WEBVTT 00:00:00.000 --> 00:00:01.428 align:middle line:90% [SQUEAKING] 00:00:01.428 --> 00:00:01.928 align:middle line:90% 00:00:01.928 --> 00:00:03.832 align:middle line:90% [RUSTLING] 00:00:03.832 --> 00:00:05.260 align:middle line:90% [CLICKING] 00:00:05.260 --> 00:00:08.942 align:middle line:90% 00:00:08.942 --> 00:00:10.400 align:middle line:84% IAN BALL: Today we're going to talk 00:00:10.400 --> 00:00:12.560 align:middle line:90% about imperfect competition. 00:00:12.560 --> 00:00:17.780 align:middle line:84% I want to start with just a small review of what we've done, 00:00:17.780 --> 00:00:19.700 align:middle line:84% and then we'll move to imperfect competition. 00:00:19.700 --> 00:00:21.158 align:middle line:84% I think this fits in with a broader 00:00:21.158 --> 00:00:24.480 align:middle line:84% theme of the course where or a broader approach in the course 00:00:24.480 --> 00:00:26.880 align:middle line:84% where we're going to start with some simple examples 00:00:26.880 --> 00:00:28.680 align:middle line:90% to try to motivate the theory. 00:00:28.680 --> 00:00:31.280 align:middle line:84% Then we'll dig deep into the theory 00:00:31.280 --> 00:00:33.360 align:middle line:84% and maybe prove some theorems, and then we'll 00:00:33.360 --> 00:00:35.880 align:middle line:84% apply the theory to some substantive economic 00:00:35.880 --> 00:00:36.497 align:middle line:90% applications. 00:00:36.497 --> 00:00:38.080 align:middle line:84% Today is going to be one of those days 00:00:38.080 --> 00:00:40.800 align:middle line:84% where we dig into a substantive economic application. 00:00:40.800 --> 00:00:43.180 align:middle line:84% So if you don't have much of an econ background, 00:00:43.180 --> 00:00:46.100 align:middle line:84% some of what we covered today may be new to you. 00:00:46.100 --> 00:00:47.820 align:middle line:84% If you have take a lot of econ courses, 00:00:47.820 --> 00:00:50.120 align:middle line:90% this may be a bit of a review. 00:00:50.120 --> 00:00:52.600 align:middle line:84% But just a reminder of what we've done so far, 00:00:52.600 --> 00:00:55.440 align:middle line:84% we've been studying strategic form games, 00:00:55.440 --> 00:00:59.090 align:middle line:84% and we've looked at various solution concepts. 00:00:59.090 --> 00:01:01.650 align:middle line:84% And we've said that, in a strategic form game, 00:01:01.650 --> 00:01:06.050 align:middle line:84% we applied this procedure of iterated elimination of strictly 00:01:06.050 --> 00:01:07.730 align:middle line:90% dominated strategies. 00:01:07.730 --> 00:01:13.390 align:middle line:84% And we generated these nested sets of strategies. 00:01:13.390 --> 00:01:15.270 align:middle line:84% And at the end, we got to S infinity. 00:01:15.270 --> 00:01:18.090 align:middle line:84% And remember, what we said is that stronger assumptions 00:01:18.090 --> 00:01:20.610 align:middle line:84% about rationality and higher-order 00:01:20.610 --> 00:01:23.930 align:middle line:84% knowledge of rationality allowed us to get sharper predictions 00:01:23.930 --> 00:01:26.250 align:middle line:90% about how players will play. 00:01:26.250 --> 00:01:29.170 align:middle line:84% And at the end, when we get to S infinity, 00:01:29.170 --> 00:01:33.250 align:middle line:84% what we further know is that a subset 00:01:33.250 --> 00:01:36.130 align:middle line:84% of the rationalizable strategies are-- maybe 00:01:36.130 --> 00:01:38.250 align:middle line:84% I'll jump down to what we showed last time. 00:01:38.250 --> 00:01:45.130 align:middle line:84% We showed these two relationships. 00:01:45.130 --> 00:01:48.610 align:middle line:84% So we showed that every dominant strategy equilibrium 00:01:48.610 --> 00:01:51.610 align:middle line:84% is a Nash equilibrium, specifically a pure strategy 00:01:51.610 --> 00:01:53.050 align:middle line:90% Nash equilibrium. 00:01:53.050 --> 00:01:55.050 align:middle line:84% And we showed that every pure strategy Nash 00:01:55.050 --> 00:01:58.730 align:middle line:90% equilibrium is rationalizable. 00:01:58.730 --> 00:02:00.690 align:middle line:84% But there's actually one more inequality-- 00:02:00.690 --> 00:02:02.530 align:middle line:90% or inclusion we can put here. 00:02:02.530 --> 00:02:06.250 align:middle line:84% And here I'll put mixed-strategy Nash equilibrium 00:02:06.250 --> 00:02:09.050 align:middle line:90% with positive probability. 00:02:09.050 --> 00:02:11.990 align:middle line:84% So let me define what I did here. 00:02:11.990 --> 00:02:14.850 align:middle line:84% And the proof of this inclusion is quite similar to the proof 00:02:14.850 --> 00:02:18.210 align:middle line:84% that we did in class last Thursday. 00:02:18.210 --> 00:02:20.330 align:middle line:84% So I'd encourage you to go through the argument 00:02:20.330 --> 00:02:22.190 align:middle line:84% and see if you can extend it to this case. 00:02:22.190 --> 00:02:26.530 align:middle line:84% So here what I mean is this is the set of all strategy profiles 00:02:26.530 --> 00:02:34.530 align:middle line:84% that are played with positive probability 00:02:34.530 --> 00:02:37.270 align:middle line:84% in some mixed-strategy Nash equilibrium. 00:02:37.270 --> 00:02:52.050 align:middle line:90% 00:02:52.050 --> 00:02:54.070 align:middle line:84% So just to make sure we're on the same page, 00:02:54.070 --> 00:02:57.780 align:middle line:84% why is it the case that every pure strategy Nash equilibrium 00:02:57.780 --> 00:02:59.620 align:middle line:90% is an element of this set? 00:02:59.620 --> 00:03:01.980 align:middle line:84% Why is every pure strategy Nash equilibrium 00:03:01.980 --> 00:03:05.060 align:middle line:84% in this set of positive probability mixed-strategy Nash 00:03:05.060 --> 00:03:06.320 align:middle line:90% equilibrium profiles? 00:03:06.320 --> 00:03:10.220 align:middle line:90% 00:03:10.220 --> 00:03:10.900 align:middle line:90% Yeah. 00:03:10.900 --> 00:03:12.525 align:middle line:84% AUDIENCE: I don't remember [INAUDIBLE]. 00:03:12.525 --> 00:03:14.000 align:middle line:90% IAN BALL: That's fine, yeah. 00:03:14.000 --> 00:03:15.820 align:middle line:84% AUDIENCE: [INAUDIBLE] strategy [INAUDIBLE]. 00:03:15.820 --> 00:03:16.520 align:middle line:90% IAN BALL: Yeah, exactly. 00:03:16.520 --> 00:03:18.145 align:middle line:84% Every pure strategy and mixed strategy, 00:03:18.145 --> 00:03:19.240 align:middle line:90% so that's the first step. 00:03:19.240 --> 00:03:21.180 align:middle line:84% And then the second step is to say, well, 00:03:21.180 --> 00:03:24.140 align:middle line:84% if something is a pure strategy Nash equilibrium, 00:03:24.140 --> 00:03:27.260 align:middle line:84% it's also a mixed-strategy Nash equilibrium where everyone just 00:03:27.260 --> 00:03:29.660 align:middle line:84% plays their component of that strategy profile 00:03:29.660 --> 00:03:31.220 align:middle line:90% with probability 1. 00:03:31.220 --> 00:03:34.100 align:middle line:84% So since that's also a mixed-strategy Nash equilibrium, 00:03:34.100 --> 00:03:37.540 align:middle line:84% is this strategy profile played with positive probability 00:03:37.540 --> 00:03:39.520 align:middle line:84% in some mixed-strategy Nash equilibrium? 00:03:39.520 --> 00:03:42.260 align:middle line:84% Yes, in fact, it's played with probability 1 00:03:42.260 --> 00:03:44.560 align:middle line:84% in a particular mixed-strategy Nash equilibrium. 00:03:44.560 --> 00:03:47.360 align:middle line:84% So it's clear that this is a subset of this. 00:03:47.360 --> 00:03:49.380 align:middle line:84% The argument that this is a subset of this 00:03:49.380 --> 00:03:51.143 align:middle line:90% is maybe a little more involved. 00:03:51.143 --> 00:03:53.060 align:middle line:84% But as I said, it's quite similar to the proof 00:03:53.060 --> 00:03:54.540 align:middle line:90% we did last week. 00:03:54.540 --> 00:03:56.740 align:middle line:84% OK, so that's the theory up to the point 00:03:56.740 --> 00:03:58.100 align:middle line:90% that we've done so far. 00:03:58.100 --> 00:04:01.780 align:middle line:84% And let me now move to the main application for today, 00:04:01.780 --> 00:04:03.680 align:middle line:90% which is imperfect competition. 00:04:03.680 --> 00:04:13.340 align:middle line:90% 00:04:13.340 --> 00:04:15.422 align:middle line:84% And to understand imperfect competition, 00:04:15.422 --> 00:04:17.339 align:middle line:84% I think it's helpful to think of it as falling 00:04:17.339 --> 00:04:19.420 align:middle line:90% between two extreme cases. 00:04:19.420 --> 00:04:22.079 align:middle line:84% So on the one hand, we have perfect competition. 00:04:22.079 --> 00:04:28.980 align:middle line:90% 00:04:28.980 --> 00:04:32.040 align:middle line:84% And then at the other extreme, we have monopoly. 00:04:32.040 --> 00:04:34.660 align:middle line:90% 00:04:34.660 --> 00:04:37.760 align:middle line:84% And then imperfect competition falls somewhere in between. 00:04:37.760 --> 00:04:38.680 align:middle line:90% So I'll put it here. 00:04:38.680 --> 00:04:46.500 align:middle line:90% 00:04:46.500 --> 00:04:50.720 align:middle line:84% Now, formally defining these concepts can be a little tricky, 00:04:50.720 --> 00:04:52.890 align:middle line:84% but let me give some ideas about what we mean. 00:04:52.890 --> 00:04:54.265 align:middle line:84% And again, people use these terms 00:04:54.265 --> 00:04:56.723 align:middle line:84% in slightly different meanings, in slightly different ways, 00:04:56.723 --> 00:04:57.830 align:middle line:90% in different contexts. 00:04:57.830 --> 00:04:59.750 align:middle line:84% But perfect competition, we normally 00:04:59.750 --> 00:05:02.730 align:middle line:84% think of that as a setting where there's many small firms. 00:05:02.730 --> 00:05:08.630 align:middle line:90% 00:05:08.630 --> 00:05:11.370 align:middle line:84% Monopoly is a situation where we just have one firm. 00:05:11.370 --> 00:05:14.790 align:middle line:84% They're the only firm offering a particular good or product. 00:05:14.790 --> 00:05:18.408 align:middle line:90% So here, we have one firm. 00:05:18.408 --> 00:05:19.950 align:middle line:84% Usually, that one firm would be large 00:05:19.950 --> 00:05:21.670 align:middle line:90% since they're the only firm. 00:05:21.670 --> 00:05:24.690 align:middle line:84% And then imperfect competition lies somewhere in between. 00:05:24.690 --> 00:05:28.350 align:middle line:84% We normally think that there are maybe a few large firms. 00:05:28.350 --> 00:05:30.910 align:middle line:84% This is sometimes also called oligopoly. 00:05:30.910 --> 00:05:34.250 align:middle line:90% So a few maybe large firms. 00:05:34.250 --> 00:05:39.030 align:middle line:90% 00:05:39.030 --> 00:05:42.130 align:middle line:84% And the implication of this is that, in perfect competition, 00:05:42.130 --> 00:05:44.910 align:middle line:84% when we have many small firms, each firm 00:05:44.910 --> 00:05:46.570 align:middle line:90% is what's called a price taker. 00:05:46.570 --> 00:05:51.590 align:middle line:90% 00:05:51.590 --> 00:05:52.690 align:middle line:90% What do I mean by that? 00:05:52.690 --> 00:05:54.650 align:middle line:90% I'm some small firm in a market. 00:05:54.650 --> 00:05:58.190 align:middle line:84% I can't influence what the market price is for the product 00:05:58.190 --> 00:05:59.470 align:middle line:90% that I'm selling. 00:05:59.470 --> 00:06:01.710 align:middle line:84% So the classic example of this would 00:06:01.710 --> 00:06:05.690 align:middle line:84% be maybe commodities markets, like wheat or corn. 00:06:05.690 --> 00:06:08.750 align:middle line:90% 00:06:08.750 --> 00:06:13.030 align:middle line:84% So if I'm a small farmer and I'm choosing how much corn 00:06:13.030 --> 00:06:15.870 align:middle line:84% to produce or to sell in the market this year, 00:06:15.870 --> 00:06:19.670 align:middle line:84% my decision about how much my particular farm produces 00:06:19.670 --> 00:06:23.190 align:middle line:84% is unlikely to affect the global market price for corn 00:06:23.190 --> 00:06:25.750 align:middle line:84% because there's many, many firms and many, many farms 00:06:25.750 --> 00:06:27.830 align:middle line:84% in the world that are producing corn. 00:06:27.830 --> 00:06:29.430 align:middle line:84% And another important aspect of this 00:06:29.430 --> 00:06:31.930 align:middle line:84% is that these are homogeneous products, 00:06:31.930 --> 00:06:35.270 align:middle line:84% and that's another common attribute 00:06:35.270 --> 00:06:37.470 align:middle line:90% of perfect competition. 00:06:37.470 --> 00:06:40.070 align:middle line:84% If we're all producing corn, but my corn 00:06:40.070 --> 00:06:42.650 align:middle line:84% is special and better than everyone else's corn. 00:06:42.650 --> 00:06:45.230 align:middle line:84% Now, I might not be such a small player anymore. 00:06:45.230 --> 00:06:48.000 align:middle line:90% 00:06:48.000 --> 00:06:50.260 align:middle line:84% Then in the case of imperfect competition, 00:06:50.260 --> 00:06:52.480 align:middle line:84% where we have a few large firms, we normally 00:06:52.480 --> 00:06:55.540 align:middle line:84% think of what we say is that these firms have market power. 00:06:55.540 --> 00:06:58.400 align:middle line:90% 00:06:58.400 --> 00:07:00.840 align:middle line:90% What does market power mean? 00:07:00.840 --> 00:07:02.873 align:middle line:84% It's really the opposite of being a price taker. 00:07:02.873 --> 00:07:05.040 align:middle line:84% Though, we can think of this kind of as a continuum. 00:07:05.040 --> 00:07:08.400 align:middle line:84% With a price taker, I have no control over the market 00:07:08.400 --> 00:07:10.480 align:middle line:90% price for some item. 00:07:10.480 --> 00:07:13.800 align:middle line:84% If I have market power, then my production decisions 00:07:13.800 --> 00:07:16.800 align:middle line:84% can have some effect on what the market price will be. 00:07:16.800 --> 00:07:18.620 align:middle line:84% So when we have a few large firms, 00:07:18.620 --> 00:07:22.560 align:middle line:84% if someone floods the market with a lot of their goods, 00:07:22.560 --> 00:07:25.000 align:middle line:84% then the market price of that good may fall. 00:07:25.000 --> 00:07:26.960 align:middle line:84% That's an example of market power. 00:07:26.960 --> 00:07:28.400 align:middle line:84% So if there's a few countries that 00:07:28.400 --> 00:07:31.800 align:middle line:84% produce oil in the world and one of them, say Saudi Arabia, 00:07:31.800 --> 00:07:34.180 align:middle line:84% produces much, much more oil this year, 00:07:34.180 --> 00:07:36.680 align:middle line:84% then that's probably going to have some effect on the market 00:07:36.680 --> 00:07:37.380 align:middle line:90% price for oil. 00:07:37.380 --> 00:07:41.800 align:middle line:84% It's probably going to bring down the market price for oil. 00:07:41.800 --> 00:07:45.000 align:middle line:84% When we have a few large firms, maybe an example of this, 00:07:45.000 --> 00:07:48.220 align:middle line:84% there's different degrees of imperfect competition. 00:07:48.220 --> 00:07:53.380 align:middle line:84% But maybe I think cell phone companies are a good example. 00:07:53.380 --> 00:07:56.240 align:middle line:84% In the US, you maybe have two or three large cell phone carriers 00:07:56.240 --> 00:07:58.200 align:middle line:90% that have their large networks. 00:07:58.200 --> 00:07:59.920 align:middle line:84% But we don't have a lot of small firms, 00:07:59.920 --> 00:08:02.920 align:middle line:84% and there's some barriers to entry. 00:08:02.920 --> 00:08:07.920 align:middle line:84% Another example of market power could be due to location. 00:08:07.920 --> 00:08:10.120 align:middle line:84% So it may be that even if there's 00:08:10.120 --> 00:08:12.560 align:middle line:84% a lot of firms producing a good, there 00:08:12.560 --> 00:08:14.320 align:middle line:84% may only be a small number of firms 00:08:14.320 --> 00:08:17.040 align:middle line:90% producing in a particular area. 00:08:17.040 --> 00:08:18.960 align:middle line:84% And this is going to be really relevant when 00:08:18.960 --> 00:08:21.320 align:middle line:90% transportation costs are high. 00:08:21.320 --> 00:08:25.080 align:middle line:84% So for instance, maybe there's a lot 00:08:25.080 --> 00:08:27.960 align:middle line:84% of coffee shops in the world, but right around MIT, 00:08:27.960 --> 00:08:29.600 align:middle line:90% there may only be a few. 00:08:29.600 --> 00:08:31.780 align:middle line:84% And if you take your coffee over long distances, 00:08:31.780 --> 00:08:32.900 align:middle line:90% it's going to get cold. 00:08:32.900 --> 00:08:35.340 align:middle line:84% So you're not really considering a coffee shop in New York 00:08:35.340 --> 00:08:37.048 align:middle line:84% even if New York, maybe has better coffee 00:08:37.048 --> 00:08:39.120 align:middle line:90% than some places in Boston. 00:08:39.120 --> 00:08:41.039 align:middle line:84% Another source of market power could 00:08:41.039 --> 00:08:44.770 align:middle line:90% be product differentiation. 00:08:44.770 --> 00:08:47.650 align:middle line:84% And this is what I was getting at with the corn example. 00:08:47.650 --> 00:08:49.250 align:middle line:84% Corn is the opposite case where we 00:08:49.250 --> 00:08:50.970 align:middle line:90% don't see much differentiation. 00:08:50.970 --> 00:08:52.650 align:middle line:90% But let's think about Apple. 00:08:52.650 --> 00:08:55.530 align:middle line:84% There's a lot of different companies that produce phones, 00:08:55.530 --> 00:09:00.010 align:middle line:84% but you might find Apple iPhones to be a different product 00:09:00.010 --> 00:09:02.090 align:middle line:84% than a Samsung phone or a Google phone 00:09:02.090 --> 00:09:03.710 align:middle line:84% or a phone produced by another firm. 00:09:03.710 --> 00:09:05.570 align:middle line:84% So even if there are many companies that 00:09:05.570 --> 00:09:08.890 align:middle line:84% are producing a smartphone, if these companies 00:09:08.890 --> 00:09:10.968 align:middle line:84% produce slightly differentiated products, 00:09:10.968 --> 00:09:13.010 align:middle line:84% then Apple has a bit of flexibility in what price 00:09:13.010 --> 00:09:13.950 align:middle line:90% it charges. 00:09:13.950 --> 00:09:16.937 align:middle line:84% If an iPhone is a bit more expensive than a Samsung phone, 00:09:16.937 --> 00:09:18.770 align:middle line:84% a lot of people will still choose that phone 00:09:18.770 --> 00:09:20.070 align:middle line:90% because they like Apple more. 00:09:20.070 --> 00:09:22.730 align:middle line:84% And the same with Samsung, there may be some Samsung loyalists 00:09:22.730 --> 00:09:24.090 align:middle line:90% out there. 00:09:24.090 --> 00:09:26.770 align:middle line:84% And then monopoly is the case, the extreme case 00:09:26.770 --> 00:09:28.690 align:middle line:90% where we have a single firm. 00:09:28.690 --> 00:09:30.470 align:middle line:90% So they still have market power. 00:09:30.470 --> 00:09:32.610 align:middle line:84% Maybe they have extreme market power. 