WEBVTT 00:00:00.000 --> 00:00:00.980 align:middle line:90% 00:00:00.980 --> 00:00:02.940 align:middle line:90% [SQUEAKING] 00:00:02.940 --> 00:00:04.410 align:middle line:90% [RUSTLING] 00:00:04.410 --> 00:00:07.350 align:middle line:90% [CLICKING] 00:00:07.350 --> 00:00:17.460 align:middle line:90% 00:00:17.460 --> 00:00:20.760 align:middle line:84% GLENN ELLISON: OK, let me go ahead and get started. 00:00:20.760 --> 00:00:26.460 align:middle line:84% So today I'm starting my week on static competition. 00:00:26.460 --> 00:00:29.670 align:middle line:84% So think about what's going on here. 00:00:29.670 --> 00:00:33.190 align:middle line:84% So far, the first two weeks have mostly been monopoly models. 00:00:33.190 --> 00:00:38.490 align:middle line:84% Obviously, most industries or most things of interest 00:00:38.490 --> 00:00:39.940 align:middle line:90% have multiple firms in it. 00:00:39.940 --> 00:00:41.850 align:middle line:84% So I'm going to now start every lecture 00:00:41.850 --> 00:00:43.350 align:middle line:84% for the rest of the term, it's going 00:00:43.350 --> 00:00:46.440 align:middle line:90% to be multiple firms competing. 00:00:46.440 --> 00:00:48.640 align:middle line:84% When Tirole goes through his book, 00:00:48.640 --> 00:00:51.870 align:middle line:84% he does this long-run to short-run chart 00:00:51.870 --> 00:00:56.040 align:middle line:84% where he talks about in the short-run firms can basically 00:00:56.040 --> 00:00:58.900 align:middle line:84% do nothing in competing with each other than setting prices. 00:00:58.900 --> 00:01:01.740 align:middle line:84% And then you get a sequence of variables that take 00:01:01.740 --> 00:01:03.310 align:middle line:90% longer and longer to adjust. 00:01:03.310 --> 00:01:07.115 align:middle line:84% And I think the way his book is written is, in some sense, 00:01:07.115 --> 00:01:08.490 align:middle line:84% the way we solve models is always 00:01:08.490 --> 00:01:11.233 align:middle line:84% by backward-- like multi-stage games by backward induction. 00:01:11.233 --> 00:01:13.900 align:middle line:84% You solve the last stage and the next to last stage and the next 00:01:13.900 --> 00:01:14.860 align:middle line:90% to last stage. 00:01:14.860 --> 00:01:17.380 align:middle line:84% And so his book is written this way, where 00:01:17.380 --> 00:01:18.640 align:middle line:90% you go backward from here. 00:01:18.640 --> 00:01:22.602 align:middle line:84% And that's how my course is written. 00:01:22.602 --> 00:01:24.310 align:middle line:84% Although, these days it's really going to 00:01:24.310 --> 00:01:27.790 align:middle line:84% be an awful lot of discussion of this and then other things 00:01:27.790 --> 00:01:30.970 align:middle line:90% just as individual topics. 00:01:30.970 --> 00:01:35.770 align:middle line:84% So the next few weeks, it's going to be short-run things. 00:01:35.770 --> 00:01:37.840 align:middle line:84% When we're discussing short-run competition, 00:01:37.840 --> 00:01:38.870 align:middle line:90% what do we talk about? 00:01:38.870 --> 00:01:42.830 align:middle line:84% One of the big things we talk about is markups. 00:01:42.830 --> 00:01:44.890 align:middle line:84% We talk about markups a lot because markups 00:01:44.890 --> 00:01:46.130 align:middle line:90% lead to deadweight loss. 00:01:46.130 --> 00:01:48.550 align:middle line:90% That's a major welfare concern. 00:01:48.550 --> 00:01:50.825 align:middle line:84% But they're also going to be, just 00:01:50.825 --> 00:01:53.200 align:middle line:84% like in price discrimination, you get that second welfare 00:01:53.200 --> 00:01:57.650 align:middle line:84% concern of the misallocation of the goods that are being sold. 00:01:57.650 --> 00:02:00.710 align:middle line:84% We'll also get mispurchasing of goods 00:02:00.710 --> 00:02:02.910 align:middle line:84% that becomes another consideration here as well. 00:02:02.910 --> 00:02:04.660 align:middle line:84% So what I'm going to do in this lecture is 00:02:04.660 --> 00:02:07.420 align:middle line:84% I'm going to start with all of the classic stuff in I/O 00:02:07.420 --> 00:02:09.880 align:middle line:84% that people don't do anymore but do that as, 00:02:09.880 --> 00:02:11.920 align:middle line:84% I think, background for things that 00:02:11.920 --> 00:02:15.880 align:middle line:84% is how modern studies of competition are done. 00:02:15.880 --> 00:02:18.240 align:middle line:84% So anyway, I start-- and I'm talking 00:02:18.240 --> 00:02:19.480 align:middle line:90% about old historical stuff. 00:02:19.480 --> 00:02:24.860 align:middle line:84% And I added some pictures of the old, dead white guys 00:02:24.860 --> 00:02:26.100 align:middle line:90% who developed these things. 00:02:26.100 --> 00:02:32.090 align:middle line:84% So there's Cournot, Cournot competition 1838. 00:02:32.090 --> 00:02:34.073 align:middle line:84% So obviously, Cournot was thinking 00:02:34.073 --> 00:02:35.990 align:middle line:84% about a world that's very different from ours, 00:02:35.990 --> 00:02:38.900 align:middle line:84% a world in which many of the things that people bought 00:02:38.900 --> 00:02:44.330 align:middle line:84% were completely undifferentiated goods, like wheat and corn 00:02:44.330 --> 00:02:48.650 align:middle line:84% and wool, or whatever, where just a product is a product. 00:02:48.650 --> 00:02:51.060 align:middle line:84% And there's a universal market for it. 00:02:51.060 --> 00:02:54.217 align:middle line:84% So Cournot thought about a model where you had n firms. 00:02:54.217 --> 00:02:56.300 align:middle line:84% There was some homogeneous good that they were all 00:02:56.300 --> 00:02:57.950 align:middle line:84% producing that had inverse demand 00:02:57.950 --> 00:03:02.900 align:middle line:84% P of X. The producers have cost functions, ci of xi that 00:03:02.900 --> 00:03:09.920 align:middle line:84% depend on what is the quantity produced by Firm I. 00:03:09.920 --> 00:03:12.870 align:middle line:84% In some sense, Cournot invented Nash equilibrium. 00:03:12.870 --> 00:03:14.380 align:middle line:90% So Cournot thought of a model. 00:03:14.380 --> 00:03:16.640 align:middle line:84% He had this timing where the firms are simultaneously 00:03:16.640 --> 00:03:19.755 align:middle line:90% choosing outputs x1 through xn. 00:03:19.755 --> 00:03:21.380 align:middle line:84% When they choose those outputs, they're 00:03:21.380 --> 00:03:23.740 align:middle line:84% going to all bring their goods to the market. 00:03:23.740 --> 00:03:26.300 align:middle line:84% There's going to be a market-determined price. 00:03:26.300 --> 00:03:31.220 align:middle line:84% And all the firms are choosing their quantity, 00:03:31.220 --> 00:03:33.710 align:middle line:84% assuming that the quantities chosen by the other firms 00:03:33.710 --> 00:03:34.730 align:middle line:90% are all held fixed. 00:03:34.730 --> 00:03:37.700 align:middle line:84% And that's going to be the optimality condition, OK? 00:03:37.700 --> 00:03:40.790 align:middle line:90% 00:03:40.790 --> 00:03:43.170 align:middle line:84% OK, what happens in Cournot competition? 00:03:43.170 --> 00:03:46.790 align:middle line:84% So in Cournot competition, the firm 00:03:46.790 --> 00:03:57.580 align:middle line:84% is maximizing over xi, xi times P of xi 00:03:57.580 --> 00:04:06.400 align:middle line:84% plus sum over j different from i xj minus ci of xi. 00:04:06.400 --> 00:04:09.880 align:middle line:84% So that's every firm's maximization problem, 00:04:09.880 --> 00:04:14.230 align:middle line:84% is maximize quantity times the market price minus the cost. 00:04:14.230 --> 00:04:18.100 align:middle line:84% Your quantity affects how much you produce. 00:04:18.100 --> 00:04:20.320 align:middle line:84% It ends up affecting the market price 00:04:20.320 --> 00:04:23.890 align:middle line:84% through its impact on the aggregate supply. 00:04:23.890 --> 00:04:28.300 align:middle line:84% And it obviously affects your cost of production. 00:04:28.300 --> 00:04:29.930 align:middle line:90% So what do we get? 00:04:29.930 --> 00:04:32.120 align:middle line:84% Well, if a profile is a Nash equilibrium, 00:04:32.120 --> 00:04:37.580 align:middle line:84% it's got to satisfy first-order condition for this for each i. 00:04:37.580 --> 00:04:39.735 align:middle line:84% What does the first-order condition look like? 00:04:39.735 --> 00:04:42.850 align:middle line:90% 00:04:42.850 --> 00:04:46.180 align:middle line:84% So first, it's this times the derivative of this gives you, 00:04:46.180 --> 00:04:50.200 align:middle line:84% you get a P of the sum of the xi's minus the derivative 00:04:50.200 --> 00:04:52.130 align:middle line:90% of this is marginal cost. 00:04:52.130 --> 00:04:59.150 align:middle line:84% The third term in the thing is xi times the derivative of that. 00:04:59.150 --> 00:05:04.450 align:middle line:84% So we get Pi prime times xi star equals 0. 00:05:04.450 --> 00:05:07.690 align:middle line:84% So this is what the classic Cournot first-order 00:05:07.690 --> 00:05:08.730 align:middle line:90% condition looks like. 00:05:08.730 --> 00:05:15.080 align:middle line:90% 00:05:15.080 --> 00:05:16.980 align:middle line:90% What are some implications? 00:05:16.980 --> 00:05:22.640 align:middle line:84% So first of all, price ends up greater than marginal cost. 00:05:22.640 --> 00:05:26.840 align:middle line:84% This is price minus marginal cost is the first term. 00:05:26.840 --> 00:05:29.940 align:middle line:84% If xi is a positive number, P prime is a negative number. 00:05:29.940 --> 00:05:33.710 align:middle line:84% So this is price minus marginal cost equals minus Pi 00:05:33.710 --> 00:05:37.220 align:middle line:90% prime xi is a positive number. 00:05:37.220 --> 00:05:38.690 align:middle line:90% Production in a Cournot-- 00:05:38.690 --> 00:05:41.460 align:middle line:84% so we get a second welfare loss in a Cournot oligopoly. 00:05:41.460 --> 00:05:44.610 align:middle line:84% So the first welfare loss is there's deadweight loss. 00:05:44.610 --> 00:05:47.310 align:middle line:84% Second is production is inefficient in a Cournot 00:05:47.310 --> 00:05:48.530 align:middle line:90% oligopoly. 00:05:48.530 --> 00:05:52.100 align:middle line:84% Production is inefficient in an asymmetric oligopoly 00:05:52.100 --> 00:05:55.910 align:middle line:84% because if the firms are asymmetric in equilibrium, 00:05:55.910 --> 00:05:58.250 align:middle line:84% x1 is going to be different from x2. 