00:17:17.030 align:middle line:90% 00:17:17.030 --> 00:17:20.420 align:middle line:84% Anyway, I put a couple other examples on there. 00:17:20.420 --> 00:17:25.714 align:middle line:84% Here, I always like finding examples of factors limiting 00:17:25.714 --> 00:17:27.589 align:middle line:84% price discrimination and how, sometimes, it's 00:17:27.589 --> 00:17:29.422 align:middle line:84% harder to price discriminate than you think. 00:17:29.422 --> 00:17:30.840 align:middle line:90% And sometimes, it's easier. 00:17:30.840 --> 00:17:32.940 align:middle line:84% So here's the, it's harder than you think. 00:17:32.940 --> 00:17:35.840 align:middle line:84% There's a story of an Italian supermarket 00:17:35.840 --> 00:17:39.680 align:middle line:84% that had a 20% discount on groceries for anyone over 60. 00:17:39.680 --> 00:17:41.180 align:middle line:84% And they thought that this was going 00:17:41.180 --> 00:17:44.930 align:middle line:84% to be a fantastic plan because senior citizens are 00:17:44.930 --> 00:17:45.810 align:middle line:90% more price-sensitive. 00:17:45.810 --> 00:17:47.310 align:middle line:84% They're willing to shop around more. 00:17:47.310 --> 00:17:48.690 align:middle line:90% They may go to multiple stores. 00:17:48.690 --> 00:17:50.300 align:middle line:84% We'll just offer them all a discount. 00:17:50.300 --> 00:17:51.870 align:middle line:90% And they will buy the goods. 00:17:51.870 --> 00:17:54.470 align:middle line:84% And what they realized, apparently only after a year, 00:17:54.470 --> 00:17:57.110 align:middle line:84% was that a number of seniors in that town 00:17:57.110 --> 00:18:00.270 align:middle line:84% had started businesses of shopping for other people. 00:18:00.270 --> 00:18:02.582 align:middle line:84% And they had become professional shoppers. 00:18:02.582 --> 00:18:04.290 align:middle line:84% You would go hand them your grocery list. 00:18:04.290 --> 00:18:06.470 align:middle line:84% They would walk into the store, buy all the goods, 00:18:06.470 --> 00:18:09.350 align:middle line:84% get the 20% discount, and then split 00:18:09.350 --> 00:18:12.350 align:middle line:84% the money with the customers, who were happy to-- 00:18:12.350 --> 00:18:14.750 align:middle line:84% in some sense, it was a forerunner 00:18:14.750 --> 00:18:15.972 align:middle line:90% to Instacart or whatever. 00:18:15.972 --> 00:18:17.180 align:middle line:90% They would take the discount. 00:18:17.180 --> 00:18:18.600 align:middle line:90% They would give you the stuff. 00:18:18.600 --> 00:18:21.200 align:middle line:84% And then everyone was everyone was better off. 00:18:21.200 --> 00:18:23.887 align:middle line:84% And I guess, when the firm realized that, they decided, 00:18:23.887 --> 00:18:25.970 align:middle line:84% maybe this wasn't such a good price discrimination 00:18:25.970 --> 00:18:27.590 align:middle line:90% scheme after all. 00:18:27.590 --> 00:18:30.465 align:middle line:84% Second example, this is a classic photo. 00:18:30.465 --> 00:18:31.590 align:middle line:90% It doesn't come up so well. 00:18:31.590 --> 00:18:34.048 align:middle line:84% At least, if I turn off these lights, you'll see it better. 00:18:34.048 --> 00:18:37.760 align:middle line:84% But for those of you who are familiar with the Dutch and 00:18:37.760 --> 00:18:41.060 align:middle line:84% French flags, the Dutch and French flags 00:18:41.060 --> 00:18:44.000 align:middle line:84% are very similar, although one is, the stripes are vertical. 00:18:44.000 --> 00:18:45.930 align:middle line:84% And the other, the stripes are horizontal. 00:18:45.930 --> 00:18:49.940 align:middle line:84% But if you're a company that decides to sell pillows online 00:18:49.940 --> 00:18:52.760 align:middle line:84% and you want to make a Dutch flag pillow, 00:18:52.760 --> 00:18:55.790 align:middle line:84% it would look kind of like this, a red stripe, a white stripe, 00:18:55.790 --> 00:18:56.610 align:middle line:90% and a blue stripe. 00:18:56.610 --> 00:18:58.770 align:middle line:84% If you want to make a French flag pillow, 00:18:58.770 --> 00:19:00.812 align:middle line:84% it would look like a blue stripe, a white stripe, 00:19:00.812 --> 00:19:03.140 align:middle line:90% and a red stripe. 00:19:03.140 --> 00:19:06.650 align:middle line:84% Obviously, at some point, they realized, well, 00:19:06.650 --> 00:19:09.530 align:middle line:84% it's the same pillow, just turned on its side. 00:19:09.530 --> 00:19:13.260 align:middle line:84% But somehow, on their website, the website had the two of them 00:19:13.260 --> 00:19:14.020 align:middle line:90% there. 00:19:14.020 --> 00:19:16.140 align:middle line:84% I don't know if Dutch people pay less for pillows 00:19:16.140 --> 00:19:17.070 align:middle line:90% than French people do. 00:19:17.070 --> 00:19:19.720 align:middle line:84% But they had, the Dutch pillow was $9.99. 00:19:19.720 --> 00:19:21.580 align:middle line:90% The French pillow was $15.99. 00:19:21.580 --> 00:19:23.805 align:middle line:84% And I guess you had to count on people 00:19:23.805 --> 00:19:25.680 align:middle line:84% not realizing they could buy the wrong pillow 00:19:25.680 --> 00:19:28.920 align:middle line:84% and just turn it sideways to get the pillow that they-- 00:19:28.920 --> 00:19:30.780 align:middle line:84% the French people could get the Dutch pillow 00:19:30.780 --> 00:19:32.780 align:middle line:84% and turn it on its side and get it more cheaply. 00:19:32.780 --> 00:19:35.910 align:middle line:84% I mean, the reds and the blues are not exactly the same 00:19:35.910 --> 00:19:38.597 align:middle line:84% on the three pillows, on the flags themselves. 00:19:38.597 --> 00:19:40.680 align:middle line:84% But I'm sure, if you bought those pillows, they're 00:19:40.680 --> 00:19:43.560 align:middle line:84% the same pillow, just turned sideways. 00:19:43.560 --> 00:19:46.470 align:middle line:84% And apparently, arbitrage was not 00:19:46.470 --> 00:19:49.310 align:middle line:84% enough to prevent that scheme from working to some degree. 00:19:49.310 --> 00:19:53.250 align:middle line:90% 00:19:53.250 --> 00:20:00.030 align:middle line:84% OK, so, next step, third degree discrimination. 00:20:00.030 --> 00:20:04.920 align:middle line:84% So, suppose the monopolist now can distinguish between classes 00:20:04.920 --> 00:20:09.520 align:middle line:84% of consumers but is limited to using simple linear pricing 00:20:09.520 --> 00:20:10.270 align:middle line:90% within each group. 00:20:10.270 --> 00:20:13.860 align:middle line:84% So for instance, maybe this pillow retailer actually 00:20:13.860 --> 00:20:15.700 align:middle line:90% has two different websites. 00:20:15.700 --> 00:20:17.730 align:middle line:84% They have a Dutch website that's only in Dutch 00:20:17.730 --> 00:20:20.050 align:middle line:84% and a French website that's only in French. 00:20:20.050 --> 00:20:21.902 align:middle line:84% And so they can just set different prices 00:20:21.902 --> 00:20:22.860 align:middle line:90% in different countries. 00:20:22.860 --> 00:20:25.483 align:middle line:84% And consumers can't see the other website. 00:20:25.483 --> 00:20:28.890 align:middle line:90% 00:20:28.890 --> 00:20:31.380 align:middle line:84% So anyway, so I'm going to have two groups. 00:20:31.380 --> 00:20:32.440 align:middle line:90% i equals 1 and 2. 00:20:32.440 --> 00:20:35.370 align:middle line:84% This will also be students and non-students. 00:20:35.370 --> 00:20:39.210 align:middle line:84% Each group has a demand, Xi, of p. 00:20:39.210 --> 00:20:41.940 align:middle line:84% And then, again, I'm going to go with the constant marginal cost 00:20:41.940 --> 00:20:44.250 align:middle line:90% of c. 00:20:44.250 --> 00:20:47.250 align:middle line:84% Here, I think what I'm going to do is think about group 1 00:20:47.250 --> 00:20:50.820 align:middle line:84% as being the students, or the low demand consumers, 00:20:50.820 --> 00:20:56.820 align:middle line:84% and group 2 as being the higher demand consumers. 00:20:56.820 --> 00:21:00.273 align:middle line:90% OK, so this is population 2. 00:21:00.273 --> 00:21:03.000 align:middle line:90% 00:21:03.000 --> 00:21:04.410 align:middle line:90% I put price in this axis. 00:21:04.410 --> 00:21:06.000 align:middle line:90% I guess I switched. 00:21:06.000 --> 00:21:09.390 align:middle line:90% So this is x1 of p. 00:21:09.390 --> 00:21:12.360 align:middle line:90% This is x2 of p. 00:21:12.360 --> 00:21:14.132 align:middle line:84% So, at any price, the students are 00:21:14.132 --> 00:21:15.840 align:middle line:84% willing to pay less than the non-students 00:21:15.840 --> 00:21:18.780 align:middle line:84% because, presumably, they have less money. 00:21:18.780 --> 00:21:22.770 align:middle line:84% So anyway, with discrimination, what are you going to do? 00:21:22.770 --> 00:21:25.050 align:middle line:84% Within each population, i, you're 00:21:25.050 --> 00:21:29.340 align:middle line:84% just going to maximize pi minus c times Xi of pi. 00:21:29.340 --> 00:21:32.580 align:middle line:84% This is just the monopoly pricing problem. 00:21:32.580 --> 00:21:35.130 align:middle line:84% So the monopoly pricing problem has the marginal revenue 00:21:35.130 --> 00:21:37.620 align:middle line:84% equals marginal cost first order condition. 00:21:37.620 --> 00:21:41.040 align:middle line:84% Price minus cost over price is 1 over the negative 1 00:21:41.040 --> 00:21:44.130 align:middle line:84% over the elasticity of demand, just like it was last week. 00:21:44.130 --> 00:21:51.520 align:middle line:84% And so, let me just say here, let's suppose we have cost here. 00:21:51.520 --> 00:21:54.630 align:middle line:90% So this is p1*. 00:21:54.630 --> 00:21:57.480 align:middle line:90% And then, this is cost. 00:21:57.480 --> 00:21:59.970 align:middle line:90% This is p2*. 00:21:59.970 --> 00:22:02.490 align:middle line:84% So I'm going to assume that-- label the markets, 00:22:02.490 --> 00:22:04.770 align:middle line:84% that the monopoly price in market 1 00:22:04.770 --> 00:22:07.175 align:middle line:84% is smaller than the monopoly price in market 2. 00:22:07.175 --> 00:22:10.780 align:middle line:90% 00:22:10.780 --> 00:22:13.060 align:middle line:84% So third degree discrimination, if you're 00:22:13.060 --> 00:22:16.120 align:middle line:84% allowed to practice it, is just monopoly pricing market 00:22:16.120 --> 00:22:16.710 align:middle line:90% by market. 00:22:16.710 --> 00:22:22.760 align:middle line:90% 00:22:22.760 --> 00:22:24.470 align:middle line:84% Interesting questions that come up 00:22:24.470 --> 00:22:26.720 align:middle line:84% in third degree discrimination is, 00:22:26.720 --> 00:22:29.870 align:middle line:84% what if you decide that discrimination should not 00:22:29.870 --> 00:22:34.140 align:middle line:84% be allowed and we want to ban price discrimination? 00:22:34.140 --> 00:22:37.835 align:middle line:90% 00:22:37.835 --> 00:22:38.710 align:middle line:90% You know what we say? 00:22:38.710 --> 00:22:41.350 align:middle line:84% And generally, we have a funny relationship 00:22:41.350 --> 00:22:42.850 align:middle line:84% with price discrimination in the US. 00:22:42.850 --> 00:22:45.058 align:middle line:84% So there is something called the Robinson-Patman Act, 00:22:45.058 --> 00:22:48.310 align:middle line:84% which dates to the early 20th century. 00:22:48.310 --> 00:22:51.360 align:middle line:84% Robinson-Patman Act bans price discrimination. 00:22:51.360 --> 00:22:54.120 align:middle line:84% But it bans price discrimination to the extent 00:22:54.120 --> 00:22:56.050 align:middle line:90% that it harms competition. 00:22:56.050 --> 00:22:58.590 align:middle line:84% And so, it was originally developed for things 00:22:58.590 --> 00:23:03.990 align:middle line:84% like not allowing the railroads to charge 00:23:03.990 --> 00:23:07.140 align:middle line:84% one firm more for shipping oil than another firm for shipping 00:23:07.140 --> 00:23:09.420 align:middle line:84% oil in order to create an oil monopoly on the East 00:23:09.420 --> 00:23:12.390 align:middle line:84% Coast of the US, or something like that. 00:23:12.390 --> 00:23:17.850 align:middle line:84% It's typically not applied to retail price discrimination 00:23:17.850 --> 00:23:19.530 align:middle line:84% or price discrimination that isn't 00:23:19.530 --> 00:23:22.140 align:middle line:84% going to be harming competition of something, where 00:23:22.140 --> 00:23:26.340 align:middle line:84% you're providing an intermediate input to some downstream firms. 00:23:26.340 --> 00:23:29.250 align:middle line:84% But there's some times when we think that price discrimination 00:23:29.250 --> 00:23:30.510 align:middle line:90% is OK. 00:23:30.510 --> 00:23:34.260 align:middle line:84% Somehow, it's OK to give senior citizen discounts. 00:23:34.260 --> 00:23:37.440 align:middle line:90% 00:23:37.440 --> 00:23:39.360 align:middle line:84% It's OK to give student discounts. 00:23:39.360 --> 00:23:41.740 align:middle line:84% But it's not OK to charge people extra. 00:23:41.740 --> 00:23:43.173 align:middle line:90% So I don't quite know how it is. 00:23:43.173 --> 00:23:44.340 align:middle line:90% It's like, discounts are OK. 00:23:44.340 --> 00:23:48.780 align:middle line:84% Charging someone more would be totally inappropriate. 00:23:48.780 --> 00:23:52.703 align:middle line:84% If you had a women's surcharge that is, 00:23:52.703 --> 00:23:54.120 align:middle line:84% we have a price in our restaurant. 00:23:54.120 --> 00:23:56.010 align:middle line:90% And women have to pay 10% more. 00:23:56.010 --> 00:23:58.406 align:middle line:84% That would be considered completely inappropriate. 00:23:58.406 --> 00:24:02.520 align:middle line:90% 00:24:02.520 --> 00:24:08.400 align:middle line:84% Or if there's a big storm, we have a surcharge 00:24:08.400 --> 00:24:11.760 align:middle line:84% on gasoline or firewood or whatever, 00:24:11.760 --> 00:24:14.100 align:middle line:84% because there's been some natural disaster. 00:24:14.100 --> 00:24:16.900 align:middle line:84% Discrimination there is just completely inappropriate. 00:24:16.900 --> 00:24:22.110 align:middle line:84% And there are anti-price-gouging laws that prevent that. 00:24:22.110 --> 00:24:24.900 align:middle line:84% So anyway, what are we going to do in this market 00:24:24.900 --> 00:24:28.403 align:middle line:84% if you decide to ban price discrimination? 