00:09:32.610 --> 00:09:35.030 align:middle line:84% It's always hard to find an example of a pure monopoly, 00:09:35.030 --> 00:09:35.810 align:middle line:90% but can you think of any? 00:09:35.810 --> 00:09:37.310 align:middle line:84% Are there any cases that you've come 00:09:37.310 --> 00:09:39.850 align:middle line:84% across where you think there's really only one firm that's 00:09:39.850 --> 00:09:42.810 align:middle line:84% selling a particular good or offering a certain service 00:09:42.810 --> 00:09:45.930 align:middle line:90% or product? 00:09:45.930 --> 00:09:46.782 align:middle line:90% Yeah. 00:09:46.782 --> 00:09:47.490 align:middle line:90% AUDIENCE: Subway. 00:09:47.490 --> 00:09:49.407 align:middle line:84% IAN BALL: The subway is a great example, yeah. 00:09:49.407 --> 00:09:51.690 align:middle line:90% 00:09:51.690 --> 00:09:56.850 align:middle line:84% So the subway, say the MBTA in Boston. 00:09:56.850 --> 00:09:58.562 align:middle line:90% There's only one game in town. 00:09:58.562 --> 00:10:00.270 align:middle line:84% You can't just, as a private company say, 00:10:00.270 --> 00:10:01.978 align:middle line:84% I'm going to start digging up the streets 00:10:01.978 --> 00:10:03.850 align:middle line:84% and building my own subway system. 00:10:03.850 --> 00:10:06.230 align:middle line:84% Now, of course, what counts as a monopoly, 00:10:06.230 --> 00:10:08.730 align:middle line:84% it always depends on what we consider a close substitute. 00:10:08.730 --> 00:10:11.090 align:middle line:84% So it is true that, instead of taking the subway, 00:10:11.090 --> 00:10:13.630 align:middle line:84% you could take a Bluebike, or you could take a Lyft. 00:10:13.630 --> 00:10:15.310 align:middle line:84% That's some kind of a substitute. 00:10:15.310 --> 00:10:17.210 align:middle line:84% But in terms of getting on a train that 00:10:17.210 --> 00:10:19.210 align:middle line:84% goes quickly underground and doesn't have 00:10:19.210 --> 00:10:20.770 align:middle line:84% any contact with traffic, that really 00:10:20.770 --> 00:10:24.050 align:middle line:84% is something that only the MBTA, only a government monopoly 00:10:24.050 --> 00:10:25.310 align:middle line:90% is able to provide. 00:10:25.310 --> 00:10:26.590 align:middle line:90% What are some other examples? 00:10:26.590 --> 00:10:27.110 align:middle line:90% Yeah. 00:10:27.110 --> 00:10:28.790 align:middle line:84% AUDIENCE: This is more of a monopsony, 00:10:28.790 --> 00:10:31.110 align:middle line:84% but if you're in a coal mining town 00:10:31.110 --> 00:10:33.490 align:middle line:84% and there's only one mining company. 00:10:33.490 --> 00:10:36.373 align:middle line:84% IAN BALL: Right, that's a great example. 00:10:36.373 --> 00:10:38.290 align:middle line:84% Yeah, maybe monopsony, maybe I won't put it up 00:10:38.290 --> 00:10:39.830 align:middle line:84% here just to avoid confusion with monopsony. 00:10:39.830 --> 00:10:42.163 align:middle line:84% But that's the case where you're the only buyer in town. 00:10:42.163 --> 00:10:45.020 align:middle line:90% You're the consumer of labor. 00:10:45.020 --> 00:10:47.740 align:middle line:84% Maybe, in that context, if there's 00:10:47.740 --> 00:10:50.003 align:middle line:84% a labor market in that town, if there's a labor union, 00:10:50.003 --> 00:10:51.920 align:middle line:84% that might be a monopoly in that town as well. 00:10:51.920 --> 00:10:53.740 align:middle line:84% But that's a great example of a monopsony. 00:10:53.740 --> 00:10:54.550 align:middle line:90% Yeah, in the back. 00:10:54.550 --> 00:10:56.300 align:middle line:84% AUDIENCE: Normally, like private companies 00:10:56.300 --> 00:10:59.420 align:middle line:84% are contracted for power or something by the government. 00:10:59.420 --> 00:11:01.340 align:middle line:84% IAN BALL: Yeah, so often, utilities, and I 00:11:01.340 --> 00:11:02.820 align:middle line:90% put cell phones up here. 00:11:02.820 --> 00:11:04.440 align:middle line:90% It's a close call. 00:11:04.440 --> 00:11:08.860 align:middle line:84% But some utilities, especially in a local market, 00:11:08.860 --> 00:11:10.487 align:middle line:84% if you have an apartment here in Boston 00:11:10.487 --> 00:11:12.820 align:middle line:84% and you try to find your internet provider or your phone 00:11:12.820 --> 00:11:13.320 align:middle line:90% provider-- 00:11:13.320 --> 00:11:15.720 align:middle line:84% I guess, people don't have landline phones anymore. 00:11:15.720 --> 00:11:17.460 align:middle line:84% But your internet provider, you may only 00:11:17.460 --> 00:11:19.348 align:middle line:90% have one effective option. 00:11:19.348 --> 00:11:20.640 align:middle line:90% So that's another good example. 00:11:20.640 --> 00:11:21.080 align:middle line:90% Yeah. 00:11:21.080 --> 00:11:23.372 align:middle line:84% AUDIENCE: I'm not sure if that is imperfect competition 00:11:23.372 --> 00:11:26.380 align:middle line:84% or monopoly, but pharmaceutical companies and drugs they make. 00:11:26.380 --> 00:11:28.775 align:middle line:84% IAN BALL: Great, so I think, again, there's 00:11:28.775 --> 00:11:31.400 align:middle line:84% sometimes blurry lines between imperfect competition, monopoly. 00:11:31.400 --> 00:11:33.920 align:middle line:84% But I think a great example of this would be a patent. 00:11:33.920 --> 00:11:37.320 align:middle line:84% So if I'm a private company and I produce a drug, 00:11:37.320 --> 00:11:39.245 align:middle line:84% I spend a lot of money developing this drug, 00:11:39.245 --> 00:11:41.620 align:middle line:84% I'm then given a certain period of time by the government 00:11:41.620 --> 00:11:43.800 align:middle line:84% where I'm the exclusive supplier of that drug. 00:11:43.800 --> 00:11:47.157 align:middle line:84% Now, again, whether a monopolist or not might depend on, 00:11:47.157 --> 00:11:48.740 align:middle line:84% well, is there a very close substitute 00:11:48.740 --> 00:11:50.740 align:middle line:84% for that drug that's offered by another company? 00:11:50.740 --> 00:11:53.300 align:middle line:84% But if I really come along with a completely new drug, 00:11:53.300 --> 00:11:55.162 align:middle line:90% I have a government monopoly. 00:11:55.162 --> 00:11:56.620 align:middle line:84% The government says, no one else is 00:11:56.620 --> 00:11:57.940 align:middle line:84% allowed to produce the drug that you're 00:11:57.940 --> 00:12:00.100 align:middle line:84% producing for some period of time, and the goal of that 00:12:00.100 --> 00:12:02.468 align:middle line:84% is to give firms the incentive to invest in these drugs 00:12:02.468 --> 00:12:04.260 align:middle line:84% because developing them is quite expensive. 00:12:04.260 --> 00:12:05.960 align:middle line:90% Any final examples? 00:12:05.960 --> 00:12:08.100 align:middle line:90% These are all good. 00:12:08.100 --> 00:12:09.760 align:middle line:84% I think another big one is sports. 00:12:09.760 --> 00:12:13.260 align:middle line:84% So the NFL, the MLB, there was actually a Supreme Court ruling 00:12:13.260 --> 00:12:16.540 align:middle line:84% that gave the MLB an official exemption 00:12:16.540 --> 00:12:19.140 align:middle line:90% from anti-monopoly laws. 00:12:19.140 --> 00:12:23.660 align:middle line:84% So the NFL, we take it for granted that there's 00:12:23.660 --> 00:12:25.460 align:middle line:90% a draft for the NFL. 00:12:25.460 --> 00:12:27.140 align:middle line:84% Why is there not a draft when you guys 00:12:27.140 --> 00:12:29.820 align:middle line:84% are trying to get jobs at tech companies after you graduate? 00:12:29.820 --> 00:12:31.500 align:middle line:84% Well, they wouldn't all participate in a draft. 00:12:31.500 --> 00:12:32.680 align:middle line:84% They're competing against each other. 00:12:32.680 --> 00:12:34.222 align:middle line:84% So the reason why we can have a draft 00:12:34.222 --> 00:12:36.020 align:middle line:84% is that it's legal for these firms 00:12:36.020 --> 00:12:39.570 align:middle line:84% to band together and enter this collective agreement 00:12:39.570 --> 00:12:41.590 align:middle line:84% where they all engage in a draft and they 00:12:41.590 --> 00:12:43.328 align:middle line:84% agree to follow the rules of this draft. 00:12:43.328 --> 00:12:45.870 align:middle line:84% If Google and Facebook tried to have a draft for MIT students 00:12:45.870 --> 00:12:47.950 align:middle line:84% after you graduated and have first-round picks 00:12:47.950 --> 00:12:50.710 align:middle line:84% and second-round picks, that would violate antitrust laws. 00:12:50.710 --> 00:12:53.670 align:middle line:84% But the NFL and the MLB, et cetera have 00:12:53.670 --> 00:12:55.650 align:middle line:84% gotten a special government exemption, 00:12:55.650 --> 00:12:57.990 align:middle line:84% and that allows them to do various things, 00:12:57.990 --> 00:13:00.210 align:middle line:84% bargain with broadcasters in a collective way, 00:13:00.210 --> 00:13:02.065 align:middle line:84% have things like a draft, have restrictions 00:13:02.065 --> 00:13:04.190 align:middle line:84% on the building of new stadiums and the development 00:13:04.190 --> 00:13:05.350 align:middle line:90% of new teams. 00:13:05.350 --> 00:13:07.540 align:middle line:84% OK, so this is a bit of actual economics, 00:13:07.540 --> 00:13:09.290 align:middle line:84% maybe more applied economics for us today. 00:13:09.290 --> 00:13:12.493 align:middle line:84% But now let's move into some of the classical theoretical models 00:13:12.493 --> 00:13:13.410 align:middle line:90% that can explain this. 00:13:13.410 --> 00:13:15.190 align:middle line:84% Maybe one more, I guess, I had in my notes 00:13:15.190 --> 00:13:18.390 align:middle line:84% that I didn't say would be the US postal Service. 00:13:18.390 --> 00:13:20.170 align:middle line:84% Again, it's a bit of a partial monopoly. 00:13:20.170 --> 00:13:23.530 align:middle line:84% There's very specific services that no one else can provide, 00:13:23.530 --> 00:13:25.710 align:middle line:84% but it does compete with, say, UPS and FedEx 00:13:25.710 --> 00:13:26.890 align:middle line:90% for certain other services. 00:13:26.890 --> 00:13:29.570 align:middle line:84% So some of these things are a bit-- are not so clear cut. 00:13:29.570 --> 00:13:31.730 align:middle line:84% And of course, when firms go to court, 00:13:31.730 --> 00:13:33.470 align:middle line:84% this is exactly what they argue about. 00:13:33.470 --> 00:13:36.070 align:middle line:84% So firms love to argue that there are actually 00:13:36.070 --> 00:13:38.010 align:middle line:84% a lot of close substitutes for their products, 00:13:38.010 --> 00:13:39.910 align:middle line:84% and they're not really a monopolist in this small market 00:13:39.910 --> 00:13:42.452 align:middle line:84% because really they're operating in this much broader market. 00:13:42.452 --> 00:13:44.908 align:middle line:84% So firms always want to argue that the market they're in 00:13:44.908 --> 00:13:46.950 align:middle line:84% is not some narrowly defined market where they're 00:13:46.950 --> 00:13:49.792 align:middle line:84% the only player but, in fact, a much broader market where 00:13:49.792 --> 00:13:51.250 align:middle line:84% there's other forms of competition. 00:13:51.250 --> 00:13:52.470 align:middle line:84% So if I were the subway and I wanted 00:13:52.470 --> 00:13:53.890 align:middle line:84% to say I'm not a monopolist, I would say, 00:13:53.890 --> 00:13:55.432 align:middle line:84% no, I'm in the transportation market, 00:13:55.432 --> 00:13:57.270 align:middle line:84% and there's tons of forms of transportation 00:13:57.270 --> 00:13:59.170 align:middle line:84% whereas if I wanted to argue that they were monopolist, 00:13:59.170 --> 00:13:59.750 align:middle line:90% I might say-- 00:13:59.750 --> 00:14:04.590 align:middle line:84% I might define transportation a lot more narrowly. 00:14:04.590 --> 00:14:06.170 align:middle line:84% So now that we have that background, 00:14:06.170 --> 00:14:09.990 align:middle line:84% let's get into a few classical game-theoretic models that 00:14:09.990 --> 00:14:12.190 align:middle line:84% try to understand the interaction of firms 00:14:12.190 --> 00:14:14.470 align:middle line:84% in imperfect competition and in monopoly. 00:14:14.470 --> 00:14:16.830 align:middle line:84% And the first ingredient for these models 00:14:16.830 --> 00:14:20.228 align:middle line:84% is going to be defining what demand is. 00:14:20.228 --> 00:14:22.770 align:middle line:84% So again, if you take an econ class, you will have seen this. 00:14:22.770 --> 00:14:25.310 align:middle line:84% But demand captures at a given price, 00:14:25.310 --> 00:14:28.510 align:middle line:84% how many units of a product am I willing to purchase? 00:14:28.510 --> 00:14:31.350 align:middle line:84% And naturally, your demand for a product 00:14:31.350 --> 00:14:32.950 align:middle line:90% is going to depend on the price. 00:14:32.950 --> 00:14:35.040 align:middle line:84% Generally, people will buy more of something 00:14:35.040 --> 00:14:37.647 align:middle line:84% if the price of that good is lower. 00:14:37.647 --> 00:14:39.480 align:middle line:84% But let's go through a really simple example 00:14:39.480 --> 00:14:41.317 align:middle line:84% to try to make this more concrete. 00:14:41.317 --> 00:14:43.900 align:middle line:84% Let's think about-- let's say it can be the demand for apples. 00:14:43.900 --> 00:14:45.020 align:middle line:90% It doesn't really matter. 00:14:45.020 --> 00:14:47.562 align:middle line:84% And let's say, in this economy, there's only three consumers. 00:14:47.562 --> 00:14:51.000 align:middle line:84% We'll call them consumer 1, consumer 2, and consumer 3. 00:14:51.000 --> 00:14:56.238 align:middle line:84% And apples, I would say, are not an infinitely divisible good. 00:14:56.238 --> 00:14:57.780 align:middle line:84% I mean, you could sell half an Apple, 00:14:57.780 --> 00:14:58.780 align:middle line:90% but that's really not done. 00:14:58.780 --> 00:15:00.040 align:middle line:84% We're going to think of these as-- 00:15:00.040 --> 00:15:02.290 align:middle line:84% you're only going to be able to buy 1, 2, or 3 apples. 00:15:02.290 --> 00:15:05.620 align:middle line:84% You can't buy 1.75, or you can't buy a lottery over apples. 00:15:05.620 --> 00:15:08.080 align:middle line:84% Though, maybe you could at some point. 00:15:08.080 --> 00:15:10.040 align:middle line:84% So let's look at consumer 1, and let's say 00:15:10.040 --> 00:15:13.780 align:middle line:84% that their valuation for the first apple they get is $1. 00:15:13.780 --> 00:15:16.600 align:middle line:84% That's how much it's worth to them to get an apple. 00:15:16.600 --> 00:15:18.360 align:middle line:90% But they only want 1 Apple. 00:15:18.360 --> 00:15:20.480 align:middle line:84% Once they get that first apple, the value 00:15:20.480 --> 00:15:23.240 align:middle line:84% they get from a second Apple, the marginal value 00:15:23.240 --> 00:15:25.080 align:middle line:84% of an additional Apple drops to 0 00:15:25.080 --> 00:15:26.678 align:middle line:84% because they're just not that hungry. 00:15:26.678 --> 00:15:28.220 align:middle line:84% And apples are perishable, so they're 00:15:28.220 --> 00:15:30.280 align:middle line:84% not-- it's going to go bad by next week 00:15:30.280 --> 00:15:32.800 align:middle line:90% when they want another apple. 00:15:32.800 --> 00:15:34.400 align:middle line:90% Then we have consumer two. 00:15:34.400 --> 00:15:37.460 align:middle line:84% They are similar to consumer 1 in that they only value 1 Apple, 00:15:37.460 --> 00:15:39.560 align:middle line:84% but they value that first Apple a bit more. 00:15:39.560 --> 00:15:42.080 align:middle line:84% So for consumer 2, let's say that first Apple 00:15:42.080 --> 00:15:44.360 align:middle line:90% is worth $2 to them. 00:15:44.360 --> 00:15:46.220 align:middle line:84% But again, they only need 1 Apple, 00:15:46.220 --> 00:15:50.320 align:middle line:84% so after that, their value drops to 0. 00:15:50.320 --> 00:15:52.720 align:middle line:84% And then consumer three really loves apples. 00:15:52.720 --> 00:15:55.880 align:middle line:84% And for them, the first Apple is worth 3, 00:15:55.880 --> 00:15:58.960 align:middle line:84% and they actually would even be willing to get a second apple. 00:15:58.960 --> 00:16:00.760 align:middle line:84% Once they have the first, the second one 00:16:00.760 --> 00:16:03.800 align:middle line:84% isn't quite as valuable, but it does have positive value. 00:16:03.800 --> 00:16:06.760 align:middle line:84% So that's going to be $1 for the second apple and then 0 00:16:06.760 --> 00:16:07.300 align:middle line:90% after that. 00:16:07.300 --> 00:16:09.200 align:middle line:84% And after that, it's going to keep being 0. 00:16:09.200 --> 00:16:14.040 align:middle line:84% They don't all of a sudden want the 10th apple. 00:16:14.040 --> 00:16:18.920 align:middle line:84% So once we understand the individual consumers' demand, 00:16:18.920 --> 00:16:21.108 align:middle line:84% we can put it together to create a market demand, 00:16:21.108 --> 00:16:23.400 align:middle line:84% but let's just make sure we understand the individual's 00:16:23.400 --> 00:16:23.900 align:middle line:90% demand. 00:16:23.900 --> 00:16:29.040 align:middle line:84% So let's say I'm consumer 3, and the price of apples is $4. 00:16:29.040 --> 00:16:30.710 align:middle line:90% How many apples will I demand? 00:16:30.710 --> 00:16:33.490 align:middle line:90% 00:16:33.490 --> 00:16:34.350 align:middle line:90% None, right? 00:16:34.350 --> 00:16:36.990 align:middle line:84% Because even this first apple is not worth it to me, 00:16:36.990 --> 00:16:40.130 align:middle line:84% so if the price is $4, I'm not going to purchase any apples. 00:16:40.130 --> 00:16:42.410 align:middle line:84% But if the price is $2, then I'm going 00:16:42.410 --> 00:16:45.570 align:middle line:84% to buy exactly 1 apple because the first Apple is worth 3 00:16:45.570 --> 00:16:49.650 align:middle line:84% to me, so it's worth it for me to buy that first apple at $2. 00:16:49.650 --> 00:16:51.890 align:middle line:84% But now, once I've already bought 1 Apple, 00:16:51.890 --> 00:16:55.530 align:middle line:84% the additional value I get from a second Apple is only $1, 00:16:55.530 --> 00:16:57.330 align:middle line:84% but I'd have to pay $2 to get it, 00:16:57.330 --> 00:16:59.690 align:middle line:84% and therefore it's not worth it for me. 00:16:59.690 --> 00:17:01.710 align:middle line:84% So using each of these individuals, 00:17:01.710 --> 00:17:04.470 align:middle line:84% we can compute each of these individual's demand. 00:17:04.470 --> 00:17:07.190 align:middle line:84% So this is going to yield an individual demand. 00:17:07.190 --> 00:17:11.690 align:middle line:90% 00:17:11.690 --> 00:17:15.329 align:middle line:84% But if I'm a firm and I'm considering what price to charge 00:17:15.329 --> 00:17:18.730 align:middle line:84% for my apples, I don't really care about individual demand. 00:17:18.730 --> 00:17:20.810 align:middle line:84% I don't care if James is buying my apple. 00:17:20.810 --> 00:17:22.810 align:middle line:84% I care about how many people in the whole market 00:17:22.810 --> 00:17:24.150 align:middle line:90% are going to buy my apples. 00:17:24.150 --> 00:17:27.190 align:middle line:84% So what's relevant to the firm is not the individual demand, 00:17:27.190 --> 00:17:28.710 align:middle line:84% but what's called the market demand. 