00:05:58.250 --> 00:06:02.420 align:middle line:84% If x1 is different from x2 and P prime is the same for everyone, 00:06:02.420 --> 00:06:04.670 align:middle line:84% because it's evaluated at the aggregate demand, 00:06:04.670 --> 00:06:07.290 align:middle line:84% then that means-- then the P is the same for everyone. 00:06:07.290 --> 00:06:10.490 align:middle line:84% That means the c primes have to be different. 00:06:10.490 --> 00:06:15.680 align:middle line:84% So in an asymmetric Cournot oligopoly, 00:06:15.680 --> 00:06:18.548 align:middle line:84% the realized marginal costs are different. 00:06:18.548 --> 00:06:20.090 align:middle line:84% So the quantity that's being produced 00:06:20.090 --> 00:06:23.110 align:middle line:90% is being produced inefficiently. 00:06:23.110 --> 00:06:25.750 align:middle line:84% OK, example to think about this is for-- 00:06:25.750 --> 00:06:29.000 align:middle line:90% 00:06:29.000 --> 00:06:32.270 align:middle line:84% if you think about the model for producing oil in the world today 00:06:32.270 --> 00:06:34.050 align:middle line:84% is something like a Cournot oligopoly. 00:06:34.050 --> 00:06:35.180 align:middle line:90% There's a set of countries. 00:06:35.180 --> 00:06:38.210 align:middle line:84% Every country, the ones we're centrally producing 00:06:38.210 --> 00:06:41.380 align:middle line:84% are choosing how much to produce. 00:06:41.380 --> 00:06:44.390 align:middle line:84% If each country is maximizing its production, 00:06:44.390 --> 00:06:46.040 align:middle line:84% then you're going to have countries 00:06:46.040 --> 00:06:48.440 align:middle line:84% like Saudi Arabia has oil that they could pump out 00:06:48.440 --> 00:06:51.050 align:middle line:84% of the ground for $5 a barrel or $10 a barrel 00:06:51.050 --> 00:06:53.010 align:middle line:84% that they're not pumping it out of the ground. 00:06:53.010 --> 00:06:56.910 align:middle line:84% Canada is getting oil out of tar sands for $50 a barrel. 00:06:56.910 --> 00:07:01.190 align:middle line:84% And there's an inefficiency there from low-cost producers 00:07:01.190 --> 00:07:03.740 align:middle line:84% not producing, while high-cost producers are producing, 00:07:03.740 --> 00:07:06.260 align:middle line:90% holding the quantity fixed. 00:07:06.260 --> 00:07:10.860 align:middle line:84% OK, firm outputs are usually strategic substitutes. 00:07:10.860 --> 00:07:15.380 align:middle line:84% So if you look at a Cournot model, if I put q1 on this axis 00:07:15.380 --> 00:07:20.690 align:middle line:84% and do what's the best response for Firm 2 to an output of q1, 00:07:20.690 --> 00:07:24.230 align:middle line:84% you get this downward-sloping line. 00:07:24.230 --> 00:07:26.790 align:middle line:84% And the equilibrium looks like this. 00:07:26.790 --> 00:07:33.680 align:middle line:84% If I put q2 on this axis and graph BR1 of q2, 00:07:33.680 --> 00:07:37.190 align:middle line:84% Cournot equilibrium is typically this intersection 00:07:37.190 --> 00:07:40.590 align:middle line:90% of two downward-sloping lines. 00:07:40.590 --> 00:07:43.620 align:middle line:84% OK, that's what it normally looks like. 00:07:43.620 --> 00:07:45.398 align:middle line:84% It doesn't have to look like that. 00:07:45.398 --> 00:07:47.440 align:middle line:84% And the Cournot equilibrium is not always unique. 00:07:47.440 --> 00:07:49.560 align:middle line:84% You could imagine if you could somehow 00:07:49.560 --> 00:07:51.570 align:middle line:84% draw these things with wiggles in them 00:07:51.570 --> 00:07:55.370 align:middle line:84% so that they intersect multiple times. 00:07:55.370 --> 00:08:02.200 align:middle line:84% OK, fourth result of this, take this expression, price 00:08:02.200 --> 00:08:07.330 align:middle line:84% minus cost is minus xi star P prime, and then 00:08:07.330 --> 00:08:09.940 align:middle line:90% divide both sides by price. 00:08:09.940 --> 00:08:13.960 align:middle line:84% I get an expression that looks very much like the monopoly 00:08:13.960 --> 00:08:16.630 align:middle line:84% pricing expression, except it has 00:08:16.630 --> 00:08:19.270 align:middle line:84% an xi star on the right-hand side instead of having 00:08:19.270 --> 00:08:21.590 align:middle line:90% an x star on the right side. 00:08:21.590 --> 00:08:24.320 align:middle line:84% But in some sense this is the monopoly first-order condition. 00:08:24.320 --> 00:08:26.770 align:middle line:84% So because this is the monopoly first-order condition, 00:08:26.770 --> 00:08:29.410 align:middle line:84% except with an xi here instead of a capital X 00:08:29.410 --> 00:08:33.130 align:middle line:84% here, I get this expression, price 00:08:33.130 --> 00:08:37.419 align:middle line:84% minus marginal cost over price is minus xi over x star 00:08:37.419 --> 00:08:39.280 align:middle line:90% times 1 over epsilon. 00:08:39.280 --> 00:08:43.390 align:middle line:84% So if we think about how does competition reduce markups 00:08:43.390 --> 00:08:46.930 align:middle line:84% in the Cournot model, obviously, elasticities-- 00:08:46.930 --> 00:08:48.880 align:middle line:84% if you don't have a constant elasticity demand 00:08:48.880 --> 00:08:51.970 align:middle line:84% curve, elasticities also change as output changes, 00:08:51.970 --> 00:08:54.510 align:middle line:84% because the elasticity is nonconstant. 00:08:54.510 --> 00:08:58.090 align:middle line:84% But if you think about the constant elasticity intuition, 00:08:58.090 --> 00:09:00.880 align:middle line:84% this is going to say that, in N firm oligopoly, 00:09:00.880 --> 00:09:04.060 align:middle line:84% prices are going to go down roughly like 1 over n. 00:09:04.060 --> 00:09:05.830 align:middle line:84% And this is one of the features that 00:09:05.830 --> 00:09:08.800 align:middle line:84% made Cournot popular is that people have this intuition. 00:09:08.800 --> 00:09:10.910 align:middle line:90% With monopoly, prices are high. 00:09:10.910 --> 00:09:14.140 align:middle line:84% As you get more competition in, prices ought to decline, 00:09:14.140 --> 00:09:17.290 align:middle line:84% and they ought to decline in some decreasing 00:09:17.290 --> 00:09:18.910 align:middle line:90% returns to competition way. 00:09:18.910 --> 00:09:21.550 align:middle line:84% And they ought to asymptote to perfect competition 00:09:21.550 --> 00:09:23.920 align:middle line:84% as the number of firms goes to infinity. 00:09:23.920 --> 00:09:25.730 align:middle line:84% And Cournot has those properties, 00:09:25.730 --> 00:09:27.640 align:middle line:84% and that's one of the reasons why it 00:09:27.640 --> 00:09:29.220 align:middle line:90% became a popular model to use. 00:09:29.220 --> 00:09:32.530 align:middle line:90% 00:09:32.530 --> 00:09:36.490 align:middle line:84% OK, notice that, like marginal costs 00:09:36.490 --> 00:09:38.840 align:middle line:84% are different with asymmetric firms, 00:09:38.840 --> 00:09:41.500 align:middle line:84% Lerner indexes are different with asymmetric firms 00:09:41.500 --> 00:09:46.060 align:middle line:84% because each firm's markup is xi over x star. 00:09:46.060 --> 00:09:48.980 align:middle line:84% And so the xi's are not all 1 over n at equilibrium. 00:09:48.980 --> 00:09:51.040 align:middle line:90% The markups are different. 00:09:51.040 --> 00:09:54.310 align:middle line:84% So we can think about what is the average markup 00:09:54.310 --> 00:09:56.390 align:middle line:90% in an industry across firms? 00:09:56.390 --> 00:10:00.130 align:middle line:84% So let's define the industry-wide Lerner 00:10:00.130 --> 00:10:06.100 align:middle line:84% index to be price minus average marginal cost over price, 00:10:06.100 --> 00:10:10.360 align:middle line:84% where we take a weighted average of the marginal costs, 00:10:10.360 --> 00:10:13.580 align:middle line:90% giving weight xi over x star. 00:10:13.580 --> 00:10:16.330 align:middle line:84% So we give more weight to the firms that are producing more. 00:10:16.330 --> 00:10:21.070 align:middle line:84% So this is price minus average marginal cost over price. 00:10:21.070 --> 00:10:23.890 align:middle line:84% Theorem is that-- and you can just-- 00:10:23.890 --> 00:10:26.560 align:middle line:84% this is just basically taking a weighted average of these, 00:10:26.560 --> 00:10:27.880 align:middle line:90% weighting them by xi. 00:10:27.880 --> 00:10:34.310 align:middle line:84% So the theorem is that the industry-average Lerner index 00:10:34.310 --> 00:10:39.710 align:middle line:84% is negative H over epsilon, where H is the sum of xi 00:10:39.710 --> 00:10:42.590 align:middle line:90% over x star squared. 00:10:42.590 --> 00:10:46.310 align:middle line:84% OK, so H is the sum of the squared market shares. 00:10:46.310 --> 00:10:50.960 align:middle line:84% And so the Cournot model predicts that-- 00:10:50.960 --> 00:10:53.480 align:middle line:90% 00:10:53.480 --> 00:10:57.800 align:middle line:84% the Cournot model predicts that the markup in an industry 00:10:57.800 --> 00:11:01.700 align:middle line:84% depends on sum of squared market shares. 00:11:01.700 --> 00:11:04.970 align:middle line:84% And sum of squared markup shares is a summary statistic 00:11:04.970 --> 00:11:06.300 align:middle line:90% for how large markups are. 00:11:06.300 --> 00:11:11.150 align:middle line:84% And this was sufficiently influential that if you go back 00:11:11.150 --> 00:11:14.060 align:middle line:84% and read how US merger guidelines were designed 00:11:14.060 --> 00:11:18.950 align:middle line:84% in the 1950s, they explicitly refer to Herfindahl indexes. 00:11:18.950 --> 00:11:21.590 align:middle line:84% And they're explicitly referring to Herfindahl indexes 00:11:21.590 --> 00:11:24.335 align:middle line:90% in the sense of like if-- 00:11:24.335 --> 00:11:26.960 align:middle line:84% I forget what the numbers are, but they're something like this. 00:11:26.960 --> 00:11:30.740 align:middle line:84% If the Herfindahl index in an industry is less than 0.18, 00:11:30.740 --> 00:11:32.790 align:middle line:90% then we will allow mergers. 00:11:32.790 --> 00:11:38.330 align:middle line:84% And if the Herfindahl index is between 0.18 and 0.28 00:11:38.330 --> 00:11:41.720 align:middle line:90% and the delta H-- 00:11:41.720 --> 00:11:43.880 align:middle line:84% then what we'll do is look at whether delta H is 00:11:43.880 --> 00:11:47.120 align:middle line:90% less than or greater than 0.01. 00:11:47.120 --> 00:11:50.525 align:middle line:84% And they will tend to consider mergers as questionable 00:11:50.525 --> 00:11:53.150 align:middle line:84% or not, depending on whether the change in the Herfindahl index 00:11:53.150 --> 00:11:55.247 align:middle line:90% is bigger or smaller than 0.01. 