00:24:28.403 --> 00:24:30.070 align:middle line:84% Well, you're just going to maximize over 00:24:30.070 --> 00:24:35.400 align:middle line:84% a single price, p, p minus c, x1 of p, plus p minus cX2 of p. 00:24:35.400 --> 00:24:38.770 align:middle line:90% 00:24:38.770 --> 00:24:41.520 align:middle line:84% If you want to think about what the first order condition looks 00:24:41.520 --> 00:24:44.430 align:middle line:90% like, you just have-- 00:24:44.430 --> 00:24:50.130 align:middle line:84% the single good case we had this was d-pi i-dp You just are 00:24:50.130 --> 00:24:54.180 align:middle line:84% adding that up across the two markets and getting 00:24:54.180 --> 00:24:57.210 align:middle line:84% the derivative of profit with respect to p in market 1, 00:24:57.210 --> 00:25:01.380 align:middle line:84% plus d(pi)/d(p) in market 2 equals 0. 00:25:01.380 --> 00:25:02.595 align:middle line:90% What's that going to do? 00:25:02.595 --> 00:25:07.770 align:middle line:84% The most standard result is that, if demand is well-behaved, 00:25:07.770 --> 00:25:11.370 align:middle line:84% by which I mean two things, demand is single-peaked 00:25:11.370 --> 00:25:15.360 align:middle line:84% and it's concave in p when p is less than p2*, 00:25:15.360 --> 00:25:17.940 align:middle line:84% then what the firm does is, when you ban discrimination, 00:25:17.940 --> 00:25:20.020 align:middle line:84% they just choose an intermediate price. 00:25:20.020 --> 00:25:24.700 align:middle line:84% The consumers, the students, are hurt by the price going up. 00:25:24.700 --> 00:25:27.750 align:middle line:84% The non-students are helped by the price going down. 00:25:27.750 --> 00:25:30.690 align:middle line:90% And why is that going to happen? 00:25:30.690 --> 00:25:31.865 align:middle line:90% If you think about it-- 00:25:31.865 --> 00:25:37.440 align:middle line:90% 00:25:37.440 --> 00:25:44.440 align:middle line:84% OK, so, this thing has a-- this was the monopoly price here. 00:25:44.440 --> 00:25:53.160 align:middle line:84% So if I look at d(pi1)/d(P), that's what it looks like. 00:25:53.160 --> 00:25:56.130 align:middle line:84% d(pi)/d(P), if profit is concave, 00:25:56.130 --> 00:25:58.180 align:middle line:84% then d-pi dp is downward-sloping. 00:25:58.180 --> 00:26:01.200 align:middle line:90% It crosses 0 at p1*. 00:26:01.200 --> 00:26:08.790 align:middle line:84% And in this example, if I graph d(pi2)/d(P), again, 00:26:08.790 --> 00:26:10.060 align:middle line:90% it's downward-sloping. 00:26:10.060 --> 00:26:11.520 align:middle line:90% It crosses 0 at p2*. 00:26:11.520 --> 00:26:14.480 align:middle line:90% 00:26:14.480 --> 00:26:16.280 align:middle line:84% So then, if you ask, well, what if I just 00:26:16.280 --> 00:26:21.020 align:middle line:84% add this one and this one, I have one function 00:26:21.020 --> 00:26:23.420 align:middle line:90% that's going negative here. 00:26:23.420 --> 00:26:27.050 align:middle line:84% I have another function that's going negative here. 00:26:27.050 --> 00:26:32.090 align:middle line:84% The optimal price, p*, is just the amount by which this one is 00:26:32.090 --> 00:26:34.590 align:middle line:84% negative equals the amount by this one is positive, 00:26:34.590 --> 00:26:37.430 align:middle line:84% so that the sum of the two first order conditions is 0. 00:26:37.430 --> 00:26:41.090 align:middle line:84% And as I've drawn it, here, this one is positive. 00:26:41.090 --> 00:26:42.200 align:middle line:90% And this one's 0. 00:26:42.200 --> 00:26:44.700 align:middle line:84% Here, this one's positive, and this one's negative. 00:26:44.700 --> 00:26:48.230 align:middle line:84% So obviously, the p* is going to be in between. 00:26:48.230 --> 00:26:54.830 align:middle line:84% And what I needed to do to say that is that, 00:26:54.830 --> 00:26:58.280 align:middle line:84% if these things are concave, then those first order 00:26:58.280 --> 00:27:00.060 align:middle line:84% conditions are both downward-sloping. 00:27:00.060 --> 00:27:02.227 align:middle line:84% And so, when they're downward-sloping, this happens. 00:27:02.227 --> 00:27:07.070 align:middle line:90% 00:27:07.070 --> 00:27:11.930 align:middle line:84% Just one comment on elasticities, 00:27:11.930 --> 00:27:17.690 align:middle line:84% still, we just have this new demand, x of p, 00:27:17.690 --> 00:27:23.150 align:middle line:84% which is equal to x1 of p plus x2 of p. 00:27:23.150 --> 00:27:27.990 align:middle line:84% Your inverse elasticity pricing based on this aggregate demand-- 00:27:27.990 --> 00:27:31.610 align:middle line:84% and just to note, when you look at an aggregate demand, 00:27:31.610 --> 00:27:34.280 align:middle line:84% the elasticity in a market that's 00:27:34.280 --> 00:27:36.710 align:middle line:84% a component of two sub-markets is just 00:27:36.710 --> 00:27:38.780 align:middle line:84% a weighted average of the elasticities 00:27:38.780 --> 00:27:41.052 align:middle line:90% in the individual markets. 00:27:41.052 --> 00:27:43.010 align:middle line:84% And it's a weighted average of the elasticities 00:27:43.010 --> 00:27:46.730 align:middle line:84% in the individual markets, but where you're waiting 00:27:46.730 --> 00:27:48.570 align:middle line:90% by the share of the market. 00:27:48.570 --> 00:27:51.200 align:middle line:84% So if there's a market that has more customers buying 00:27:51.200 --> 00:27:55.880 align:middle line:84% at that price, it gets a larger weight than one that's smaller. 00:27:55.880 --> 00:27:58.310 align:middle line:84% So it is the case that this is, again, another reason 00:27:58.310 --> 00:27:59.960 align:middle line:84% to think about why it's intermediate 00:27:59.960 --> 00:28:02.690 align:middle line:84% is, you have the high elasticity market. 00:28:02.690 --> 00:28:04.610 align:middle line:84% You have the low elasticity market. 00:28:04.610 --> 00:28:06.955 align:middle line:84% The combined market has an intermediate elasticity, 00:28:06.955 --> 00:28:08.830 align:middle line:84% which is a weighted average of the other two. 00:28:08.830 --> 00:28:12.360 align:middle line:84% So, therefore, it's in between, OK? 00:28:12.360 --> 00:28:15.630 align:middle line:90% 00:28:15.630 --> 00:28:18.193 align:middle line:84% Well, this is what we think of as the normal case. 00:28:18.193 --> 00:28:21.180 align:middle line:90% 00:28:21.180 --> 00:28:26.370 align:middle line:84% I was assuming that pi* is concave. 00:28:26.370 --> 00:28:32.250 align:middle line:84% Profit functions are never concave, pretty much. 00:28:32.250 --> 00:28:34.260 align:middle line:84% What do profit functions look like? 00:28:34.260 --> 00:28:38.370 align:middle line:90% We normally draw them like this. 00:28:38.370 --> 00:28:40.710 align:middle line:84% But we ignore the fact that profits 00:28:40.710 --> 00:28:43.290 align:middle line:84% don't go to negative infinity as p goes to infinity. 00:28:43.290 --> 00:28:46.300 align:middle line:84% As p goes to infinity, people stop buying your product. 00:28:46.300 --> 00:28:49.290 align:middle line:84% So what profit functions look like in practice is, 00:28:49.290 --> 00:28:50.430 align:middle line:90% they go like this. 00:28:50.430 --> 00:28:53.730 align:middle line:84% And then they asymptote to 0 as p goes to infinity. 00:28:53.730 --> 00:28:56.970 align:middle line:84% So they're concave part of the time. 00:28:56.970 --> 00:29:01.430 align:middle line:84% And then they become convex, as p gets large. 00:29:01.430 --> 00:29:04.160 align:middle line:84% And if you think about what happens 00:29:04.160 --> 00:29:08.180 align:middle line:84% when this is what profits look like, 00:29:08.180 --> 00:29:12.620 align:middle line:84% imagine what I have is the profit in the low demand market 00:29:12.620 --> 00:29:15.020 align:middle line:90% looks like this. 00:29:15.020 --> 00:29:19.310 align:middle line:84% And the profit in the high demand market 00:29:19.310 --> 00:29:22.490 align:middle line:90% looks like this, OK? 00:29:22.490 --> 00:29:25.360 align:middle line:84% What do I get when I add those two together? 00:29:25.360 --> 00:29:27.400 align:middle line:84% I get something that goes like this. 00:29:27.400 --> 00:29:31.700 align:middle line:90% 00:29:31.700 --> 00:29:39.500 align:middle line:84% In some sense, after some point, when this one 00:29:39.500 --> 00:29:41.390 align:middle line:84% becomes essentially 0, this curve 00:29:41.390 --> 00:29:44.300 align:middle line:90% just coincides with this curve. 00:29:44.300 --> 00:29:46.820 align:middle line:84% So if I'm adding together one profit that 00:29:46.820 --> 00:29:49.350 align:middle line:84% looks like this and one profit that looks like this, 00:29:49.350 --> 00:29:51.860 align:middle line:84% there may be this bump over here on the left side, 00:29:51.860 --> 00:29:54.440 align:middle line:84% or maybe there isn't even a bump on the left side. 00:29:54.440 --> 00:29:59.960 align:middle line:84% But the maximizer here can just coincide. 00:29:59.960 --> 00:30:03.530 align:middle line:84% If this one, imagine, no student is willing to pay more than $100 00:30:03.530 --> 00:30:06.150 align:middle line:84% for a ticket to the A.R.T. or something like that. 00:30:06.150 --> 00:30:07.700 align:middle line:90% Then this just hits 0. 00:30:07.700 --> 00:30:10.560 align:middle line:84% When this hits 0, these things coincide. 00:30:10.560 --> 00:30:12.650 align:middle line:84% And what you do is you just abandon 00:30:12.650 --> 00:30:15.700 align:middle line:84% market 1 and monopoly price in market 2. 00:30:15.700 --> 00:30:19.890 align:middle line:90% 00:30:19.890 --> 00:30:26.970 align:middle line:84% So if you have that case where the concavity is not 00:30:26.970 --> 00:30:29.430 align:middle line:84% applying in the relevant region, you don't necessarily 00:30:29.430 --> 00:30:31.240 align:middle line:84% get the intermediate pricing result. 00:30:31.240 --> 00:30:34.680 align:middle line:84% You can get the just price to market 2 result. 00:30:34.680 --> 00:30:39.150 align:middle line:84% If you just price to market 2, then, clearly, 00:30:39.150 --> 00:30:42.390 align:middle line:84% if when you price discriminate, you just price to market 2 00:30:42.390 --> 00:30:44.370 align:middle line:84% and you eliminate the student discount, 00:30:44.370 --> 00:30:46.890 align:middle line:84% then, clearly, everybody is worse off. 00:30:46.890 --> 00:30:49.050 align:middle line:84% The monopolist makes less money because it's now 00:30:49.050 --> 00:30:50.913 align:middle line:84% no longer selling to any students. 00:30:50.913 --> 00:30:52.830 align:middle line:84% The students are worse off because they're not 00:30:52.830 --> 00:30:53.770 align:middle line:90% buying any tickets. 00:30:53.770 --> 00:30:56.860 align:middle line:84% They get zero surplus instead of getting positive surplus. 00:30:56.860 --> 00:31:03.720 align:middle line:84% So that's a case where there's a clear profit and social welfare 00:31:03.720 --> 00:31:05.640 align:middle line:84% and consumer surplus advantage to allowing 00:31:05.640 --> 00:31:07.150 align:middle line:90% price discrimination. 00:31:07.150 --> 00:31:12.800 align:middle line:90% 00:31:12.800 --> 00:31:15.710 align:middle line:84% In general, the monopoly result is fully general. 00:31:15.710 --> 00:31:17.660 align:middle line:84% Monopolies always benefit from price 00:31:17.660 --> 00:31:20.870 align:middle line:84% discriminating because they could always choose not to. 00:31:20.870 --> 00:31:23.420 align:middle line:84% The monopolist could be told, OK, this customer is in France. 00:31:23.420 --> 00:31:25.700 align:middle line:84% This customer is in the Netherlands. 00:31:25.700 --> 00:31:27.840 align:middle line:84% They could just ignore that and set the same price. 00:31:27.840 --> 00:31:30.650 align:middle line:84% So the fact that they choose to set different prices 00:31:30.650 --> 00:31:33.020 align:middle line:84% means they're always better off discriminating. 00:31:33.020 --> 00:31:37.190 align:middle line:84% But whether consumer surplus and social welfare change, 00:31:37.190 --> 00:31:40.610 align:middle line:90% that's a different story. 00:31:40.610 --> 00:31:42.440 align:middle line:84% This normal case, we have the sense 00:31:42.440 --> 00:31:45.030 align:middle line:84% that some consumers would like you to stop discriminating. 00:31:45.030 --> 00:31:47.420 align:middle line:84% Some don't want you to stop discriminating. 00:31:47.420 --> 00:31:48.865 align:middle line:90% But that's not always true. 00:31:48.865 --> 00:31:52.630 align:middle line:90% 00:31:52.630 --> 00:31:56.410 align:middle line:90% OK, a little more about welfare. 00:31:56.410 --> 00:32:00.340 align:middle line:84% So to think about aggregate social welfare of price 00:32:00.340 --> 00:32:03.280 align:middle line:84% discrimination, you have to think about two 00:32:03.280 --> 00:32:05.090 align:middle line:90% different welfare effects. 00:32:05.090 --> 00:32:08.920 align:middle line:84% So, one welfare effect of price discrimination, or not 00:32:08.920 --> 00:32:11.150 align:middle line:84% allowing price discrimination, is deadweight loss. 00:32:11.150 --> 00:32:12.910 align:middle line:84% How many consumers are there who would 00:32:12.910 --> 00:32:14.530 align:middle line:84% be willing to pay what it cost, who 00:32:14.530 --> 00:32:18.640 align:middle line:84% would like to buy the good at cost, who don't get served? 00:32:18.640 --> 00:32:23.380 align:middle line:84% And then, the new problem we get in price discrimination 00:32:23.380 --> 00:32:26.590 align:middle line:84% is misallocation of goods sold, that when 00:32:26.590 --> 00:32:28.450 align:middle line:84% you sell the goods at different prices, 00:32:28.450 --> 00:32:32.300 align:middle line:84% there are high value people who are not buying the good. 00:32:32.300 --> 00:32:36.010 align:middle line:84% And there are people with lower values who are getting the good. 00:32:36.010 --> 00:32:41.290 align:middle line:84% So, for instance, let's think of a hypothetical world 00:32:41.290 --> 00:32:45.070 align:middle line:84% where, somehow, Apple has two markets 00:32:45.070 --> 00:32:47.620 align:middle line:90% to which they sell iPhones. 00:32:47.620 --> 00:32:51.520 align:middle line:84% They sell iPhones to people who want to use them as phones. 00:32:51.520 --> 00:32:53.060 align:middle line:84% And they also sell iPhones to people 00:32:53.060 --> 00:32:55.280 align:middle line:84% who want to use them as paper weights. 