00:17:28.710 --> 00:17:30.835 align:middle line:84% And that's what we're going to try to capture here. 00:17:30.835 --> 00:17:34.010 align:middle line:84% So what is the market demand for apples 00:17:34.010 --> 00:17:38.610 align:middle line:84% in this very simple market that only has three consumers? 00:17:38.610 --> 00:17:40.530 align:middle line:84% Well, what we're going to do is we're 00:17:40.530 --> 00:17:43.890 align:middle line:84% going to need to plot the demand for apples 00:17:43.890 --> 00:17:45.850 align:middle line:90% as a function of the price. 00:17:45.850 --> 00:17:48.010 align:middle line:84% And there's a long convention in economics 00:17:48.010 --> 00:17:50.690 align:middle line:84% that we always put price on the vertical axis. 00:17:50.690 --> 00:17:53.730 align:middle line:84% So if you think of quantity as a function of price, 00:17:53.730 --> 00:17:55.610 align:middle line:84% that may feel kind of backwards to you 00:17:55.610 --> 00:17:59.930 align:middle line:84% from the way it's done in math, but this is just 00:17:59.930 --> 00:18:01.267 align:middle line:90% a historical convention. 00:18:01.267 --> 00:18:03.350 align:middle line:84% Some people argue that there's good reason for it. 00:18:03.350 --> 00:18:05.230 align:middle line:84% But we'll just take it as a convention, 00:18:05.230 --> 00:18:07.230 align:middle line:84% and we're always going to write things this way. 00:18:07.230 --> 00:18:09.530 align:middle line:90% So we have price and quantity. 00:18:09.530 --> 00:18:13.650 align:middle line:84% And on the vertical axis, let me make some marks. 00:18:13.650 --> 00:18:15.610 align:middle line:84% By drawing won't be perfect, but let's 00:18:15.610 --> 00:18:19.950 align:middle line:90% say this is $1, $2, $3, $4, $5. 00:18:19.950 --> 00:18:22.930 align:middle line:90% 00:18:22.930 --> 00:18:26.580 align:middle line:84% So what we want to do is, for each price, 00:18:26.580 --> 00:18:29.620 align:middle line:84% we want to compute what is the total quantity demanded 00:18:29.620 --> 00:18:32.620 align:middle line:90% at that price by the market? 00:18:32.620 --> 00:18:36.380 align:middle line:84% So if the price is 5, what is the total market demand 00:18:36.380 --> 00:18:37.240 align:middle line:90% for apples? 00:18:37.240 --> 00:18:39.800 align:middle line:90% 00:18:39.800 --> 00:18:40.300 align:middle line:90% AUDIENCE: 0. 00:18:40.300 --> 00:18:41.092 align:middle line:90% IAN BALL: 0, right? 00:18:41.092 --> 00:18:42.500 align:middle line:90% No one's willing to buy at 5. 00:18:42.500 --> 00:18:45.220 align:middle line:84% And in fact, no one's willing to buy at 4 either. 00:18:45.220 --> 00:18:48.000 align:middle line:84% So if we start up here, demand is just 0. 00:18:48.000 --> 00:18:50.080 align:middle line:84% I'll try to make it shaded so you can see it. 00:18:50.080 --> 00:18:51.160 align:middle line:90% It's 0, 0, 0. 00:18:51.160 --> 00:18:53.180 align:middle line:90% But then something happens at 3. 00:18:53.180 --> 00:18:59.140 align:middle line:84% When the price drops down to 3, well, now this person, player 3, 00:18:59.140 --> 00:19:01.800 align:middle line:84% is willing to buy exactly 1 apple. 00:19:01.800 --> 00:19:06.160 align:middle line:84% So the market demand is going to jump to 1 when the price hits 3. 00:19:06.160 --> 00:19:10.340 align:middle line:84% And I should put some marks here. 00:19:10.340 --> 00:19:14.780 align:middle line:84% So here, maybe I'll put it at a line like this, 00:19:14.780 --> 00:19:19.860 align:middle line:84% it's going to jump up to 1 apple when the price hits 3. 00:19:19.860 --> 00:19:22.140 align:middle line:90% And then it's going to stay. 00:19:22.140 --> 00:19:26.460 align:middle line:84% If the price is, say, 250, well, that's 00:19:26.460 --> 00:19:28.880 align:middle line:84% going to make the third consumer pretty happy. 00:19:28.880 --> 00:19:30.860 align:middle line:84% If the price is now only 250, he's 00:19:30.860 --> 00:19:34.040 align:middle line:84% actually going to make a surplus from this first purchase, 00:19:34.040 --> 00:19:36.460 align:middle line:84% but it's not going to entice him to buy another apple. 00:19:36.460 --> 00:19:38.940 align:middle line:84% And it's also not going to entice either of these players 00:19:38.940 --> 00:19:39.960 align:middle line:90% to buy an apple. 00:19:39.960 --> 00:19:42.100 align:middle line:84% So the demand is going to be constant 00:19:42.100 --> 00:19:44.260 align:middle line:90% until we hit a price of 2. 00:19:44.260 --> 00:19:48.900 align:middle line:84% And then at a price of 2, how many apples will be demanded? 00:19:48.900 --> 00:19:51.780 align:middle line:84% Now 2 because the third player is still 00:19:51.780 --> 00:19:53.980 align:middle line:84% going to demand an Apple, but now the second player 00:19:53.980 --> 00:19:56.580 align:middle line:84% is going to demand one apple as well. 00:19:56.580 --> 00:20:01.480 align:middle line:84% So now we're going to have this step again up to 2. 00:20:01.480 --> 00:20:02.980 align:middle line:84% OK, I think you can see the pattern, 00:20:02.980 --> 00:20:04.647 align:middle line:84% but let's try to understand what happens 00:20:04.647 --> 00:20:07.740 align:middle line:90% when we get to a price of one. 00:20:07.740 --> 00:20:09.220 align:middle line:84% Now what is demand going to be when 00:20:09.220 --> 00:20:13.460 align:middle line:84% the price gets to be 1 or maybe a little bit below 1? 00:20:13.460 --> 00:20:14.780 align:middle line:90% Now it's 4. 00:20:14.780 --> 00:20:16.060 align:middle line:90% And notice what happens. 00:20:16.060 --> 00:20:18.500 align:middle line:84% When the price hits 1, the first player 00:20:18.500 --> 00:20:20.900 align:middle line:84% is now willing to buy 1 apple, but that's not 00:20:20.900 --> 00:20:22.180 align:middle line:90% the only thing that happens. 00:20:22.180 --> 00:20:25.310 align:middle line:84% Now the third player is willing to buy a second apple instead 00:20:25.310 --> 00:20:26.370 align:middle line:90% of only 1 apple. 00:20:26.370 --> 00:20:28.570 align:middle line:84% + now demand increases for two reasons. 00:20:28.570 --> 00:20:31.190 align:middle line:84% We have new consumers entering the market choosing to buy 00:20:31.190 --> 00:20:32.630 align:middle line:90% who didn't previously buy. 00:20:32.630 --> 00:20:34.830 align:middle line:84% And we also have this apple lover 00:20:34.830 --> 00:20:37.470 align:middle line:84% increasing the number of apples that he buys from 1 apple 00:20:37.470 --> 00:20:38.630 align:middle line:90% to 2 apples. 00:20:38.630 --> 00:20:42.390 align:middle line:84% So now it's going to jump up to 4, 00:20:42.390 --> 00:20:45.130 align:middle line:84% and then it's going to stay like this. 00:20:45.130 --> 00:20:49.510 align:middle line:84% So we have some jumps in the demand curve, 00:20:49.510 --> 00:20:52.270 align:middle line:90% and it looks like this. 00:20:52.270 --> 00:20:53.950 align:middle line:90% So that's our demand curve. 00:20:53.950 --> 00:20:56.910 align:middle line:84% It looks kind of jagged, and the reason 00:20:56.910 --> 00:21:00.190 align:middle line:84% is that we're only considering a market with three people. 00:21:00.190 --> 00:21:01.950 align:middle line:84% But if I'm a supermarket selling apples, 00:21:01.950 --> 00:21:04.770 align:middle line:84% I'm, hopefully, selling to more than just three people. 00:21:04.770 --> 00:21:06.670 align:middle line:84% So in reality, we're going to be aggregating 00:21:06.670 --> 00:21:08.290 align:middle line:90% a lot of these individuals. 00:21:08.290 --> 00:21:09.910 align:middle line:84% And the more individuals we aggregate 00:21:09.910 --> 00:21:11.730 align:middle line:84% as we change the scale of our graph, 00:21:11.730 --> 00:21:13.410 align:middle line:84% it's going to get smoother and smoother. 00:21:13.410 --> 00:21:22.750 align:middle line:84% So in our idealized model, with maybe many consumers, 00:21:22.750 --> 00:21:27.678 align:middle line:84% we're going to visualize this as a continuous function. 00:21:27.678 --> 00:21:29.970 align:middle line:84% Now, you might argue, well, it's still really discrete. 00:21:29.970 --> 00:21:31.730 align:middle line:84% Prices are discrete, people are discrete. 00:21:31.730 --> 00:21:34.210 align:middle line:84% But to make the math a bit cleaner, 00:21:34.210 --> 00:21:35.990 align:middle line:84% I think not much is lost, and a lot 00:21:35.990 --> 00:21:37.990 align:middle line:84% is actually gained in terms of tractability 00:21:37.990 --> 00:21:39.410 align:middle line:90% if we make it continuous. 00:21:39.410 --> 00:21:42.590 align:middle line:84% So we might think of a demand function that looks something 00:21:42.590 --> 00:21:46.870 align:middle line:90% like this just as an example. 00:21:46.870 --> 00:21:49.190 align:middle line:84% So again, the interpretation is the same-- 00:21:49.190 --> 00:21:52.110 align:middle line:84% as the price goes down, the total number of apples 00:21:52.110 --> 00:21:53.790 align:middle line:90% demanded increases. 00:21:53.790 --> 00:21:56.010 align:middle line:84% And again, it increases for different reasons. 00:21:56.010 --> 00:21:58.350 align:middle line:84% It can increase because some consumers start 00:21:58.350 --> 00:22:00.350 align:middle line:84% buying who didn't previously buy, 00:22:00.350 --> 00:22:04.070 align:middle line:84% and other consumers increase the number that they actually buy. 00:22:04.070 --> 00:22:06.870 align:middle line:84% So we're going to call this the demand function, 00:22:06.870 --> 00:22:15.030 align:middle line:84% and we think of this as a function Q of P. 00:22:15.030 --> 00:22:18.090 align:middle line:84% So I always have to turn my head when I think about this. 00:22:18.090 --> 00:22:20.360 align:middle line:84% We have price on the vertical axis. 00:22:20.360 --> 00:22:22.080 align:middle line:84% We have demand, the total quantity 00:22:22.080 --> 00:22:24.400 align:middle line:90% demanded on the horizontal axis. 00:22:24.400 --> 00:22:27.240 align:middle line:90% And Q is a function of P. 00:22:27.240 --> 00:22:30.680 align:middle line:84% Now, it's also sometimes helpful to think of it the other way, 00:22:30.680 --> 00:22:35.580 align:middle line:84% to think if I wanted a certain number of apples to me demanded, 00:22:35.580 --> 00:22:38.200 align:middle line:84% what is the price that I would have to set in order 00:22:38.200 --> 00:22:39.920 align:middle line:90% to ensure that was the demand? 00:22:39.920 --> 00:22:43.160 align:middle line:84% So instead of thinking of the function from prices 00:22:43.160 --> 00:22:45.920 align:middle line:84% to quantities, we can think of it the other way-- 00:22:45.920 --> 00:22:48.720 align:middle line:90% from quantities to prices. 00:22:48.720 --> 00:22:52.640 align:middle line:84% And we sometimes call this P of Q. 00:22:52.640 --> 00:22:55.280 align:middle line:84% And this is often called the inverse demand function 00:22:55.280 --> 00:22:57.940 align:middle line:84% because, mathematically, this is just the inverse. 00:22:57.940 --> 00:23:01.440 align:middle line:84% If we think of Q of P as just a function, then P of Q 00:23:01.440 --> 00:23:03.780 align:middle line:84% is literally the inverse of that function. 00:23:03.780 --> 00:23:13.320 align:middle line:90% 00:23:13.320 --> 00:23:15.640 align:middle line:84% So in problem sets and when we set things up, 00:23:15.640 --> 00:23:18.200 align:middle line:84% sometimes we'll describe demand in terms 00:23:18.200 --> 00:23:21.320 align:middle line:84% of the demand function, the demand as a function of price. 00:23:21.320 --> 00:23:24.060 align:middle line:84% And sometimes, we'll write down the inverse demand, 00:23:24.060 --> 00:23:27.120 align:middle line:84% which is the price as a function of quantity. 00:23:27.120 --> 00:23:29.600 align:middle line:84% These are just different mathematical representations 00:23:29.600 --> 00:23:31.400 align:middle line:84% of exactly the same object, which 00:23:31.400 --> 00:23:35.480 align:middle line:84% is a correspondence between prices and quantities. 00:23:35.480 --> 00:23:36.740 align:middle line:90% Any questions on this? 00:23:36.740 --> 00:23:39.800 align:middle line:90% 00:23:39.800 --> 00:23:42.840 align:middle line:84% So now that we've set up demand, we'll 00:23:42.840 --> 00:23:44.420 align:middle line:90% start with the monopoly problem. 00:23:44.420 --> 00:23:45.962 align:middle line:84% The monopoly problem is a bit easier. 00:23:45.962 --> 00:23:47.587 align:middle line:84% We don't really have to do game theory. 00:23:47.587 --> 00:23:49.860 align:middle line:84% And you've probably seen this in other econ courses. 00:23:49.860 --> 00:23:51.277 align:middle line:84% And then we'll move to competition 00:23:51.277 --> 00:23:53.400 align:middle line:84% where we really have to take into account 00:23:53.400 --> 00:23:55.060 align:middle line:90% interaction between the firms. 00:23:55.060 --> 00:24:02.640 align:middle line:90% 00:24:02.640 --> 00:24:05.100 align:middle line:84% So now let's look at the monopoly problem. 00:24:05.100 --> 00:24:11.360 align:middle line:90% 00:24:11.360 --> 00:24:13.400 align:middle line:84% So what we imagine is I'm a monopolist. 00:24:13.400 --> 00:24:16.690 align:middle line:84% I'm the only person selling some good. 00:24:16.690 --> 00:24:18.490 align:middle line:84% Say it's apples, but usually, that's 00:24:18.490 --> 00:24:20.650 align:middle line:90% not a good example of monopoly. 00:24:20.650 --> 00:24:22.650 align:middle line:84% And what we're going to assume is 00:24:22.650 --> 00:24:33.410 align:middle line:84% that the monopolist has some constant marginal cost c, which 00:24:33.410 --> 00:24:36.290 align:middle line:90% is greater than or equal to 0. 00:24:36.290 --> 00:24:38.710 align:middle line:84% What do I mean by constant marginal cost? 00:24:38.710 --> 00:24:42.170 align:middle line:84% What I mean is if the monopolist wants 00:24:42.170 --> 00:24:50.130 align:middle line:84% to produce Q units of a good, then the cost of those Q units 00:24:50.130 --> 00:24:59.690 align:middle line:90% is just c times Q. 00:24:59.690 --> 00:25:03.810 align:middle line:84% So here, Q is just a number, c is just a number. 00:25:03.810 --> 00:25:06.070 align:middle line:84% We might think that, at some point, 00:25:06.070 --> 00:25:08.670 align:middle line:84% it becomes really costly to produce an additional unit. 00:25:08.670 --> 00:25:11.850 align:middle line:84% So often, we think that costs in general, at some scales, 00:25:11.850 --> 00:25:15.913 align:middle line:84% become convex eventually, that if you have to really increase 00:25:15.913 --> 00:25:17.330 align:middle line:84% production and start hiring people 00:25:17.330 --> 00:25:19.370 align:middle line:84% to work overtime and plant the apples too 00:25:19.370 --> 00:25:21.830 align:middle line:84% close to each other in the farmland and all these things, 00:25:21.830 --> 00:25:23.152 align:middle line:90% costs become convex. 00:25:23.152 --> 00:25:25.110 align:middle line:84% That's probably realistic in a lot of settings, 00:25:25.110 --> 00:25:27.930 align:middle line:84% but let's stick to constant marginal cost for now 00:25:27.930 --> 00:25:29.870 align:middle line:84% over a certain range of production. 00:25:29.870 --> 00:25:32.450 align:middle line:84% That's probably pretty realistic. 00:25:32.450 --> 00:25:35.025 align:middle line:84% And now we have to specify the demand. 00:25:35.025 --> 00:25:36.650 align:middle line:84% So let's understand here the difference 00:25:36.650 --> 00:25:46.170 align:middle line:84% that these are assumptions about the firm, which in this case 00:25:46.170 --> 00:25:47.850 align:middle line:90% is a monopolist. 00:25:47.850 --> 00:25:50.250 align:middle line:84% And now, when we write down things about demand, 00:25:50.250 --> 00:25:52.750 align:middle line:84% we're not making assumptions about the firm anymore. 00:25:52.750 --> 00:25:56.090 align:middle line:84% We're making assumptions about the population of consumers who 00:25:56.090 --> 00:25:57.952 align:middle line:90% are buying that firm's product. 00:25:57.952 --> 00:25:59.410 align:middle line:84% So what we're going to assume, just 00:25:59.410 --> 00:26:02.490 align:middle line:84% to make the math pretty easy, is we'll 00:26:02.490 --> 00:26:10.010 align:middle line:84% assume that our demand is Q of P equals-- 00:26:10.010 --> 00:26:13.740 align:middle line:84% well, we want to just say 1 minus P, 00:26:13.740 --> 00:26:17.332 align:middle line:84% so that as the price goes up, the demand goes down. 00:26:17.332 --> 00:26:18.040 align:middle line:90% That makes sense. 00:26:18.040 --> 00:26:20.900 align:middle line:84% People buy less when the price is higher. 00:26:20.900 --> 00:26:23.920 align:middle line:84% But the problem is, well, if the price gets really high, 00:26:23.920 --> 00:26:25.660 align:middle line:84% then this demand would be negative. 00:26:25.660 --> 00:26:27.120 align:middle line:90% And that's a problem. 00:26:27.120 --> 00:26:28.960 align:middle line:84% We don't think that demand is ever negative. 00:26:28.960 --> 00:26:33.340 align:middle line:84% So we're going to write the maximum of 1 minus P 00:26:33.340 --> 00:26:38.020 align:middle line:84% And 0 so that, once the price gets high enough, specifically 00:26:38.020 --> 00:26:42.040 align:middle line:84% when the price gets above 1, demand is just going to be 0. 00:26:42.040 --> 00:26:43.640 align:middle line:84% No one's willing to buy at that price, 00:26:43.640 --> 00:26:46.260 align:middle line:84% but demand won't actually become negative. 00:26:46.260 --> 00:26:49.340 align:middle line:84% Now, when we solve things, we often 00:26:49.340 --> 00:26:52.620 align:middle line:84% kind of cheat a little bit, and we forget about the max. 00:26:52.620 --> 00:26:55.860 align:middle line:84% And we hope that, at the end, the prices we consider 00:26:55.860 --> 00:26:57.640 align:middle line:84% won't be big enough that this matters. 00:26:57.640 --> 00:27:01.185 align:middle line:84% So what we'll often do is we'll reason as if the max isn't here 00:27:01.185 --> 00:27:03.060 align:middle line:84% and hope that at the end, our answer involves 00:27:03.060 --> 00:27:04.660 align:middle line:90% a price that's less than 1. 00:27:04.660 --> 00:27:07.000 align:middle line:84% And if it does, that's not going to be a problem. 00:27:07.000 --> 00:27:08.640 align:middle line:84% But if we found a price greater than 1, 00:27:08.640 --> 00:27:09.920 align:middle line:90% then we'd have some issues. 00:27:09.920 --> 00:27:11.820 align:middle line:84% So that's just something to keep in mind 00:27:11.820 --> 00:27:15.580 align:middle line:84% when you're working with these kinds of demand functions. 00:27:15.580 --> 00:27:23.580 align:middle line:84% And let's remind us that this is an assumption, well, not just 00:27:23.580 --> 00:27:26.680 align:middle line:84% about one consumer because we have many, many consumers, 00:27:26.680 --> 00:27:29.120 align:middle line:84% so it's assumption about the population of consumers. 00:27:29.120 --> 00:27:35.820 align:middle line:90% 00:27:35.820 --> 00:27:38.700 align:middle line:84% Sometimes hear about demand-side and supply-side economics. 