00:11:55.247 --> 00:11:57.830 align:middle line:84% And then, for industries where the Herfindahl index is already 00:11:57.830 --> 00:12:02.040 align:middle line:84% above 0.28, then they're going to be-- then 00:12:02.040 --> 00:12:04.040 align:middle line:84% they're going to be-- then mergers are typically 00:12:04.040 --> 00:12:05.340 align:middle line:90% not going to be allowed. 00:12:05.340 --> 00:12:09.050 align:middle line:84% But this is just-- because the Herfindahl index 00:12:09.050 --> 00:12:10.640 align:middle line:84% had this role in the theorem that it 00:12:10.640 --> 00:12:13.530 align:middle line:84% was a measure of how competitive an industry was, 00:12:13.530 --> 00:12:16.620 align:middle line:84% it took this very central role in competition. 00:12:16.620 --> 00:12:18.170 align:middle line:90% And if you look at the-- 00:12:18.170 --> 00:12:23.370 align:middle line:84% I discussed the industry cross section I/O from the 1960s, 00:12:23.370 --> 00:12:26.552 align:middle line:84% constant regressions of mark-ups on Herfindahl indexes 00:12:26.552 --> 00:12:29.010 align:middle line:84% because the Herfindahl index was supposed to be the correct 00:12:29.010 --> 00:12:32.340 align:middle line:84% measure of how concentrated an industry was. 00:12:32.340 --> 00:12:35.310 align:middle line:84% One thing to note, though, you definitely 00:12:35.310 --> 00:12:38.730 align:middle line:84% should not be thinking of the Herfindahl index as a welfare 00:12:38.730 --> 00:12:41.130 align:middle line:84% proxy because you think about it, 00:12:41.130 --> 00:12:44.250 align:middle line:84% it's measuring mark-ups relative to the cost they're there. 00:12:44.250 --> 00:12:46.020 align:middle line:84% So, for instance, if you have two firms 00:12:46.020 --> 00:12:49.500 align:middle line:84% that are perfectly symmetric, the Herfindahl index is 0.5. 00:12:49.500 --> 00:12:52.620 align:middle line:84% It's 1/2 squared plus 1/2 squared is 0.5. 00:12:52.620 --> 00:12:54.930 align:middle line:84% Suppose one of those firms gets more efficient 00:12:54.930 --> 00:12:56.650 align:middle line:90% and lowers its cost. 00:12:56.650 --> 00:13:00.990 align:middle line:84% When it lowers its cost, everyone is better off. 00:13:00.990 --> 00:13:04.170 align:middle line:84% Social welfare goes up, but the Herfindahl index also 00:13:04.170 --> 00:13:06.060 align:middle line:84% goes up because the firm with a lower cost 00:13:06.060 --> 00:13:09.365 align:middle line:84% now starts producing a higher share of the output. 00:13:09.365 --> 00:13:14.100 align:middle line:90% 00:13:14.100 --> 00:13:17.310 align:middle line:90% In the old days, one could-- 00:13:17.310 --> 00:13:20.160 align:middle line:84% and let me say, I think big mistake students still 00:13:20.160 --> 00:13:22.290 align:middle line:84% make today is trying to be too original. 00:13:22.290 --> 00:13:23.790 align:middle line:84% I think almost the best way to do 00:13:23.790 --> 00:13:25.707 align:middle line:84% research, especially when you're starting out, 00:13:25.707 --> 00:13:28.030 align:middle line:84% is always to take some existing paper and improve on it 00:13:28.030 --> 00:13:31.038 align:middle line:84% because if you take an existing paper, you improve on it. 00:13:31.038 --> 00:13:33.580 align:middle line:84% You've got something better than an existing published paper. 00:13:33.580 --> 00:13:36.900 align:middle line:84% Whereas, you start from scratch with some creative idea. 00:13:36.900 --> 00:13:37.920 align:middle line:90% You spend years on it. 00:13:37.920 --> 00:13:40.337 align:middle line:84% And then you realize two years later that what you've done 00:13:40.337 --> 00:13:43.000 align:middle line:84% has created a worse version of something that already exists. 00:13:43.000 --> 00:13:46.050 align:middle line:84% Whereas, if you start with the existing frontier paper, 00:13:46.050 --> 00:13:47.560 align:middle line:90% you know where the frontier is. 00:13:47.560 --> 00:13:48.370 align:middle line:90% You improve on it. 00:13:48.370 --> 00:13:50.750 align:middle line:84% You've got a new frontier paper, OK? 00:13:50.750 --> 00:13:55.470 align:middle line:84% Anyway, back in the day, Cournot was 1838. 00:13:55.470 --> 00:13:59.220 align:middle line:84% Bertrand, 45 years later, picks up Cournot's paper and says, 00:13:59.220 --> 00:14:02.040 align:middle line:84% I can come up with an interesting comment on Cournot. 00:14:02.040 --> 00:14:07.410 align:middle line:84% So his comment on Cournot was that many firms 00:14:07.410 --> 00:14:10.720 align:middle line:84% don't choose the quantity that they're going to produce. 00:14:10.720 --> 00:14:14.020 align:middle line:84% What they do is instead set a price for their product 00:14:14.020 --> 00:14:16.750 align:middle line:84% and then sell however much at that price 00:14:16.750 --> 00:14:19.780 align:middle line:90% as people are willing to buy. 00:14:19.780 --> 00:14:22.690 align:middle line:84% So you just flipped around this discussion 00:14:22.690 --> 00:14:25.960 align:middle line:84% from firms choosing quantities, treating everyone's quantity 00:14:25.960 --> 00:14:28.190 align:middle line:84% as fixed, to firms choosing prices. 00:14:28.190 --> 00:14:31.150 align:middle line:84% And his comment is basically that predictions 00:14:31.150 --> 00:14:33.440 align:middle line:84% of Cournot's model change dramatically 00:14:33.440 --> 00:14:35.110 align:middle line:84% if you make that simple flip from firms 00:14:35.110 --> 00:14:37.763 align:middle line:84% are choosing quantities, assuming quantities 00:14:37.763 --> 00:14:39.430 align:middle line:84% are fixed, to firms are choosing prices, 00:14:39.430 --> 00:14:41.320 align:middle line:90% assuming prices are fixed. 00:14:41.320 --> 00:14:46.570 align:middle line:84% So anyway, Bertrand's model, let x be a market demand function. 00:14:46.570 --> 00:14:49.450 align:middle line:84% Assume that x is weakly decreasing 00:14:49.450 --> 00:14:52.810 align:middle line:84% and that P times x of P is bounded. 00:14:52.810 --> 00:14:56.260 align:middle line:84% Assume that all firms have unit cost c. 00:14:56.260 --> 00:14:58.280 align:middle line:84% Firms simultaneously announce prices. 00:14:58.280 --> 00:15:00.760 align:middle line:84% All demand goes to the lowest price firms. 00:15:00.760 --> 00:15:05.420 align:middle line:84% Then, we don't get this Cournot continuity. 00:15:05.420 --> 00:15:07.270 align:middle line:84% We get an immediate discontinuity, 00:15:07.270 --> 00:15:10.130 align:middle line:84% which is two firms is enough for perfect competition. 00:15:10.130 --> 00:15:14.080 align:middle line:84% So the unique equilibrium of this model is P1 star 00:15:14.080 --> 00:15:17.960 align:middle line:90% equals P2 star equals c. 00:15:17.960 --> 00:15:20.630 align:middle line:84% And this is what Frank Fisher and his writing 00:15:20.630 --> 00:15:23.040 align:middle line:90% about economic theory would say. 00:15:23.040 --> 00:15:24.810 align:middle line:90% This is an exemplifying theory. 00:15:24.810 --> 00:15:28.420 align:middle line:84% You make these somewhat extreme assumptions, 00:15:28.420 --> 00:15:31.313 align:middle line:84% that is, firms announced prices, and all demand 00:15:31.313 --> 00:15:33.730 align:middle line:84% goes to the lowest price firm, even if it's one penny less 00:15:33.730 --> 00:15:34.610 align:middle line:90% than the other firm. 00:15:34.610 --> 00:15:37.810 align:middle line:84% But what you show is that, with these assumptions, 00:15:37.810 --> 00:15:40.150 align:middle line:84% you get of extreme outcome, which 00:15:40.150 --> 00:15:42.340 align:middle line:84% is competition works differently from Cournot, 00:15:42.340 --> 00:15:43.812 align:middle line:90% and it's a discontinuous thing. 00:15:43.812 --> 00:15:45.520 align:middle line:84% And any number of firms is enough to have 00:15:45.520 --> 00:15:46.660 align:middle line:90% perfect competition. 00:15:46.660 --> 00:15:49.180 align:middle line:90% 00:15:49.180 --> 00:15:52.630 align:middle line:84% One version of this model that still does get used 00:15:52.630 --> 00:15:55.960 align:middle line:84% is if you think about firms that have asymmetric costs, 00:15:55.960 --> 00:15:59.420 align:middle line:84% you have two firms with cost c1 star and c2 star. 00:15:59.420 --> 00:16:01.360 align:middle line:90% What's the equilibrium? 00:16:01.360 --> 00:16:05.380 align:middle line:84% The equilibrium is the firms end up both pricing at c2 star 00:16:05.380 --> 00:16:08.760 align:middle line:84% with all of the demand going to the firm with the lower cost. 00:16:08.760 --> 00:16:10.510 align:middle line:84% If you want, you can think of it as Firm 1 00:16:10.510 --> 00:16:14.080 align:middle line:84% is charging c2 minus epsilon and getting all the demand. 00:16:14.080 --> 00:16:17.770 align:middle line:84% But when you have asymmetric Cournot, 00:16:17.770 --> 00:16:21.470 align:middle line:84% prices are determined by the second lowest cost in a market. 00:16:21.470 --> 00:16:23.270 align:middle line:84% And I think that's the important intuition. 00:16:23.270 --> 00:16:25.240 align:middle line:84% That's the second lowest cost determines 00:16:25.240 --> 00:16:29.630 align:middle line:84% what happens in markets that are this very intense price 00:16:29.630 --> 00:16:31.793 align:middle line:84% competition or undifferentiated products. 00:16:31.793 --> 00:16:34.460 align:middle line:84% AUDIENCE: Does this change if we don't have complete information 00:16:34.460 --> 00:16:35.365 align:middle line:90% on the cost? 00:16:35.365 --> 00:16:38.552 align:middle line:90% 00:16:38.552 --> 00:16:40.010 align:middle line:84% GLENN ELLISON: Yeah, so let me see. 00:16:40.010 --> 00:16:42.550 align:middle line:84% So if you did this model where you had-- 00:16:42.550 --> 00:16:44.410 align:middle line:84% AUDIENCE: Like private info, like you 00:16:44.410 --> 00:16:47.087 align:middle line:84% don't have any knowledge on their distribution. 00:16:47.087 --> 00:16:48.670 align:middle line:84% GLENN ELLISON: Yeah, so in some sense, 00:16:48.670 --> 00:16:52.360 align:middle line:84% if you have private information on costs, 00:16:52.360 --> 00:16:54.910 align:middle line:84% this is some sense that's what we normally 00:16:54.910 --> 00:16:57.130 align:middle line:90% refer to as an auction model. 00:16:57.130 --> 00:16:57.980 align:middle line:90% It's an auction. 