00:32:55.280 --> 00:32:57.590 align:middle line:84% And somehow, they have this ability 00:32:57.590 --> 00:32:59.390 align:middle line:90% to restrict you when you buy it. 00:32:59.390 --> 00:33:02.130 align:middle line:84% I'm in the paperweight market or I'm in the phone market. 00:33:02.130 --> 00:33:04.047 align:middle line:84% And if you only buy in the paperweight market, 00:33:04.047 --> 00:33:06.440 align:middle line:84% they ensure that the phone actually won't ever work. 00:33:06.440 --> 00:33:07.740 align:middle line:90% It's still a working phone. 00:33:07.740 --> 00:33:09.560 align:middle line:84% They just somehow manage to block you 00:33:09.560 --> 00:33:11.840 align:middle line:90% from ever getting service on it. 00:33:11.840 --> 00:33:15.350 align:middle line:84% If you imagine that world, it would be a funny world 00:33:15.350 --> 00:33:17.960 align:middle line:84% where you have some people who would 00:33:17.960 --> 00:33:20.630 align:middle line:84% like to pay $700 for an iPhone and who 00:33:20.630 --> 00:33:24.500 align:middle line:84% don't get to have an iPhone because the price is $799. 00:33:24.500 --> 00:33:26.330 align:middle line:90% And then you have other people-- 00:33:26.330 --> 00:33:28.020 align:middle line:90% or maybe it's a kids toy. 00:33:28.020 --> 00:33:31.700 align:middle line:84% It's an iPhone kids toy that's actually a functioning iPhone. 00:33:31.700 --> 00:33:34.800 align:middle line:90% And they get to buy it for $50. 00:33:34.800 --> 00:33:37.040 align:middle line:84% And then, so you have someone who 00:33:37.040 --> 00:33:41.608 align:middle line:84% has this value for $50 for this toy who's 00:33:41.608 --> 00:33:43.400 align:middle line:84% getting to use the toy, and someone someone 00:33:43.400 --> 00:33:45.960 align:middle line:84% who's buying the phone at $700 isn't getting it. 00:33:45.960 --> 00:33:47.803 align:middle line:84% There's this gains from trade where, 00:33:47.803 --> 00:33:49.220 align:middle line:84% if the person owning the toy phone 00:33:49.220 --> 00:33:51.740 align:middle line:84% could hand it to the person who wants to use the phone, 00:33:51.740 --> 00:33:55.550 align:middle line:84% there'd be this big gain in social surplus. 00:33:55.550 --> 00:34:02.300 align:middle line:84% But you're going to get that any time you have a senior citizen 00:34:02.300 --> 00:34:02.820 align:middle line:90% discount. 00:34:02.820 --> 00:34:05.270 align:middle line:84% Someone who doesn't even really want to go to the play 00:34:05.270 --> 00:34:07.721 align:middle line:84% is there and paying because it's only $15. 00:34:07.721 --> 00:34:09.679 align:middle line:84% And it was cheaper than going to the movie they 00:34:09.679 --> 00:34:10.802 align:middle line:90% would have rather seen. 00:34:10.802 --> 00:34:12.260 align:middle line:84% And then, you have someone else who 00:34:12.260 --> 00:34:14.552 align:middle line:84% would have liked to go who would be willing to pay $60, 00:34:14.552 --> 00:34:15.300 align:middle line:90% but isn't there. 00:34:15.300 --> 00:34:16.739 align:middle line:90% And there would be this-- 00:34:16.739 --> 00:34:18.739 align:middle line:84% you could just make this swap of, I'll trade you 00:34:18.739 --> 00:34:20.090 align:middle line:90% my play ticket. 00:34:20.090 --> 00:34:22.280 align:middle line:84% And I'll give you a ticket to the movie 00:34:22.280 --> 00:34:24.080 align:middle line:90% in the theater next door. 00:34:24.080 --> 00:34:26.480 align:middle line:90% We're both better off. 00:34:26.480 --> 00:34:31.300 align:middle line:84% Anyway, so there's that misallocation of goods utility. 00:34:31.300 --> 00:34:34.760 align:middle line:84% A proposition just highlighting the second effect 00:34:34.760 --> 00:34:38.389 align:middle line:84% is, if third degree discrimination doesn't increase 00:34:38.389 --> 00:34:41.120 align:middle line:84% total output relative to uniform pricing, 00:34:41.120 --> 00:34:43.187 align:middle line:90% then it reduces social welfare. 00:34:43.187 --> 00:34:45.770 align:middle line:84% And this is going to be because if it doesn't increase output, 00:34:45.770 --> 00:34:48.060 align:middle line:84% it's not helping with deadweight loss. 00:34:48.060 --> 00:34:50.210 align:middle line:84% And so, if it's not helping with deadweight loss, 00:34:50.210 --> 00:34:51.332 align:middle line:90% it creates misallocation. 00:34:51.332 --> 00:34:54.199 align:middle line:84% And therefore, people are worse off. 00:34:54.199 --> 00:34:56.920 align:middle line:90% So here's a proof. 00:34:56.920 --> 00:35:00.880 align:middle line:84% So imagine, we start from a situation 00:35:00.880 --> 00:35:03.160 align:middle line:90% where we have uniform pricing. 00:35:03.160 --> 00:35:08.860 align:middle line:84% And then we switch to discriminatory pricing. 00:35:08.860 --> 00:35:13.570 align:middle line:84% And I'm going to write delta x1 and delta x2 00:35:13.570 --> 00:35:17.620 align:middle line:90% for how does demand change. 00:35:17.620 --> 00:35:20.935 align:middle line:84% So I'm going to write delta xi to be 00:35:20.935 --> 00:35:29.110 align:middle line:84% xi under discriminatory pricing, minus-- 00:35:29.110 --> 00:35:31.900 align:middle line:84% under discriminatory pricing, minus the xi 00:35:31.900 --> 00:35:33.045 align:middle line:90% under uniform pricing. 00:35:33.045 --> 00:35:36.200 align:middle line:90% 00:35:36.200 --> 00:35:37.607 align:middle line:90% So here's a picture here. 00:35:37.607 --> 00:35:39.440 align:middle line:84% I guess I'll use this one instead of drawing 00:35:39.440 --> 00:35:40.550 align:middle line:90% a new one on the board. 00:35:40.550 --> 00:35:46.190 align:middle line:84% So if we had uniform pricing, this was going to be the price, 00:35:46.190 --> 00:35:47.340 align:middle line:90% p*. 00:35:47.340 --> 00:35:50.540 align:middle line:84% This would be the number of units sold, x*. 00:35:50.540 --> 00:35:52.920 align:middle line:84% And then, so this is the student market. 00:35:52.920 --> 00:35:56.120 align:middle line:84% These are the lower value consumers. 00:35:56.120 --> 00:35:58.850 align:middle line:84% When you start discriminating, you give them a price cut. 00:35:58.850 --> 00:36:01.740 align:middle line:84% You cut their price from p to p*. 00:36:01.740 --> 00:36:03.620 align:middle line:90% We get a positive delta xi. 00:36:03.620 --> 00:36:06.190 align:middle line:84% They buy this many units instead of this many units. 00:36:06.190 --> 00:36:10.010 align:middle line:90% 00:36:10.010 --> 00:36:12.170 align:middle line:84% So a comment is, if I think about, 00:36:12.170 --> 00:36:14.550 align:middle line:84% what is the welfare gain in this market, 00:36:14.550 --> 00:36:16.010 align:middle line:84% the welfare gain in this market is, 00:36:16.010 --> 00:36:19.010 align:middle line:84% I've reduced deadweight loss by this much, 00:36:19.010 --> 00:36:24.790 align:middle line:84% this trapezoid here, because all of these units that were not 00:36:24.790 --> 00:36:26.540 align:middle line:84% formally getting purchased are now getting 00:36:26.540 --> 00:36:28.470 align:middle line:90% purchased at the lower price. 00:36:28.470 --> 00:36:30.710 align:middle line:84% And then this is the amount of surplus 00:36:30.710 --> 00:36:34.250 align:middle line:84% that's being generated on each of those units that's 00:36:34.250 --> 00:36:35.460 align:middle line:90% being purchased. 00:36:35.460 --> 00:36:38.480 align:middle line:84% So what I get is, if you think about this trapezoid, 00:36:38.480 --> 00:36:41.090 align:middle line:84% it's bounded by the big rectangle 00:36:41.090 --> 00:36:42.360 align:middle line:90% and the little rectangle. 00:36:42.360 --> 00:36:47.660 align:middle line:84% And so that tells me that p* minus c times delta xi, 00:36:47.660 --> 00:36:50.990 align:middle line:84% that's the big rectangle, is bigger than delta Wi, 00:36:50.990 --> 00:36:54.930 align:middle line:84% is bigger than pi* minus c, times delta xi. 00:36:54.930 --> 00:36:59.900 align:middle line:84% So pi* minus c is the area of this little rectangle. 00:36:59.900 --> 00:37:02.090 align:middle line:84% That doesn't quite line up, but underneath. 00:37:02.090 --> 00:37:05.070 align:middle line:84% And then p* minus c is the height of the big rectangle. 00:37:05.070 --> 00:37:08.210 align:middle line:84% So the change in welfare is bounded between those two. 00:37:08.210 --> 00:37:10.230 align:middle line:90% Notice, the same is true-- 00:37:10.230 --> 00:37:15.390 align:middle line:84% if there's another market where I reduce, I raise the price 00:37:15.390 --> 00:37:20.520 align:middle line:84% and I reduce the demand, again, the loss 00:37:20.520 --> 00:37:23.400 align:middle line:84% is going to be this trapezoid over here. 00:37:23.400 --> 00:37:26.340 align:middle line:84% And the loss with that trapezoid is going to be bounded between 00:37:26.340 --> 00:37:30.630 align:middle line:84% two rectangles, one being the p* minus c, which is now negative, 00:37:30.630 --> 00:37:33.340 align:middle line:84% the other being the pi* minus c, which is here. 00:37:33.340 --> 00:37:35.880 align:middle line:84% And with the negative numbers, the same inequality 00:37:35.880 --> 00:37:36.605 align:middle line:90% is still true. 00:37:36.605 --> 00:37:39.240 align:middle line:90% 00:37:39.240 --> 00:37:41.980 align:middle line:84% It's now, pi* minus c is the big negative number. 00:37:41.980 --> 00:37:43.510 align:middle line:84% This is the small negative number. 00:37:43.510 --> 00:37:45.420 align:middle line:84% It is in between the big negative number 00:37:45.420 --> 00:37:48.120 align:middle line:90% and the small negative number. 00:37:48.120 --> 00:37:55.850 align:middle line:84% So if I just now add that across markets, summing over i, 00:37:55.850 --> 00:37:57.290 align:middle line:90% I sum this over markets, i. 00:37:57.290 --> 00:38:01.710 align:middle line:84% I get p* minus c times the sum of delta xi is bigger than 00:38:01.710 --> 00:38:04.260 align:middle line:84% the change in welfare, which is bigger than the sum over i 00:38:04.260 --> 00:38:07.140 align:middle line:90% of pi* minus c delta xi. 00:38:07.140 --> 00:38:10.200 align:middle line:84% And the left one is the one that's really involved 00:38:10.200 --> 00:38:11.970 align:middle line:90% in proving the proposition. 00:38:11.970 --> 00:38:16.380 align:middle line:84% If the sum of the delta xi*, if the sum of the delta xi's is 0 00:38:16.380 --> 00:38:20.430 align:middle line:84% or negative, then this is 0 or a negative number. 00:38:20.430 --> 00:38:22.920 align:middle line:84% And it's bigger than the change in welfare. 00:38:22.920 --> 00:38:25.200 align:middle line:84% So the change in welfare is negative 00:38:25.200 --> 00:38:26.795 align:middle line:90% if output hasn't gone up. 00:38:26.795 --> 00:38:36.360 align:middle line:90% 00:38:36.360 --> 00:38:39.050 align:middle line:90% OK, so some comments on here. 00:38:39.050 --> 00:38:43.080 align:middle line:90% 00:38:43.080 --> 00:38:44.443 align:middle line:90% This is a result about welfare. 00:38:44.443 --> 00:38:46.860 align:middle line:84% It's highlighting that there's that misallocation of goods 00:38:46.860 --> 00:38:47.710 align:middle line:90% sold. 00:38:47.710 --> 00:38:50.200 align:middle line:90% Obviously, output can go up. 00:38:50.200 --> 00:38:53.130 align:middle line:84% If output goes up, and output goes up by enough, 00:38:53.130 --> 00:38:58.230 align:middle line:84% then welfare can be higher with price discrimination. 00:38:58.230 --> 00:39:02.100 align:middle line:84% One example of that would be in the model 00:39:02.100 --> 00:39:06.072 align:middle line:84% where you only serve one market when you're discriminating. 00:39:06.072 --> 00:39:07.530 align:middle line:84% Then, obviously, output has gone up 00:39:07.530 --> 00:39:10.980 align:middle line:84% by the amount at which the students are buying things. 00:39:10.980 --> 00:39:14.250 align:middle line:84% Equity concerns can go either way. 00:39:14.250 --> 00:39:16.360 align:middle line:84% We think about-- price discrimination, 00:39:16.360 --> 00:39:19.350 align:middle line:84% also, I said, is a transfer between groups, 00:39:19.350 --> 00:39:22.480 align:middle line:84% between the high demand group to the low demand group. 00:39:22.480 --> 00:39:28.450 align:middle line:84% What we think about that depends on the examples. 00:39:28.450 --> 00:39:30.240 align:middle line:84% So for instance, one case where we 00:39:30.240 --> 00:39:32.610 align:middle line:84% might think equity says we should discriminate 00:39:32.610 --> 00:39:34.900 align:middle line:84% is financial aid for undergraduate colleges 00:39:34.900 --> 00:39:36.550 align:middle line:90% in the US. 00:39:36.550 --> 00:39:38.553 align:middle line:84% Colleges charge very, very different prices 00:39:38.553 --> 00:39:39.470 align:middle line:90% to different students. 00:39:39.470 --> 00:39:41.530 align:middle line:84% They charge much less to low income students 00:39:41.530 --> 00:39:43.490 align:middle line:84% than they charge to high income students. 00:39:43.490 --> 00:39:46.210 align:middle line:84% We tend to think of banning price discrimination there would 00:39:46.210 --> 00:39:49.630 align:middle line:84% be a bad thing because it would be raising the prices paid 00:39:49.630 --> 00:39:55.060 align:middle line:84% by all the low income students, who perhaps have a higher 00:39:55.060 --> 00:39:56.375 align:middle line:90% marginal utility of income. 00:39:56.375 --> 00:39:58.750 align:middle line:84% Another example, though, that goes the opposite direction 00:39:58.750 --> 00:39:59.780 align:middle line:90% is health insurance. 00:39:59.780 --> 00:40:02.770 align:middle line:84% If you allow health insurance companies to discriminate, 00:40:02.770 --> 00:40:05.480 align:middle line:84% the people who should pay the high price are the sick people. 00:40:05.480 --> 00:40:09.850 align:middle line:84% And so, if you ban discrimination-- 00:40:09.850 --> 00:40:12.160 align:middle line:84% if you allow discrimination for health insurance, 00:40:12.160 --> 00:40:17.830 align:middle line:84% there, allowing discrimination will be charging high prices 00:40:17.830 --> 00:40:18.650 align:middle line:90% to sick people. 00:40:18.650 --> 00:40:19.750 align:middle line:84% Maybe we don't want to allow you to charge 00:40:19.750 --> 00:40:21.667 align:middle line:84% high prices to sick people for equity reasons. 