00:27:38.700 --> 00:27:41.380 align:middle line:84% These are assumptions about the supply side, the supplier 00:27:41.380 --> 00:27:43.100 align:middle line:84% of the good, and these are assumptions 00:27:43.100 --> 00:27:47.380 align:middle line:84% about the demand side, the consumers who consume the good. 00:27:47.380 --> 00:27:49.393 align:middle line:84% So now let's draw this, and I want 00:27:49.393 --> 00:27:50.560 align:middle line:90% to be a little more precise. 00:27:50.560 --> 00:27:52.400 align:middle line:84% Not only is c greater than or equal to 0, 00:27:52.400 --> 00:27:55.780 align:middle line:84% but let's actually say it's between 0 and 1. 00:27:55.780 --> 00:27:57.780 align:middle line:84% It's going to make things a bit easier. 00:27:57.780 --> 00:28:01.100 align:middle line:84% It could be exactly 0, but let's say it's strictly positive, 00:28:01.100 --> 00:28:03.940 align:middle line:90% and it's between 0 and 1. 00:28:03.940 --> 00:28:06.680 align:middle line:90% So now let's draw this demand. 00:28:06.680 --> 00:28:09.750 align:middle line:90% 00:28:09.750 --> 00:28:13.510 align:middle line:84% So as usual, I'm going to have quantity on the horizontal axis 00:28:13.510 --> 00:28:15.330 align:middle line:90% and price on the vertical axis. 00:28:15.330 --> 00:28:18.150 align:middle line:90% 00:28:18.150 --> 00:28:23.430 align:middle line:90% And let me mark 1 and 1. 00:28:23.430 --> 00:28:25.810 align:middle line:84% Of course, this just makes the numbers easy, 00:28:25.810 --> 00:28:28.330 align:middle line:84% but if you want to think of this depending on the product, 00:28:28.330 --> 00:28:31.810 align:middle line:84% maybe this is $0.01 or $1 or $100 or $1,000, 00:28:31.810 --> 00:28:33.090 align:middle line:90% but we'll just call it 1. 00:28:33.090 --> 00:28:34.710 align:middle line:84% And similarly, maybe this is tons 00:28:34.710 --> 00:28:36.760 align:middle line:90% of apples or bushels of apples. 00:28:36.760 --> 00:28:38.510 align:middle line:84% It could be various things, but we'll just 00:28:38.510 --> 00:28:41.510 align:middle line:90% use these simple units here. 00:28:41.510 --> 00:28:43.010 align:middle line:84% And what does this demand look like? 00:28:43.010 --> 00:28:45.750 align:middle line:84% Well, if the price is greater than 1, 00:28:45.750 --> 00:28:48.110 align:middle line:84% then no one's willing to buy at all. 00:28:48.110 --> 00:28:54.470 align:middle line:84% So the demand looks like that until we get to 1. 00:28:54.470 --> 00:28:58.790 align:middle line:84% If the price is exactly 1, then demand is 0. 00:28:58.790 --> 00:29:02.570 align:middle line:84% And on the other hand, if the price is 0, then demand is 1. 00:29:02.570 --> 00:29:05.070 align:middle line:84% So we know that there's-- here's another point on the demand 00:29:05.070 --> 00:29:06.070 align:middle line:90% curve. 00:29:06.070 --> 00:29:08.170 align:middle line:84% And because of the form of our demand, 00:29:08.170 --> 00:29:10.095 align:middle line:84% this is what's called a linear demand. 00:29:10.095 --> 00:29:11.470 align:middle line:84% So the demand curve is just going 00:29:11.470 --> 00:29:14.510 align:middle line:84% to be a straight line that connects our point here 00:29:14.510 --> 00:29:15.950 align:middle line:90% and our point here. 00:29:15.950 --> 00:29:19.110 align:middle line:84% So maybe I'll draw it something like this. 00:29:19.110 --> 00:29:23.710 align:middle line:84% If my axes were straight, this should be, I guess, 00:29:23.710 --> 00:29:24.810 align:middle line:90% an isosceles triangle. 00:29:24.810 --> 00:29:27.750 align:middle line:84% But maybe I haven't done it quite right. 00:29:27.750 --> 00:29:34.710 align:middle line:84% OK, and just so we understand, at any price P here, 00:29:34.710 --> 00:29:38.530 align:middle line:84% this value is Q of P, let's understand. 00:29:38.530 --> 00:29:41.230 align:middle line:84% So at this price here, I walk horizontally 00:29:41.230 --> 00:29:44.210 align:middle line:84% to the value of the function Q of P. I come down, 00:29:44.210 --> 00:29:46.710 align:middle line:84% and that's the value Q of P here, which is, in this case, 00:29:46.710 --> 00:29:50.190 align:middle line:90% is exactly 1 minus P. 00:29:50.190 --> 00:29:53.790 align:middle line:84% So now I need to represent one more thing on the graph. 00:29:53.790 --> 00:29:55.630 align:middle line:84% So far, the graph is only representing 00:29:55.630 --> 00:29:57.270 align:middle line:90% the demand side of the market. 00:29:57.270 --> 00:30:00.130 align:middle line:84% Now, I also want to represent the firm's costs. 00:30:00.130 --> 00:30:05.900 align:middle line:84% So let me put c here, and I'll draw a horizontal line here. 00:30:05.900 --> 00:30:09.220 align:middle line:84% So this is going to represent the firm's cost of production. 00:30:09.220 --> 00:30:11.800 align:middle line:90% 00:30:11.800 --> 00:30:16.840 align:middle line:84% And now let's understand, if the firm were to set a price of P, 00:30:16.840 --> 00:30:18.340 align:middle line:90% what would their profits be? 00:30:18.340 --> 00:30:21.640 align:middle line:90% So let's try to write this down. 00:30:21.640 --> 00:30:24.320 align:middle line:84% I want to understand what is pi of P? 00:30:24.320 --> 00:30:26.920 align:middle line:84% So this is-- suppose I'm the monopolist. 00:30:26.920 --> 00:30:29.120 align:middle line:90% I choose to set a price of p. 00:30:29.120 --> 00:30:30.900 align:middle line:90% What are my profits going to be? 00:30:30.900 --> 00:30:32.340 align:middle line:90% If I set this price of p? 00:30:32.340 --> 00:30:35.920 align:middle line:90% 00:30:35.920 --> 00:30:38.520 align:middle line:84% Well, let's break it down into two parts. 00:30:38.520 --> 00:30:41.840 align:middle line:84% The first is my profit per unit that I sell. 00:30:41.840 --> 00:30:45.440 align:middle line:84% So for each unit that I sell, I sell it at a price of p, 00:30:45.440 --> 00:30:48.120 align:middle line:84% but I have to pay a cost of c to produce it. 00:30:48.120 --> 00:30:53.140 align:middle line:84% So my profit per unit is p minus c. 00:30:53.140 --> 00:30:59.200 align:middle line:90% 00:30:59.200 --> 00:31:01.860 align:middle line:84% But then the question is I'm getting this profit per unit. 00:31:01.860 --> 00:31:03.720 align:middle line:84% But how many units do I actually sell? 00:31:03.720 --> 00:31:07.020 align:middle line:84% So it's going to be p minus c times Q of p. 00:31:07.020 --> 00:31:11.640 align:middle line:90% 00:31:11.640 --> 00:31:13.480 align:middle line:84% And now we see the basic trade-off 00:31:13.480 --> 00:31:15.200 align:middle line:90% that the monopolist faces. 00:31:15.200 --> 00:31:18.480 align:middle line:84% What happens when the monopolist raises their price? 00:31:18.480 --> 00:31:22.800 align:middle line:84% They increase their profit per unit. 00:31:22.800 --> 00:31:25.080 align:middle line:84% If I increase the price of apples, each apple I sell 00:31:25.080 --> 00:31:25.780 align:middle line:90% is great for me. 00:31:25.780 --> 00:31:28.120 align:middle line:84% I'm making a lot of money on each apple I sell. 00:31:28.120 --> 00:31:30.600 align:middle line:84% But when I raise that price, I'm not 00:31:30.600 --> 00:31:32.080 align:middle line:90% going to sell as many apples. 00:31:32.080 --> 00:31:34.440 align:middle line:84% So the number of units that I sell goes down. 00:31:34.440 --> 00:31:36.400 align:middle line:84% And the basic trade-off for the monopolist 00:31:36.400 --> 00:31:39.760 align:middle line:84% is to balance these two effects, the per-unit profits 00:31:39.760 --> 00:31:44.360 align:middle line:84% against the total number of units that are sold. 00:31:44.360 --> 00:31:49.260 align:middle line:84% And let's write this, for prices that are between 0 and 1, 00:31:49.260 --> 00:31:52.060 align:middle line:84% this is going to take the form like this. 00:31:52.060 --> 00:31:58.000 align:middle line:84% So in general, Q of p is the maximum of 1 minus p and 0. 00:31:58.000 --> 00:32:00.650 align:middle line:84% But as long as p is not too big, then this is just 00:32:00.650 --> 00:32:02.290 align:middle line:90% going to reduce to 1 minus p. 00:32:02.290 --> 00:32:05.850 align:middle line:84% And I can substitute this in here. 00:32:05.850 --> 00:32:08.450 align:middle line:84% Now we can nicely see this graphically. 00:32:08.450 --> 00:32:11.130 align:middle line:84% Graphically, if I look at this price p, 00:32:11.130 --> 00:32:19.410 align:middle line:84% well, this is going to be the amount that I sell. 00:32:19.410 --> 00:32:22.170 align:middle line:84% And p minus c is my profit per unit. 00:32:22.170 --> 00:32:28.850 align:middle line:84% So what I see is I can actually shade in my profit 00:32:28.850 --> 00:32:31.490 align:middle line:90% as this square or rectangle. 00:32:31.490 --> 00:32:41.090 align:middle line:84% So the shaded rectangle equals profit. 00:32:41.090 --> 00:32:42.890 align:middle line:84% Let's make sure we understand it. 00:32:42.890 --> 00:32:45.010 align:middle line:84% I could actually look at the entire rectangle 00:32:45.010 --> 00:32:47.170 align:middle line:84% all the way down to the horizontal axis. 00:32:47.170 --> 00:32:50.930 align:middle line:84% That would represent revenue because that entire rectangle, 00:32:50.930 --> 00:32:57.630 align:middle line:84% its area is its height, which is the price, times its width, 00:32:57.630 --> 00:32:59.250 align:middle line:90% which is the demand. 00:32:59.250 --> 00:33:02.570 align:middle line:84% So the entire rectangle tells me the price 00:33:02.570 --> 00:33:04.650 align:middle line:90% times the amount that I sell. 00:33:04.650 --> 00:33:05.630 align:middle line:90% That's revenue. 00:33:05.630 --> 00:33:07.690 align:middle line:84% That's the amount of money I take in. 00:33:07.690 --> 00:33:09.370 align:middle line:84% But I'm not counting this little part 00:33:09.370 --> 00:33:11.770 align:middle line:84% of the rectangle in my profit because this 00:33:11.770 --> 00:33:14.650 align:middle line:84% is the cost I have to pay to produce that amount. 00:33:14.650 --> 00:33:22.330 align:middle line:84% So remember, profit is profit which equals revenue minus cost, 00:33:22.330 --> 00:33:24.930 align:middle line:84% revenue meaning the total amount of money that I take 00:33:24.930 --> 00:33:27.770 align:middle line:84% in and cost being the amount that I 00:33:27.770 --> 00:33:31.130 align:middle line:84% have to pay in order to produce the amount that I sell. 00:33:31.130 --> 00:33:33.510 align:middle line:84% So I don't want to make the graph too ugly, 00:33:33.510 --> 00:33:36.890 align:middle line:90% but this would be the cost. 00:33:36.890 --> 00:33:39.610 align:middle line:84% I have to pay a cost of c per unit, 00:33:39.610 --> 00:33:43.930 align:middle line:84% and then the width here is the number of units that I sell. 00:33:43.930 --> 00:33:45.750 align:middle line:84% So what is the monopolist trying to do? 00:33:45.750 --> 00:33:47.330 align:middle line:84% They're trying to choose this price 00:33:47.330 --> 00:33:50.210 align:middle line:90% p to maximize their profit. 00:33:50.210 --> 00:33:54.370 align:middle line:84% That is, choose this price p to make this rectangle-- 00:33:54.370 --> 00:33:57.923 align:middle line:84% to make the area of this rectangle as large as possible. 00:33:57.923 --> 00:34:00.340 align:middle line:84% Now, let's just understand some extreme cases, some things 00:34:00.340 --> 00:34:01.580 align:middle line:90% they wouldn't want to do. 00:34:01.580 --> 00:34:03.980 align:middle line:84% What if they set the price to be 1? 00:34:03.980 --> 00:34:06.260 align:middle line:90% What would their profit be? 00:34:06.260 --> 00:34:06.960 align:middle line:90% 0, right? 00:34:06.960 --> 00:34:09.980 align:middle line:84% If they set the price to 1, no one's going to buy. 00:34:09.980 --> 00:34:12.659 align:middle line:90% What if they set the price to c? 00:34:12.659 --> 00:34:14.659 align:middle line:90% Then their profit is also 0. 00:34:14.659 --> 00:34:16.219 align:middle line:84% A lot of people are going to buy, 00:34:16.219 --> 00:34:18.679 align:middle line:84% but if they're charging exactly what their cost is, 00:34:18.679 --> 00:34:19.940 align:middle line:90% they're not making any money. 00:34:19.940 --> 00:34:22.260 align:middle line:84% And in fact, if they set a price below c, 00:34:22.260 --> 00:34:24.820 align:middle line:84% they'd actually be losing money because their revenue would 00:34:24.820 --> 00:34:26.940 align:middle line:90% be smaller than their cost. 00:34:26.940 --> 00:34:28.820 align:middle line:84% So it's pretty clear that the price should 00:34:28.820 --> 00:34:31.168 align:middle line:90% be somewhere between 1 and c. 00:34:31.168 --> 00:34:32.960 align:middle line:84% And let's actually figure out what that is. 00:34:32.960 --> 00:34:39.179 align:middle line:84% So let's now find the optimal monopoly price. 00:34:39.179 --> 00:34:41.520 align:middle line:84% So maybe I'll call it the monopoly problem. 00:34:41.520 --> 00:34:45.802 align:middle line:90% 00:34:45.802 --> 00:34:47.260 align:middle line:84% Well, what is the monopolist doing? 00:34:47.260 --> 00:34:53.340 align:middle line:84% They're maximizing over the price p 00:34:53.340 --> 00:35:00.060 align:middle line:84% of pi of p, which equals p minus c times 1 minus p. 00:35:00.060 --> 00:35:02.040 align:middle line:84% Now, again, you could say I'm not-- 00:35:02.040 --> 00:35:05.260 align:middle line:84% this is not quite correct because, technically, 00:35:05.260 --> 00:35:07.220 align:middle line:84% for some prices they might choose, 00:35:07.220 --> 00:35:09.980 align:middle line:84% this is not a reflection of demand. 00:35:09.980 --> 00:35:13.780 align:middle line:84% But this is the correct formula for the reasonable range 00:35:13.780 --> 00:35:15.640 align:middle line:90% of prices between 0 and 1. 00:35:15.640 --> 00:35:17.700 align:middle line:84% And if I check at the end that the price I get 00:35:17.700 --> 00:35:20.360 align:middle line:84% is between 0 and 1, then everything's going to be OK. 00:35:20.360 --> 00:35:22.540 align:middle line:84% But recognize that I'm not literally 00:35:22.540 --> 00:35:25.420 align:middle line:84% claiming that if my price is 10, then 00:35:25.420 --> 00:35:28.220 align:middle line:84% my profit is going to be negative 00:35:28.220 --> 00:35:30.120 align:middle line:84% because if I set a price of 10, in fact, 00:35:30.120 --> 00:35:34.500 align:middle line:84% my profit will be 0 because no one's going to buy the good. 00:35:34.500 --> 00:35:36.960 align:middle line:84% Well, how do we maximize a single variable function? 00:35:36.960 --> 00:35:39.420 align:middle line:84% We take derivatives and set them to 0. 00:35:39.420 --> 00:35:42.480 align:middle line:84% You can check that this is going to be a concave function. 00:35:42.480 --> 00:35:44.020 align:middle line:84% So if we set the derivative to 0, 00:35:44.020 --> 00:35:46.460 align:middle line:84% we'll actually find the maximizer. 00:35:46.460 --> 00:35:50.140 align:middle line:84% And so the derivative pi prime of p, 00:35:50.140 --> 00:35:53.150 align:middle line:84% well, we're just going to use the product rule. 00:35:53.150 --> 00:35:56.910 align:middle line:84% So we take the derivative of the first term times the second. 00:35:56.910 --> 00:35:59.230 align:middle line:84% The derivative of the first term is 1. 00:35:59.230 --> 00:36:01.210 align:middle line:84% So we just multiply that by the second term, 00:36:01.210 --> 00:36:03.910 align:middle line:90% and we get 1 minus p. 00:36:03.910 --> 00:36:07.070 align:middle line:84% Then we have the first term p minus c 00:36:07.070 --> 00:36:09.670 align:middle line:84% times the derivative of the second term, which 00:36:09.670 --> 00:36:11.350 align:middle line:90% is negative 1. 00:36:11.350 --> 00:36:13.470 align:middle line:90% So we get negative 1 here. 00:36:13.470 --> 00:36:17.170 align:middle line:84% So we get 1 minus p plus minus 1 times p minus c. 00:36:17.170 --> 00:36:19.230 align:middle line:90% Let's try to simplify this. 00:36:19.230 --> 00:36:26.310 align:middle line:84% Well, we're actually going to get 1 plus c. 00:36:26.310 --> 00:36:27.550 align:middle line:90% minus 2p. 00:36:27.550 --> 00:36:32.110 align:middle line:90% 00:36:32.110 --> 00:36:39.230 align:middle line:84% So we want to set this to 0 and solve for 0 equals this. 00:36:39.230 --> 00:36:42.470 align:middle line:84% We're going to pull the 2p to the other side and divide by p. 00:36:42.470 --> 00:36:46.350 align:middle line:84% And what we can see is that the monopoly price p star 00:36:46.350 --> 00:36:49.110 align:middle line:90% is going to be 1 plus c over 2. 00:36:49.110 --> 00:36:52.150 align:middle line:90% 00:36:52.150 --> 00:36:53.970 align:middle line:84% So in fact, it will be the price. 00:36:53.970 --> 00:36:56.430 align:middle line:84% What is 1 plus c over 2, geometrically? 00:36:56.430 --> 00:37:00.070 align:middle line:84% It's the midpoint between 1 and c. 00:37:00.070 --> 00:37:03.470 align:middle line:84% And if you draw this correctly, the optimal price 1 00:37:03.470 --> 00:37:07.430 align:middle line:84% plus c over 2 will, actually, make this rectangle a square. 00:37:07.430 --> 00:37:10.190 align:middle line:84% I won't try to show it here because I think my picture isn't 00:37:10.190 --> 00:37:12.350 align:middle line:84% exactly to scale, but what you'll find 00:37:12.350 --> 00:37:16.830 align:middle line:90% is that this will be a square. 00:37:16.830 --> 00:37:20.090 align:middle line:84% And this is actually a nice geometric fact. 00:37:20.090 --> 00:37:21.825 align:middle line:84% So you could do all the calculus here. 00:37:21.825 --> 00:37:23.450 align:middle line:84% I mean, it's not too hard in this case, 00:37:23.450 --> 00:37:24.950 align:middle line:90% but it sometimes gets messier. 00:37:24.950 --> 00:37:32.950 align:middle line:84% One way to think about this is, well, p minus c plus 1 minus p, 00:37:32.950 --> 00:37:35.150 align:middle line:90% that turns out to be constant. 00:37:35.150 --> 00:37:37.350 align:middle line:84% So what you're actually being asked to do here 00:37:37.350 --> 00:37:41.230 align:middle line:84% is to find a rectangle of maximal area 00:37:41.230 --> 00:37:43.470 align:middle line:90% given a fixed perimeter. 00:37:43.470 --> 00:37:45.590 align:middle line:84% So this is just a reflection of the geometric fact 00:37:45.590 --> 00:37:47.870 align:middle line:84% that if I fix a perimeter, and I ask 00:37:47.870 --> 00:37:50.460 align:middle line:84% you to find the rectangle of largest area, 00:37:50.460 --> 00:37:52.460 align:middle line:84% given that perimeter, it's going to be a square. 00:37:52.460 --> 00:37:56.040 align:middle line:84% So that's actually why we get a square here. 00:37:56.040 --> 00:37:59.480 align:middle line:84% But that's just a fact to keep in mind. 00:37:59.480 --> 00:38:02.440 align:middle line:90% So now we found p star. 00:38:02.440 --> 00:38:05.360 align:middle line:90% Let's now find Q star. 00:38:05.360 --> 00:38:09.800 align:middle line:84% So Q of p star is going to be what? 00:38:09.800 --> 00:38:13.120 align:middle line:90% Well, q of p is just 1 minus p. 00:38:13.120 --> 00:38:21.980 align:middle line:84% So we're going to get 1 minus 1 plus c over 2. 00:38:21.980 --> 00:38:24.560 align:middle line:90% 00:38:24.560 --> 00:38:28.880 align:middle line:84% And if we simplify that, we can think of this as 2 over 2. 