00:16:57.980 --> 00:17:00.230 align:middle line:84% I don't know what the value of the painting is to you. 00:17:00.230 --> 00:17:02.522 align:middle line:84% You don't know what the value of the painting is to me. 00:17:02.522 --> 00:17:05.829 align:middle line:84% So I bid something, giving myself 00:17:05.829 --> 00:17:09.640 align:middle line:84% some expected markup because if I bid cost, then if I win 00:17:09.640 --> 00:17:12.440 align:middle line:84% or if I lose, I'm unhappy both ways. 00:17:12.440 --> 00:17:14.440 align:middle line:84% And so I bid something in between. 00:17:14.440 --> 00:17:16.480 align:middle line:84% In the buying something, I bid something 00:17:16.480 --> 00:17:19.700 align:middle line:90% in between my value and 0. 00:17:19.700 --> 00:17:22.480 align:middle line:84% And you do the same thing, and we get positive markups 00:17:22.480 --> 00:17:23.710 align:middle line:90% for that reason. 00:17:23.710 --> 00:17:29.500 align:middle line:84% Yeah, so that becomes like in the-- 00:17:29.500 --> 00:17:32.720 align:middle line:84% values uniform 0, 1 model, you bid v over 2 is the equilibrium. 00:17:32.720 --> 00:17:35.450 align:middle line:84% So in some sense that is a model. 00:17:35.450 --> 00:17:38.060 align:middle line:84% You end up reconstructing something like Cournot 00:17:38.060 --> 00:17:39.460 align:middle line:90% that you get positive markups. 00:17:39.460 --> 00:17:41.293 align:middle line:84% And as the number of firms goes to infinity, 00:17:41.293 --> 00:17:42.150 align:middle line:90% the markups go to 0. 00:17:42.150 --> 00:17:45.300 align:middle line:84% So that would be another way to get a Cournot-like prediction. 00:17:45.300 --> 00:17:47.810 align:middle line:90% 00:17:47.810 --> 00:17:49.670 align:middle line:90% Anyway, I do talk about-- 00:17:49.670 --> 00:17:52.100 align:middle line:84% I'll do auctions in like week eight or whatever. 00:17:52.100 --> 00:17:54.268 align:middle line:90% But we actually get that-- 00:17:54.268 --> 00:17:56.060 align:middle line:84% the place where that analogy is more direct 00:17:56.060 --> 00:17:57.540 align:middle line:90% is like procurement auctions. 00:17:57.540 --> 00:18:00.590 align:middle line:84% You have auctions for contracts to pave a road 00:18:00.590 --> 00:18:02.180 align:middle line:90% in the city of Cambridge. 00:18:02.180 --> 00:18:03.970 align:middle line:84% And those are allocated by auction. 00:18:03.970 --> 00:18:06.470 align:middle line:84% And exactly, you don't know what the rival's costs are going 00:18:06.470 --> 00:18:08.120 align:middle line:90% to be for that paving job. 00:18:08.120 --> 00:18:11.750 align:middle line:84% So both of you bid some markup, hoping to win, yeah. 00:18:11.750 --> 00:18:14.370 align:middle line:90% 00:18:14.370 --> 00:18:21.700 align:middle line:84% OK, comment on-- again, go forward another 46 years. 00:18:21.700 --> 00:18:27.180 align:middle line:84% Comment on-- Cournot comment on Bertrand competition 00:18:27.180 --> 00:18:28.740 align:middle line:90% by Harold Hotelling. 00:18:28.740 --> 00:18:32.490 align:middle line:84% And I wanted to put him here because Harold Hotelling is 00:18:32.490 --> 00:18:34.950 align:middle line:90% my great, great grand advisor. 00:18:34.950 --> 00:18:38.240 align:middle line:84% So Hotelling was Arrow's advisor. 00:18:38.240 --> 00:18:39.720 align:middle line:90% Arrow was Maskin's advisor. 00:18:39.720 --> 00:18:42.100 align:middle line:90% Maskin was Fudenberg's advisor. 00:18:42.100 --> 00:18:43.440 align:middle line:90% Drew was my advisor. 00:18:43.440 --> 00:18:46.860 align:middle line:84% So anyway, I have some fondness for Harold Hotelling. 00:18:46.860 --> 00:18:50.340 align:middle line:90% And he was actually-- 00:18:50.340 --> 00:18:54.360 align:middle line:84% so if you go look at my advisor family tree, 00:18:54.360 --> 00:18:57.090 align:middle line:84% they're all mathematicians beyond some point. 00:18:57.090 --> 00:19:00.385 align:middle line:84% So you get to all those French mathematicians, whose names you 00:19:00.385 --> 00:19:02.010 align:middle line:84% hear in probability theory or whatever, 00:19:02.010 --> 00:19:06.910 align:middle line:84% because Hotelling had his PhD in math rather than in economics. 00:19:06.910 --> 00:19:09.665 align:middle line:84% So my family tree goes back three branches in economics. 00:19:09.665 --> 00:19:11.790 align:middle line:84% And then everyone's a mathematician from that point 00:19:11.790 --> 00:19:14.740 align:middle line:84% forward, like for Hotelling's advisors. 00:19:14.740 --> 00:19:17.503 align:middle line:90% But anyway, Hotelling, through-- 00:19:17.503 --> 00:19:19.420 align:middle line:84% well, mostly through having advised Ken Arrow, 00:19:19.420 --> 00:19:23.770 align:middle line:84% Hotelling does have over 1,000 descendants, 00:19:23.770 --> 00:19:25.930 align:middle line:90% grand advisees or whatever. 00:19:25.930 --> 00:19:28.330 align:middle line:84% So anyway, so Hotelling-- and actually, I 00:19:28.330 --> 00:19:29.870 align:middle line:90% love Hotelling's writing also. 00:19:29.870 --> 00:19:34.780 align:middle line:84% You get him to-- he's got a very, in some sense, 00:19:34.780 --> 00:19:38.050 align:middle line:84% self-confident but trying-to-be-understated style 00:19:38.050 --> 00:19:40.400 align:middle line:90% of this, of-- 00:19:40.400 --> 00:19:42.400 align:middle line:84% "after the work of the late Professor Edgeworth, 00:19:42.400 --> 00:19:43.858 align:middle line:84% one may doubt that anything further 00:19:43.858 --> 00:19:45.760 align:middle line:84% can be said on the theory of competition. 00:19:45.760 --> 00:19:48.980 align:middle line:84% However, one important feature seems to have escaped scrutiny. 00:19:48.980 --> 00:19:53.068 align:middle line:84% This is the fact that of all the purchases of commodities, 00:19:53.068 --> 00:19:54.610 align:middle line:84% some buy from one, some from another, 00:19:54.610 --> 00:19:56.560 align:middle line:84% in spite of the moderate differences in price." 00:19:56.560 --> 00:19:58.393 align:middle line:84% And that's saying that price reaction should 00:19:58.393 --> 00:20:00.850 align:middle line:84% be continuous rather than nondifferentiable 00:20:00.850 --> 00:20:03.447 align:middle line:84% as they are in Bertrand's model and then working out 00:20:03.447 --> 00:20:04.280 align:middle line:90% the [? direction. ?] 00:20:04.280 --> 00:20:08.680 align:middle line:84% So anyway, Hotelling's model is-- 00:20:08.680 --> 00:20:11.980 align:middle line:84% and in some sense, Hotelling has opened the path 00:20:11.980 --> 00:20:13.570 align:middle line:84% that everyone has followed since, 00:20:13.570 --> 00:20:16.840 align:middle line:84% which is thinking about competition in terms 00:20:16.840 --> 00:20:19.840 align:middle line:84% of heterogeneous consumer populations 00:20:19.840 --> 00:20:25.120 align:middle line:84% and some underlying type space of heterogeneous consumers. 00:20:25.120 --> 00:20:28.360 align:middle line:84% So he had this sort of line, where he 00:20:28.360 --> 00:20:34.750 align:middle line:90% had consumers arranged on 0, 1. 00:20:34.750 --> 00:20:37.630 align:middle line:84% And actually, Hotelling spent a lot of his career at UCLA 00:20:37.630 --> 00:20:40.390 align:middle line:84% and I think was thinking about this as a beach in Southern 00:20:40.390 --> 00:20:42.160 align:middle line:90% California. 00:20:42.160 --> 00:20:44.200 align:middle line:84% And so Hotelling did have this model 00:20:44.200 --> 00:20:49.150 align:middle line:84% you can think of as you've got the two 00:20:49.150 --> 00:20:53.980 align:middle line:84% stands on the beach, each one selling drinks and hot dogs 00:20:53.980 --> 00:20:55.310 align:middle line:90% and ice cream or whatever. 00:20:55.310 --> 00:20:57.160 align:middle line:84% And then you have all the customers, 00:20:57.160 --> 00:20:59.787 align:middle line:84% who are lying on blankets somewhere along the beach. 00:20:59.787 --> 00:21:01.870 align:middle line:84% And then when they want to get something to drink, 00:21:01.870 --> 00:21:04.020 align:middle line:84% they pick up, and they walk to the nearest stand. 00:21:04.020 --> 00:21:05.770 align:middle line:84% And then they buy something, and then they 00:21:05.770 --> 00:21:08.170 align:middle line:84% walk back to where they were sitting on the beach. 00:21:08.170 --> 00:21:11.470 align:middle line:84% So his model is we have these consumers, 00:21:11.470 --> 00:21:14.710 align:middle line:90% and they have the utilities. 00:21:14.710 --> 00:21:16.130 align:middle line:90% So I put theta on this axis. 00:21:16.130 --> 00:21:18.750 align:middle line:90% 00:21:18.750 --> 00:21:20.760 align:middle line:84% So then if I graph the utility that you 00:21:20.760 --> 00:21:28.080 align:middle line:84% get buying consumer of type theta buying from Firm 1, 00:21:28.080 --> 00:21:32.310 align:middle line:84% I get some utility that looks like this, v minus t 00:21:32.310 --> 00:21:35.550 align:middle line:90% times theta minus P1. 00:21:35.550 --> 00:21:40.140 align:middle line:84% So that would be my utility of buying from Firm 1. 00:21:40.140 --> 00:21:46.740 align:middle line:84% And then, consumers also have a utility of buying from Firm 2. 00:21:46.740 --> 00:21:50.130 align:middle line:90% So let me on this axis put v-- 00:21:50.130 --> 00:21:57.120 align:middle line:84% this is v minus t1 minus theta minus P2. 00:21:57.120 --> 00:22:03.450 align:middle line:84% So the argument is t is my disutility per unit 00:22:03.450 --> 00:22:04.960 align:middle line:90% of distance walking. 00:22:04.960 --> 00:22:07.410 align:middle line:84% And so my utility from buying the product from Firm 1 00:22:07.410 --> 00:22:09.750 align:middle line:84% is v minus t times theta, because theta 00:22:09.750 --> 00:22:12.910 align:middle line:90% captures my distance, minus P1. 00:22:12.910 --> 00:22:16.170 align:middle line:84% And if I buy from Firm 2, it's v minus t times 1 00:22:16.170 --> 00:22:17.810 align:middle line:90% minus theta minus P2. 00:22:17.810 --> 00:22:21.200 align:middle line:90% 00:22:21.200 --> 00:22:23.660 align:middle line:84% And so he did this in a one-dimensional-- 00:22:23.660 --> 00:22:26.660 align:middle line:84% this one-dimensional type space captures your preference 00:22:26.660 --> 00:22:28.820 align:middle line:90% for both goods. 00:22:28.820 --> 00:22:31.580 align:middle line:84% And so we assume there's a constant marginal cost c. 00:22:31.580 --> 00:22:35.510 align:middle line:84% He considered, again, the Nash equilibrium 00:22:35.510 --> 00:22:38.180 align:middle line:84% before Nash of firms simultaneously announced 00:22:38.180 --> 00:22:40.280 align:middle line:90% prices P1 and P2. 