00:40:21.667 --> 00:40:25.970 align:middle line:90% 00:40:25.970 --> 00:40:32.120 align:middle line:84% OK, here is a corollary of the previous theorem, which 00:40:32.120 --> 00:40:35.210 align:middle line:90% I think is important to know. 00:40:35.210 --> 00:40:40.400 align:middle line:84% Suppose that demands in all these sub-markets are linear 00:40:40.400 --> 00:40:43.870 align:middle line:84% and that all markets are served under uniform pricing. 00:40:43.870 --> 00:40:45.890 align:middle line:84% Then third degree price discrimination 00:40:45.890 --> 00:40:48.320 align:middle line:90% always reduces welfare. 00:40:48.320 --> 00:40:52.160 align:middle line:84% So, again, why demand should be linear, I don't know. 00:40:52.160 --> 00:40:53.660 align:middle line:84% But it's a common benchmark that you 00:40:53.660 --> 00:40:56.210 align:middle line:84% might use as your first thought if you're studying a market. 00:40:56.210 --> 00:41:01.340 align:middle line:84% And this theorem says that, if the demands are linear, then 00:41:01.340 --> 00:41:02.780 align:middle line:84% third degree price discrimination 00:41:02.780 --> 00:41:05.780 align:middle line:90% reduces social welfare. 00:41:05.780 --> 00:41:07.140 align:middle line:90% What's the argument for that? 00:41:07.140 --> 00:41:11.210 align:middle line:84% The argument for this is going to be that the sum-- 00:41:11.210 --> 00:41:15.350 align:middle line:84% in the linear model, the sum of the delta xi's is always 00:41:15.350 --> 00:41:16.760 align:middle line:90% equal to 0. 00:41:16.760 --> 00:41:20.090 align:middle line:84% And because the output is unchanged, 00:41:20.090 --> 00:41:24.050 align:middle line:84% then discrimination hurts social welfare. 00:41:24.050 --> 00:41:26.760 align:middle line:90% How do I show that? 00:41:26.760 --> 00:41:28.840 align:middle line:84% This is algebra, so I won't go through it. 00:41:28.840 --> 00:41:32.675 align:middle line:84% But this was something I think I've shown you 00:41:32.675 --> 00:41:34.800 align:middle line:84% over and over again when I've been drawing pictures 00:41:34.800 --> 00:41:35.830 align:middle line:90% on the board. 00:41:35.830 --> 00:41:37.865 align:middle line:84% Suppose you have a linear demand curve. 00:41:37.865 --> 00:41:40.530 align:middle line:90% 00:41:40.530 --> 00:41:45.420 align:middle line:90% So this is my x of p. 00:41:45.420 --> 00:41:47.490 align:middle line:90% And this is p on this axis. 00:41:47.490 --> 00:41:51.060 align:middle line:90% I draw my cost in here. 00:41:51.060 --> 00:41:55.470 align:middle line:84% And then I ask, what's the monopoly price when I set-- 00:41:55.470 --> 00:41:58.530 align:middle line:84% what's the monopoly price when I have cost of c 00:41:58.530 --> 00:42:00.360 align:middle line:84% and I have a linear demand curve? 00:42:00.360 --> 00:42:02.820 align:middle line:90% It's exactly in the middle. 00:42:02.820 --> 00:42:06.900 align:middle line:84% So the rectangle that maximizes this 00:42:06.900 --> 00:42:14.190 align:middle line:84% is to set p halfway in between the price that's competitive. 00:42:14.190 --> 00:42:18.120 align:middle line:84% Oops, what am I doing wrong here? 00:42:18.120 --> 00:42:20.670 align:middle line:90% Sorry, that's not what I wanted. 00:42:20.670 --> 00:42:23.220 align:middle line:90% I wanted x here and p here. 00:42:23.220 --> 00:42:30.060 align:middle line:84% So if I set price equal to cost, then this 00:42:30.060 --> 00:42:33.330 align:middle line:84% is the x in a competitive market. 00:42:33.330 --> 00:42:37.470 align:middle line:90% This is the 0. 00:42:37.470 --> 00:42:42.660 align:middle line:84% x monopoly equals 1/2 [INAUDIBLE] competitive. 00:42:42.660 --> 00:42:45.220 align:middle line:84% And then this is the monopoly price here. 00:42:45.220 --> 00:42:47.993 align:middle line:84% So if I put this on the x axis, I'm 00:42:47.993 --> 00:42:49.660 align:middle line:84% trying to figure out the monopoly price. 00:42:49.660 --> 00:42:54.690 align:middle line:84% It's always halfway in between 0 and what a competitive firm 00:42:54.690 --> 00:42:55.500 align:middle line:90% would charge-- 00:42:55.500 --> 00:42:59.550 align:middle line:90% would produce, OK? 00:42:59.550 --> 00:43:07.270 align:middle line:84% So xi* is just one half of the competitive output. 00:43:07.270 --> 00:43:12.750 align:middle line:84% So if you sum across markets, what you just find 00:43:12.750 --> 00:43:19.020 align:middle line:84% is that the sum of the xi's is just one half 00:43:19.020 --> 00:43:21.600 align:middle line:84% of the sum of what you'd get under perfect competition 00:43:21.600 --> 00:43:23.650 align:middle line:90% in each market together. 00:43:23.650 --> 00:43:25.403 align:middle line:84% And if you think about perfect competition 00:43:25.403 --> 00:43:26.820 align:middle line:84% with all the markets combined, you 00:43:26.820 --> 00:43:29.145 align:middle line:84% set p equal to c, that's still one 00:43:29.145 --> 00:43:31.020 align:middle line:84% half of what you get with perfect competition 00:43:31.020 --> 00:43:32.550 align:middle line:90% in all markets. 00:43:32.550 --> 00:43:35.940 align:middle line:84% So if I combine the markets together, 00:43:35.940 --> 00:43:38.820 align:middle line:84% I get one half of the competitive market 00:43:38.820 --> 00:43:40.300 align:middle line:90% as the total output. 00:43:40.300 --> 00:43:41.880 align:middle line:84% And if I separate the markets, I get 00:43:41.880 --> 00:43:44.100 align:middle line:84% one half of the competitive output in market 1, 00:43:44.100 --> 00:43:46.560 align:middle line:84% plus one half of the competitive output in market 2, 00:43:46.560 --> 00:43:49.380 align:middle line:84% plus one half of the competitive output in market n. 00:43:49.380 --> 00:43:51.810 align:middle line:84% That's just-- because the competitive output 00:43:51.810 --> 00:43:54.690 align:middle line:84% is always the demand at price equal to c, 00:43:54.690 --> 00:43:57.350 align:middle line:90% those two things are equal. 00:43:57.350 --> 00:43:59.790 align:middle line:84% So the sum of one half of the competitive outputs, 00:43:59.790 --> 00:44:02.880 align:middle line:84% market by market, is one half of the competitive output 00:44:02.880 --> 00:44:05.130 align:middle line:90% in all the markets together. 00:44:05.130 --> 00:44:10.620 align:middle line:84% So with linear demand curves, because of this feature 00:44:10.620 --> 00:44:15.630 align:middle line:84% that you sell exactly half the competitive output, 00:44:15.630 --> 00:44:17.955 align:middle line:90% output is unchanged under-- 00:44:17.955 --> 00:44:21.100 align:middle line:90% 00:44:21.100 --> 00:44:23.100 align:middle line:84% output is unchanged if you allow discrimination. 00:44:23.100 --> 00:44:26.730 align:middle line:84% Therefore, discrimination reduces social welfare, OK? 00:44:26.730 --> 00:44:29.480 align:middle line:90% 00:44:29.480 --> 00:44:31.460 align:middle line:84% I covered this theorem because I think 00:44:31.460 --> 00:44:35.750 align:middle line:84% it highlights a very general concern, which is, often, 00:44:35.750 --> 00:44:38.270 align:middle line:84% people, when they're doing structural estimation of models, 00:44:38.270 --> 00:44:40.790 align:middle line:84% they assume some theoretical structure, 00:44:40.790 --> 00:44:43.430 align:middle line:84% whether on the demand curves or on the utility functions. 00:44:43.430 --> 00:44:45.650 align:middle line:84% And then they estimate some number of parameters. 00:44:45.650 --> 00:44:47.990 align:middle line:84% And then they comment on something of interest. 00:44:47.990 --> 00:44:49.917 align:middle line:90% So this gives you an example. 00:44:49.917 --> 00:44:51.500 align:middle line:84% Suppose someone comes to you and says, 00:44:51.500 --> 00:44:53.070 align:middle line:90% OK, I'm going to write a paper. 00:44:53.070 --> 00:44:55.790 align:middle line:84% I'm concerned about price discrimination 00:44:55.790 --> 00:44:58.135 align:middle line:90% in health insurance markets. 00:44:58.135 --> 00:45:00.260 align:middle line:84% I'm going to imagine that, instead of being allowed 00:45:00.260 --> 00:45:03.530 align:middle line:84% to discriminate and charge different health-related prices, 00:45:03.530 --> 00:45:06.237 align:middle line:84% I'm going to charge equal prices in all market. 00:45:06.237 --> 00:45:08.570 align:middle line:84% And I'm going to see what's the effect on social welfare 00:45:08.570 --> 00:45:12.170 align:middle line:84% of forcing the firm to charge a uniform price across all classes 00:45:12.170 --> 00:45:14.990 align:middle line:84% of consumers instead of discriminating by consumers. 00:45:14.990 --> 00:45:17.630 align:middle line:84% And the student tells me, oh, wait, for simplicity, 00:45:17.630 --> 00:45:19.380 align:middle line:84% I'm going to assume that demand curves are 00:45:19.380 --> 00:45:20.780 align:middle line:90% linear in every market. 00:45:20.780 --> 00:45:23.868 align:middle line:84% Well, then, I already know what the results of the paper are. 00:45:23.868 --> 00:45:25.410 align:middle line:84% I know that the paper is going to say 00:45:25.410 --> 00:45:28.890 align:middle line:84% that charging uniform price has increased social welfare. 00:45:28.890 --> 00:45:30.360 align:middle line:84% And it's increased social welfare 00:45:30.360 --> 00:45:33.630 align:middle line:84% because it's implicit in this demand specification 00:45:33.630 --> 00:45:41.310 align:middle line:84% that you increase social welfare when you ban discrimination. 00:45:41.310 --> 00:45:44.430 align:middle line:84% And I think it's just a very important thing to know, 00:45:44.430 --> 00:45:47.225 align:middle line:84% that if you're thinking about writing about a model 00:45:47.225 --> 00:45:48.600 align:middle line:84% to investigate some question, you 00:45:48.600 --> 00:45:50.350 align:middle line:84% have to know whether the answer is already 00:45:50.350 --> 00:45:53.340 align:middle line:84% determined by this functional form you've chosen. 00:45:53.340 --> 00:45:57.570 align:middle line:84% And again, why is linear demand curves not right? 00:45:57.570 --> 00:46:02.160 align:middle line:84% In part, social welfare is about how much utility people 00:46:02.160 --> 00:46:04.150 align:middle line:90% are getting beyond-- 00:46:04.150 --> 00:46:08.130 align:middle line:84% what's the consumer surplus that people are getting? 00:46:08.130 --> 00:46:11.455 align:middle line:84% It gets very different if demand looks like this, 00:46:11.455 --> 00:46:13.830 align:middle line:84% and if there are some people who really like the product, 00:46:13.830 --> 00:46:15.300 align:middle line:84% or if it goes like that and there's 00:46:15.300 --> 00:46:18.060 align:middle line:90% nobody who likes it very much. 00:46:18.060 --> 00:46:21.180 align:middle line:84% In some sense, prices are determined 00:46:21.180 --> 00:46:22.650 align:middle line:84% by elasticities, which are just-- 00:46:22.650 --> 00:46:24.062 align:middle line:90% determine these slopes here. 00:46:24.062 --> 00:46:26.020 align:middle line:84% If you actually want to understand whether it's 00:46:26.020 --> 00:46:27.790 align:middle line:84% increasing or decreasing welfare, 00:46:27.790 --> 00:46:29.650 align:middle line:84% you'd have to be able to think about, 00:46:29.650 --> 00:46:31.840 align:middle line:90% can I estimate these things? 00:46:31.840 --> 00:46:34.540 align:middle line:84% How much consumer surplus is here, 00:46:34.540 --> 00:46:36.777 align:middle line:84% relative to what the monopolist does, 00:46:36.777 --> 00:46:38.860 align:middle line:84% which is based on the elasticity at this one point 00:46:38.860 --> 00:46:40.930 align:middle line:90% the monopolist is choosing. 00:46:40.930 --> 00:46:47.590 align:middle line:84% And you need to be aware that this assumption is 00:46:47.590 --> 00:46:51.010 align:middle line:90% picking the answer for you. 00:46:51.010 --> 00:46:53.980 align:middle line:90% I don't know that it's not-- 00:46:53.980 --> 00:46:56.395 align:middle line:84% it may be a useful rule of thumb just to keep in mind. 00:46:56.395 --> 00:46:59.020 align:middle line:84% If, in the linear model, there's no effect on aggregate output, 00:46:59.020 --> 00:47:00.770 align:middle line:84% maybe we would think that aggregate output 00:47:00.770 --> 00:47:02.530 align:middle line:90% effects typically are small. 00:47:02.530 --> 00:47:05.595 align:middle line:84% But again, it's all based in the linearity there. 00:47:05.595 --> 00:47:08.840 align:middle line:90% 00:47:08.840 --> 00:47:10.910 align:middle line:90% OK, what is general? 00:47:10.910 --> 00:47:15.320 align:middle line:84% So there's a recent paper by Bergemann, Brooks, and Morris 00:47:15.320 --> 00:47:21.080 align:middle line:84% that asked this question, what can we say generally 00:47:21.080 --> 00:47:23.930 align:middle line:84% about when you allow a monopolist to discriminate? 00:47:23.930 --> 00:47:26.180 align:middle line:84% Will welfare-- we know that, you allow 00:47:26.180 --> 00:47:28.040 align:middle line:84% monopolist to discriminate, profits go up. 00:47:28.040 --> 00:47:29.940 align:middle line:90% Will social welfare go up? 00:47:29.940 --> 00:47:32.140 align:middle line:84% Will consumer surplus go up or down? 00:47:32.140 --> 00:47:33.680 align:middle line:90% What are the trade-offs? 00:47:33.680 --> 00:47:35.840 align:middle line:84% And what Bergemann, Brooks, and Morris note 00:47:35.840 --> 00:47:39.500 align:middle line:84% is that it depends on what information 00:47:39.500 --> 00:47:41.910 align:middle line:84% the monopolist has about the consumers. 00:47:41.910 --> 00:47:44.210 align:middle line:84% So let's think about the standard example 00:47:44.210 --> 00:47:49.820 align:middle line:84% where the consumer's values are uniform, 0, 1, c equals 0. 00:47:49.820 --> 00:47:53.750 align:middle line:84% If the monopolist has no information about the consumers, 00:47:53.750 --> 00:47:56.142 align:middle line:84% then it doesn't matter if you allow him to discriminate. 00:47:56.142 --> 00:47:58.100 align:middle line:84% He has no information on which to discriminate. 00:47:58.100 --> 00:48:00.220 align:middle line:84% What's the monopolist going to do? 00:48:00.220 --> 00:48:04.250 align:middle line:84% This is your standard monopoly pricing, p equals 1/2. 00:48:04.250 --> 00:48:05.610 align:middle line:90% Profit is 1/4. 