00:38:28.880 --> 00:38:33.880 align:middle line:84% So we're going to get 1 minus c over 2. 00:38:33.880 --> 00:38:37.520 align:middle line:84% So what this says is, it's going to be optimal for the monopolist 00:38:37.520 --> 00:38:42.360 align:middle line:84% to set a price of 1 plus c over 2, and when they set that price, 00:38:42.360 --> 00:38:44.120 align:middle line:84% the number of units they're going to sell 00:38:44.120 --> 00:38:45.480 align:middle line:90% is 1 minus c over 2. 00:38:45.480 --> 00:38:48.235 align:middle line:90% 00:38:48.235 --> 00:38:49.860 align:middle line:84% Now, the first thing we should observe, 00:38:49.860 --> 00:38:52.760 align:middle line:84% which I think makes sense, is that the price 00:38:52.760 --> 00:38:55.160 align:middle line:84% the monopolist finds it optimal to charge 00:38:55.160 --> 00:38:57.905 align:middle line:84% is increasing in their production costs. 00:38:57.905 --> 00:38:58.780 align:middle line:90% And this makes sense. 00:38:58.780 --> 00:39:00.322 align:middle line:84% So whenever you solve these problems, 00:39:00.322 --> 00:39:02.375 align:middle line:84% I think it's good to go through the intuition. 00:39:02.375 --> 00:39:04.000 align:middle line:84% Does it make sense that, when something 00:39:04.000 --> 00:39:07.220 align:middle line:84% is more expensive to produce, I charge a higher price? 00:39:07.220 --> 00:39:08.760 align:middle line:84% Yeah, that certainly makes sense. 00:39:08.760 --> 00:39:11.440 align:middle line:84% And in fact, it's often helpful to decompose 00:39:11.440 --> 00:39:15.800 align:middle line:90% this in a very special way. 00:39:15.800 --> 00:39:23.880 align:middle line:84% So we can actually write this as c plus 1 minus c over 2. 00:39:23.880 --> 00:39:25.340 align:middle line:90% Let's check that that agrees. 00:39:25.340 --> 00:39:28.720 align:middle line:90% This is 1/2 plus 1/2 half of c. 00:39:28.720 --> 00:39:34.040 align:middle line:84% And this is c minus c over 2, so we still have 1/2 c. 00:39:34.040 --> 00:39:35.100 align:middle line:90% And then we have a 1/2. 00:39:35.100 --> 00:39:38.840 align:middle line:90% So the algebra works out. 00:39:38.840 --> 00:39:42.200 align:middle line:84% And it's helpful to decompose it this way because c 00:39:42.200 --> 00:39:45.280 align:middle line:90% is the cost of production. 00:39:45.280 --> 00:39:47.490 align:middle line:90% So this term has a name. 00:39:47.490 --> 00:39:53.290 align:middle line:84% Has anyone heard what we might call this term here? 00:39:53.290 --> 00:39:54.750 align:middle line:90% This is often called the markup. 00:39:54.750 --> 00:39:55.917 align:middle line:90% And you might talk about it. 00:39:55.917 --> 00:39:58.550 align:middle line:84% You go to a store, say, wow, that's a really high markup. 00:39:58.550 --> 00:40:00.675 align:middle line:84% If you go to a restaurant, I could buy this chicken 00:40:00.675 --> 00:40:02.270 align:middle line:84% at a grocery store for this price. 00:40:02.270 --> 00:40:03.670 align:middle line:84% But this restaurant is charging a lot more. 00:40:03.670 --> 00:40:04.420 align:middle line:90% That's the markup. 00:40:04.420 --> 00:40:06.930 align:middle line:84% It's the difference between the price you're paying 00:40:06.930 --> 00:40:09.350 align:middle line:84% and the cost that they're actually paying to produce it. 00:40:09.350 --> 00:40:11.110 align:middle line:90% So this is called the markup. 00:40:11.110 --> 00:40:13.850 align:middle line:90% 00:40:13.850 --> 00:40:16.770 align:middle line:84% So we see that monopolists charge a markup. 00:40:16.770 --> 00:40:20.270 align:middle line:84% They don't charge a price equal to their cost of production. 00:40:20.270 --> 00:40:22.530 align:middle line:84% They charge a price that's strictly higher 00:40:22.530 --> 00:40:23.933 align:middle line:90% than their cost of production. 00:40:23.933 --> 00:40:25.850 align:middle line:84% And that's because they're taking advantage of 00:40:25.850 --> 00:40:29.330 align:middle line:84% or exploiting their monopoly power. 00:40:29.330 --> 00:40:30.690 align:middle line:90% Great. 00:40:30.690 --> 00:40:34.250 align:middle line:84% So now let's move to the actual game theory 00:40:34.250 --> 00:40:40.950 align:middle line:84% and think about what happens if we have multiple firms. 00:40:40.950 --> 00:40:50.290 align:middle line:90% 00:40:50.290 --> 00:40:52.790 align:middle line:84% So now what if there are multiple firms? 00:40:52.790 --> 00:41:06.210 align:middle line:90% 00:41:06.210 --> 00:41:10.610 align:middle line:84% Well, we have to think, how are these firms going to compete? 00:41:10.610 --> 00:41:12.650 align:middle line:84% It's not so clear what they're doing. 00:41:12.650 --> 00:41:15.650 align:middle line:84% And we're actually going to study two classical models 00:41:15.650 --> 00:41:17.570 align:middle line:90% of how firms compete. 00:41:17.570 --> 00:41:23.230 align:middle line:84% So one model is what's called quantity competition. 00:41:23.230 --> 00:41:28.085 align:middle line:90% 00:41:28.085 --> 00:41:30.210 align:middle line:84% And here, I think the model you should have in mind 00:41:30.210 --> 00:41:31.390 align:middle line:90% is you're a farmer. 00:41:31.390 --> 00:41:32.790 align:middle line:90% You think of two farmers. 00:41:32.790 --> 00:41:35.810 align:middle line:84% They're choosing how many apples to bring to the market. 00:41:35.810 --> 00:41:37.930 align:middle line:84% And once they get to the market, the price 00:41:37.930 --> 00:41:39.570 align:middle line:84% that they can get at the market depends 00:41:39.570 --> 00:41:41.810 align:middle line:84% on how many apples people bring to the market. 00:41:41.810 --> 00:41:45.020 align:middle line:84% So here, in quantity competition, 00:41:45.020 --> 00:41:46.560 align:middle line:90% firms choose quantities. 00:41:46.560 --> 00:41:52.380 align:middle line:90% 00:41:52.380 --> 00:41:54.840 align:middle line:84% And then the market chooses the price. 00:41:54.840 --> 00:41:58.140 align:middle line:90% 00:41:58.140 --> 00:42:01.140 align:middle line:90% Maybe sets price. 00:42:01.140 --> 00:42:03.780 align:middle line:84% So this is the oil example I gave earlier. 00:42:03.780 --> 00:42:06.260 align:middle line:84% If the US-- say, I gave Saudi Arabia before. 00:42:06.260 --> 00:42:08.140 align:middle line:84% Let's say the US, if the US increases 00:42:08.140 --> 00:42:10.580 align:middle line:84% its oil or its natural gas production 00:42:10.580 --> 00:42:13.860 align:middle line:84% and floods the market, that's going to decrease the market 00:42:13.860 --> 00:42:15.300 align:middle line:90% price of oil. 00:42:15.300 --> 00:42:17.020 align:middle line:84% So the US isn't just saying this is 00:42:17.020 --> 00:42:19.100 align:middle line:90% the price of oil I'm charging. 00:42:19.100 --> 00:42:20.700 align:middle line:84% They produce more oil, and then they 00:42:20.700 --> 00:42:23.420 align:middle line:84% have to take the price that they're given. 00:42:23.420 --> 00:42:25.415 align:middle line:84% So that's the model of quantity competition. 00:42:25.415 --> 00:42:27.540 align:middle line:84% The other model is maybe the more traditional model 00:42:27.540 --> 00:42:31.900 align:middle line:84% that you think of price competition, 00:42:31.900 --> 00:42:34.520 align:middle line:84% where, here, firms choose prices. 00:42:34.520 --> 00:42:36.220 align:middle line:84% You have two stores side by side. 00:42:36.220 --> 00:42:37.780 align:middle line:84% They each post a sign that says, this 00:42:37.780 --> 00:42:41.380 align:middle line:84% is how much it costs to buy this item at our store. 00:42:41.380 --> 00:42:44.880 align:middle line:90% So here, firms choose prices. 00:42:44.880 --> 00:42:49.980 align:middle line:90% 00:42:49.980 --> 00:42:53.220 align:middle line:84% And then those prices determine how much consumers actually 00:42:53.220 --> 00:42:55.060 align:middle line:90% buy from each store. 00:42:55.060 --> 00:42:58.500 align:middle line:84% So then you could say the market sets demand. 00:42:58.500 --> 00:43:01.140 align:middle line:90% Or I'll say quantities-- 00:43:01.140 --> 00:43:07.900 align:middle line:84% maybe I'll say the market chooses demand-- 00:43:07.900 --> 00:43:09.000 align:middle line:90% or chooses quantity. 00:43:09.000 --> 00:43:11.860 align:middle line:90% 00:43:11.860 --> 00:43:13.143 align:middle line:90% So I see two stores. 00:43:13.143 --> 00:43:15.560 align:middle line:84% They each have a sign that says how much they're charging. 00:43:15.560 --> 00:43:18.100 align:middle line:84% And I choose which store to go to. 00:43:18.100 --> 00:43:20.140 align:middle line:84% So I think these are two very natural ways 00:43:20.140 --> 00:43:23.108 align:middle line:90% of thinking about competition. 00:43:23.108 --> 00:43:24.900 align:middle line:84% We're going to find in the next few minutes 00:43:24.900 --> 00:43:27.300 align:middle line:84% that these actually give very different answers. 00:43:27.300 --> 00:43:31.060 align:middle line:84% So I think there's the math, which allows 00:43:31.060 --> 00:43:33.112 align:middle line:90% us to analyze these two models. 00:43:33.112 --> 00:43:34.820 align:middle line:84% And then I think the job of the economist 00:43:34.820 --> 00:43:36.860 align:middle line:84% is to try to figure out which of these models 00:43:36.860 --> 00:43:39.990 align:middle line:84% is more appropriate in a particular situation. 00:43:39.990 --> 00:43:42.150 align:middle line:84% Because they both seem reasonable, 00:43:42.150 --> 00:43:43.822 align:middle line:84% and I gave a few examples of markets 00:43:43.822 --> 00:43:45.530 align:middle line:84% that might fit one better than the other, 00:43:45.530 --> 00:43:47.930 align:middle line:84% but whenever we have two models that both seem reasonable, 00:43:47.930 --> 00:43:49.050 align:middle line:84% they give very different results, 00:43:49.050 --> 00:43:51.508 align:middle line:84% we really have to think hard about which is the right model 00:43:51.508 --> 00:43:53.510 align:middle line:84% to capture the situation we have in mind. 00:43:53.510 --> 00:43:56.350 align:middle line:84% So it turns out this one came first. 00:43:56.350 --> 00:43:59.855 align:middle line:90% This is a model by Cournot. 00:43:59.855 --> 00:44:01.230 align:middle line:84% It's easy to remember these dates 00:44:01.230 --> 00:44:02.810 align:middle line:90% because they mirror each other. 00:44:02.810 --> 00:44:05.153 align:middle line:90% This was in 1838. 00:44:05.153 --> 00:44:07.070 align:middle line:84% And then, in this model, the price competition 00:44:07.070 --> 00:44:10.920 align:middle line:84% is by Bertrand, and this is actually 1883. 00:44:10.920 --> 00:44:12.670 align:middle line:84% I mean, the dates don't matter, but I just 00:44:12.670 --> 00:44:16.430 align:middle line:84% think it's fun that the dates are like that. 00:44:16.430 --> 00:44:19.450 align:middle line:84% And Cournot came along, wrote down this model. 00:44:19.450 --> 00:44:23.530 align:middle line:84% He was motivated by, actually, spring water, 00:44:23.530 --> 00:44:26.695 align:middle line:84% these two firms that were sitting on a spring and were, 00:44:26.695 --> 00:44:29.070 align:middle line:84% I don't know, bottling or I don't know how water was sold 00:44:29.070 --> 00:44:32.510 align:middle line:84% in the 1800s, putting water into buckets and selling it. 00:44:32.510 --> 00:44:35.230 align:middle line:84% And then Bertrand wrote an angry article 00:44:35.230 --> 00:44:37.670 align:middle line:84% a few years later saying, this is a crazy way 00:44:37.670 --> 00:44:38.730 align:middle line:90% to model competition. 00:44:38.730 --> 00:44:40.890 align:middle line:90% Firms don't choose quantities. 00:44:40.890 --> 00:44:41.973 align:middle line:90% They choose prices. 00:44:41.973 --> 00:44:44.390 align:middle line:84% And today, modern industrial organization economists still 00:44:44.390 --> 00:44:46.550 align:middle line:84% think about different ways of modeling competition 00:44:46.550 --> 00:44:48.210 align:middle line:84% and what's the right way to think about it. 00:44:48.210 --> 00:44:50.330 align:middle line:84% There's no right way, but in different situations, 00:44:50.330 --> 00:44:51.430 align:middle line:90% which one is better. 00:44:51.430 --> 00:44:55.310 align:middle line:84% OK, So let's go through these formal models. 00:44:55.310 --> 00:44:56.730 align:middle line:90% So we'll start with Cournot. 00:44:56.730 --> 00:44:58.810 align:middle line:90% We'll go chronologically. 00:44:58.810 --> 00:45:08.950 align:middle line:90% 00:45:08.950 --> 00:45:11.310 align:middle line:84% So this is sometimes known as quantity competition. 00:45:11.310 --> 00:45:13.450 align:middle line:84% Sometimes called Cournot competition. 00:45:13.450 --> 00:45:14.490 align:middle line:90% Those are synonymous. 00:45:14.490 --> 00:45:17.650 align:middle line:84% So maybe here I'll call it Cournot competition. 00:45:17.650 --> 00:45:22.190 align:middle line:90% 00:45:22.190 --> 00:45:23.410 align:middle line:90% So what's the model? 00:45:23.410 --> 00:45:29.830 align:middle line:84% We have two firms, and we'll call those firms 1 and 2. 00:45:29.830 --> 00:45:32.950 align:middle line:84% And each firm has the same constant marginal cost 00:45:32.950 --> 00:45:34.960 align:middle line:90% of production. 00:45:34.960 --> 00:45:46.580 align:middle line:84% So we'll say constant marginal cost c at both firms. 00:45:46.580 --> 00:45:50.320 align:middle line:90% 00:45:50.320 --> 00:45:53.740 align:middle line:84% And let's assume c is between 0 and 1, just as we did before. 00:45:53.740 --> 00:45:57.920 align:middle line:90% 00:45:57.920 --> 00:46:01.153 align:middle line:90% And now we have market demand. 00:46:01.153 --> 00:46:03.320 align:middle line:84% We're actually going to look at the inverse demand-- 00:46:03.320 --> 00:46:05.487 align:middle line:84% because it's a bit more convenient in this setting-- 00:46:05.487 --> 00:46:11.330 align:middle line:90% 00:46:11.330 --> 00:46:16.720 align:middle line:90% P of q equals 1 minus q. 00:46:16.720 --> 00:46:19.560 align:middle line:84% But notice here that this inverse demand is actually 00:46:19.560 --> 00:46:22.120 align:middle line:84% exactly the same demand we had before. 00:46:22.120 --> 00:46:25.240 align:middle line:84% Because if p of Q equals 1 minus q, well, 00:46:25.240 --> 00:46:27.680 align:middle line:84% how do I-- let's solve for Q. That 00:46:27.680 --> 00:46:30.240 align:middle line:90% means Q is equal to 1 minus p. 00:46:30.240 --> 00:46:32.560 align:middle line:84% So this is exactly the inverse demand 00:46:32.560 --> 00:46:35.880 align:middle line:84% that is associated with this demand over here. 00:46:35.880 --> 00:46:39.520 align:middle line:84% So these are just two different ways of writing it. 00:46:39.520 --> 00:46:44.080 align:middle line:84% And again with the understanding that if quantity gets too big, 00:46:44.080 --> 00:46:45.260 align:middle line:90% then the price is just 0. 00:46:45.260 --> 00:46:46.760 align:middle line:84% So if I want it to be really formal, 00:46:46.760 --> 00:46:52.860 align:middle line:84% I would say the maximum of 1 minus q and 0. 00:46:52.860 --> 00:46:57.680 align:middle line:90% 00:46:57.680 --> 00:46:59.760 align:middle line:90% But this is a crucial point. 00:46:59.760 --> 00:47:04.140 align:middle line:84% This Q here is the market quantity. 00:47:04.140 --> 00:47:10.080 align:middle line:90% 00:47:10.080 --> 00:47:13.960 align:middle line:84% So the price at the market depends on how much 00:47:13.960 --> 00:47:16.360 align:middle line:90% water is brought to market. 00:47:16.360 --> 00:47:18.840 align:middle line:84% But the amount of water or apples brought to market 00:47:18.840 --> 00:47:22.600 align:middle line:84% depends on the entire market, not just an individual firm. 00:47:22.600 --> 00:47:28.760 align:middle line:84% So the crucial thing here is that, each firm i, 00:47:28.760 --> 00:47:32.910 align:middle line:90% chooses a quantity qi. 00:47:32.910 --> 00:47:35.970 align:middle line:84% So firm 1 chooses their quantity, q1. 00:47:35.970 --> 00:47:38.490 align:middle line:84% And firm 2 chooses their quantity, q2. 00:47:38.490 --> 00:47:40.543 align:middle line:90% And notice this is lowercase. 00:47:40.543 --> 00:47:43.210 align:middle line:84% So we're generally going to use lowercase to denote the quantity 00:47:43.210 --> 00:47:45.810 align:middle line:90% chosen by a particular firm. 00:47:45.810 --> 00:47:50.610 align:middle line:84% But the individual choices of the firms, when added together, 00:47:50.610 --> 00:47:52.770 align:middle line:84% determine what the market demand is. 00:47:52.770 --> 00:47:56.530 align:middle line:84% So in this case, the market quantity Q 00:47:56.530 --> 00:47:59.930 align:middle line:84% is going to be the sum of the amount produced by each firm. 00:47:59.930 --> 00:48:04.510 align:middle line:84% So this is going to be q1 plus q2. 00:48:04.510 --> 00:48:13.170 align:middle line:90% 00:48:13.170 --> 00:48:15.970 align:middle line:84% And the final assumption-- maybe I'll write it explicitly 00:48:15.970 --> 00:48:18.110 align:middle line:90% is that firms maximize profits. 00:48:18.110 --> 00:48:20.930 align:middle line:90% 00:48:20.930 --> 00:48:22.730 align:middle line:84% Expected profit-- or I guess there's 00:48:22.730 --> 00:48:26.130 align:middle line:90% no [INAUDIBLE] say profit. 00:48:26.130 --> 00:48:28.730 align:middle line:84% Now, remember, this is an important assumption. 00:48:28.730 --> 00:48:31.050 align:middle line:84% Going back to what we said before, when we set up 00:48:31.050 --> 00:48:34.850 align:middle line:84% game theory, we said what people maximize is utility, 00:48:34.850 --> 00:48:37.450 align:middle line:84% and utility is not always the same as money. 00:48:37.450 --> 00:48:39.890 align:middle line:84% So another way of saying firms maximize profit 00:48:39.890 --> 00:48:42.930 align:middle line:90% is that firms are risk neutral. 00:48:42.930 --> 00:48:45.250 align:middle line:84% Their von Neumann-Morgenstern utility 00:48:45.250 --> 00:48:48.450 align:middle line:84% function as a function of money is just linear. 00:48:48.450 --> 00:48:50.090 align:middle line:90% Is this a reasonable assumption? 00:48:50.090 --> 00:48:51.030 align:middle line:90% In some contexts, yes. 00:48:51.030 --> 00:48:52.225 align:middle line:90% In other contexts, no. 00:48:52.225 --> 00:48:53.850 align:middle line:84% So maybe in other contexts, we'd really 00:48:53.850 --> 00:48:56.742 align:middle line:84% want to think of a firm that's risk averse over their profits. 00:48:56.742 --> 00:48:58.950 align:middle line:84% But in this model, we're assuming their risk neutral. 00:48:58.950 --> 00:49:02.610 align:middle line:84% So all they're trying to do is maximize profits. 00:49:02.610 --> 00:49:06.250 align:middle line:84% OK, so now let's write down what the profits are. 00:49:06.250 --> 00:49:08.410 align:middle line:90% So let's look at firm 1. 00:49:08.410 --> 00:49:10.930 align:middle line:84% It's easier to reason from one firm's perspective. 00:49:10.930 --> 00:49:13.930 align:middle line:84% Though, it's always going to be symmetric. 