00:22:40.280 --> 00:22:43.410 align:middle line:84% And then, firms announce those prices. 00:22:43.410 --> 00:22:44.690 align:middle line:90% It's a simultaneous move game. 00:22:44.690 --> 00:22:47.107 align:middle line:84% And then, consumers decide who to buy from, 00:22:47.107 --> 00:22:48.690 align:middle line:84% and then the firms earn their profits. 00:22:48.690 --> 00:22:53.460 align:middle line:84% And we just look for the static Nash equilibrium. 00:22:53.460 --> 00:22:59.520 align:middle line:84% The standard case we discuss in this model is if v is large, 00:22:59.520 --> 00:23:02.820 align:middle line:84% then there's some consumer theta hat 00:23:02.820 --> 00:23:05.430 align:middle line:84% who's indifferent between buying the two products. 00:23:05.430 --> 00:23:12.600 align:middle line:84% So this consumer theta hat has v minus t theta hat minus P1 00:23:12.600 --> 00:23:19.650 align:middle line:84% equals v minus t 1 minus theta hat minus P2. 00:23:19.650 --> 00:23:21.390 align:middle line:84% So at those prices, that consumer 00:23:21.390 --> 00:23:23.880 align:middle line:84% is indifferent between the two products. 00:23:23.880 --> 00:23:26.610 align:middle line:84% You solve that equation, and it tells you that the indifferent 00:23:26.610 --> 00:23:36.550 align:middle line:84% consumer theta hat is 1/2 plus P2 minus P1 over 2t. 00:23:36.550 --> 00:23:40.332 align:middle line:90% 00:23:40.332 --> 00:23:41.790 align:middle line:84% With that indifferent consumer-- do 00:23:41.790 --> 00:23:43.900 align:middle line:84% I have it on the next slide or not? 00:23:43.900 --> 00:23:49.067 align:middle line:84% So with that indifferent consumer, then you get x1 of P1, 00:23:49.067 --> 00:23:55.780 align:middle line:84% P2 is 1/2 plus P2 minus P1 over 2t. 00:23:55.780 --> 00:24:07.090 align:middle line:84% And x2 of P1 P2 is 1/2 minus P2 minus P1 over 2t, OK? 00:24:07.090 --> 00:24:13.263 align:middle line:84% The demands add up to 1 if-- as long as this consumer is willing 00:24:13.263 --> 00:24:14.680 align:middle line:84% to-- as long as v is large enough, 00:24:14.680 --> 00:24:16.250 align:middle line:90% this consumer is willing to buy. 00:24:16.250 --> 00:24:18.560 align:middle line:84% So everyone buys from one firm or the other. 00:24:18.560 --> 00:24:21.550 align:middle line:84% So there's no deadweight loss in this model. 00:24:21.550 --> 00:24:29.910 align:middle line:84% Demands end up being independent of v. So this is if, whatever, 00:24:29.910 --> 00:24:41.700 align:middle line:84% v minus t times 1/2 plus P2 minus P1 over 2t minus P1 00:24:41.700 --> 00:24:42.820 align:middle line:90% greater than equal to 0. 00:24:42.820 --> 00:24:47.440 align:middle line:84% So as long as this indifferent consumer is willing to buy, 00:24:47.440 --> 00:24:51.490 align:middle line:84% demands are completely independent of v. And just 00:24:51.490 --> 00:24:52.960 align:middle line:90% are these linear-- 00:24:52.960 --> 00:24:55.060 align:middle line:90% these are linear demand curves. 00:24:55.060 --> 00:24:58.090 align:middle line:84% So what he's done is he's just proposed 00:24:58.090 --> 00:25:01.210 align:middle line:84% this model of heterogeneous consumer populations and said, 00:25:01.210 --> 00:25:04.240 align:middle line:84% with that heterogeneous consumer population model, 00:25:04.240 --> 00:25:09.730 align:middle line:84% we just get price competition with these particular linear 00:25:09.730 --> 00:25:10.500 align:middle line:90% demand curves. 00:25:10.500 --> 00:25:14.220 align:middle line:90% 00:25:14.220 --> 00:25:16.720 align:middle line:84% And what happens when you have those linear demand curves? 00:25:16.720 --> 00:25:25.290 align:middle line:84% Well, Firm I is just maximizing price minus cost times 1/2 plus 00:25:25.290 --> 00:25:27.430 align:middle line:90% pj minus p over 2t. 00:25:27.430 --> 00:25:30.000 align:middle line:84% So, if it sets a higher price, it 00:25:30.000 --> 00:25:32.170 align:middle line:84% gets a higher markup per consumer. 00:25:32.170 --> 00:25:34.740 align:middle line:84% But the number of consumers go down, 00:25:34.740 --> 00:25:38.670 align:middle line:84% with 1 over 2t being the slope of the downward-sloping 00:25:38.670 --> 00:25:42.630 align:middle line:84% individual demand curve facing it. 00:25:42.630 --> 00:25:45.480 align:middle line:84% I take the first-order conditions for this. 00:25:45.480 --> 00:25:46.920 align:middle line:90% It's just algebra. 00:25:46.920 --> 00:25:49.380 align:middle line:84% And, given that it's a linear demand curve, 00:25:49.380 --> 00:25:51.520 align:middle line:84% we get a quadratic objective function. 00:25:51.520 --> 00:25:53.850 align:middle line:90% It has an interior maximum. 00:25:53.850 --> 00:25:57.030 align:middle line:84% And what we get is the best response for Firm I to a price 00:25:57.030 --> 00:26:03.460 align:middle line:90% pj is 1/2 of c plus t plus pj. 00:26:03.460 --> 00:26:12.210 align:middle line:84% So, if I try to graph what's happening here, P1, P2, 00:26:12.210 --> 00:26:18.570 align:middle line:84% so if P1 is 0, the best response for Firm 2 is 1/2 c plus t is 00:26:18.570 --> 00:26:19.480 align:middle line:90% positive. 00:26:19.480 --> 00:26:22.240 align:middle line:90% 00:26:22.240 --> 00:26:25.550 align:middle line:84% And then, it's a line that's upward sloping. 00:26:25.550 --> 00:26:32.060 align:middle line:84% So this is the best response for Firm 2 to a price of P1. 00:26:32.060 --> 00:26:36.100 align:middle line:90% And this is 1/2 c plus t. 00:26:36.100 --> 00:26:40.470 align:middle line:90% 00:26:40.470 --> 00:26:42.840 align:middle line:84% And then similarly, the best response 00:26:42.840 --> 00:26:51.060 align:middle line:84% for Firm 1 to a price of P2 is going to look like this. 00:26:51.060 --> 00:26:54.630 align:middle line:84% So I'm graphing Firm 1's best response. 00:26:54.630 --> 00:26:56.520 align:middle line:84% I'm graphing this thing backwards, 00:26:56.520 --> 00:26:59.510 align:middle line:84% as you do in game theory, where as P2 is higher, 00:26:59.510 --> 00:27:01.230 align:middle line:90% I'm graphing P1 is higher. 00:27:01.230 --> 00:27:04.570 align:middle line:84% But this line has slope 1/2 relative to this. 00:27:04.570 --> 00:27:07.740 align:middle line:84% This one has slope 1/2 if you view it as a function of this 00:27:07.740 --> 00:27:08.540 align:middle line:90% line. 00:27:08.540 --> 00:27:11.380 align:middle line:84% So look at these two upward-sloping lines. 00:27:11.380 --> 00:27:13.110 align:middle line:90% They intersect. 00:27:13.110 --> 00:27:14.970 align:middle line:90% That's the equilibrium. 00:27:14.970 --> 00:27:18.905 align:middle line:84% And we get P1 star equals P2 star equals c plus t. 00:27:18.905 --> 00:27:23.540 align:middle line:90% 00:27:23.540 --> 00:27:28.320 align:middle line:84% So what are the economic implications here? 00:27:28.320 --> 00:27:32.270 align:middle line:84% One is that markups are proportional to the product 00:27:32.270 --> 00:27:34.130 align:middle line:90% differentiation parameter t. 00:27:34.130 --> 00:27:36.470 align:middle line:84% So it's the amount of product differentiation 00:27:36.470 --> 00:27:41.400 align:middle line:84% in a market that ends up determining 00:27:41.400 --> 00:27:42.595 align:middle line:90% how large are the markups? 00:27:42.595 --> 00:27:45.810 align:middle line:90% 00:27:45.810 --> 00:27:48.960 align:middle line:84% The hotter it is and the more unpleasant 00:27:48.960 --> 00:27:52.230 align:middle line:84% it is to walk across the sand, the higher will be the prices. 00:27:52.230 --> 00:27:56.220 align:middle line:84% And people today, I think, use this model not just 00:27:56.220 --> 00:28:00.660 align:middle line:84% for differentiation in physical space driving, 00:28:00.660 --> 00:28:04.175 align:middle line:84% but differentiation in taste space as well. 00:28:04.175 --> 00:28:05.550 align:middle line:84% So if you think about competition 00:28:05.550 --> 00:28:08.800 align:middle line:84% between Coke and Pepsi, how much do you like Coke? 00:28:08.800 --> 00:28:09.970 align:middle line:90% How much do you like Pepsi? 00:28:09.970 --> 00:28:14.342 align:middle line:84% There are some people who love Coke and dislike Pepsi. 00:28:14.342 --> 00:28:16.300 align:middle line:84% There are some who love Pepsi and dislike Coke. 00:28:16.300 --> 00:28:17.675 align:middle line:84% There are some who are completely 00:28:17.675 --> 00:28:18.850 align:middle line:90% indifferent between the two. 00:28:18.850 --> 00:28:22.020 align:middle line:84% The amount of taste heterogeneity 00:28:22.020 --> 00:28:24.510 align:middle line:90% is what determines the markups. 00:28:24.510 --> 00:28:26.580 align:middle line:84% And numerically, with these linear demand curves, 00:28:26.580 --> 00:28:28.860 align:middle line:84% it's the amount by which people at one end 00:28:28.860 --> 00:28:30.247 align:middle line:90% of the line versus the other-- 00:28:30.247 --> 00:28:31.830 align:middle line:84% it's the relative preference of people 00:28:31.830 --> 00:28:33.670 align:middle line:84% at one end of the line versus the other. 00:28:33.670 --> 00:28:37.060 align:middle line:84% This person thinks Pepsi is t better than Coke. 00:28:37.060 --> 00:28:39.517 align:middle line:84% That person thinks Coke is t better than Pepsi. t is 00:28:39.517 --> 00:28:40.475 align:middle line:90% the equilibrium markup. 00:28:40.475 --> 00:28:43.746 align:middle line:90% 00:28:43.746 --> 00:28:47.780 align:middle line:84% You can do an n firm circular version of this. 00:28:47.780 --> 00:28:49.850 align:middle line:90% So imagine that you have-- 00:28:49.850 --> 00:28:53.560 align:middle line:84% obviously, there are lots of parts of the United States-- 00:28:53.560 --> 00:28:55.880 align:middle line:84% well, obviously, you'd have to go all the way down 00:28:55.880 --> 00:28:56.810 align:middle line:90% to South America. 00:28:56.810 --> 00:28:58.893 align:middle line:84% And some parts, no one's going to be on the beach. 00:28:58.893 --> 00:29:01.460 align:middle line:84% But you could imagine a giant beach that's-- 00:29:01.460 --> 00:29:03.890 align:middle line:84% we have a resort island where the beach is just 00:29:03.890 --> 00:29:06.800 align:middle line:90% circle around the whole thing. 