00:48:05.610 --> 00:48:08.700 align:middle line:90% Consumer surplus is 1/8. 00:48:08.700 --> 00:48:10.890 align:middle line:84% In their figure, that's this point here. 00:48:10.890 --> 00:48:13.170 align:middle line:90% Consumer surplus is 1/8. 00:48:13.170 --> 00:48:17.880 align:middle line:90% Producer surplus is 1/4, OK? 00:48:17.880 --> 00:48:20.700 align:middle line:90% 00:48:20.700 --> 00:48:23.850 align:middle line:84% One extreme is, what if the monopolist 00:48:23.850 --> 00:48:26.200 align:middle line:84% can perform first degree price discrimination? 00:48:26.200 --> 00:48:28.350 align:middle line:90% The monopolist knows everything. 00:48:28.350 --> 00:48:30.690 align:middle line:84% If the monopolist knows everything, 00:48:30.690 --> 00:48:35.140 align:middle line:84% then the monopolist charges each consumer their full value. 00:48:35.140 --> 00:48:37.800 align:middle line:84% We know there that the monopolist's profit 00:48:37.800 --> 00:48:41.490 align:middle line:90% has gone up tremendously. 00:48:41.490 --> 00:48:44.630 align:middle line:84% And we know that the consumer surplus has been driven to 0. 00:48:44.630 --> 00:48:48.870 align:middle line:84% So here, if the monopolist knows everything about the consumers, 00:48:48.870 --> 00:48:52.260 align:middle line:84% then the answer to what happens if you allow discrimination is, 00:48:52.260 --> 00:48:54.420 align:middle line:90% profit goes up-- 00:48:54.420 --> 00:48:55.740 align:middle line:90% profit goes up. 00:48:55.740 --> 00:48:57.480 align:middle line:90% Consumer surplus goes down. 00:48:57.480 --> 00:49:00.830 align:middle line:84% Social welfare goes up because we're above the 45 degree line. 00:49:00.830 --> 00:49:04.980 align:middle line:90% 00:49:04.980 --> 00:49:07.350 align:middle line:84% But they note, in the paper, thinking 00:49:07.350 --> 00:49:09.840 align:middle line:84% the same kind of reasoning as Roesler and Szentes, 00:49:09.840 --> 00:49:15.510 align:middle line:84% there are other situations where consumer surplus and profit will 00:49:15.510 --> 00:49:19.150 align:middle line:84% also go up if you allow the monopolist to discriminate, 00:49:19.150 --> 00:49:21.140 align:middle line:90% that they both go up. 00:49:21.140 --> 00:49:24.590 align:middle line:84% Here's their interesting and clever example. 00:49:24.590 --> 00:49:28.450 align:middle line:84% So suppose what we have is, we have this demand curve that 00:49:28.450 --> 00:49:33.180 align:middle line:84% comes from there being consumers with every different-- 00:49:33.180 --> 00:49:35.860 align:middle line:84% these sub-populations of consumers 00:49:35.860 --> 00:49:38.080 align:middle line:90% with every different value. 00:49:38.080 --> 00:49:41.380 align:middle line:84% Suppose what the monopolist gets is this signal that says, 00:49:41.380 --> 00:49:43.420 align:middle line:90% one of two things is true. 00:49:43.420 --> 00:49:51.220 align:middle line:84% Either the consumer is someone whose value-- 00:49:51.220 --> 00:49:56.620 align:middle line:84% so this is going to be my f of v, given my signal. 00:49:56.620 --> 00:50:02.380 align:middle line:84% The consumer either has a value between 0.01 and 0.02, 00:50:02.380 --> 00:50:06.160 align:middle line:84% or the consumer's value is, with small probability, 00:50:06.160 --> 00:50:11.080 align:middle line:84% drawn from a uniform distribution on 0.02 up to 1. 00:50:11.080 --> 00:50:14.170 align:middle line:84% So this signal means there's no way their value is 00:50:14.170 --> 00:50:15.950 align:middle line:90% between 0 and 0.01. 00:50:15.950 --> 00:50:18.360 align:middle line:90% Very likely, it's between-- 00:50:18.360 --> 00:50:20.070 align:middle line:84% all consumers with values in this range 00:50:20.070 --> 00:50:21.400 align:middle line:90% will have that signal. 00:50:21.400 --> 00:50:24.580 align:middle line:84% And then there's some small possibility of a false positive. 00:50:24.580 --> 00:50:27.450 align:middle line:84% And it's actually a consumer with a value drawn from here, 00:50:27.450 --> 00:50:29.400 align:middle line:90% OK? 00:50:29.400 --> 00:50:32.730 align:middle line:90% What does your profit look like? 00:50:32.730 --> 00:50:45.460 align:middle line:84% Well, your profit is increasing in price until you get to 0.01. 00:50:45.460 --> 00:50:52.720 align:middle line:84% As you drop your price from 0.01 to 0.02, per consumer profit, 00:50:52.720 --> 00:50:54.866 align:middle line:90% you'd lose many customers. 00:50:54.866 --> 00:50:58.560 align:middle line:90% 00:50:58.560 --> 00:51:01.920 align:middle line:84% But then, once you raise your price, 00:51:01.920 --> 00:51:03.433 align:middle line:84% you then are just making more money. 00:51:03.433 --> 00:51:05.100 align:middle line:84% Now, all these consumers have gone away. 00:51:05.100 --> 00:51:06.780 align:middle line:84% And you're making more money off these consumers 00:51:06.780 --> 00:51:08.010 align:middle line:90% as you raise your price. 00:51:08.010 --> 00:51:11.580 align:middle line:84% And you have something that looks like this. 00:51:11.580 --> 00:51:14.040 align:middle line:84% In this sub-population, it's like your standard monopoly 00:51:14.040 --> 00:51:16.350 align:middle line:90% pricing. 00:51:16.350 --> 00:51:20.280 align:middle line:84% And what they note is that, by very clever choice of how 00:51:20.280 --> 00:51:23.220 align:middle line:84% many people to put in this band, I 00:51:23.220 --> 00:51:28.620 align:middle line:84% can make it so that this profit level and this profit level 00:51:28.620 --> 00:51:30.900 align:middle line:90% coincide. 00:51:30.900 --> 00:51:35.670 align:middle line:84% So I'm exactly indifferent between two prices, 0.01, 00:51:35.670 --> 00:51:37.610 align:middle line:90% or my standard 0.5 price. 00:51:37.610 --> 00:51:40.340 align:middle line:90% 00:51:40.340 --> 00:51:43.280 align:middle line:84% And so, if you give the monopolist a signal that says, 00:51:43.280 --> 00:51:45.365 align:middle line:84% there's a few consumers with this-- 00:51:45.365 --> 00:51:47.900 align:middle line:90% 00:51:47.900 --> 00:51:48.930 align:middle line:90% here's this signal. 00:51:48.930 --> 00:51:51.950 align:middle line:84% You get this signal, or you get this signal occasionally. 00:51:51.950 --> 00:51:54.617 align:middle line:84% And then, the rest of the time, you just get the regular signal. 00:51:54.617 --> 00:51:55.790 align:middle line:90% It's a regular customer. 00:51:55.790 --> 00:52:00.253 align:middle line:90% Then, when you get this signal-- 00:52:00.253 --> 00:52:02.420 align:middle line:84% and then, you have the other signal that tells you-- 00:52:02.420 --> 00:52:04.070 align:middle line:84% the complementary signal would tell me 00:52:04.070 --> 00:52:10.130 align:middle line:84% that the consumer might have a value here, no chance 00:52:10.130 --> 00:52:11.090 align:middle line:90% to have a value here. 00:52:11.090 --> 00:52:13.583 align:middle line:84% And then they may have a value like that. 00:52:13.583 --> 00:52:15.000 align:middle line:84% So that's my complementary signal. 00:52:15.000 --> 00:52:18.380 align:middle line:84% It's either this signal or this signal, OK? 00:52:18.380 --> 00:52:24.980 align:middle line:84% Well, when I get this signal, my optimal price is p equals 0.5. 00:52:24.980 --> 00:52:27.660 align:middle line:84% When I get this signal, I'm indifferent between 0.01 00:52:27.660 --> 00:52:28.830 align:middle line:90% and 0.5. 00:52:28.830 --> 00:52:32.390 align:middle line:84% So if I charge 0.01 when I get this signal, 00:52:32.390 --> 00:52:35.270 align:middle line:84% I've just created consumer surplus. 00:52:35.270 --> 00:52:37.730 align:middle line:84% And I haven't affected profits at all. 00:52:37.730 --> 00:52:40.980 align:middle line:84% So what I'm able to do is move along this line 00:52:40.980 --> 00:52:44.680 align:middle line:84% and just keep profits exactly at the same thing 00:52:44.680 --> 00:52:49.503 align:middle line:84% I get charging 0.5 to every one, and give consumer surplus. 00:52:49.503 --> 00:52:50.920 align:middle line:84% And then you can think about this. 00:52:50.920 --> 00:52:52.020 align:middle line:84% I could do the same argument, adding 00:52:52.020 --> 00:52:53.290 align:middle line:90% more and more such signals. 00:52:53.290 --> 00:52:58.660 align:middle line:84% I can do a 0.02 to 0.03 signal, a 0.03 to 0.04, 0.04 to 0.05. 00:52:58.660 --> 00:53:01.740 align:middle line:84% I can give the monopolist many, many, many signals, 00:53:01.740 --> 00:53:04.200 align:middle line:84% and just, by doing that, get the monopolist 00:53:04.200 --> 00:53:07.680 align:middle line:84% to have more and more groups to which it offers a discount 00:53:07.680 --> 00:53:10.565 align:middle line:84% and increase consumer surplus up to some point here. 00:53:10.565 --> 00:53:18.830 align:middle line:90% 00:53:18.830 --> 00:53:20.850 align:middle line:90% It turns out, I can also-- 00:53:20.850 --> 00:53:23.390 align:middle line:84% so that's their clever construction 00:53:23.390 --> 00:53:25.595 align:middle line:84% for how I get from here, going in this direction. 00:53:25.595 --> 00:53:28.220 align:middle line:84% It turns out I can also do the same kind of clever construction 00:53:28.220 --> 00:53:29.660 align:middle line:90% and go in that direction. 00:53:29.660 --> 00:53:32.270 align:middle line:84% I can make the monopolist indifferent between 0.5 00:53:32.270 --> 00:53:34.105 align:middle line:90% and a very high price. 00:53:34.105 --> 00:53:36.230 align:middle line:84% And then, once the monopolist is indifferent to 0.5 00:53:36.230 --> 00:53:39.500 align:middle line:84% and a very high price, they start charging the high price 00:53:39.500 --> 00:53:40.730 align:middle line:90% to all these. 00:53:40.730 --> 00:53:44.270 align:middle line:84% There's a special signal that tells you that. 00:53:44.270 --> 00:53:47.630 align:middle line:84% There's some chance, there's this excess probability 00:53:47.630 --> 00:53:49.130 align:middle line:90% that the value is up here. 00:53:49.130 --> 00:53:50.820 align:middle line:90% And otherwise, it's uniform. 00:53:50.820 --> 00:53:53.535 align:middle line:84% When you get those signals, they're 00:53:53.535 --> 00:53:55.160 align:middle line:84% in between charging the very high price 00:53:55.160 --> 00:53:59.930 align:middle line:84% in selling to these consumers only, or setting the 0.5 price. 00:53:59.930 --> 00:54:05.150 align:middle line:84% And so, by using other signals, I can keep the profit-- 00:54:05.150 --> 00:54:08.670 align:middle line:84% here, the profit went up as consumer surplus went to 0. 00:54:08.670 --> 00:54:12.750 align:middle line:84% Here, I can have the monopolist profit stay the same and drive 00:54:12.750 --> 00:54:15.540 align:middle line:90% consumer surplus to 0. 00:54:15.540 --> 00:54:18.330 align:middle line:84% And their general result is, by this choice 00:54:18.330 --> 00:54:20.920 align:middle line:84% of clever distributions of signals, 00:54:20.920 --> 00:54:27.480 align:middle line:84% what they show is that, really, what price discrimination does 00:54:27.480 --> 00:54:29.790 align:middle line:84% to consumer surplus and to social welfare 00:54:29.790 --> 00:54:32.250 align:middle line:90% is just totally indeterminate. 00:54:32.250 --> 00:54:37.170 align:middle line:84% If the monopolist has some types of information structures, 00:54:37.170 --> 00:54:38.730 align:middle line:84% it always raises the monopoly profit. 00:54:38.730 --> 00:54:41.590 align:middle line:84% But it can raise or lower consumer surplus. 00:54:41.590 --> 00:54:44.130 align:middle line:84% And because it can go above or below this 45 degree line, 00:54:44.130 --> 00:54:47.220 align:middle line:84% it can raise or lower total social welfare. 00:54:47.220 --> 00:54:50.700 align:middle line:84% And it's all a function of, what information 00:54:50.700 --> 00:54:52.380 align:middle line:90% does the monopolist have? 00:54:52.380 --> 00:54:53.970 align:middle line:84% And is it the type of information 00:54:53.970 --> 00:54:56.713 align:middle line:84% that makes the monopolist want to charge low prices, 00:54:56.713 --> 00:54:59.130 align:middle line:84% or is it the type of information that wants the monopolist 00:54:59.130 --> 00:55:00.335 align:middle line:90% to charge high prices? 00:55:00.335 --> 00:55:04.600 align:middle line:90% 00:55:04.600 --> 00:55:06.370 align:middle line:84% AUDIENCE: So this result goes away 00:55:06.370 --> 00:55:09.580 align:middle line:84% if the monopolist is allowed to design their own information 00:55:09.580 --> 00:55:10.110 align:middle line:90% scheme? 00:55:10.110 --> 00:55:11.277 align:middle line:90% GLENN ELLISON: That's right. 00:55:11.277 --> 00:55:14.770 align:middle line:84% So this is very much thinking about the-- the monopolist is 00:55:14.770 --> 00:55:18.130 align:middle line:84% given a scheme that, it's given a scheme like you either 00:55:18.130 --> 00:55:20.380 align:middle line:84% know that the person is astute, because it's 00:55:20.380 --> 00:55:22.630 align:middle line:90% third degree discrimination. 00:55:22.630 --> 00:55:24.860 align:middle line:84% You need to be able to price based on the signals 00:55:24.860 --> 00:55:25.930 align:middle line:90% that you're given. 00:55:25.930 --> 00:55:29.050 align:middle line:84% You've got demand in Mississippi, demand in Kansas, 00:55:29.050 --> 00:55:29.890 align:middle line:90% demand in Boston. 00:55:29.890 --> 00:55:30.730 align:middle line:90% That's all you know. 00:55:30.730 --> 00:55:32.710 align:middle line:90% Or you've got student demand. 00:55:32.710 --> 00:55:37.120 align:middle line:90% You've got non-student demand. 00:55:37.120 --> 00:55:42.130 align:middle line:84% So, obviously, the monopolist wants perfect information 00:55:42.130 --> 00:55:43.670 align:middle line:90% and wants to go here. 00:55:43.670 --> 00:55:46.448 align:middle line:84% And so, the more useful information the monopolist has, 00:55:46.448 --> 00:55:47.990 align:middle line:84% the higher it's going to get up here. 00:55:47.990 --> 00:55:52.120 align:middle line:84% But if the sub-populations are what they are, 00:55:52.120 --> 00:55:54.550 align:middle line:90% it can go either way, yeah. 00:55:54.550 --> 00:55:59.530 align:middle line:90% 00:55:59.530 --> 00:56:01.810 align:middle line:84% Yeah, because I think, on the monopolist's side, 00:56:01.810 --> 00:56:04.150 align:middle line:84% the real intuition is, you want to know everything 00:56:04.150 --> 00:56:05.210 align:middle line:90% and do first degree. 