00:49:13.930 --> 00:49:18.290 align:middle line:84% I'm going to write pi 1 of q1, q2. 00:49:18.290 --> 00:49:20.010 align:middle line:84% So let's just understand pi is often 00:49:20.010 --> 00:49:23.170 align:middle line:84% used for profits just because it's the Greek pi, like p 00:49:23.170 --> 00:49:24.450 align:middle line:90% for profit. 00:49:24.450 --> 00:49:26.070 align:middle line:84% And we already used p for prices, 00:49:26.070 --> 00:49:28.100 align:middle line:90% so we use pi for profits. 00:49:28.100 --> 00:49:30.380 align:middle line:84% What I want to understand is I'm firm 1. 00:49:30.380 --> 00:49:33.780 align:middle line:84% What is the profit that I get if I 00:49:33.780 --> 00:49:36.300 align:middle line:84% produce a quantity of q1 and the other firm 00:49:36.300 --> 00:49:39.020 align:middle line:90% produces a quantity of q2? 00:49:39.020 --> 00:49:40.660 align:middle line:90% Well, let's understand this. 00:49:40.660 --> 00:49:43.680 align:middle line:84% Well, just as before, we can decompose this into two parts. 00:49:43.680 --> 00:49:47.240 align:middle line:84% We have to keep track of my profit per unit, 00:49:47.240 --> 00:49:49.402 align:middle line:84% and then the number of units I have. 00:49:49.402 --> 00:49:50.860 align:middle line:84% The number of units I have is easy. 00:49:50.860 --> 00:49:51.920 align:middle line:90% Let's write that down. 00:49:51.920 --> 00:49:56.700 align:middle line:84% That's q1-- q1, the number of units I sell. 00:49:56.700 --> 00:50:01.100 align:middle line:84% But then what is going to be my profit per unit? 00:50:01.100 --> 00:50:02.860 align:middle line:90% Thoughts here? 00:50:02.860 --> 00:50:06.680 align:middle line:84% So what do I want to multiply q1 by? 00:50:06.680 --> 00:50:10.723 align:middle line:90% AUDIENCE: 1 minus q1 plus q2. 00:50:10.723 --> 00:50:12.640 align:middle line:84% IAN BALL: Yes, there's a parentheses in there. 00:50:12.640 --> 00:50:13.223 align:middle line:90% Yeah, exactly. 00:50:13.223 --> 00:50:15.980 align:middle line:90% So let me write it-- 00:50:15.980 --> 00:50:18.300 align:middle line:90% let me first write it as this. 00:50:18.300 --> 00:50:21.860 align:middle line:84% And then I'll break it down in the way you suggested. 00:50:21.860 --> 00:50:24.900 align:middle line:84% So q1 is the amount I'm producing. 00:50:24.900 --> 00:50:26.900 align:middle line:90% What is my profit per unit? 00:50:26.900 --> 00:50:28.660 align:middle line:84% Well, my profit is just the price 00:50:28.660 --> 00:50:32.380 align:middle line:84% that I'm able to sell it for minus the cost of production. 00:50:32.380 --> 00:50:34.620 align:middle line:84% But the tricky thing here is, what is the price? 00:50:34.620 --> 00:50:37.700 align:middle line:84% Well, the price is determined by the market demand. 00:50:37.700 --> 00:50:41.580 align:middle line:84% And therefore, it's p of the market quantity-- sorry, 00:50:41.580 --> 00:50:43.240 align:middle line:84% not market demand, market quantity-- 00:50:43.240 --> 00:50:46.900 align:middle line:84% which is the sum of q1 plus q2, the market supply. 00:50:46.900 --> 00:50:49.300 align:middle line:84% And this is what makes this a game theory problem. 00:50:49.300 --> 00:50:53.140 align:middle line:84% Because how will I do as firm 1 depends not only 00:50:53.140 --> 00:50:55.560 align:middle line:84% on what I produce and what I bring to market, 00:50:55.560 --> 00:50:58.620 align:middle line:84% but also on what my opponent brings to market, q2. 00:50:58.620 --> 00:51:01.780 align:middle line:84% Why does it matter how much my opponent produces? 00:51:01.780 --> 00:51:03.660 align:middle line:84% Because how much my opponent produces 00:51:03.660 --> 00:51:06.580 align:middle line:84% affects the price at which I sell my goods. 00:51:06.580 --> 00:51:08.500 align:middle line:84% So now we have a strategic interaction 00:51:08.500 --> 00:51:11.180 align:middle line:90% between the two firms. 00:51:11.180 --> 00:51:13.200 align:middle line:84% And let's write this out once more. 00:51:13.200 --> 00:51:19.820 align:middle line:84% We have q1 times, well, p of q1 plus q2 is just 1 minus-- 00:51:19.820 --> 00:51:21.560 align:middle line:90% in parentheses q1 plus q2. 00:51:21.560 --> 00:51:26.530 align:middle line:84% So that's 1 minus q1 minus q2 minus c. 00:51:26.530 --> 00:51:31.670 align:middle line:90% 00:51:31.670 --> 00:51:33.530 align:middle line:84% So now it doesn't really make sense to say, 00:51:33.530 --> 00:51:35.228 align:middle line:90% what is my optimal quantity? 00:51:35.228 --> 00:51:37.770 align:middle line:84% With the monopolist, we just said what price should I charge? 00:51:37.770 --> 00:51:38.670 align:middle line:90% That was easy. 00:51:38.670 --> 00:51:43.590 align:middle line:84% Now the optimal quantity for me depends upon the quantity 00:51:43.590 --> 00:51:45.910 align:middle line:90% that the other firm produces. 00:51:45.910 --> 00:51:48.370 align:middle line:84% So instead of just talking about an optimal quantity, 00:51:48.370 --> 00:51:49.970 align:middle line:84% we have to talk about a best response. 00:51:49.970 --> 00:51:51.130 align:middle line:90% Now we have a game. 00:51:51.130 --> 00:51:52.750 align:middle line:90% Let's understand this as a game. 00:51:52.750 --> 00:51:55.510 align:middle line:84% A strategy for firm 1 is a quantity. 00:51:55.510 --> 00:51:57.990 align:middle line:84% A strategy for firm 2 is also a quantity. 00:51:57.990 --> 00:52:00.810 align:middle line:84% And the utility of firm 1 is given like this. 00:52:00.810 --> 00:52:03.450 align:middle line:84% And we can symmetrically write down the utility for firm 2. 00:52:03.450 --> 00:52:06.550 align:middle line:84% So now we have a game, and we can talk about best responses. 00:52:06.550 --> 00:52:15.030 align:middle line:84% So a best response by firm 1 to a quantity q2 is equal to what? 00:52:15.030 --> 00:52:16.110 align:middle line:90% Well? 00:52:16.110 --> 00:52:18.950 align:middle line:84% We need to maximize this expression. 00:52:18.950 --> 00:52:21.370 align:middle line:84% And this kind of expression comes up a lot. 00:52:21.370 --> 00:52:22.970 align:middle line:84% So I want to-- you can do the algebra, 00:52:22.970 --> 00:52:24.845 align:middle line:84% but I think it's nice to know a little trick. 00:52:24.845 --> 00:52:28.230 align:middle line:84% So if you're ever maximizing something 00:52:28.230 --> 00:52:30.130 align:middle line:90% like this where a is positive-- 00:52:30.130 --> 00:52:32.870 align:middle line:90% 00:52:32.870 --> 00:52:37.590 align:middle line:84% so I'm choosing x, to maximize x times a minus x, 00:52:37.590 --> 00:52:39.370 align:middle line:84% you can just derive this with calculus. 00:52:39.370 --> 00:52:41.990 align:middle line:84% But what you'll find is x equals a over 2. 00:52:41.990 --> 00:52:43.430 align:middle line:90% That's always the optimum. 00:52:43.430 --> 00:52:45.797 align:middle line:84% And this kind of form comes up again and again. 00:52:45.797 --> 00:52:47.630 align:middle line:84% So it's just a nice thing to know right away 00:52:47.630 --> 00:52:49.510 align:middle line:90% for exams and quizzes. 00:52:49.510 --> 00:52:53.190 align:middle line:84% Again, it's the fact that a rectangle 00:52:53.190 --> 00:52:56.890 align:middle line:84% of constant perimeter, its area is maximized by a square. 00:52:56.890 --> 00:52:59.693 align:middle line:84% If I take x equals a over 2, then both of these terms 00:52:59.693 --> 00:53:00.610 align:middle line:90% are equal to a over 2. 00:53:00.610 --> 00:53:01.693 align:middle line:90% That's the geometry of it. 00:53:01.693 --> 00:53:03.410 align:middle line:90% You can do calculus to solve it. 00:53:03.410 --> 00:53:05.810 align:middle line:84% But now we can immediately find what my best response is. 00:53:05.810 --> 00:53:08.890 align:middle line:84% We just have to be careful to figure out what the a is. 00:53:08.890 --> 00:53:11.470 align:middle line:84% So we have to think, OK, I'm firm 1. 00:53:11.470 --> 00:53:13.030 align:middle line:90% I'm choosing q1. 00:53:13.030 --> 00:53:15.990 align:middle line:84% So from my perspective, what part of this do I control? 00:53:15.990 --> 00:53:19.430 align:middle line:84% And what part of this is a constant? 00:53:19.430 --> 00:53:20.240 align:middle line:90% Yeah. 00:53:20.240 --> 00:53:22.878 align:middle line:84% AUDIENCE: q1 is controlled [INAUDIBLE]. 00:53:22.878 --> 00:53:24.420 align:middle line:84% IAN BALL: Right, so q1 is controlled. 00:53:24.420 --> 00:53:29.420 align:middle line:84% So the a here is 1 minus q2 minus c. 00:53:29.420 --> 00:53:33.320 align:middle line:84% We can think of this as the constant a minus q1 00:53:33.320 --> 00:53:36.000 align:middle line:90% where a is 1 minus q2 minus c. 00:53:36.000 --> 00:53:39.520 align:middle line:84% So if I just do this out, I see that my best response is 1 minus 00:53:39.520 --> 00:53:42.540 align:middle line:90% q2 minus c divided by 2. 00:53:42.540 --> 00:53:51.520 align:middle line:90% 00:53:51.520 --> 00:53:54.400 align:middle line:84% OK, and again, let's ask if this makes sense. 00:53:54.400 --> 00:53:58.000 align:middle line:84% So as before, we see that the amount I produce 00:53:58.000 --> 00:54:00.000 align:middle line:90% is decreasing in the cost. 00:54:00.000 --> 00:54:02.785 align:middle line:84% So if the cost of production is higher, I produce less. 00:54:02.785 --> 00:54:03.660 align:middle line:90% Does this make sense? 00:54:03.660 --> 00:54:05.700 align:middle line:84% Can someone give intuition for this? 00:54:05.700 --> 00:54:08.360 align:middle line:84% Why do I want to produce less when the cost of production 00:54:08.360 --> 00:54:09.020 align:middle line:90% is higher? 00:54:09.020 --> 00:54:12.198 align:middle line:90% 00:54:12.198 --> 00:54:13.740 align:middle line:84% Why don't I just keep producing more? 00:54:13.740 --> 00:54:17.760 align:middle line:90% 00:54:17.760 --> 00:54:18.300 align:middle line:90% Thoughts? 00:54:18.300 --> 00:54:21.040 align:middle line:90% 00:54:21.040 --> 00:54:24.520 align:middle line:84% Well, my amount of production affects the market price. 00:54:24.520 --> 00:54:27.440 align:middle line:84% So if the cost is really high, it's only worth it for me 00:54:27.440 --> 00:54:29.560 align:middle line:84% to produce if the market price is high, 00:54:29.560 --> 00:54:31.380 align:middle line:84% which means I can't keep producing a lot. 00:54:31.380 --> 00:54:33.520 align:middle line:84% Otherwise, I'd pull the market price down too low. 00:54:33.520 --> 00:54:36.760 align:middle line:84% So again, a higher cost means I produce less simply 00:54:36.760 --> 00:54:41.040 align:middle line:84% because I require a higher price to make it worth it. 00:54:41.040 --> 00:54:44.000 align:middle line:84% And then it's also decreasing in q2. 00:54:44.000 --> 00:54:46.640 align:middle line:84% So the more that my competitor produces, 00:54:46.640 --> 00:54:48.400 align:middle line:90% the less that I produce. 00:54:48.400 --> 00:54:49.420 align:middle line:90% Does that make sense? 00:54:49.420 --> 00:54:56.440 align:middle line:90% 00:54:56.440 --> 00:54:58.240 align:middle line:90% Well, if my-- yeah. 00:54:58.240 --> 00:54:58.920 align:middle line:90% Go ahead. 00:54:58.920 --> 00:55:00.295 align:middle line:84% AUDIENCE: They are producing more 00:55:00.295 --> 00:55:01.580 align:middle line:90% than the price is going down. 00:55:01.580 --> 00:55:02.580 align:middle line:90% IAN BALL: Exactly right. 00:55:02.580 --> 00:55:05.400 align:middle line:84% So the more they produce, the lower the price 00:55:05.400 --> 00:55:07.940 align:middle line:84% I'm going to face for a given amount of my production. 00:55:07.940 --> 00:55:10.840 align:middle line:84% And therefore, it's optimal for me to produce less. 00:55:10.840 --> 00:55:13.980 align:middle line:84% So now we've computed the best responses. 00:55:13.980 --> 00:55:15.480 align:middle line:84% I've only done it one way, but we 00:55:15.480 --> 00:55:17.570 align:middle line:84% can see what it's going to be for the other firm. 00:55:17.570 --> 00:55:20.390 align:middle line:84% BR2 of q1 is just going to be symmetric. 00:55:20.390 --> 00:55:24.570 align:middle line:84% It's going to be 1 minus q1 minus c over 2. 00:55:24.570 --> 00:55:28.850 align:middle line:84% So if I'm firm 2 and firm 1 is choosing a quantity of q1, 00:55:28.850 --> 00:55:33.130 align:middle line:84% this is the optimal quantity for firm 2 to produce. 00:55:33.130 --> 00:55:36.770 align:middle line:84% And now I want to solve for an equilibrium, which 00:55:36.770 --> 00:55:40.530 align:middle line:90% means I need-- 00:55:40.530 --> 00:55:42.190 align:middle line:84% maybe I'll just write it like this. 00:55:42.190 --> 00:55:47.250 align:middle line:90% 00:55:47.250 --> 00:55:49.930 align:middle line:90% Maybe I'll put these in here. 00:55:49.930 --> 00:55:51.910 align:middle line:84% So what is my equilibrium condition? 00:55:51.910 --> 00:55:55.370 align:middle line:84% In equilibrium, each firm is playing a best response 00:55:55.370 --> 00:55:57.610 align:middle line:90% to the other firm's quantity. 00:55:57.610 --> 00:56:01.210 align:middle line:84% So I need q1 star, what firm 1 is choosing, 00:56:01.210 --> 00:56:05.330 align:middle line:84% to be a best response to what q2, firm 2, is choosing. 00:56:05.330 --> 00:56:08.770 align:middle line:84% And I need the amount of produced by firm 2, q2 star, 00:56:08.770 --> 00:56:11.490 align:middle line:84% to be a best response for firm 2 to the amount produced 00:56:11.490 --> 00:56:14.290 align:middle line:90% by firm 1. 00:56:14.290 --> 00:56:17.450 align:middle line:84% So I now have a system of equations. 00:56:17.450 --> 00:56:19.610 align:middle line:84% But let's understand, my system of equations 00:56:19.610 --> 00:56:21.770 align:middle line:90% is a linear system of equations. 00:56:21.770 --> 00:56:24.930 align:middle line:84% And it has two equations and two unknowns. 00:56:24.930 --> 00:56:27.770 align:middle line:84% And in general, we can solve those systems pretty easily. 00:56:27.770 --> 00:56:30.610 align:middle line:84% We could go through the algebra, but I'll spare you the algebra. 00:56:30.610 --> 00:56:37.730 align:middle line:84% And what we'll get is q1 star equals q2 star equals 00:56:37.730 --> 00:56:39.830 align:middle line:90% 1 minus c over 3. 00:56:39.830 --> 00:56:51.370 align:middle line:90% 00:56:51.370 --> 00:56:53.130 align:middle line:84% And let's ask, what is the market 00:56:53.130 --> 00:56:55.770 align:middle line:90% price going to be in this case? 00:56:55.770 --> 00:57:03.530 align:middle line:84% Well, the market price is going to be 1 minus q1 minus q2. 00:57:03.530 --> 00:57:06.570 align:middle line:84% But each of these is 1 minus c over 3, 00:57:06.570 --> 00:57:08.370 align:middle line:90% but I subtract that twice. 00:57:08.370 --> 00:57:14.440 align:middle line:90% So I get 1 minus 2/3 1 minus c. 00:57:14.440 --> 00:57:18.620 align:middle line:90% 00:57:18.620 --> 00:57:21.460 align:middle line:84% And again, it's nice to pull c out. 00:57:21.460 --> 00:57:23.040 align:middle line:90% So we can do a little trick. 00:57:23.040 --> 00:57:24.100 align:middle line:90% This is c. 00:57:24.100 --> 00:57:26.140 align:middle line:90% Let's add c and subtract c. 00:57:26.140 --> 00:57:31.200 align:middle line:84% And what we get is c plus 1 minus c over 3. 00:57:31.200 --> 00:57:42.740 align:middle line:90% 00:57:42.740 --> 00:57:45.140 align:middle line:84% So one thing we can make a comparison 00:57:45.140 --> 00:57:46.340 align:middle line:90% with our monopoly case. 00:57:46.340 --> 00:57:49.020 align:middle line:84% In our monopoly case where we had only one firm, 00:57:49.020 --> 00:57:52.420 align:middle line:84% the markup was 1 minus c1 over 2. 00:57:52.420 --> 00:57:55.020 align:middle line:84% Here, when we have two firms competing in Cournot, 00:57:55.020 --> 00:57:57.420 align:middle line:90% the markup is 1 minus c over 3. 00:57:57.420 --> 00:58:03.260 align:middle line:84% So we see that we have a smaller markup, which maybe makes sense. 00:58:03.260 --> 00:58:05.540 align:middle line:84% And we can actually generalize this. 00:58:05.540 --> 00:58:09.120 align:middle line:84% So let's understand it intuitively. 00:58:09.120 --> 00:58:22.980 align:middle line:90% 00:58:22.980 --> 00:58:31.560 align:middle line:84% So let's look at the general case with n firms. 00:58:31.560 --> 00:58:34.022 align:middle line:90% 00:58:34.022 --> 00:58:35.980 align:middle line:84% And this we can actually just guess by the form 00:58:35.980 --> 00:58:36.730 align:middle line:90% that we have here. 00:58:36.730 --> 00:58:39.120 align:middle line:84% So I'm not going to go through the derivation, 00:58:39.120 --> 00:58:42.100 align:middle line:84% but I'm just going to write down the answer. 00:58:42.100 --> 00:58:44.660 align:middle line:84% And it's pretty easy to check using the same argument. 00:58:44.660 --> 00:58:46.580 align:middle line:90% So we have n firms. 00:58:46.580 --> 00:58:50.260 align:middle line:84% How much is each firm going to produce? 00:58:50.260 --> 00:58:54.220 align:middle line:84% Maybe I'll write q1 star equals qn star. 00:58:54.220 --> 00:58:56.140 align:middle line:84% So it turns out with n firms, we're 00:58:56.140 --> 00:58:57.880 align:middle line:84% going to have a symmetric equilibrium, 00:58:57.880 --> 00:59:00.620 align:middle line:84% every firm is going to produce the same amount, 00:59:00.620 --> 00:59:03.200 align:middle line:84% and based on our pattern, with two firms, 00:59:03.200 --> 00:59:05.980 align:middle line:84% they each produce 1 minus c over 3. 00:59:05.980 --> 00:59:10.230 align:middle line:84% And notice in the monopoly case, we got-- 00:59:10.230 --> 00:59:11.430 align:middle line:90% did we solve for q? 00:59:11.430 --> 00:59:14.082 align:middle line:90% 1 minus c over 2. 00:59:14.082 --> 00:59:16.290 align:middle line:84% Now, in the monopoly case, they were choosing prices. 00:59:16.290 --> 00:59:17.870 align:middle line:84% But actually, with a monopolist, whether you choose 00:59:17.870 --> 00:59:20.190 align:middle line:84% price or quantity doesn't make a difference. 00:59:20.190 --> 00:59:22.390 align:middle line:84% So with one firm, we got 1 minus c over 2. 00:59:22.390 --> 00:59:25.593 align:middle line:84% With two firms, we got 1 minus c over 3. 00:59:25.593 --> 00:59:27.010 align:middle line:84% It's a pretty clear pattern there. 00:59:27.010 --> 00:59:31.070 align:middle line:84% It's always 1 minus c divided by the number of firms plus 1. 00:59:31.070 --> 00:59:36.843 align:middle line:84% So this is 1 minus c over n plus 1. 00:59:36.843 --> 00:59:38.010 align:middle line:90% So I think this makes sense. 00:59:38.010 --> 00:59:40.670 align:middle line:84% Let's again go through our intuition. 00:59:40.670 --> 00:59:43.250 align:middle line:84% Each firm produces less when the cost is higher. 00:59:43.250 --> 00:59:44.430 align:middle line:90% That makes sense. 00:59:44.430 --> 00:59:47.670 align:middle line:84% Each firm also produces less when the number of other firms 00:59:47.670 --> 00:59:48.630 align:middle line:90% goes up. 00:59:48.630 --> 00:59:53.070 align:middle line:84% So the more firms there are, the less each firm produces. 