00:29:06.800 --> 00:29:11.240 align:middle line:84% If you put n firms around this, it's 00:29:11.240 --> 00:29:14.510 align:middle line:84% as if the competition between any of these two firms 00:29:14.510 --> 00:29:17.660 align:middle line:84% is now going to be like t times 1 over n 00:29:17.660 --> 00:29:20.660 align:middle line:84% is going to be the effective distance between them. 00:29:20.660 --> 00:29:23.450 align:middle line:84% And so if t times 1 over n becomes the effective distance 00:29:23.450 --> 00:29:28.940 align:middle line:84% between them, you're going to get P star equals 00:29:28.940 --> 00:29:31.730 align:middle line:90% c plus t times 1 over n. 00:29:31.730 --> 00:29:35.492 align:middle line:84% So this is a model where it can be like Cournot. 00:29:35.492 --> 00:29:36.950 align:middle line:84% And, as you put more and more firms 00:29:36.950 --> 00:29:39.620 align:middle line:84% into the same finite dimensional product space, 00:29:39.620 --> 00:29:41.750 align:middle line:84% markups decline and are continuous 00:29:41.750 --> 00:29:44.470 align:middle line:84% with perfect competition as n goes to infinity. 00:29:44.470 --> 00:29:47.895 align:middle line:90% 00:29:47.895 --> 00:29:49.270 align:middle line:84% Anyway, I'll just say this later. 00:29:49.270 --> 00:29:50.187 align:middle line:90% Actions are strategic. 00:29:50.187 --> 00:29:53.462 align:middle line:84% Complements just means that the reaction curves 00:29:53.462 --> 00:29:55.420 align:middle line:84% look different from how they looked in Cournot. 00:29:55.420 --> 00:29:57.613 align:middle line:84% Here, it's an intersection of upward-sloping lines. 00:29:57.613 --> 00:29:59.863 align:middle line:84% Cournot was an intersection of downward-sloping lines. 00:29:59.863 --> 00:30:02.640 align:middle line:90% 00:30:02.640 --> 00:30:05.850 align:middle line:84% Understanding some of the implications of the model, 00:30:05.850 --> 00:30:10.080 align:middle line:84% that's going to matter later, OK? 00:30:10.080 --> 00:30:15.380 align:middle line:84% OK, any questions on Hotelling's model? 00:30:15.380 --> 00:30:19.160 align:middle line:90% All right, OK. 00:30:19.160 --> 00:30:24.260 align:middle line:84% OK, so vertical differentiation, final thing we think of 00:30:24.260 --> 00:30:28.700 align:middle line:84% is that there's many examples like Coke and Pepsi. 00:30:28.700 --> 00:30:30.920 align:middle line:84% Clearly, one is the better product, and one is-- 00:30:30.920 --> 00:30:33.470 align:middle line:84% sorry, two products are just a matter of taste, 00:30:33.470 --> 00:30:35.180 align:middle line:90% whether you a versus b. 00:30:35.180 --> 00:30:36.710 align:middle line:84% There are other examples we think 00:30:36.710 --> 00:30:39.050 align:middle line:84% of where differentiation consists of one product 00:30:39.050 --> 00:30:41.630 align:middle line:90% is better and one is worse. 00:30:41.630 --> 00:30:49.940 align:middle line:84% So if you think about do people want to buy the BMW, 00:30:49.940 --> 00:30:53.120 align:middle line:84% or do they want the Toyota Yaris or something? 00:30:53.120 --> 00:30:55.880 align:middle line:84% Everybody would rather have the BMW. 00:30:55.880 --> 00:30:57.740 align:middle line:84% Everyone admits that this product a 00:30:57.740 --> 00:30:59.258 align:middle line:90% is better than product b. 00:30:59.258 --> 00:31:00.800 align:middle line:84% But the question is, how much are you 00:31:00.800 --> 00:31:03.530 align:middle line:84% willing to pay for product a versus product b? 00:31:03.530 --> 00:31:06.352 align:middle line:84% You could have, again, maybe some people 00:31:06.352 --> 00:31:07.310 align:middle line:90% still like flip phones. 00:31:07.310 --> 00:31:09.830 align:middle line:84% But you have the modern phone competing 00:31:09.830 --> 00:31:12.910 align:middle line:84% against the old flip phone, with just a keypad 00:31:12.910 --> 00:31:14.160 align:middle line:90% and a little screen like this. 00:31:14.160 --> 00:31:17.730 align:middle line:84% Everyone agrees that the modern phone is the better phone. 00:31:17.730 --> 00:31:19.260 align:middle line:84% But people just differ in how much 00:31:19.260 --> 00:31:21.600 align:middle line:84% they're willing to pay for the better product. 00:31:21.600 --> 00:31:24.813 align:middle line:84% So the consumer preferences here are going 00:31:24.813 --> 00:31:25.980 align:middle line:90% to be vertical rather than-- 00:31:25.980 --> 00:31:27.855 align:middle line:84% what we call vertical rather than horizontal. 00:31:27.855 --> 00:31:29.740 align:middle line:90% So do this example. 00:31:29.740 --> 00:31:31.890 align:middle line:90% I've got two firms. 00:31:31.890 --> 00:31:33.420 align:middle line:90% They have goods of quality. 00:31:33.420 --> 00:31:35.290 align:middle line:90% SL is my flip phone. 00:31:35.290 --> 00:31:37.290 align:middle line:90% SH is my iPhone. 00:31:37.290 --> 00:31:39.683 align:middle line:84% And the low-quality phone, everyone would agree, 00:31:39.683 --> 00:31:41.225 align:middle line:84% is worse than the high-quality phone. 00:31:41.225 --> 00:31:43.790 align:middle line:90% 00:31:43.790 --> 00:31:46.130 align:middle line:84% We have consumers have types, again, 00:31:46.130 --> 00:31:49.230 align:middle line:84% distributed on a unit interval, or sorry, nonunit interval 00:31:49.230 --> 00:31:51.800 align:middle line:84% now, theta lower bar, theta upper bar. 00:31:51.800 --> 00:31:53.480 align:middle line:84% And the utility functions are going 00:31:53.480 --> 00:31:56.900 align:middle line:84% to be the consumer-- utility of a consumer of type theta buying 00:31:56.900 --> 00:32:00.050 align:middle line:90% product i is theta si minus pi. 00:32:00.050 --> 00:32:04.247 align:middle line:84% So the theta is your marginal value of a unit of quality. 00:32:04.247 --> 00:32:06.080 align:middle line:84% You could also just think of this as a model 00:32:06.080 --> 00:32:08.300 align:middle line:84% where consumers are differentiated by income 00:32:08.300 --> 00:32:13.070 align:middle line:84% and have a different marginal value of income. 00:32:13.070 --> 00:32:15.860 align:middle line:84% And therefore, they have all the same utility 00:32:15.860 --> 00:32:17.370 align:middle line:84% that they get from higher quality. 00:32:17.370 --> 00:32:19.412 align:middle line:84% But just some people have more money than others. 00:32:19.412 --> 00:32:21.980 align:middle line:84% They have a greater disutility of spending money, OK? 00:32:21.980 --> 00:32:24.960 align:middle line:90% 00:32:24.960 --> 00:32:27.010 align:middle line:84% OK, and so consumers have this utility 00:32:27.010 --> 00:32:29.790 align:middle line:84% if they buy from Firm I. They get 0 utility if they 00:32:29.790 --> 00:32:33.570 align:middle line:90% buy from neither firm at all. 00:32:33.570 --> 00:32:35.850 align:middle line:84% I'm going to, for simplicity, assume a unit mass 00:32:35.850 --> 00:32:40.120 align:middle line:84% of consumers, a unit density of consumers and an interval theta 00:32:40.120 --> 00:32:41.315 align:middle line:90% lower bar, theta upper bar. 00:32:41.315 --> 00:32:43.950 align:middle line:90% 00:32:43.950 --> 00:32:47.640 align:middle line:84% OK, so what's going on here is, here, I'm 00:32:47.640 --> 00:32:50.610 align:middle line:84% typically going to have my theta space-- 00:32:50.610 --> 00:32:55.510 align:middle line:84% often, we have our theta space start at 0. 00:32:55.510 --> 00:32:58.505 align:middle line:84% But here, everybody in my model is going to like quality. 00:32:58.505 --> 00:32:59.880 align:middle line:84% So I'm going to think of a model. 00:32:59.880 --> 00:33:01.588 align:middle line:84% We have this sort of interval theta lower 00:33:01.588 --> 00:33:05.010 align:middle line:90% bar, theta upper bar. 00:33:05.010 --> 00:33:10.080 align:middle line:84% And so consumers are arrayed on this interval 00:33:10.080 --> 00:33:11.165 align:middle line:90% of positive values. 00:33:11.165 --> 00:33:13.710 align:middle line:90% 00:33:13.710 --> 00:33:19.770 align:middle line:84% So again, consider the same game that Bertrand and Hotelling 00:33:19.770 --> 00:33:20.610 align:middle line:90% considered. 00:33:20.610 --> 00:33:24.060 align:middle line:84% Firms simultaneously choose prices PL and PH. 00:33:24.060 --> 00:33:26.130 align:middle line:84% Taking the other firm's price is fixed, 00:33:26.130 --> 00:33:28.470 align:middle line:84% consumers decide who to buy from. 00:33:28.470 --> 00:33:30.850 align:middle line:90% And then firms earn profits. 00:33:30.850 --> 00:33:33.310 align:middle line:90% That's the end of the game. 00:33:33.310 --> 00:33:36.340 align:middle line:90% What do the utilities look like? 00:33:36.340 --> 00:33:42.820 align:middle line:84% Here, let me first draw a line like this. 00:33:42.820 --> 00:33:47.080 align:middle line:84% This is the line theta SL minus PL. 00:33:47.080 --> 00:33:52.000 align:middle line:84% So it starts at negative Pl, and then it 00:33:52.000 --> 00:33:54.830 align:middle line:90% goes up with a slope of SL. 00:33:54.830 --> 00:33:56.700 align:middle line:84% This is the utility that you get-- 00:33:56.700 --> 00:33:59.660 align:middle line:90% 00:33:59.660 --> 00:34:01.860 align:middle line:90% this is UL of theta. 00:34:01.860 --> 00:34:10.698 align:middle line:84% That's the utility you get buying from Firm L. Equalas 00:34:10.698 --> 00:34:13.120 align:middle line:90% UL of theta. 00:34:13.120 --> 00:34:15.670 align:middle line:84% OK, then other line I'm going to draw 00:34:15.670 --> 00:34:20.350 align:middle line:84% is Firm H has the higher quality product. 00:34:20.350 --> 00:34:23.710 align:middle line:84% So if you had type 0, which nobody does, 00:34:23.710 --> 00:34:27.370 align:middle line:84% you'd get utility negative PH from buying that product. 00:34:27.370 --> 00:34:30.670 align:middle line:84% But then I'm going to assume that's a steeper-sloping line, 00:34:30.670 --> 00:34:34.750 align:middle line:90% like this, theta SH minus PH. 00:34:34.750 --> 00:34:39.790 align:middle line:84% It's a steeper-sloping line because SH is bigger than SL, 00:34:39.790 --> 00:34:43.690 align:middle line:90% and the slope is S, OK? 00:34:43.690 --> 00:34:45.219 align:middle line:90% So what happens in this model? 00:34:45.219 --> 00:34:48.050 align:middle line:84% Again, there's some-- in equilibrium, 00:34:48.050 --> 00:34:52.730 align:middle line:84% there's be some indifferent consumer of type theta hat. 00:34:52.730 --> 00:34:58.010 align:middle line:84% Consumers with types above theta hat, so these guys 00:34:58.010 --> 00:35:03.080 align:middle line:90% all buy the high-quality good. 00:35:03.080 --> 00:35:05.030 align:middle line:84% These consumers, the upper envelope, 00:35:05.030 --> 00:35:10.720 align:middle line:84% is these guys buy the low-quality good. 00:35:10.720 --> 00:35:13.330 align:middle line:84% As I've drawn it, there's another point that's 00:35:13.330 --> 00:35:15.070 align:middle line:90% of importance called theta-- 00:35:15.070 --> 00:35:15.940 align:middle line:90% I'll call it theta-- 00:35:15.940 --> 00:35:19.320 align:middle line:84% I named theta prime in the slides. 