00:56:05.210 --> 00:56:07.580 align:middle line:84% And if you can do that, that's what you're going to do. 00:56:07.580 --> 00:56:11.050 align:middle line:84% But as you're getting there, it's 00:56:11.050 --> 00:56:14.170 align:middle line:84% possible you're going there this way or this way 00:56:14.170 --> 00:56:15.170 align:middle line:90% and reducing welfare. 00:56:15.170 --> 00:56:16.300 align:middle line:84% It could be, you're going there this way 00:56:16.300 --> 00:56:18.090 align:middle line:84% and increasing welfare on the path there. 00:56:18.090 --> 00:56:23.550 align:middle line:90% 00:56:23.550 --> 00:56:27.417 align:middle line:84% OK, so the final thing I'm going to do today, 00:56:27.417 --> 00:56:28.875 align:middle line:84% well, actually, next to last thing, 00:56:28.875 --> 00:56:31.080 align:middle line:90% is second degree discrimination. 00:56:31.080 --> 00:56:36.480 align:middle line:84% So now, we're back in the case of the iPhone 128 00:56:36.480 --> 00:56:39.900 align:middle line:84% and the iPhone 512, where the monopolist can't observe 00:56:39.900 --> 00:56:43.140 align:middle line:84% the consumer preferences and is relying on the self-selection 00:56:43.140 --> 00:56:47.670 align:middle line:84% to get the high value consumers to buy the high-end good. 00:56:47.670 --> 00:56:51.900 align:middle line:84% So I'm going to have consumers have some unknown type, theta, 00:56:51.900 --> 00:56:54.040 align:middle line:84% that's unobserved by the monopolist. 00:56:54.040 --> 00:57:00.300 align:middle line:84% They get utility, v of q theta if they buy a quality, q, good, 00:57:00.300 --> 00:57:01.560 align:middle line:90% and their type is theta. 00:57:01.560 --> 00:57:05.280 align:middle line:84% And they pay a total price of T. I'm 00:57:05.280 --> 00:57:07.740 align:middle line:84% going to assume that the utility is that everyone 00:57:07.740 --> 00:57:10.740 align:middle line:90% agrees that quality is good. 00:57:10.740 --> 00:57:13.650 align:middle line:84% The higher theta consumers have a higher willingness 00:57:13.650 --> 00:57:14.805 align:middle line:90% to pay for any good. 00:57:14.805 --> 00:57:17.910 align:middle line:90% 00:57:17.910 --> 00:57:22.810 align:middle line:84% Cross-partial of v with respect to q and theta is positive. 00:57:22.810 --> 00:57:25.950 align:middle line:84% So the higher theta, people have a higher valuation and a higher 00:57:25.950 --> 00:57:28.710 align:middle line:90% marginal valuation for quality. 00:57:28.710 --> 00:57:31.410 align:middle line:84% And I'm going to assume that there are diminishing returns 00:57:31.410 --> 00:57:32.440 align:middle line:90% to quality. 00:57:32.440 --> 00:57:37.170 align:middle line:84% So second derivative of v with respect to q is negative. 00:57:37.170 --> 00:57:41.640 align:middle line:84% I'm going to, and this is really a labeling of quality, 00:57:41.640 --> 00:57:44.850 align:middle line:84% I'm going to assume that the cost of producing a quality, q, 00:57:44.850 --> 00:57:46.920 align:middle line:90% good is c times q. 00:57:46.920 --> 00:57:51.120 align:middle line:84% So you can think of that as just determining how we call-- 00:57:51.120 --> 00:57:55.150 align:middle line:84% we don't want to call a 128 versus 512 four times as good. 00:57:55.150 --> 00:57:58.950 align:middle line:84% The q is defined in terms of how much the cost of producing 00:57:58.950 --> 00:58:02.100 align:middle line:90% that quality is. 00:58:02.100 --> 00:58:05.710 align:middle line:84% For now, I'm just going to assume there are two types. 00:58:05.710 --> 00:58:09.490 align:middle line:84% And I'm going to write vi of q for the-- 00:58:09.490 --> 00:58:11.770 align:middle line:84% so I'm going to write v1 of q and v2 of q 00:58:11.770 --> 00:58:13.968 align:middle line:84% for what the utility function is for the low types 00:58:13.968 --> 00:58:14.760 align:middle line:90% and the high types. 00:58:14.760 --> 00:58:17.370 align:middle line:90% 00:58:17.370 --> 00:58:23.670 align:middle line:84% Again, if the thetas were observable, first. 00:58:23.670 --> 00:58:25.690 align:middle line:84% this would be first degree discrimination model. 00:58:25.690 --> 00:58:27.065 align:middle line:84% I would just, for every consumer, 00:58:27.065 --> 00:58:30.180 align:middle line:84% sell them the efficient quality for them 00:58:30.180 --> 00:58:32.960 align:middle line:84% and charge them their full surplus that they get from it. 00:58:32.960 --> 00:58:36.180 align:middle line:90% 00:58:36.180 --> 00:58:40.410 align:middle line:84% With theta unobserved, this isn't going to work. 00:58:40.410 --> 00:58:43.450 align:middle line:84% In the perfect price discrimination scheme, 00:58:43.450 --> 00:58:47.070 align:middle line:84% the type theta equals 2 consumers get zero utility when 00:58:47.070 --> 00:58:50.730 align:middle line:90% they buy q2* at a price of T2*. 00:58:50.730 --> 00:58:53.940 align:middle line:84% These were the first degree levels. 00:58:53.940 --> 00:58:57.960 align:middle line:84% So they get zero utility from buying the first degree 00:58:57.960 --> 00:58:59.580 align:middle line:90% packaging for them. 00:58:59.580 --> 00:59:03.540 align:middle line:84% But they're going to get positive utility from buying q1* 00:59:03.540 --> 00:59:08.070 align:middle line:84% at a price of T1* because the low types get non-negative 00:59:08.070 --> 00:59:12.900 align:middle line:84% utility from buying a quality q1* good at price T1*. 00:59:12.900 --> 00:59:17.350 align:middle line:84% The theta 2 types always get more utility than the theta 1 00:59:17.350 --> 00:59:18.590 align:middle line:90% get from any utility. 00:59:18.590 --> 00:59:21.400 align:middle line:84% Therefore, the theta 2 types would 00:59:21.400 --> 00:59:23.740 align:middle line:84% be better off not buying the package designed for them, 00:59:23.740 --> 00:59:25.150 align:middle line:90% and instead-- 00:59:25.150 --> 00:59:30.663 align:middle line:84% so in some sense, if the business class tickets 00:59:30.663 --> 00:59:32.830 align:middle line:84% were the full willingness to pay of the businessmen, 00:59:32.830 --> 00:59:35.620 align:middle line:84% they would go to fly in coach and get a positive surplus 00:59:35.620 --> 00:59:37.890 align:middle line:84% from sitting in a coach seat at the coach price. 00:59:37.890 --> 00:59:41.780 align:middle line:90% 00:59:41.780 --> 00:59:45.690 align:middle line:84% OK, so what do you want to do with theta unobservable? 00:59:45.690 --> 00:59:47.870 align:middle line:84% This is your standard screening problem. 00:59:47.870 --> 00:59:50.790 align:middle line:90% You have two types. 00:59:50.790 --> 00:59:52.640 align:middle line:84% You offer a menu that has two options. 00:59:52.640 --> 00:59:55.470 align:middle line:84% And you let the consumers choose between those two options. 00:59:55.470 --> 00:59:57.900 align:middle line:84% So consumers are given the option, 00:59:57.900 --> 01:00:01.280 align:middle line:84% you can either buy a quality q1 good at a price of T1 01:00:01.280 --> 01:00:05.300 align:middle line:84% or a quality q2 good at a price of T2. 01:00:05.300 --> 01:00:08.940 align:middle line:84% Monopolist maximization problem, I'm mazimizing. 01:00:08.940 --> 01:00:12.330 align:middle line:84% So I have a equal masses of consumers of each type here. 01:00:12.330 --> 01:00:16.190 align:middle line:84% I'm getting the price I get from the low types, 01:00:16.190 --> 01:00:18.230 align:middle line:84% plus the price I get from the high types, 01:00:18.230 --> 01:00:21.000 align:middle line:84% minus the cost of producing all the goods. 01:00:21.000 --> 01:00:23.960 align:middle line:84% And then I have these four standard constraints 01:00:23.960 --> 01:00:27.830 align:middle line:84% like you're used to seeing in mechanism design problems. 01:00:27.830 --> 01:00:32.086 align:middle line:84% The IR constraints, that stands for individual rationality. 01:00:32.086 --> 01:00:39.510 align:middle line:90% 01:00:39.510 --> 01:00:43.260 align:middle line:84% The constraints say that the low type consumers 01:00:43.260 --> 01:00:45.660 align:middle line:84% have to be getting at least as much utility from the good 01:00:45.660 --> 01:00:48.090 align:middle line:84% they're buying as what they're paying for it, 01:00:48.090 --> 01:00:50.100 align:middle line:90% as do the high types. 01:00:50.100 --> 01:01:04.090 align:middle line:84% And then, the IC constraints, the incentive compatibility, 01:01:04.090 --> 01:01:06.280 align:middle line:84% the incentive compatibility constraints 01:01:06.280 --> 01:01:10.420 align:middle line:84% say that the utility that the low types get 01:01:10.420 --> 01:01:12.970 align:middle line:84% from buying the package designed for them 01:01:12.970 --> 01:01:16.012 align:middle line:84% is at least as good as the utility they would get if they 01:01:16.012 --> 01:01:17.470 align:middle line:84% bought the package that was instead 01:01:17.470 --> 01:01:20.860 align:middle line:84% designed for the high types and paid the high-type price. 01:01:20.860 --> 01:01:24.587 align:middle line:84% And similarly, the businessmen have 01:01:24.587 --> 01:01:26.170 align:middle line:84% to be getting at least as much utility 01:01:26.170 --> 01:01:28.750 align:middle line:84% from sitting in business class as they would 01:01:28.750 --> 01:01:32.110 align:middle line:84% get if they instead sat in coach, got the coach quality, 01:01:32.110 --> 01:01:33.590 align:middle line:90% and paid the coach price. 01:01:33.590 --> 01:01:36.040 align:middle line:84% So each group has to be willing to buy the package 01:01:36.040 --> 01:01:38.197 align:middle line:84% that you're selling to them in equilibrium, 01:01:38.197 --> 01:01:39.780 align:middle line:84% relative to the other group's package. 01:01:39.780 --> 01:01:45.440 align:middle line:90% 01:01:45.440 --> 01:01:47.330 align:middle line:84% The first step in solving problems like this 01:01:47.330 --> 01:01:49.670 align:middle line:84% is always to figure out which constraints are binding 01:01:49.670 --> 01:01:51.960 align:middle line:84% and which constraints are not binding. 01:01:51.960 --> 01:01:57.320 align:middle line:84% Here, one observation is that the IR2 constraint is not 01:01:57.320 --> 01:01:58.970 align:middle line:90% going to be binding. 01:01:58.970 --> 01:02:03.110 align:middle line:84% And the argument here is simply that the students 01:02:03.110 --> 01:02:06.950 align:middle line:84% are willing to fly on the plane in coach. 01:02:06.950 --> 01:02:10.040 align:middle line:84% The IC constraint says that the businessmen 01:02:10.040 --> 01:02:13.170 align:middle line:84% have to prefer what they're getting to flying in coach. 01:02:13.170 --> 01:02:14.820 align:middle line:84% They have positive utility from that. 01:02:14.820 --> 01:02:16.897 align:middle line:84% So therefore, they're automatically 01:02:16.897 --> 01:02:18.980 align:middle line:84% willing to buy because they would get more utility 01:02:18.980 --> 01:02:21.500 align:middle line:90% from the coach class seat. 01:02:21.500 --> 01:02:23.990 align:middle line:84% And then, I would say the second thing is just 01:02:23.990 --> 01:02:26.150 align:middle line:84% a guess, although I'll show you, it's true. 01:02:26.150 --> 01:02:29.300 align:middle line:90% IC1 seems unlikely to bind. 01:02:29.300 --> 01:02:32.300 align:middle line:84% If you're thinking about, what's the airline's pricing problem, 01:02:32.300 --> 01:02:34.880 align:middle line:84% you never have the problem of, the students are going to buy 01:02:34.880 --> 01:02:38.570 align:middle line:84% the $3,000 ticket if you're not careful. 01:02:38.570 --> 01:02:42.470 align:middle line:84% The problem is keeping the wealthy people 01:02:42.470 --> 01:02:44.630 align:middle line:84% from buying the cheap product, not 01:02:44.630 --> 01:02:47.110 align:middle line:84% keeping the poor people from buying the expensive product. 01:02:47.110 --> 01:02:49.940 align:middle line:90% 01:02:49.940 --> 01:02:53.630 align:middle line:84% So once I eliminate those two, the simplified problem 01:02:53.630 --> 01:02:59.390 align:middle line:84% is, I'm maximizing my profits subject to just two constraints. 01:02:59.390 --> 01:03:02.540 align:middle line:84% The low types have to be willing to buy 01:03:02.540 --> 01:03:04.550 align:middle line:90% the product I'm selling them. 01:03:04.550 --> 01:03:08.220 align:middle line:84% And the high types have to prefer the expensive product 01:03:08.220 --> 01:03:10.580 align:middle line:84% I'm trying to sell them to the cheaper product I'm 01:03:10.580 --> 01:03:11.635 align:middle line:90% selling to the low types. 01:03:11.635 --> 01:03:14.610 align:middle line:90% 01:03:14.610 --> 01:03:18.030 align:middle line:84% So if you look at this problem now, 01:03:18.030 --> 01:03:20.550 align:middle line:84% so I'm doing this constrained optimization, 01:03:20.550 --> 01:03:23.790 align:middle line:84% I want to make the Ts as big as I can. 01:03:23.790 --> 01:03:26.740 align:middle line:84% What are the constraints on making the Ts as big as I can? 01:03:26.740 --> 01:03:30.400 align:middle line:84% So for T1, if I raise it, that's good. 01:03:30.400 --> 01:03:33.070 align:middle line:84% It makes this constraint easier to satisfy. 01:03:33.070 --> 01:03:35.400 align:middle line:84% So the only reason not to raise T1 01:03:35.400 --> 01:03:38.220 align:middle line:84% is because this constraint is going to be violated. 01:03:38.220 --> 01:03:40.230 align:middle line:84% So clearly, in equilibrium, I'm going 01:03:40.230 --> 01:03:46.860 align:middle line:84% to set T1 equal to v1 one q1 and have this constraint be binding. 01:03:46.860 --> 01:03:48.600 align:middle line:84% And then, also, I'm going to want 01:03:48.600 --> 01:03:52.030 align:middle line:84% to raise the price to the high types as much as I can. 01:03:52.030 --> 01:03:54.360 align:middle line:84% What prevents me from doing that is only that T2 01:03:54.360 --> 01:03:55.980 align:middle line:90% appears in this constraint. 01:03:55.980 --> 01:03:58.470 align:middle line:84% And so, I'm going to make T2 as large as I can 01:03:58.470 --> 01:04:00.690 align:middle line:84% before this constraint is violated. 01:04:00.690 --> 01:04:03.340 align:middle line:84% And so, this is going to also hold with equality. 