00:59:53.070 --> 00:59:55.910 align:middle line:84% And the reason is that the residual demand 00:59:55.910 --> 00:59:57.610 align:middle line:90% that they can capture is lower. 00:59:57.610 --> 01:00:00.652 align:middle line:84% The other firms are already capturing a lot of the market. 01:00:00.652 --> 01:00:03.110 align:middle line:84% Or another way of saying it is, the other firms are already 01:00:03.110 --> 01:00:04.950 align:middle line:90% dragging down the price. 01:00:04.950 --> 01:00:08.230 align:middle line:84% So I don't want to bring so much more. 01:00:08.230 --> 01:00:13.950 align:middle line:84% It's also good, though, to look at the total market quantity. 01:00:13.950 --> 01:00:22.310 align:middle line:84% So Q star which equals q1 star up to qn star is-- 01:00:22.310 --> 01:00:24.770 align:middle line:84% let's sum up the amount produced by each firm. 01:00:24.770 --> 01:00:27.950 align:middle line:84% So we can look at the total amount produced by the market. 01:00:27.950 --> 01:00:35.350 align:middle line:84% And what we're going to get is n over n plus 1 times 1 over c. 01:00:35.350 --> 01:00:40.230 align:middle line:84% So what we see is that this is decreasing in n, 01:00:40.230 --> 01:00:42.710 align:middle line:90% but this is increasing in n. 01:00:42.710 --> 01:00:46.350 align:middle line:84% So when there's more firms, each firm produces less. 01:00:46.350 --> 01:00:48.990 align:middle line:84% But the total amount produced by all firms 01:00:48.990 --> 01:00:50.870 align:middle line:90% is actually increasing. 01:00:50.870 --> 01:00:56.110 align:middle line:84% And as n gets really large, what is this going to approach? 01:00:56.110 --> 01:00:58.510 align:middle line:84% Just 1 minus c because n over n plus 1 01:00:58.510 --> 01:01:00.470 align:middle line:90% is going to converge to 1. 01:01:00.470 --> 01:01:02.310 align:middle line:90% So we just get 1 minus c. 01:01:02.310 --> 01:01:05.880 align:middle line:84% So I'll say, and this converges to 1 minus c as n 01:01:05.880 --> 01:01:06.780 align:middle line:90% goes to infinity. 01:01:06.780 --> 01:01:11.360 align:middle line:90% 01:01:11.360 --> 01:01:15.400 align:middle line:90% And what about the market price? 01:01:15.400 --> 01:01:18.400 align:middle line:84% Remember, it doesn't make sense to talk about the firm's price 01:01:18.400 --> 01:01:20.700 align:middle line:84% because they're all selling at the same price. 01:01:20.700 --> 01:01:24.380 align:middle line:84% So there's a firm quantity and a market quantity, 01:01:24.380 --> 01:01:25.820 align:middle line:90% but there's only a market price. 01:01:25.820 --> 01:01:29.880 align:middle line:84% There's no individual firm price in this model. 01:01:29.880 --> 01:01:32.420 align:middle line:90% Again, we can see the pattern. 01:01:32.420 --> 01:01:36.220 align:middle line:84% This is going to be c plus 1 minus c over n plus 1. 01:01:36.220 --> 01:01:39.600 align:middle line:90% 01:01:39.600 --> 01:01:41.740 align:middle line:90% And this is decreasing in it. 01:01:41.740 --> 01:01:45.000 align:middle line:90% 01:01:45.000 --> 01:01:46.620 align:middle line:84% And again, I think this makes sense. 01:01:46.620 --> 01:01:50.160 align:middle line:84% The more firms there are, the stiffer 01:01:50.160 --> 01:01:52.640 align:middle line:84% the competition between the firms, 01:01:52.640 --> 01:01:56.080 align:middle line:90% and the lower the price is. 01:01:56.080 --> 01:02:03.040 align:middle line:84% And in fact, what happens to the markup as n gets really big? 01:02:03.040 --> 01:02:05.025 align:middle line:90% The markup goes to 0. 01:02:05.025 --> 01:02:06.400 align:middle line:84% So what we see is that the market 01:02:06.400 --> 01:02:13.000 align:middle line:84% price in this case converges to c as n goes to infinity. 01:02:13.000 --> 01:02:15.880 align:middle line:84% And this exactly captures perfect competition. 01:02:15.880 --> 01:02:18.880 align:middle line:84% So when there are many, many firms competing with each other, 01:02:18.880 --> 01:02:22.680 align:middle line:84% they no longer have the market power to charge a markup. 01:02:22.680 --> 01:02:25.000 align:middle line:84% And in the limit, as we have many, many firms, 01:02:25.000 --> 01:02:27.400 align:middle line:90% every single firm-- 01:02:27.400 --> 01:02:29.920 align:middle line:84% well, every firm is going to produce a quantity such 01:02:29.920 --> 01:02:34.480 align:middle line:84% that the market price is exactly equal to cost of c. 01:02:34.480 --> 01:02:41.480 align:middle line:84% And can anyone interpret 1 minus c? 01:02:41.480 --> 01:02:44.700 align:middle line:84% Why do we get 1 minus c as the quantity in this case? 01:02:44.700 --> 01:02:48.863 align:middle line:90% 01:02:48.863 --> 01:02:50.280 align:middle line:84% It turns out this is what we might 01:02:50.280 --> 01:02:51.820 align:middle line:90% call the efficient quantity. 01:02:51.820 --> 01:02:58.053 align:middle line:90% 01:02:58.053 --> 01:02:59.220 align:middle line:90% What do I mean by efficient? 01:02:59.220 --> 01:03:02.450 align:middle line:84% Well, if it costs c to produce a good, 01:03:02.450 --> 01:03:04.590 align:middle line:84% for whom is it efficient to buy the good? 01:03:04.590 --> 01:03:07.570 align:middle line:84% It's efficient for people to buy the good if they value it 01:03:07.570 --> 01:03:09.930 align:middle line:84% more than the cost of production. 01:03:09.930 --> 01:03:13.450 align:middle line:84% But our demand curve exactly tells us 01:03:13.450 --> 01:03:16.050 align:middle line:84% that the number of people who value 01:03:16.050 --> 01:03:18.690 align:middle line:84% the product, or more precisely, the number of units 01:03:18.690 --> 01:03:21.650 align:middle line:84% of the product that have marginal utility above c 01:03:21.650 --> 01:03:23.173 align:middle line:90% is exactly 1 minus c. 01:03:23.173 --> 01:03:24.590 align:middle line:84% So what happens when we have many, 01:03:24.590 --> 01:03:27.450 align:middle line:84% many firms is we converge to an efficient outcome. 01:03:27.450 --> 01:03:30.527 align:middle line:84% The market price is exactly c, and the amount 01:03:30.527 --> 01:03:32.610 align:middle line:84% that's produced and consumed is exactly the amount 01:03:32.610 --> 01:03:35.810 align:middle line:84% that it's efficient to produce and consume. 01:03:35.810 --> 01:03:39.950 align:middle line:84% People who value each unit at more than c are going to buy it, 01:03:39.950 --> 01:03:43.370 align:middle line:84% and people who don't value it at more than c don't buy it. 01:03:43.370 --> 01:03:47.730 align:middle line:84% So we see this is an initial illustration 01:03:47.730 --> 01:03:55.190 align:middle line:84% that perfect competition leads us to efficiency. 01:03:55.190 --> 01:03:57.850 align:middle line:90% 01:03:57.850 --> 01:04:00.170 align:middle line:84% And here, perfect competition meaning the limit 01:04:00.170 --> 01:04:02.870 align:middle line:84% as the number of identical firms grows very, very large. 01:04:02.870 --> 01:04:12.090 align:middle line:90% 01:04:12.090 --> 01:04:14.030 align:middle line:90% Great, any questions about this? 01:04:14.030 --> 01:04:17.850 align:middle line:90% 01:04:17.850 --> 01:04:18.370 align:middle line:90% Yeah. 01:04:18.370 --> 01:04:24.650 align:middle line:84% AUDIENCE: Compared to some other quantity other than 1 minus c, 01:04:24.650 --> 01:04:26.985 align:middle line:84% why are those other quantities inefficient? 01:04:26.985 --> 01:04:28.610 align:middle line:84% IAN BALL: Great, so let's look at the-- 01:04:28.610 --> 01:04:35.113 align:middle line:84% do we have a demand curve somewhere? 01:04:35.113 --> 01:04:36.530 align:middle line:84% I forget if I've erased something. 01:04:36.530 --> 01:04:38.970 align:middle line:90% I may have erased it. 01:04:38.970 --> 01:04:41.530 align:middle line:84% So let me just draw a little curve here. 01:04:41.530 --> 01:04:45.890 align:middle line:84% So one way to interpret, this comes down to how we interpret 01:04:45.890 --> 01:04:56.355 align:middle line:84% demand Q of P. So what Q of P means, let's 01:04:56.355 --> 01:04:57.730 align:middle line:84% imagine just to make the argument 01:04:57.730 --> 01:05:00.800 align:middle line:84% simpler that everyone only consumes one unit of the good. 01:05:00.800 --> 01:05:02.720 align:middle line:84% So when demand's going up, as price drops, 01:05:02.720 --> 01:05:04.752 align:middle line:84% it's because more people are choosing to buy, 01:05:04.752 --> 01:05:06.960 align:middle line:84% not because a single person is buying multiple units. 01:05:06.960 --> 01:05:09.460 align:middle line:84% The argument goes through, but that'll just make it simpler. 01:05:09.460 --> 01:05:12.940 align:middle line:84% So what Q of P is, it's the number 01:05:12.940 --> 01:05:16.020 align:middle line:84% of people who are willing to buy at price p. 01:05:16.020 --> 01:05:23.090 align:middle line:90% 01:05:23.090 --> 01:05:25.340 align:middle line:84% But let's think this through a little bit differently. 01:05:25.340 --> 01:05:27.540 align:middle line:90% Who's willing to buy at price p? 01:05:27.540 --> 01:05:30.980 align:middle line:84% It's people whose value for the good is at least p. 01:05:30.980 --> 01:05:33.700 align:middle line:84% So another way of thinking of demand Q of P is-- actually, 01:05:33.700 --> 01:05:35.460 align:middle line:90% it's the number of people-- 01:05:35.460 --> 01:05:40.760 align:middle line:84% it's the number with value at least p. 01:05:40.760 --> 01:05:43.620 align:middle line:90% 01:05:43.620 --> 01:05:46.500 align:middle line:84% It's the number of people who say, for them, the apple is 01:05:46.500 --> 01:05:48.500 align:middle line:90% worth at least p. 01:05:48.500 --> 01:05:52.940 align:middle line:84% But that means that Q of c, which in our example 01:05:52.940 --> 01:05:56.220 align:middle line:84% is exactly 1 minus c, it's the demand at c, 01:05:56.220 --> 01:06:00.960 align:middle line:84% is exactly the number of people whose value is at least cost. 01:06:00.960 --> 01:06:07.940 align:middle line:90% 01:06:07.940 --> 01:06:11.000 align:middle line:84% So this captures-- if we look at everyone in the population, 01:06:11.000 --> 01:06:13.820 align:middle line:84% some people value the good at more than it costs to produce. 01:06:13.820 --> 01:06:16.280 align:middle line:84% Some people valued at less than it cost to produce. 01:06:16.280 --> 01:06:19.020 align:middle line:84% The efficient allocation is for people 01:06:19.020 --> 01:06:21.940 align:middle line:84% to get the good exactly if their value for the good 01:06:21.940 --> 01:06:24.180 align:middle line:84% exceeds the cost of producing it. 01:06:24.180 --> 01:06:26.577 align:middle line:84% And in this case, that turns out to be 1 minus c. 01:06:26.577 --> 01:06:28.660 align:middle line:84% It's the number of people whose value for the good 01:06:28.660 --> 01:06:31.100 align:middle line:90% is more than 1 minus c. 01:06:31.100 --> 01:06:32.040 align:middle line:90% Any other questions? 01:06:32.040 --> 01:06:34.860 align:middle line:90% 01:06:34.860 --> 01:06:36.700 align:middle line:84% Great, OK, so now that we've done 01:06:36.700 --> 01:06:39.140 align:middle line:84% Cournot in the last few minutes, let's 01:06:39.140 --> 01:06:41.900 align:middle line:90% move to Bertrand competition. 01:06:41.900 --> 01:06:46.860 align:middle line:90% So maybe come down. 01:06:46.860 --> 01:06:50.307 align:middle line:84% No, I guess I'm going to get stuck with these boards. 01:06:50.307 --> 01:06:51.640 align:middle line:90% I'll come all the way over here. 01:06:51.640 --> 01:07:11.150 align:middle line:90% 01:07:11.150 --> 01:07:15.870 align:middle line:84% So now let's look at Bertrand competition. 01:07:15.870 --> 01:07:17.970 align:middle line:84% So almost everything's the same as before. 01:07:17.970 --> 01:07:19.390 align:middle line:90% We still have two firms. 01:07:19.390 --> 01:07:21.550 align:middle line:84% They still have constant marginal cost of c, 01:07:21.550 --> 01:07:24.310 align:middle line:84% and demand still takes the same firm-- the same form. 01:07:24.310 --> 01:07:28.890 align:middle line:84% So firms, I'll just write it quickly, firms 1 and 2. 01:07:28.890 --> 01:07:32.470 align:middle line:90% 01:07:32.470 --> 01:07:34.530 align:middle line:90% Constant marginal cost c. 01:07:34.530 --> 01:07:38.110 align:middle line:90% 01:07:38.110 --> 01:07:40.010 align:middle line:90% And the market demand. 01:07:40.010 --> 01:07:45.358 align:middle line:90% 01:07:45.358 --> 01:07:47.150 align:middle line:84% And this time it's more convenient to write 01:07:47.150 --> 01:07:51.510 align:middle line:84% it this way, the demand Q of P equals the max of 1 01:07:51.510 --> 01:07:55.030 align:middle line:90% minus p and 0. 01:07:55.030 --> 01:08:01.230 align:middle line:84% And c where c is between 0 and 1. 01:08:01.230 --> 01:08:02.870 align:middle line:84% But now the difference with Bertrand 01:08:02.870 --> 01:08:05.770 align:middle line:84% is that we imagine that, instead of firms choosing quantities, 01:08:05.770 --> 01:08:08.790 align:middle line:90% they choose prices. 01:08:08.790 --> 01:08:20.417 align:middle line:84% So each firm i chooses a price pi. 01:08:20.417 --> 01:08:22.750 align:middle line:84% And now we have to try to understand, what are consumers 01:08:22.750 --> 01:08:23.750 align:middle line:90% going to do? 01:08:23.750 --> 01:08:26.950 align:middle line:84% If firm 1 charges a price of p1 and firm 2 01:08:26.950 --> 01:08:31.750 align:middle line:84% chooses a price of p2, what would you do as a consumer? 01:08:31.750 --> 01:08:34.950 align:middle line:90% Which firm would you buy from? 01:08:34.950 --> 01:08:36.210 align:middle line:90% The firm with the lower price. 01:08:36.210 --> 01:08:41.630 align:middle line:84% So our assumption is going to be that, whenever the firms charge 01:08:41.630 --> 01:08:46.910 align:middle line:84% different prices, all consumers buy from the lower-priced firm. 01:08:46.910 --> 01:08:48.670 align:middle line:90% And how many units do they buy? 01:08:48.670 --> 01:08:53.080 align:middle line:84% Well, they buy from the market demand at that lower price. 01:08:53.080 --> 01:09:01.420 align:middle line:84% So let's see if we can write down a formula. 01:09:01.420 --> 01:09:07.760 align:middle line:90% 01:09:07.760 --> 01:09:10.660 align:middle line:84% So mathematically, so we understand, this is a story. 01:09:10.660 --> 01:09:12.100 align:middle line:90% This is the motivating story. 01:09:12.100 --> 01:09:14.040 align:middle line:84% But mathematically, this is just a game. 01:09:14.040 --> 01:09:16.760 align:middle line:84% And we have to specify the strategies and the payoffs. 01:09:16.760 --> 01:09:18.520 align:middle line:84% We've already specified the strategies 01:09:18.520 --> 01:09:21.279 align:middle line:84% because what each firm chooses is a price. 01:09:21.279 --> 01:09:24.000 align:middle line:84% So to finish specifying this mathematically as a game, 01:09:24.000 --> 01:09:26.840 align:middle line:84% we need to say, what is each firm's payoff 01:09:26.840 --> 01:09:30.000 align:middle line:84% as a function of the price she charges 01:09:30.000 --> 01:09:32.880 align:middle line:84% and the price that the other firm charges? 01:09:32.880 --> 01:09:33.700 align:middle line:90% So let's do it. 01:09:33.700 --> 01:09:37.560 align:middle line:84% It's symmetric, so let's do it from the perspective of firm 1. 01:09:37.560 --> 01:09:42.120 align:middle line:84% What I want to understand is pi 1 of p1, p2. 01:09:42.120 --> 01:09:45.300 align:middle line:84% So as before, we're going to use pi to denote profit. 01:09:45.300 --> 01:09:48.920 align:middle line:84% I'm going to write pi 1 to say this is firm 1's profit. 01:09:48.920 --> 01:09:51.800 align:middle line:84% But now from 1's profit is not a function of the quantities 01:09:51.800 --> 01:09:57.000 align:middle line:84% we choose, but it's a function of the prices that we choose. 01:09:57.000 --> 01:10:00.400 align:middle line:84% And this is going to take a different form depending 01:10:00.400 --> 01:10:02.500 align:middle line:84% on the relative values of p1 and p2. 01:10:02.500 --> 01:10:04.320 align:middle line:84% So let me break this up into cases. 01:10:04.320 --> 01:10:07.240 align:middle line:84% There's going to be the case where p1 is less than p2. 01:10:07.240 --> 01:10:10.320 align:middle line:84% There's going to be the one where-- case where p1 equals p2 01:10:10.320 --> 01:10:12.500 align:middle line:84% and the case where p1 is greater than p2. 01:10:12.500 --> 01:10:14.933 align:middle line:90% 01:10:14.933 --> 01:10:16.600 align:middle line:84% All right, so let's try to fill this in. 01:10:16.600 --> 01:10:18.183 align:middle line:84% I think this is the easiest case here. 01:10:18.183 --> 01:10:20.280 align:middle line:84% So if I charge more than my opponent, 01:10:20.280 --> 01:10:23.200 align:middle line:90% what is my profit going to be? 01:10:23.200 --> 01:10:23.860 align:middle line:90% Just 0, right? 01:10:23.860 --> 01:10:27.400 align:middle line:90% I'm not going to sell anything. 01:10:27.400 --> 01:10:29.880 align:middle line:90% So I get 0 here. 01:10:29.880 --> 01:10:31.180 align:middle line:90% Now let's do this case. 01:10:31.180 --> 01:10:34.400 align:middle line:84% If I charge less than my opponent, well, 01:10:34.400 --> 01:10:37.593 align:middle line:84% now let's first-- let's break it up into two pieces 01:10:37.593 --> 01:10:38.260 align:middle line:90% as we always do. 01:10:38.260 --> 01:10:41.400 align:middle line:84% We need to think about, what is my profit per unit? 01:10:41.400 --> 01:10:44.480 align:middle line:84% And then what is the number of units I'm going to sell? 01:10:44.480 --> 01:10:49.230 align:middle line:84% So my profit per unit is going to be p1 minus c. 01:10:49.230 --> 01:10:54.570 align:middle line:84% I'm selling at a price of p1, and my cost is c. 01:10:54.570 --> 01:10:57.210 align:middle line:84% And notice how this is dual to what we did before. 01:10:57.210 --> 01:10:59.890 align:middle line:84% Before, I directly chose quantity, 01:10:59.890 --> 01:11:02.730 align:middle line:84% but the price depended on what the other person did. 01:11:02.730 --> 01:11:05.290 align:middle line:84% Here, I directly choose price, but the quantity 01:11:05.290 --> 01:11:08.370 align:middle line:84% depends on what the other person does and also what I do. 01:11:08.370 --> 01:11:12.510 align:middle line:90% So what is going to go in here? 01:11:12.510 --> 01:11:17.650 align:middle line:84% What is going to be the quantity I sell at price p1? 01:11:17.650 --> 01:11:20.553 align:middle line:84% Well, everyone, if they buy, is going to buy from me. 01:11:20.553 --> 01:11:21.970 align:middle line:84% So the amount that I sell is going 01:11:21.970 --> 01:11:25.130 align:middle line:84% to be the market demand at a price of p1. 