00:35:19.320 --> 00:35:22.380 align:middle line:84% Anyone with a type below theta prime 00:35:22.380 --> 00:35:26.280 align:middle line:84% is going to buy nothing because neither good is worth 00:35:26.280 --> 00:35:27.605 align:middle line:90% paying what's being charged. 00:35:27.605 --> 00:35:31.090 align:middle line:90% 00:35:31.090 --> 00:35:34.780 align:middle line:84% I've drawn this in the case where theta prime is below theta 00:35:34.780 --> 00:35:38.320 align:middle line:84% lower bar, and theta hat is between theta lower 00:35:38.320 --> 00:35:40.270 align:middle line:90% bar and theta upper bar. 00:35:40.270 --> 00:35:42.970 align:middle line:84% And in that case, what are the demands? 00:35:42.970 --> 00:35:44.950 align:middle line:84% The demand for the high-quality product 00:35:44.950 --> 00:35:48.170 align:middle line:84% is just theta upper bar minus theta hat. 00:35:48.170 --> 00:35:50.150 align:middle line:84% And the demand for the low-quality product 00:35:50.150 --> 00:35:53.520 align:middle line:84% is theta hat minus theta lower bar. 00:35:53.520 --> 00:35:55.890 align:middle line:84% If theta prime were to the right of this, 00:35:55.890 --> 00:35:57.510 align:middle line:84% the demand for the low-quality product 00:35:57.510 --> 00:35:59.600 align:middle line:84% would be theta hat minus theta prime. 00:35:59.600 --> 00:36:02.710 align:middle line:90% 00:36:02.710 --> 00:36:07.510 align:middle line:84% But anyway, I drew it like this, so this becomes the equations. 00:36:07.510 --> 00:36:16.780 align:middle line:84% And then again, this theta hat satisfies theta hat SH minus PH 00:36:16.780 --> 00:36:20.830 align:middle line:90% equals theta hat SL minus PL. 00:36:20.830 --> 00:36:28.420 align:middle line:84% So that tells you that theta hat times SH minus SL 00:36:28.420 --> 00:36:32.200 align:middle line:90% equals PH minus PL. 00:36:32.200 --> 00:36:37.240 align:middle line:84% That gives you this expression here for what 00:36:37.240 --> 00:36:39.970 align:middle line:90% the demand is for product H. 00:36:39.970 --> 00:36:45.430 align:middle line:84% So again, it's a story, and it's a story 00:36:45.430 --> 00:36:48.160 align:middle line:84% that just basically what is done is it's just given us, 00:36:48.160 --> 00:36:50.830 align:middle line:90% again, two linear demand curves. 00:36:50.830 --> 00:36:53.740 align:middle line:84% These are both-- they've got other parameters in them, 00:36:53.740 --> 00:36:54.760 align:middle line:90% and it's not so obvious. 00:36:54.760 --> 00:36:55.570 align:middle line:90% But you just look at it. 00:36:55.570 --> 00:36:57.070 align:middle line:84% It's like, yeah, that's just-- it's 00:36:57.070 --> 00:36:59.050 align:middle line:90% a linear function of PL and PH. 00:36:59.050 --> 00:37:00.550 align:middle line:84% It's a linear function of PL and PH. 00:37:00.550 --> 00:37:03.420 align:middle line:90% 00:37:03.420 --> 00:37:06.360 align:middle line:84% Hotelling was a symmetric linear model. 00:37:06.360 --> 00:37:08.990 align:middle line:84% The two demand curves looked exactly the same. 00:37:08.990 --> 00:37:11.850 align:middle line:84% Here, the demand curves look different. 00:37:11.850 --> 00:37:17.598 align:middle line:84% In particular, if the prices were equal, 00:37:17.598 --> 00:37:19.640 align:middle line:84% everyone would buy from Firm H. So in some sense, 00:37:19.640 --> 00:37:21.680 align:middle line:84% Firm H's demand is higher than Firm L's 00:37:21.680 --> 00:37:23.600 align:middle line:90% holding the price is fixed. 00:37:23.600 --> 00:37:25.495 align:middle line:84% But that's what the equations look like. 00:37:25.495 --> 00:37:32.030 align:middle line:90% 00:37:32.030 --> 00:37:35.640 align:middle line:84% But it's just a shift of demand curves. 00:37:35.640 --> 00:37:38.120 align:middle line:84% One demand curve is higher, but the demand curves 00:37:38.120 --> 00:37:40.680 align:middle line:84% are both linear with the same slope and the two variables. 00:37:40.680 --> 00:37:44.920 align:middle line:90% 00:37:44.920 --> 00:37:46.920 align:middle line:84% Any question on that, getting from the equations 00:37:46.920 --> 00:37:49.560 align:middle line:90% to the slopes? 00:37:49.560 --> 00:37:51.930 align:middle line:84% So anyway, that's what our demand model looks like. 00:37:51.930 --> 00:37:53.680 align:middle line:84% And then again, the question is like, what 00:37:53.680 --> 00:37:55.810 align:middle line:90% happens in this competition? 00:37:55.810 --> 00:38:02.452 align:middle line:84% And again, it's just it's solving a-- 00:38:02.452 --> 00:38:05.230 align:middle line:84% it's just solving two equations and two unknowns 00:38:05.230 --> 00:38:07.610 align:middle line:84% to find what the demand curves are. 00:38:07.610 --> 00:38:14.020 align:middle line:84% It really is not so different here from what Hotelling did. 00:38:14.020 --> 00:38:28.870 align:middle line:84% So if I plot P1 and P2 again, so the best response to Firm H 00:38:28.870 --> 00:38:31.090 align:middle line:84% of a price PL turns out to be-- if you remember, 00:38:31.090 --> 00:38:34.270 align:middle line:84% the other one was 1/2 p plus c plus t. 00:38:34.270 --> 00:38:39.640 align:middle line:84% So it turns out to be 1/2 p plus c plus, instead of t, 00:38:39.640 --> 00:38:43.480 align:middle line:84% we get theta upper bar minus SH minus SL, 00:38:43.480 --> 00:38:46.450 align:middle line:84% which is like the amount of differentiation that there is 00:38:46.450 --> 00:38:49.660 align:middle line:84% between the two products from the perspective of the theta 00:38:49.660 --> 00:38:50.990 align:middle line:90% upper bar consumer. 00:38:50.990 --> 00:38:53.650 align:middle line:84% So it's a lot like p plus c plus t 00:38:53.650 --> 00:38:55.263 align:middle line:84% but just with the amount of difference 00:38:55.263 --> 00:38:57.430 align:middle line:84% between the products here being from the perspective 00:38:57.430 --> 00:39:00.640 align:middle line:90% of the high theta consumer. 00:39:00.640 --> 00:39:06.670 align:middle line:84% And so what that looks like is we start again here. 00:39:06.670 --> 00:39:11.200 align:middle line:90% So we can put PL here, PH here. 00:39:11.200 --> 00:39:16.420 align:middle line:84% So it starts at 1/2 PL plus c plus something or other. 00:39:16.420 --> 00:39:19.030 align:middle line:84% So it starts at some positive thing, 00:39:19.030 --> 00:39:21.520 align:middle line:84% and it goes up with a slope of 1/2. 00:39:21.520 --> 00:39:27.420 align:middle line:84% So this is the best response for Firm H to a price of PL. 00:39:27.420 --> 00:39:37.670 align:middle line:84% And this is 1/2 of c plus theta upper bar times SH minus SL. 00:39:37.670 --> 00:39:44.640 align:middle line:84% Now, Firm L's best response is 1/2 of p plus c minus something. 00:39:44.640 --> 00:39:46.640 align:middle line:84% And so the minus something is again 00:39:46.640 --> 00:39:49.550 align:middle line:84% related to how much differentiation there is. 00:39:49.550 --> 00:39:53.530 align:middle line:84% Notice because when PH is 0, this becomes 1/2 of c minus 00:39:53.530 --> 00:39:54.030 align:middle line:90% something. 00:39:54.030 --> 00:39:55.880 align:middle line:84% This thing could even be negative, 00:39:55.880 --> 00:39:58.310 align:middle line:90% or it's certainly below c. 00:39:58.310 --> 00:40:02.930 align:middle line:84% And it could even be a negative number if differentiate, 00:40:02.930 --> 00:40:05.973 align:middle line:84% depending on how big differentiation is. 00:40:05.973 --> 00:40:08.390 align:middle line:84% But anyway, I'll draw it as starting as a positive number, 00:40:08.390 --> 00:40:10.490 align:middle line:84% but it starts from some smaller amount. 00:40:10.490 --> 00:40:14.490 align:middle line:84% And then it also goes up at a slope of 1/2. 00:40:14.490 --> 00:40:20.160 align:middle line:90% So we get BR H-- 00:40:20.160 --> 00:40:21.790 align:middle line:90% BRL of PH. 00:40:21.790 --> 00:40:24.870 align:middle line:90% Looks like that. 00:40:24.870 --> 00:40:29.070 align:middle line:84% And it starts from 1/2 of c minus theta lower bar times SH 00:40:29.070 --> 00:40:31.700 align:middle line:90% minus SL. 00:40:31.700 --> 00:40:35.630 align:middle line:84% And, given these things both have slope of 1/2, again, 00:40:35.630 --> 00:40:37.250 align:middle line:90% there's a unique intersection. 00:40:37.250 --> 00:40:38.820 align:middle line:90% And it's right there. 00:40:38.820 --> 00:40:43.820 align:middle line:84% And you can think of this as PL star comma PH star. 00:40:43.820 --> 00:40:48.200 align:middle line:84% And what we get is this asymmetric equilibrium. 00:40:48.200 --> 00:40:50.720 align:middle line:84% The formulas look the same, but this one's 00:40:50.720 --> 00:40:54.050 align:middle line:84% got twice the bigger number minus the smaller number. 00:40:54.050 --> 00:40:55.940 align:middle line:84% And this one has 1 times the bigger number 00:40:55.940 --> 00:40:57.570 align:middle line:90% minus twice the smaller number. 00:40:57.570 --> 00:41:01.310 align:middle line:84% So this is a bigger number than this one. 00:41:01.310 --> 00:41:06.620 align:middle line:84% And so what we get is, again, vertical differentiation, just 00:41:06.620 --> 00:41:09.110 align:middle line:84% like horizontal differentiation, it 00:41:09.110 --> 00:41:12.930 align:middle line:84% creates finite demand elasticities. 00:41:12.930 --> 00:41:14.470 align:middle line:90% It creates positive markups. 00:41:14.470 --> 00:41:17.270 align:middle line:84% If you put uniform distributions on the vertical tastes, 00:41:17.270 --> 00:41:19.040 align:middle line:84% it can be linear demand curves, just 00:41:19.040 --> 00:41:22.460 align:middle line:90% like the horizontal model is. 00:41:22.460 --> 00:41:26.450 align:middle line:84% In equilibrium, the differentiation, again, 00:41:26.450 --> 00:41:28.660 align:middle line:90% leads to positive markups. 00:41:28.660 --> 00:41:31.490 align:middle line:84% Leads to positive markups, but it leads to positive markups 00:41:31.490 --> 00:41:34.100 align:middle line:90% where Firm H is favored. 00:41:34.100 --> 00:41:35.436 align:middle line:90% Firm L is disfavored. 