01:04:03.340 --> 01:04:07.650 align:middle line:84% And that means, if I bring it over to this side, T2 equals T1, 01:04:07.650 --> 01:04:11.080 align:middle line:90% plus v2 of q2, minus v2 of q1. 01:04:11.080 --> 01:04:15.030 align:middle line:84% So in some sense, this is just like in the durable goods 01:04:15.030 --> 01:04:19.088 align:middle line:84% problem, where people could buy the good in the second period. 01:04:19.088 --> 01:04:21.630 align:middle line:84% So I can charge them for getting the good in the first period 01:04:21.630 --> 01:04:22.130 align:middle line:90% instead. 01:04:22.130 --> 01:04:25.830 align:middle line:84% Is there incremental utility for getting it one period earlier? 01:04:25.830 --> 01:04:28.560 align:middle line:84% Again, what I can get from selling them 01:04:28.560 --> 01:04:30.660 align:middle line:84% the higher quality good is what they 01:04:30.660 --> 01:04:32.580 align:middle line:84% would pay for the low quality good, 01:04:32.580 --> 01:04:34.710 align:middle line:84% plus the incremental utility that they 01:04:34.710 --> 01:04:36.800 align:middle line:90% get from the quality upgrade. 01:04:36.800 --> 01:04:38.860 align:middle line:84% That's the most they're going to be able to pay. 01:04:38.860 --> 01:04:46.280 align:middle line:84% And so, that's v1 q1, plus v2 of q2 minus v2 of q1. 01:04:46.280 --> 01:04:51.170 align:middle line:84% And so, once I've made these two substitutions, this for T1 01:04:51.170 --> 01:04:55.100 align:middle line:84% and this for T2, I now just have an unconstrained maximization 01:04:55.100 --> 01:04:57.350 align:middle line:90% problem. 01:04:57.350 --> 01:04:58.950 align:middle line:90% What's the answer to that? 01:04:58.950 --> 01:05:04.280 align:middle line:84% So I've just-- assuming the v's are concave functions, 01:05:04.280 --> 01:05:08.660 align:middle line:84% I just take the first order conditions for this to maximize. 01:05:08.660 --> 01:05:11.600 align:middle line:84% First, let me differentiate with respect 01:05:11.600 --> 01:05:14.750 align:middle line:84% to q2, which only appears here and here. 01:05:14.750 --> 01:05:16.700 align:middle line:84% I differentiate with respect to q2. 01:05:16.700 --> 01:05:21.625 align:middle line:84% And I get dv, d(v2)/d(q) equals c. 01:05:21.625 --> 01:05:24.170 align:middle line:90% 01:05:24.170 --> 01:05:27.260 align:middle line:84% So that just tells me that the q2 with second degree 01:05:27.260 --> 01:05:31.310 align:middle line:84% discrimination is equal to the q2* that you do with first 01:05:31.310 --> 01:05:32.900 align:middle line:90% degree discrimination. 01:05:32.900 --> 01:05:35.620 align:middle line:84% Or with the monopoly Apple equality theorem, 01:05:35.620 --> 01:05:38.360 align:middle line:84% the high types get the optimal product. 01:05:38.360 --> 01:05:40.910 align:middle line:90% And I think the sort of thing-- 01:05:40.910 --> 01:05:41.550 align:middle line:90% sense you get. 01:05:41.550 --> 01:05:43.310 align:middle line:84% Like, sometimes, I know people have 01:05:43.310 --> 01:05:48.580 align:middle line:84% this sense that there's excess consumption, or excess quantity. 01:05:48.580 --> 01:05:51.330 align:middle line:84% Like, I walk through that first class cabin on the airplane. 01:05:51.330 --> 01:05:56.260 align:middle line:84% It isn't that obscene that these people are drinking drinks 01:05:56.260 --> 01:06:00.020 align:middle line:84% from glass glasses and using metal silverware, or whatever. 01:06:00.020 --> 01:06:02.980 align:middle line:84% And you just have to think to yourself, wait, no, actually, 01:06:02.980 --> 01:06:05.153 align:middle line:84% I'm relatively low in the income distribution. 01:06:05.153 --> 01:06:06.820 align:middle line:84% And I have metal silverware at my house. 01:06:06.820 --> 01:06:09.640 align:middle line:84% And I drink out of glass cups instead of paper cups. 01:06:09.640 --> 01:06:14.860 align:middle line:84% It's just, that is, given the cost of providing metal, 01:06:14.860 --> 01:06:17.380 align:middle line:84% it seems like that's a totally reasonable price to be paying 01:06:17.380 --> 01:06:18.680 align:middle line:90% for people, or whatever. 01:06:18.680 --> 01:06:22.420 align:middle line:84% So you give them the optimal quality product 01:06:22.420 --> 01:06:25.120 align:middle line:90% and charge them for it. 01:06:25.120 --> 01:06:27.040 align:middle line:90% And then, what about q1? 01:06:27.040 --> 01:06:29.998 align:middle line:84% I differentiate this with respect to q1. 01:06:29.998 --> 01:06:30.790 align:middle line:90% I get a d(v)/d(q1). 01:06:30.790 --> 01:06:33.910 align:middle line:90% 01:06:33.910 --> 01:06:35.140 align:middle line:90% Again, it's equal to c. 01:06:35.140 --> 01:06:39.010 align:middle line:84% But then, I'm going to have two other terms, derivatives, 01:06:39.010 --> 01:06:42.170 align:middle line:90% d(v1)/d(q1) and d(v2)/d(q1). 01:06:42.170 --> 01:06:45.970 align:middle line:84% And so, what you get is d(v1)/d(q1), 01:06:45.970 --> 01:06:48.490 align:middle line:84% moving everything to the other side, equals c, 01:06:48.490 --> 01:06:51.670 align:middle line:84% plus partial of v2 with respect to q, 01:06:51.670 --> 01:06:53.920 align:middle line:84% minus partial of v1 with respect to q. 01:06:53.920 --> 01:06:56.470 align:middle line:90% 01:06:56.470 --> 01:06:59.800 align:middle line:84% Remember, the higher types have a higher incremental willingness 01:06:59.800 --> 01:07:02.680 align:middle line:84% to pay for quality at the same quality level. 01:07:02.680 --> 01:07:04.720 align:middle line:90% So this is greater than c. 01:07:04.720 --> 01:07:10.120 align:middle line:84% So the distortion is, I distort quality down for the low types 01:07:10.120 --> 01:07:13.580 align:middle line:84% and provide them with a suboptimal quality. 01:07:13.580 --> 01:07:15.580 align:middle line:84% If you've done that calculation on the airplane, 01:07:15.580 --> 01:07:17.330 align:middle line:84% I can't believe I'm sitting here in coach. 01:07:17.330 --> 01:07:19.930 align:middle line:84% And I can't open my laptop whatsoever. 01:07:19.930 --> 01:07:22.100 align:middle line:84% And my knees are pressed in the seat in front of me. 01:07:22.100 --> 01:07:25.810 align:middle line:84% Couldn't we just have moved the seats one inch further apart, 01:07:25.810 --> 01:07:27.590 align:middle line:90% take one seat out of the plane? 01:07:27.590 --> 01:07:29.300 align:middle line:84% I would be willing to pay this much more. 01:07:29.300 --> 01:07:30.770 align:middle line:90% They would make more money. 01:07:30.770 --> 01:07:32.000 align:middle line:90% Why don't they do that? 01:07:32.000 --> 01:07:34.750 align:middle line:84% Well, the answer is, yes, they could make more money 01:07:34.750 --> 01:07:36.520 align:middle line:84% in the coach cabin doing that and making 01:07:36.520 --> 01:07:37.880 align:middle line:90% the seats more comfortable. 01:07:37.880 --> 01:07:41.080 align:middle line:84% But then, the businessmen would be willing to sit in coach. 01:07:41.080 --> 01:07:44.140 align:middle line:84% So you have to make those coach seats uncomfortable enough 01:07:44.140 --> 01:07:46.580 align:middle line:84% that the businessmen will not sit in them. 01:07:46.580 --> 01:07:48.372 align:middle line:84% Your seats are the ones that are distorted. 01:07:48.372 --> 01:07:49.955 align:middle line:84% Theirs are where your knees don't bang 01:07:49.955 --> 01:07:51.290 align:middle line:90% into the seat in front of you. 01:07:51.290 --> 01:07:54.490 align:middle line:90% That's optimal quality. 01:07:54.490 --> 01:07:57.770 align:middle line:84% And so, what we do is, we distort quality down 01:07:57.770 --> 01:07:59.450 align:middle line:90% for the low types. 01:07:59.450 --> 01:08:02.780 align:middle line:84% And so, this is a new inefficiency of second degree 01:08:02.780 --> 01:08:03.900 align:middle line:90% price discrimination. 01:08:03.900 --> 01:08:06.840 align:middle line:84% We have all the old efficiencies, inefficiencies. 01:08:06.840 --> 01:08:11.270 align:middle line:84% Our new inefficiency, again, is suboptimal product quality. 01:08:11.270 --> 01:08:15.590 align:middle line:84% And the sub-optimal product quality is done-- 01:08:15.590 --> 01:08:19.189 align:middle line:84% it's because they don't have the ID to say, I'm rich 01:08:19.189 --> 01:08:21.630 align:middle line:84% or I'm poor, which seat I'm going to sit in. 01:08:21.630 --> 01:08:23.569 align:middle line:84% We have to have this extra distortion 01:08:23.569 --> 01:08:27.689 align:middle line:84% to allow them to screen without that signal, OK? 01:08:27.689 --> 01:08:30.569 align:middle line:90% 01:08:30.569 --> 01:08:31.740 align:middle line:90% What's the other comments? 01:08:31.740 --> 01:08:34.060 align:middle line:84% So the high types are getting positive surplus. 01:08:34.060 --> 01:08:35.140 align:middle line:90% The low types are not. 01:08:35.140 --> 01:08:36.934 align:middle line:84% We sometimes call that an information rent. 01:08:36.934 --> 01:08:39.899 align:middle line:90% 01:08:39.899 --> 01:08:43.529 align:middle line:84% Welfare is worse than first degree discrimination. 01:08:43.529 --> 01:08:47.550 align:middle line:84% If we could give the students their optimal seat pitch 01:08:47.550 --> 01:08:50.880 align:middle line:84% and charge them the optimal price, they would be better off. 01:08:50.880 --> 01:08:53.550 align:middle line:84% But the comparison with what would happen, for instance, 01:08:53.550 --> 01:08:58.529 align:middle line:84% if we require you to have only a single good and not 01:08:58.529 --> 01:09:01.050 align:middle line:84% have two different coach classes, that's 01:09:01.050 --> 01:09:04.020 align:middle line:90% an ambiguous distinction. 01:09:04.020 --> 01:09:06.180 align:middle line:84% So again, the fact that you may be 01:09:06.180 --> 01:09:07.950 align:middle line:84% able to create these low quality seats 01:09:07.950 --> 01:09:09.930 align:middle line:84% and serve people who would not be in the market 01:09:09.930 --> 01:09:12.569 align:middle line:84% if there were no low quality seats, social welfare 01:09:12.569 --> 01:09:15.300 align:middle line:84% can be better than if you had the only first class 01:09:15.300 --> 01:09:18.930 align:middle line:84% plane, for instance, which is what you might get if you didn't 01:09:18.930 --> 01:09:21.960 align:middle line:90% allow discrimination. 01:09:21.960 --> 01:09:27.330 align:middle line:84% OK, I would say, modern IO theory papers 01:09:27.330 --> 01:09:29.939 align:middle line:84% tend to work with a continuum of types model instead 01:09:29.939 --> 01:09:33.990 align:middle line:90% of a discrete-type model. 01:09:33.990 --> 01:09:36.279 align:middle line:84% These days, I have this awkward thing that Alex, 01:09:36.279 --> 01:09:38.279 align:middle line:84% when he teaches [14.]124, does a really good job 01:09:38.279 --> 01:09:40.240 align:middle line:84% on the continuum-type screening models. 01:09:40.240 --> 01:09:44.080 align:middle line:84% So I'm not going to cover continuum-type screening models. 01:09:44.080 --> 01:09:45.980 align:middle line:84% It's in the slides that I have here. 01:09:45.980 --> 01:09:49.015 align:middle line:90% 01:09:49.015 --> 01:09:51.390 align:middle line:84% [INAUDIBLE] is going to cover it in recitation on Friday. 01:09:51.390 --> 01:09:53.265 align:middle line:84% I think, I haven't looked at it this morning, 01:09:53.265 --> 01:09:57.870 align:middle line:84% but I think there's also a 2020 me discussing this material 01:09:57.870 --> 01:10:01.290 align:middle line:84% on Zoom video if you can't make recitation on Friday, 01:10:01.290 --> 01:10:03.960 align:middle line:84% and see me discussing the continuum of types price 01:10:03.960 --> 01:10:06.390 align:middle line:90% discrimination in a COVID world. 01:10:06.390 --> 01:10:08.435 align:middle line:84% I think that's on the website, too. 01:10:08.435 --> 01:10:11.130 align:middle line:90% 01:10:11.130 --> 01:10:15.540 align:middle line:84% But I mean, the general intuitions are just that, 01:10:15.540 --> 01:10:19.860 align:middle line:84% if you have three or four or five types instead of-- 01:10:19.860 --> 01:10:22.300 align:middle line:84% or a continuum of types instead of two types, 01:10:22.300 --> 01:10:24.590 align:middle line:84% you need to stop these guys from copying 01:10:24.590 --> 01:10:25.840 align:middle line:90% these guys buying the product. 01:10:25.840 --> 01:10:26.920 align:middle line:84% And then, for these guys, you need 01:10:26.920 --> 01:10:28.837 align:middle line:84% to stop these people from buying this product. 01:10:28.837 --> 01:10:31.220 align:middle line:84% You need to stop these people from buying this product. 01:10:31.220 --> 01:10:34.000 align:middle line:84% And so, in some sense, you get these cascading distortions, 01:10:34.000 --> 01:10:39.310 align:middle line:84% where any time I give something to the lowest type, 01:10:39.310 --> 01:10:41.890 align:middle line:84% the next lowest type gets more utility 01:10:41.890 --> 01:10:43.810 align:middle line:84% because they have to be given utility so they 01:10:43.810 --> 01:10:45.165 align:middle line:90% won't copy the lowest type. 01:10:45.165 --> 01:10:47.290 align:middle line:84% And then, because they're getting a better product, 01:10:47.290 --> 01:10:50.180 align:middle line:84% the next type up have to get a better product, and so on. 01:10:50.180 --> 01:10:52.270 align:middle line:84% So you get these places where you 01:10:52.270 --> 01:10:55.210 align:middle line:84% have very severe distortions, which is that the further you go 01:10:55.210 --> 01:10:58.788 align:middle line:84% down in the distribution, the more reasons you have to distort 01:10:58.788 --> 01:11:01.330 align:middle line:84% the package being given by the low, low types, because you're 01:11:01.330 --> 01:11:03.820 align:middle line:84% giving money to every higher type when you give them 01:11:03.820 --> 01:11:04.930 align:middle line:90% something. 01:11:04.930 --> 01:11:07.422 align:middle line:84% And then, a second intuition is, if there 01:11:07.422 --> 01:11:09.880 align:middle line:84% are types that there aren't a lot of, you want to give them 01:11:09.880 --> 01:11:14.980 align:middle line:84% a very bad deal because anything you give them, the fact 01:11:14.980 --> 01:11:17.720 align:middle line:84% that it's available raises the utility of the higher types. 