01:11:25.130 --> 01:11:29.090 align:middle line:84% But we already said the market demand at a price of p is just 1 01:11:29.090 --> 01:11:30.130 align:middle line:90% minus p. 01:11:30.130 --> 01:11:33.690 align:middle line:84% So we're going to get 1 minus p1, 01:11:33.690 --> 01:11:36.198 align:middle line:84% again, assuming p1 is less than 1, 01:11:36.198 --> 01:11:37.990 align:middle line:84% but we're going to be a little sloppy here. 01:11:37.990 --> 01:11:42.090 align:middle line:90% 01:11:42.090 --> 01:11:45.850 align:middle line:84% And now we see the same central trade off but in the other way. 01:11:45.850 --> 01:11:48.670 align:middle line:84% If I raise my price, I get more per unit, 01:11:48.670 --> 01:11:50.890 align:middle line:84% but the number of units I sell goes down. 01:11:50.890 --> 01:11:51.830 align:middle line:90% What about this case? 01:11:51.830 --> 01:11:52.430 align:middle line:90% This is a little tricky. 01:11:52.430 --> 01:11:53.680 align:middle line:90% We have to make an assumption. 01:11:53.680 --> 01:11:57.530 align:middle line:84% What happens if both firms charge exactly the same price? 01:11:57.530 --> 01:11:58.050 align:middle line:90% Yeah. 01:11:58.050 --> 01:11:59.490 align:middle line:84% AUDIENCE: You both get half of the market. 01:11:59.490 --> 01:12:00.530 align:middle line:84% IAN BALL: Right, that's the standard assumption 01:12:00.530 --> 01:12:02.250 align:middle line:84% that if consumers are indifferent, maybe 01:12:02.250 --> 01:12:05.470 align:middle line:84% they're randomize, maybe they, whatever, for whatever reason, 01:12:05.470 --> 01:12:06.650 align:middle line:90% it's going to be half/half. 01:12:06.650 --> 01:12:12.530 align:middle line:84% So it's going to be p1 minus c times 1 minus p1 over 2. 01:12:12.530 --> 01:12:15.250 align:middle line:84% So we're both charging the same price p1. 01:12:15.250 --> 01:12:18.650 align:middle line:84% The market demand is 1 minus p1, but I get half of that, 01:12:18.650 --> 01:12:21.330 align:middle line:84% and my opponent gets half of that. 01:12:21.330 --> 01:12:23.470 align:middle line:84% So now, mathematically, we're done. 01:12:23.470 --> 01:12:26.330 align:middle line:90% We've described the game. 01:12:26.330 --> 01:12:29.570 align:middle line:84% Now what we want to understand is the best response. 01:12:29.570 --> 01:12:34.490 align:middle line:84% So now let me understand the best response of firm 1 01:12:34.490 --> 01:12:37.730 align:middle line:90% to a price of p2. 01:12:37.730 --> 01:12:39.450 align:middle line:84% And there's going to be a few cases 01:12:39.450 --> 01:12:41.090 align:middle line:90% we have to be careful about. 01:12:41.090 --> 01:12:43.250 align:middle line:90% So let's break this down. 01:12:43.250 --> 01:12:46.300 align:middle line:84% The first case is if p2 is less than c. 01:12:46.300 --> 01:12:49.500 align:middle line:90% Next case is p2 equals c. 01:12:49.500 --> 01:12:52.040 align:middle line:90% Next case is c is less than p2. 01:12:52.040 --> 01:12:54.860 align:middle line:90% 01:12:54.860 --> 01:12:56.380 align:middle line:84% And this is going to be a final case 01:12:56.380 --> 01:12:57.740 align:middle line:90% at the end, which I'll get to. 01:12:57.740 --> 01:13:00.620 align:middle line:84% But let's go through it step by step. 01:13:00.620 --> 01:13:05.140 align:middle line:84% What if my opponent charges a price less than c? 01:13:05.140 --> 01:13:07.420 align:middle line:90% Strictly less than c. 01:13:07.420 --> 01:13:08.880 align:middle line:84% What price would I like to charge? 01:13:08.880 --> 01:13:09.380 align:middle line:90% Yeah. 01:13:09.380 --> 01:13:10.797 align:middle line:84% AUDIENCE: Well, at that point, you 01:13:10.797 --> 01:13:14.020 align:middle line:84% should just not because if you compete with them 01:13:14.020 --> 01:13:15.860 align:middle line:84% and actually get customers, you're not 01:13:15.860 --> 01:13:17.280 align:middle line:90% going to be making any money. 01:13:17.280 --> 01:13:19.020 align:middle line:84% IAN BALL: Great, so the only way I'm 01:13:19.020 --> 01:13:20.660 align:middle line:84% going to be able to sell to anyone 01:13:20.660 --> 01:13:24.780 align:middle line:84% is if I charge a price that's at most p2, 01:13:24.780 --> 01:13:27.140 align:middle line:84% but that price is already below c, so I'm definitely 01:13:27.140 --> 01:13:28.200 align:middle line:90% going to lose money. 01:13:28.200 --> 01:13:30.380 align:middle line:84% So the best I can do is get a payoff of 0. 01:13:30.380 --> 01:13:34.940 align:middle line:84% But what price will ensure that I get a payoff of 0? 01:13:34.940 --> 01:13:38.180 align:middle line:84% Well, 0 actually would not be a very good price to set. 01:13:38.180 --> 01:13:39.120 align:middle line:90% I need to charge. 01:13:39.120 --> 01:13:42.540 align:middle line:84% Well, let's see, there's a lot of things I could do. 01:13:42.540 --> 01:13:46.940 align:middle line:90% I can actually charge. 01:13:46.940 --> 01:13:50.100 align:middle line:84% It's a little tricky, but actually, anything above p2 01:13:50.100 --> 01:13:51.058 align:middle line:90% is going to work. 01:13:51.058 --> 01:13:52.600 align:middle line:84% So maybe I'll write it down as a set. 01:13:52.600 --> 01:13:55.380 align:middle line:84% I mean, we're being a little careful here. 01:13:55.380 --> 01:13:57.300 align:middle line:84% If my opponent charges p2, you're 01:13:57.300 --> 01:13:59.632 align:middle line:84% exactly right that my goal is to sell nothing 01:13:59.632 --> 01:14:01.340 align:middle line:84% because the only way I can sell something 01:14:01.340 --> 01:14:02.820 align:middle line:90% is if I'm losing money. 01:14:02.820 --> 01:14:04.700 align:middle line:84% How do I ensure that I sell nothing? 01:14:04.700 --> 01:14:07.260 align:middle line:84% Well, I don't even want to charge p2 because then I'll 01:14:07.260 --> 01:14:08.857 align:middle line:90% get half the market. 01:14:08.857 --> 01:14:10.440 align:middle line:84% And then I'll lose money on that half. 01:14:10.440 --> 01:14:14.140 align:middle line:84% So it has to be strictly above p2, so anything 01:14:14.140 --> 01:14:16.160 align:middle line:84% strictly above P2 up to infinity. 01:14:16.160 --> 01:14:20.040 align:middle line:84% So I'm using round parentheses to denote strict inequalities. 01:14:20.040 --> 01:14:22.700 align:middle line:90% 01:14:22.700 --> 01:14:25.740 align:middle line:84% Now, in particular, I mean, one thing that's weird about this 01:14:25.740 --> 01:14:29.300 align:middle line:84% is s might be willing to charge a price below cost, which 01:14:29.300 --> 01:14:31.257 align:middle line:84% seems really strange, but I'm willing to do it 01:14:31.257 --> 01:14:33.340 align:middle line:84% as long as the other person's price is even lower, 01:14:33.340 --> 01:14:36.180 align:middle line:84% and I'm not actually going to sell. 01:14:36.180 --> 01:14:41.070 align:middle line:84% What if my opponent charges exactly c? 01:14:41.070 --> 01:14:42.130 align:middle line:90% Now what do I-- 01:14:42.130 --> 01:14:45.310 align:middle line:90% 01:14:45.310 --> 01:14:48.365 align:middle line:90% what am I willing to charge? 01:14:48.365 --> 01:14:49.990 align:middle line:84% Again, I'm not going to be able to make 01:14:49.990 --> 01:14:53.470 align:middle line:84% any money because the best I can do is sell it at a price of c, 01:14:53.470 --> 01:14:54.550 align:middle line:90% and my cost is c. 01:14:54.550 --> 01:14:56.410 align:middle line:84% So I'm not going to make a positive profit. 01:14:56.410 --> 01:14:59.110 align:middle line:84% But I want to make sure I don't make a negative profit. 01:14:59.110 --> 01:15:00.010 align:middle line:90% So what should I do? 01:15:00.010 --> 01:15:00.787 align:middle line:90% Yeah, over here. 01:15:00.787 --> 01:15:02.370 align:middle line:84% AUDIENCE: Anywhere from c to infinity. 01:15:02.370 --> 01:15:03.310 align:middle line:84% IAN BALL: Exactly, and in this case, 01:15:03.310 --> 01:15:05.365 align:middle line:84% can I charge a price of c exactly or not? 01:15:05.365 --> 01:15:05.990 align:middle line:90% AUDIENCE: Yeah. 01:15:05.990 --> 01:15:06.657 align:middle line:90% IAN BALL: I can? 01:15:06.657 --> 01:15:08.870 align:middle line:84% And why is that different from this case here? 01:15:08.870 --> 01:15:11.830 align:middle line:84% AUDIENCE: You charge [INAUDIBLE] probability 0 at the same time. 01:15:11.830 --> 01:15:14.213 align:middle line:84% IAN BALL: Exactly, so here we have a closed parenthesis, 01:15:14.213 --> 01:15:15.130 align:middle line:90% and it goes like this. 01:15:15.130 --> 01:15:16.050 align:middle line:90% Notice the difference. 01:15:16.050 --> 01:15:18.470 align:middle line:84% If I charge exactly the same price as my opponent, 01:15:18.470 --> 01:15:20.270 align:middle line:90% I get half the market. 01:15:20.270 --> 01:15:22.430 align:middle line:84% If their price is strictly below c, then 01:15:22.430 --> 01:15:25.030 align:middle line:84% getting half the market means I lose money because I'm losing 01:15:25.030 --> 01:15:26.990 align:middle line:90% money on every unit I sell. 01:15:26.990 --> 01:15:28.790 align:middle line:84% Here, getting half the market gives me 01:15:28.790 --> 01:15:31.390 align:middle line:84% a profit of exactly 0 because each unit I sell 01:15:31.390 --> 01:15:32.950 align:middle line:90% is exactly at a price of c. 01:15:32.950 --> 01:15:37.222 align:middle line:90% 01:15:37.222 --> 01:15:42.470 align:middle line:84% Now, OK, maybe to make the cases a little easier, 01:15:42.470 --> 01:15:47.090 align:middle line:84% let's say I'm just going to say c is less than a 1/3 just to-- 01:15:47.090 --> 01:15:49.590 align:middle line:84% so I don't have to deal with really complicated inequalities 01:15:49.590 --> 01:15:49.810 align:middle line:90% here. 01:15:49.810 --> 01:15:51.435 align:middle line:84% So let's just say c is less than a 1/3. 01:15:51.435 --> 01:15:53.070 align:middle line:90% It's not so important. 01:15:53.070 --> 01:15:57.110 align:middle line:84% So now what happens if my opponent charges strictly 01:15:57.110 --> 01:16:01.430 align:middle line:84% more than c but less than or equal to 1 minus c over 2? 01:16:01.430 --> 01:16:03.870 align:middle line:84% The 1 minus c over 2 is not-- you'll 01:16:03.870 --> 01:16:07.870 align:middle line:90% see later why that comes up. 01:16:07.870 --> 01:16:09.430 align:middle line:90% No, 1 plus c over 2, sorry. 01:16:09.430 --> 01:16:15.790 align:middle line:90% 01:16:15.790 --> 01:16:18.227 align:middle line:90% So actually, I don't need-- 01:16:18.227 --> 01:16:19.810 align:middle line:84% sorry, I don't need c less than a 1/3. 01:16:19.810 --> 01:16:20.990 align:middle line:90% Never mind, ignore that. 01:16:20.990 --> 01:16:22.750 align:middle line:84% I made a mistake, and then that caused 01:16:22.750 --> 01:16:24.708 align:middle line:84% me to make another mistake conditional on that. 01:16:24.708 --> 01:16:28.850 align:middle line:84% So now my opponent's price is strictly greater than c. 01:16:28.850 --> 01:16:30.210 align:middle line:90% What price do I want to charge? 01:16:30.210 --> 01:16:37.602 align:middle line:90% 01:16:37.602 --> 01:16:39.060 align:middle line:84% Well, they're charging more than c, 01:16:39.060 --> 01:16:41.640 align:middle line:84% so I can certainly make positive profit. 01:16:41.640 --> 01:16:42.573 align:middle line:90% But what's my goal? 01:16:42.573 --> 01:16:43.740 align:middle line:90% What do I want to try to do? 01:16:43.740 --> 01:16:46.840 align:middle line:90% 01:16:46.840 --> 01:16:47.600 align:middle line:90% Yeah. 01:16:47.600 --> 01:16:50.260 align:middle line:84% AUDIENCE: Charge as small under p2 as possible. 01:16:50.260 --> 01:16:51.912 align:middle line:84% IAN BALL: I want to just undercut them. 01:16:51.912 --> 01:16:54.120 align:middle line:84% And that creates a problem here because, however much 01:16:54.120 --> 01:16:56.620 align:middle line:84% undercut them, I could undercut them by a little bit less. 01:16:56.620 --> 01:16:58.480 align:middle line:90% Let's just say I charge $1 less. 01:16:58.480 --> 01:16:59.980 align:middle line:84% Well, I'd rather charge 1 cent less. 01:16:59.980 --> 01:17:01.540 align:middle line:84% I'd rather charge 1/2 a cent less. 01:17:01.540 --> 01:17:04.060 align:middle line:84% So it turns out, technically, it's empty. 01:17:04.060 --> 01:17:06.220 align:middle line:84% There's not a best response because whatever I do, 01:17:06.220 --> 01:17:08.387 align:middle line:84% I could do strictly better because I could-- indeed, 01:17:08.387 --> 01:17:11.120 align:middle line:84% my goal is to undercut them by the smallest amount, 01:17:11.120 --> 01:17:13.080 align:middle line:84% and I can't undercut them by 0 because then I 01:17:13.080 --> 01:17:14.300 align:middle line:90% only get half the market. 01:17:14.300 --> 01:17:15.860 align:middle line:84% So I really want to be strictly-- 01:17:15.860 --> 01:17:16.818 align:middle line:90% it's the classic thing. 01:17:16.818 --> 01:17:19.300 align:middle line:84% What's the biggest number that's strictly less than 1? 01:17:19.300 --> 01:17:20.548 align:middle line:90% Well, it doesn't exist. 01:17:20.548 --> 01:17:22.840 align:middle line:84% Now, as soon as I write this down, I think you should-- 01:17:22.840 --> 01:17:25.060 align:middle line:84% some warning bells should go off, and you should say, well, 01:17:25.060 --> 01:17:26.600 align:middle line:84% is all this analysis being driven 01:17:26.600 --> 01:17:29.640 align:middle line:84% by some weird things about the real numbers and limits not 01:17:29.640 --> 01:17:30.880 align:middle line:90% existing? 01:17:30.880 --> 01:17:33.040 align:middle line:84% Or is this really something about the real world? 01:17:33.040 --> 01:17:34.560 align:middle line:84% And you should ask, well, what would 01:17:34.560 --> 01:17:37.320 align:middle line:84% happen if we required prices to be on a finite grid 01:17:37.320 --> 01:17:39.338 align:middle line:84% and say prices have to be denominated in cents? 01:17:39.338 --> 01:17:40.880 align:middle line:84% And it turns out that the conclusions 01:17:40.880 --> 01:17:42.080 align:middle line:90% will be basically the same. 01:17:42.080 --> 01:17:45.200 align:middle line:84% So whenever you have this sinking feeling that there's 01:17:45.200 --> 01:17:47.540 align:middle line:84% some weird math going on, you should ask this question, 01:17:47.540 --> 01:17:48.220 align:middle line:90% and people have. 01:17:48.220 --> 01:17:49.845 align:middle line:84% And it turns out the answer's the same, 01:17:49.845 --> 01:17:51.720 align:middle line:84% so that's why we're not too concerned. 01:17:51.720 --> 01:17:54.280 align:middle line:84% OK, and then the final case, this 01:17:54.280 --> 01:18:01.740 align:middle line:84% is the trickiest one where p2 is greater than one plus c over 2. 01:18:01.740 --> 01:18:05.000 align:middle line:90% This is a bit tricky. 01:18:05.000 --> 01:18:08.220 align:middle line:84% But what do I want to do in this case? 01:18:08.220 --> 01:18:12.880 align:middle line:84% You might think I want to just undercut my opponent. 01:18:12.880 --> 01:18:16.680 align:middle line:84% But it turns out that's not the case here. 01:18:16.680 --> 01:18:19.500 align:middle line:84% So let's recall in the monopoly case where this demand function, 01:18:19.500 --> 01:18:22.520 align:middle line:84% if I'm a monopolist, what is the optimal price for me to charge 01:18:22.520 --> 01:18:24.880 align:middle line:90% as a monopolist? 01:18:24.880 --> 01:18:28.263 align:middle line:84% It turns out it's exactly 1 plus c over 2. 01:18:28.263 --> 01:18:29.680 align:middle line:84% If I were a monopolist, that would 01:18:29.680 --> 01:18:32.250 align:middle line:90% be the best price to charge. 01:18:32.250 --> 01:18:34.210 align:middle line:84% So let's say my opponent is charging 01:18:34.210 --> 01:18:36.210 align:middle line:90% a ridiculously high price. 01:18:36.210 --> 01:18:38.690 align:middle line:84% Well, then it's as if I'm a monopolist. 01:18:38.690 --> 01:18:41.490 align:middle line:84% And what I actually want to do is charge exactly 01:18:41.490 --> 01:18:43.890 align:middle line:84% the monopoly price of 1 plus c over 2. 01:18:43.890 --> 01:18:49.490 align:middle line:90% 01:18:49.490 --> 01:18:51.570 align:middle line:84% So notice where this undercutting argument 01:18:51.570 --> 01:18:52.190 align:middle line:90% breaks down. 01:18:52.190 --> 01:18:54.380 align:middle line:84% You might think, oh, I want to just undercut them. 01:18:54.380 --> 01:18:56.130 align:middle line:84% But that is assuming that they're charging 01:18:56.130 --> 01:18:57.510 align:middle line:90% a pretty reasonable price. 01:18:57.510 --> 01:18:59.410 align:middle line:84% If they're charging such a high price 01:18:59.410 --> 01:19:02.170 align:middle line:84% that if I just undercut them, no one's going to buy from me, 01:19:02.170 --> 01:19:04.470 align:middle line:84% then just undercutting them no longer makes sense. 01:19:04.470 --> 01:19:07.830 align:middle line:84% So if they're charging strictly more than the monopoly price, 01:19:07.830 --> 01:19:09.890 align:middle line:84% then I can just charge the monopoly price. 01:19:09.890 --> 01:19:13.250 align:middle line:84% I'm charging less than them, so I get the whole market. 01:19:13.250 --> 01:19:15.490 align:middle line:84% And in fact, I get the highest possible profit 01:19:15.490 --> 01:19:17.770 align:middle line:84% because I get exactly the monopoly profit. 01:19:17.770 --> 01:19:20.670 align:middle line:84% So here, you get the monopoly profit. 01:19:20.670 --> 01:19:24.410 align:middle line:90% 01:19:24.410 --> 01:19:26.170 align:middle line:90% So now we can work this all out. 01:19:26.170 --> 01:19:28.910 align:middle line:84% We understand the best response of firm 1 to firm 2. 01:19:28.910 --> 01:19:31.510 align:middle line:84% We can compute firm 2's best response to firm 1. 01:19:31.510 --> 01:19:33.230 align:middle line:84% But it turns out, if we do all the math, 01:19:33.230 --> 01:19:41.050 align:middle line:84% there's a unique equilibrium in which p1 star 01:19:41.050 --> 01:19:44.890 align:middle line:90% equals P2 star equals c. 01:19:44.890 --> 01:19:47.010 align:middle line:90% So we both charge exactly c. 01:19:47.010 --> 01:19:50.645 align:middle line:84% And we can check, it's easy to see that this is an equilibrium. 01:19:50.645 --> 01:19:52.270 align:middle line:84% Showing it's unique is a bit more work, 01:19:52.270 --> 01:19:56.050 align:middle line:84% but seeing it's an equilibrium, if my opponent charges c, 01:19:56.050 --> 01:19:58.290 align:middle line:90% I'm willing to charge c. 01:19:58.290 --> 01:20:02.130 align:middle line:84% And therefore, if we each charge c, this is an equilibrium. 01:20:02.130 --> 01:20:04.490 align:middle line:84% Now, notice a fundamental difference 01:20:04.490 --> 01:20:06.290 align:middle line:90% between Cournot and Bertrand. 01:20:06.290 --> 01:20:09.050 align:middle line:84% With Cournot, each time we added a firm, 01:20:09.050 --> 01:20:12.290 align:middle line:84% the price got closer and closer to the efficient price of c. 01:20:12.290 --> 01:20:14.330 align:middle line:84% With Bertrand, it only takes two. 01:20:14.330 --> 01:20:16.410 align:middle line:84% As soon as we had two firms competing, 01:20:16.410 --> 01:20:19.410 align:middle line:84% this undercutting motive was so strong that we immediately 01:20:19.410 --> 01:20:23.450 align:middle line:84% got down to the efficient price of price equals marginal cost. 01:20:23.450 --> 01:20:26.720 align:middle line:84% All right, I'll end there, and I'll see everyone on Thursday. 01:20:26.720 --> 01:20:30.000 align:middle line:90%