01:11:17.720 --> 01:11:19.780 align:middle line:84% If there aren't very many people in that group, 01:11:19.780 --> 01:11:21.520 align:middle line:84% then you really want to discriminate. 01:11:21.520 --> 01:11:23.470 align:middle line:84% You want to give them a terrible product 01:11:23.470 --> 01:11:26.350 align:middle line:84% because the profit you get from giving them optimal quality 01:11:26.350 --> 01:11:28.280 align:middle line:84% is tiny when there aren't many people there. 01:11:28.280 --> 01:11:31.450 align:middle line:84% So people who are in a small fraction of the population, 01:11:31.450 --> 01:11:34.960 align:middle line:84% they also get really bad service on quality. 01:11:34.960 --> 01:11:38.630 align:middle line:84% But anyway, so there's a video on the website. 01:11:38.630 --> 01:11:42.550 align:middle line:84% I think what I want to do to jump ahead at the end is, 01:11:42.550 --> 01:11:46.840 align:middle line:90% let me just talk about bundling. 01:11:46.840 --> 01:11:55.770 align:middle line:84% So let's think about, you have a firm that's 01:11:55.770 --> 01:11:57.993 align:middle line:90% selling multiple products. 01:11:57.993 --> 01:12:00.900 align:middle line:90% 01:12:00.900 --> 01:12:03.960 align:middle line:84% What's the best way to sell multiple goods instead 01:12:03.960 --> 01:12:04.720 align:middle line:90% of a single good? 01:12:04.720 --> 01:12:07.170 align:middle line:84% So, for instance, Apple doesn't just sell phones. 01:12:07.170 --> 01:12:10.740 align:middle line:84% They sell phones, and chargers, and earbuds, 01:12:10.740 --> 01:12:13.370 align:middle line:90% and apps for the phones. 01:12:13.370 --> 01:12:17.890 align:middle line:90% 01:12:17.890 --> 01:12:20.420 align:middle line:84% Netflix doesn't just sell movie by movie. 01:12:20.420 --> 01:12:23.500 align:middle line:84% Netflix sells whole big bundles of movies. 01:12:23.500 --> 01:12:27.310 align:middle line:84% So, observation from this literature 01:12:27.310 --> 01:12:30.760 align:middle line:84% is that, often, if a firm sells multiple products that 01:12:30.760 --> 01:12:33.550 align:middle line:84% are used together, they're better off doing 01:12:33.550 --> 01:12:36.250 align:middle line:90% some kind of bundled pricing. 01:12:36.250 --> 01:12:38.630 align:middle line:84% Why do you do some kind of bundled pricing? 01:12:38.630 --> 01:12:40.630 align:middle line:84% I put it in this lecture because often, 01:12:40.630 --> 01:12:42.940 align:middle line:84% the reasons why you want to bundle goods together 01:12:42.940 --> 01:12:46.930 align:middle line:84% have something to do with price discrimination. 01:12:46.930 --> 01:12:51.040 align:middle line:84% So, the first example, due to Stigler, is, 01:12:51.040 --> 01:12:55.390 align:middle line:84% imagine you have consumers who have values for the two goods 01:12:55.390 --> 01:12:58.960 align:middle line:84% that you sell which are negatively correlated. 01:12:58.960 --> 01:13:04.168 align:middle line:84% So the example that Stigler gave is, 01:13:04.168 --> 01:13:06.460 align:middle line:84% suppose you have these types, theta, that are uniformly 01:13:06.460 --> 01:13:07.960 align:middle line:90% distributed on 0, 1. 01:13:07.960 --> 01:13:11.770 align:middle line:84% And these are about their preferences over movies. 01:13:11.770 --> 01:13:15.250 align:middle line:84% And so, a type theta consumer gets utility theta 01:13:15.250 --> 01:13:18.980 align:middle line:84% from watching some kind of superhero action movie 01:13:18.980 --> 01:13:25.172 align:middle line:84% and gets utility 1 minus theta from watching a romantic comedy. 01:13:25.172 --> 01:13:26.880 align:middle line:84% And people's preference over these things 01:13:26.880 --> 01:13:29.080 align:middle line:84% are just exactly negatively correlated. 01:13:29.080 --> 01:13:32.100 align:middle line:84% So if I'm a far right superhero movie person, 01:13:32.100 --> 01:13:34.810 align:middle line:84% I'm also the far left romantic comedy utility. 01:13:34.810 --> 01:13:37.650 align:middle line:84% And if I'm the far right romantic comedy utility, 01:13:37.650 --> 01:13:39.510 align:middle line:84% I'm the far left superhero quality. 01:13:39.510 --> 01:13:42.330 align:middle line:90% 01:13:42.330 --> 01:13:45.600 align:middle line:84% If Netflix had to price these things separately, 01:13:45.600 --> 01:13:48.330 align:middle line:84% and we have Netflix action/adventure movies 01:13:48.330 --> 01:13:52.590 align:middle line:84% and Netflix romantic comedy movies, what's going to happen? 01:13:52.590 --> 01:13:56.100 align:middle line:84% Well, if these are the values, it's going to set p* equals 1/2 01:13:56.100 --> 01:13:59.250 align:middle line:90% for each service. 01:13:59.250 --> 01:14:04.200 align:middle line:84% Every consumer is going to buy exactly one of the two services. 01:14:04.200 --> 01:14:11.250 align:middle line:84% And so, Netflix ends up earning profit 1/4 on each. 01:14:11.250 --> 01:14:12.240 align:middle line:90% I set a price of 1/2. 01:14:12.240 --> 01:14:14.700 align:middle line:90% I sell the 1/2 to the consumers. 01:14:14.700 --> 01:14:18.630 align:middle line:84% And that's the profits that I get. 01:14:18.630 --> 01:14:21.390 align:middle line:84% Suppose they instead follow this pure bundling thing, 01:14:21.390 --> 01:14:23.910 align:middle line:84% where we'll have both the action/adventure movies 01:14:23.910 --> 01:14:28.210 align:middle line:84% and the romantic comedies on the same service. 01:14:28.210 --> 01:14:29.860 align:middle line:84% Well, then, what everybody can do 01:14:29.860 --> 01:14:32.158 align:middle line:84% is, they can both watch their superhero movies. 01:14:32.158 --> 01:14:33.700 align:middle line:84% And they can watch romantic comedies, 01:14:33.700 --> 01:14:36.170 align:middle line:84% because they're both available free on the service. 01:14:36.170 --> 01:14:38.420 align:middle line:84% What utility do they get from doing that? 01:14:38.420 --> 01:14:43.450 align:middle line:84% They get utility theta plus 1 minus theta equals 1. 01:14:43.450 --> 01:14:47.440 align:middle line:84% And so, because they get utility 1, 01:14:47.440 --> 01:14:50.180 align:middle line:84% you can just set the price of the bundle equals 1. 01:14:50.180 --> 01:14:51.830 align:middle line:90% It's fully socially-efficient. 01:14:51.830 --> 01:14:54.460 align:middle line:84% We extract all of the social surplus. 01:14:54.460 --> 01:14:57.790 align:middle line:84% But one way to think about this bundle of what we're doing 01:14:57.790 --> 01:15:00.730 align:middle line:90% is, we just have the people-- 01:15:00.730 --> 01:15:03.190 align:middle line:84% we know the people who are buying the superhero movie 01:15:03.190 --> 01:15:08.180 align:middle line:84% channel have low values for the romantic movies. 01:15:08.180 --> 01:15:10.790 align:middle line:84% So we just want to charge them a lower price for that. 01:15:10.790 --> 01:15:13.990 align:middle line:84% And this combination of charging them a high price for one 01:15:13.990 --> 01:15:15.880 align:middle line:84% and a low price for one ends up being 01:15:15.880 --> 01:15:20.000 align:middle line:84% something you can do perfectly by bundling products together. 01:15:20.000 --> 01:15:23.725 align:middle line:84% So that would be one argument for bundling. 01:15:23.725 --> 01:15:27.980 align:middle line:90% 01:15:27.980 --> 01:15:31.370 align:middle line:84% There's a very nice paper by McAfee, MacMillan, and Winston 01:15:31.370 --> 01:15:35.300 align:middle line:84% that notes that Stigler gave this example making 01:15:35.300 --> 01:15:37.780 align:middle line:84% you think negative correlation is important. 01:15:37.780 --> 01:15:45.270 align:middle line:84% Actually, the same thing works with independent valuations. 01:15:45.270 --> 01:15:52.190 align:middle line:84% So suppose your values for romantic comedies 01:15:52.190 --> 01:15:56.070 align:middle line:84% and for superhero movies are completely independent draws. 01:15:56.070 --> 01:15:57.950 align:middle line:84% Then it's still the case that the firm would 01:15:57.950 --> 01:16:01.010 align:middle line:84% be better off bundling, not pure bundling 01:16:01.010 --> 01:16:02.810 align:middle line:84% like in Stigler, but with mixed bundling. 01:16:02.810 --> 01:16:04.500 align:middle line:90% You offer three packages. 01:16:04.500 --> 01:16:07.790 align:middle line:84% You offer the superhero movie channel, the romantic comedy 01:16:07.790 --> 01:16:10.970 align:middle line:90% channel, or Netflix total. 01:16:10.970 --> 01:16:14.210 align:middle line:84% And this mixed bundling scheme of offering 01:16:14.210 --> 01:16:17.780 align:middle line:84% the bundle and the two products separately strictly 01:16:17.780 --> 01:16:23.780 align:middle line:84% dominates offering the product separately, 01:16:23.780 --> 01:16:28.040 align:middle line:84% when you have independent valuations, OK? 01:16:28.040 --> 01:16:31.010 align:middle line:84% In some sense, it's an obvious statement that the mixed 01:16:31.010 --> 01:16:36.320 align:middle line:84% bundling strategy, this offer, p1, p2, and p-bundle, 01:16:36.320 --> 01:16:39.620 align:middle line:84% is at least weakly better, because you could always offer 01:16:39.620 --> 01:16:46.010 align:middle line:84% good 1 at p1*, good 2 at p2*, and price the bundle at p1* plus 01:16:46.010 --> 01:16:48.890 align:middle line:84% p2*, the bundle, in some sense, superfluous. 01:16:48.890 --> 01:16:51.920 align:middle line:84% But it doesn't hurt the monopolist's profits. 01:16:51.920 --> 01:16:54.140 align:middle line:84% But what McAfee, MacMillan, and Winston show 01:16:54.140 --> 01:16:58.410 align:middle line:84% is that, in fact, it strictly raises profits. 01:16:58.410 --> 01:17:01.290 align:middle line:84% And so, I'll just go through this as quickly as I can. 01:17:01.290 --> 01:17:07.250 align:middle line:84% So, start from the situation where you have p1*, p2*, 01:17:07.250 --> 01:17:09.470 align:middle line:90% and the price of the bundle. 01:17:09.470 --> 01:17:13.400 align:middle line:84% Then what's going to happen is, these consumers 01:17:13.400 --> 01:17:16.650 align:middle line:84% for which v1 is large are going to buy good 1. 01:17:16.650 --> 01:17:19.710 align:middle line:84% These for whom v2 is large are going to buy good 2. 01:17:19.710 --> 01:17:21.950 align:middle line:84% And then people here are going to buy the bundle. 01:17:21.950 --> 01:17:26.110 align:middle line:90% 01:17:26.110 --> 01:17:28.840 align:middle line:84% Imagine that what the monopolist does now is, 01:17:28.840 --> 01:17:31.810 align:middle line:84% it raises the price of good 2 by epsilon 01:17:31.810 --> 01:17:34.930 align:middle line:84% and leaves the bundle price unchanged. 01:17:34.930 --> 01:17:37.690 align:middle line:84% Who is going to react when you raise the price of good 2, 01:17:37.690 --> 01:17:40.130 align:middle line:84% when you leave the bundle price unchanged? 01:17:40.130 --> 01:17:45.310 align:middle line:84% Well, these consumers who would have formerly 01:17:45.310 --> 01:17:51.250 align:middle line:84% bought just good 2, now that good 2 has gone up in price, 01:17:51.250 --> 01:17:52.930 align:middle line:84% they're going to switch from buying 01:17:52.930 --> 01:17:56.020 align:middle line:90% good 2 to buying the bundle. 01:17:56.020 --> 01:17:59.230 align:middle line:84% And so we get this first order gain in profits 01:17:59.230 --> 01:18:02.530 align:middle line:84% from all of these people who were buying just good 2, 01:18:02.530 --> 01:18:07.480 align:middle line:84% now also buying good 1 from me, which has a positive markup. 01:18:07.480 --> 01:18:09.200 align:middle line:90% What do I lose? 01:18:09.200 --> 01:18:15.250 align:middle line:84% I lose these people who would have bought good 2 at p2*, 01:18:15.250 --> 01:18:18.010 align:middle line:84% but now don't want to pay p2* plus epsilon because it's not 01:18:18.010 --> 01:18:19.280 align:middle line:90% worth it to them. 01:18:19.280 --> 01:18:30.290 align:middle line:84% But we know that d(pi2)/d(p2) evaluated at p2* equals 0. 01:18:30.290 --> 01:18:34.010 align:middle line:84% So the fact that I lose these customers 01:18:34.010 --> 01:18:36.740 align:middle line:84% and charge a price here, I was the first order-indifferent 01:18:36.740 --> 01:18:39.540 align:middle line:84% between this price and this price anyway in this market. 01:18:39.540 --> 01:18:41.600 align:middle line:84% So I've got a second order loss from raising 01:18:41.600 --> 01:18:46.912 align:middle line:84% the price, a first order benefit from cutting the price-- 01:18:46.912 --> 01:18:48.620 align:middle line:84% sorry, from raising the price and getting 01:18:48.620 --> 01:18:50.550 align:middle line:90% them to buy the bundle instead. 01:18:50.550 --> 01:18:54.558 align:middle line:84% And therefore, I'm strictly better off by bundling. 01:18:54.558 --> 01:18:56.850 align:middle line:84% And so, that's the basic argument in McAfee, MacMillan, 01:18:56.850 --> 01:19:00.110 align:middle line:84% and Winston, is that mixed bundling is obviously 01:19:00.110 --> 01:19:01.350 align:middle line:90% weakly optimal. 01:19:01.350 --> 01:19:03.800 align:middle line:84% And if you just think about starting from that weakly 01:19:03.800 --> 01:19:05.403 align:middle line:84% optimal thing, and then just raising 01:19:05.403 --> 01:19:07.070 align:middle line:84% the price of the two goods individually, 01:19:07.070 --> 01:19:08.840 align:middle line:90% that's always better for you. 01:19:08.840 --> 01:19:11.150 align:middle line:84% So the fact that you can bundle and have people 01:19:11.150 --> 01:19:14.570 align:middle line:84% have this option to switch to the bundle, which lets you sell 01:19:14.570 --> 01:19:16.290 align:middle line:90% extra goods is good for you. 01:19:16.290 --> 01:19:18.440 align:middle line:84% And so, you do generally want to bundle 01:19:18.440 --> 01:19:20.690 align:middle line:84% if you're in this case, where values for the two goods 01:19:20.690 --> 01:19:21.810 align:middle line:90% are independent. 01:19:21.810 --> 01:19:24.410 align:middle line:90% 01:19:24.410 --> 01:19:26.010 align:middle line:90% OK, so I am out of time. 01:19:26.010 --> 01:19:28.720 align:middle line:90% So why don't I just stop there? 01:19:28.720 --> 01:19:41.000 align:middle line:90%