00:41:35.436 --> 00:41:38.230 align:middle line:90% 00:41:38.230 --> 00:41:42.340 align:middle line:84% Notice also that if theta upper bar and theta lower bar 00:41:42.340 --> 00:41:45.250 align:middle line:84% are too close together, this doesn't work, 00:41:45.250 --> 00:41:47.710 align:middle line:84% and Firm L just has to drop out of the market 00:41:47.710 --> 00:41:51.760 align:middle line:84% because the equilibrium looks like theta upper bar minus 2 00:41:51.760 --> 00:41:53.830 align:middle line:90% theta lower bar over 3. 00:41:53.830 --> 00:41:57.220 align:middle line:84% As theta lower bar approaches 1/2 of theta upper bar, 00:41:57.220 --> 00:41:59.800 align:middle line:90% Firm 2 is just pricing at cost. 00:41:59.800 --> 00:42:07.000 align:middle line:84% If firm theta lower bar was even closer to theta upper bar, what 00:42:07.000 --> 00:42:09.620 align:middle line:84% you'd get in equilibrium is Firm L would just be shut out. 00:42:09.620 --> 00:42:11.867 align:middle line:84% It would be driven down to pricing-- 00:42:11.867 --> 00:42:14.450 align:middle line:84% to play [INAUDIBLE], that would have to be pricing below cost. 00:42:14.450 --> 00:42:16.075 align:middle line:84% It eventually doesn't price below cost. 00:42:16.075 --> 00:42:18.750 align:middle line:84% It can't compete in the market, OK? 00:42:18.750 --> 00:42:23.100 align:middle line:84% So vertical differentiation, like horizontal differentiation, 00:42:23.100 --> 00:42:25.660 align:middle line:84% produces finite demand elasticities. 00:42:25.660 --> 00:42:34.530 align:middle line:84% It can give us, again, standard Cournot-like markups. 00:42:34.530 --> 00:42:39.130 align:middle line:84% It doesn't give us a model where Cournot is-- 00:42:39.130 --> 00:42:42.170 align:middle line:84% it's like Cournot had that continuity n goes to infinity. 00:42:42.170 --> 00:42:43.820 align:middle line:90% Price heads to cost. 00:42:43.820 --> 00:42:46.180 align:middle line:84% Here, this doesn't happen because there's only room 00:42:46.180 --> 00:42:49.000 align:middle line:90% for a finite number of firms. 00:42:49.000 --> 00:42:50.560 align:middle line:84% You start taking this space, and you 00:42:50.560 --> 00:42:53.950 align:middle line:84% try to have three or four or five or 10 different firms 00:42:53.950 --> 00:42:54.800 align:middle line:90% selling to this. 00:42:54.800 --> 00:42:57.740 align:middle line:84% At some point, the firms get too close together. 00:42:57.740 --> 00:43:00.460 align:middle line:84% The firms that are below just get shut out of the market 00:43:00.460 --> 00:43:01.340 align:middle line:90% and can't compete. 00:43:01.340 --> 00:43:02.750 align:middle line:84% And so it's only the high-quality firms 00:43:02.750 --> 00:43:03.833 align:middle line:90% that are making any sales. 00:43:03.833 --> 00:43:06.880 align:middle line:84% And so there's some minimum level of markups 00:43:06.880 --> 00:43:08.560 align:middle line:84% you're going to have to get there. 00:43:08.560 --> 00:43:11.800 align:middle line:84% Although, obviously, as the firms 00:43:11.800 --> 00:43:14.350 align:middle line:84% crowd the space, the difference between the SH firm 00:43:14.350 --> 00:43:16.142 align:middle line:84% and the SH minus epsilon firm, you're only 00:43:16.142 --> 00:43:17.350 align:middle line:90% going to get epsilon profits. 00:43:17.350 --> 00:43:23.970 align:middle line:84% But you're going to get it with just a few firms active, OK? 00:43:23.970 --> 00:43:27.510 align:middle line:84% OK, and obviously, I think modern IO-- in reality, 00:43:27.510 --> 00:43:29.940 align:middle line:84% we think that vertical differentiation 00:43:29.940 --> 00:43:33.370 align:middle line:84% and horizontal differentiation are present in most markets. 00:43:33.370 --> 00:43:37.097 align:middle line:84% We think most products, there's some extent 00:43:37.097 --> 00:43:39.180 align:middle line:84% to which we think product a is better than product 00:43:39.180 --> 00:43:41.520 align:middle line:84% b that everyone would agree on or almost everyone 00:43:41.520 --> 00:43:42.160 align:middle line:90% would agree on. 00:43:42.160 --> 00:43:44.463 align:middle line:84% And then there's other horizontal aspects. 00:43:44.463 --> 00:43:47.130 align:middle line:84% Everyone wants a phone that has better battery life and a better 00:43:47.130 --> 00:43:49.135 align:middle line:84% screen resolution and a better camera. 00:43:49.135 --> 00:43:50.760 align:middle line:84% But then there are other things, people 00:43:50.760 --> 00:43:53.730 align:middle line:84% like the look and feel of a versus b and are going to have-- 00:43:53.730 --> 00:43:55.832 align:middle line:84% know the operating system of a versus b 00:43:55.832 --> 00:43:58.040 align:middle line:84% and are going to have horizontal and vertical tastes. 00:43:58.040 --> 00:44:04.510 align:middle line:90% 00:44:04.510 --> 00:44:08.210 align:middle line:84% So let me go back to horizontal differentiation now. 00:44:08.210 --> 00:44:13.330 align:middle line:84% And this is motivated by how the empirical literature and IO has 00:44:13.330 --> 00:44:14.180 align:middle line:90% developed. 00:44:14.180 --> 00:44:19.920 align:middle line:90% So generally, the standard-- 00:44:19.920 --> 00:44:25.990 align:middle line:84% Hotelling is a very nice model of competition on a line. 00:44:25.990 --> 00:44:29.040 align:middle line:84% Hotelling is not as good a model once you have three firms 00:44:29.040 --> 00:44:30.335 align:middle line:90% instead of two firms. 00:44:30.335 --> 00:44:31.710 align:middle line:84% Because you have three firms, you 00:44:31.710 --> 00:44:35.100 align:middle line:84% have to think about where do we put the three firms and product 00:44:35.100 --> 00:44:35.640 align:middle line:90% space. 00:44:35.640 --> 00:44:38.250 align:middle line:90% One thing you could do is-- 00:44:38.250 --> 00:44:39.900 align:middle line:90% what did I do with my eraser? 00:44:39.900 --> 00:44:42.090 align:middle line:90% There it is. 00:44:42.090 --> 00:44:46.580 align:middle line:84% You could, if you're someone who likes high school geometry, 00:44:46.580 --> 00:44:49.565 align:middle line:84% you could go back to your youth and say, OK, here's 00:44:49.565 --> 00:44:50.440 align:middle line:90% what I'm going to do. 00:44:50.440 --> 00:44:53.220 align:middle line:84% I'm going to have the three-firm Hotelling model. 00:44:53.220 --> 00:44:58.560 align:middle line:84% And I have Firm 1 here, Firm 2 here, Firm 3 here. 00:44:58.560 --> 00:45:01.290 align:middle line:84% And there's going to be this set of consumers 00:45:01.290 --> 00:45:03.540 align:middle line:84% who are indifferent between Firm 1 and Firm 2 00:45:03.540 --> 00:45:06.300 align:middle line:84% based on their prices and a set of firms 00:45:06.300 --> 00:45:11.070 align:middle line:84% indifferent between Firm 1 and 3 based on their prices 00:45:11.070 --> 00:45:16.030 align:middle line:84% and a set of firms indifferent between Firm 1 and 2 00:45:16.030 --> 00:45:19.150 align:middle line:90% based on their prices. 00:45:19.150 --> 00:45:22.000 align:middle line:84% I think that has to go through the same point. 00:45:22.000 --> 00:45:24.603 align:middle line:84% And so we're going to get these three different regions. 00:45:24.603 --> 00:45:27.110 align:middle line:90% 00:45:27.110 --> 00:45:31.940 align:middle line:84% So in equilibrium, these guys buy from 1. 00:45:31.940 --> 00:45:34.730 align:middle line:90% These guys buy from 2. 00:45:34.730 --> 00:45:37.268 align:middle line:90% And these guys buy from Firm 3. 00:45:37.268 --> 00:45:39.560 align:middle line:84% I'm going to use everything I remember from high school 00:45:39.560 --> 00:45:41.390 align:middle line:84% geometry to figure out the areas of those things 00:45:41.390 --> 00:45:42.765 align:middle line:84% and how the areas of those things 00:45:42.765 --> 00:45:45.150 align:middle line:84% are functions of P1 and P2 and P3. 00:45:45.150 --> 00:45:48.170 align:middle line:84% And then, when I get to 4, I'm going to make it a tetrahedron. 00:45:48.170 --> 00:45:50.520 align:middle line:84% And I'm going to draw all the volumes of those things. 00:45:50.520 --> 00:45:54.350 align:middle line:84% But it quickly becomes just an intractable mess 00:45:54.350 --> 00:45:55.590 align:middle line:90% with lots of corners. 00:45:55.590 --> 00:45:58.680 align:middle line:84% And you also think, why were we doing this in the first place? 00:45:58.680 --> 00:46:01.010 align:middle line:84% It wasn't like we felt that people were uniformly-- 00:46:01.010 --> 00:46:03.390 align:middle line:84% uniformly distributed on the beach seemed OK. 00:46:03.390 --> 00:46:08.780 align:middle line:84% Once you get between competition between Google and Samsung 00:46:08.780 --> 00:46:12.320 align:middle line:84% and Apple to sell modern phones, is it 00:46:12.320 --> 00:46:14.430 align:middle line:90% really uniform on a triangle? 00:46:14.430 --> 00:46:16.280 align:middle line:90% Why do we believe that anyway? 00:46:16.280 --> 00:46:17.780 align:middle line:84% So what people do instead is they've 00:46:17.780 --> 00:46:21.950 align:middle line:84% switched to this kind of utility spectrum, where 00:46:21.950 --> 00:46:24.680 align:middle line:84% in some sense what Hotelling was trying to do 00:46:24.680 --> 00:46:28.470 align:middle line:84% was fit two firms into a one-dimensional space. 00:46:28.470 --> 00:46:30.840 align:middle line:84% And fitting two firms into a one-dimensional space 00:46:30.840 --> 00:46:33.690 align:middle line:84% was a great idea to make it more tractable. 00:46:33.690 --> 00:46:38.520 align:middle line:84% Fitting three firms into a two-dimensional space, 00:46:38.520 --> 00:46:39.820 align:middle line:90% it just gets awkward. 00:46:39.820 --> 00:46:42.720 align:middle line:84% And so the observation is, why not just stick with 00:46:42.720 --> 00:46:46.290 align:middle line:84% an n-dimensional space for n firms instead of an n minus 00:46:46.290 --> 00:46:48.550 align:middle line:90% 1-dimensional space for n firms? 00:46:48.550 --> 00:46:50.790 align:middle line:84% And so what people do is assume the utility that 00:46:50.790 --> 00:46:52.650 align:middle line:90% Firm I gets from by-- 00:46:52.650 --> 00:46:54.750 align:middle line:84% utility that consumer I gets buying 00:46:54.750 --> 00:47:00.420 align:middle line:84% from Firm J is vj, which is like the vertical quality of product 00:47:00.420 --> 00:47:06.240 align:middle line:84% j, minus alpha times pj, the price of Firm J, 00:47:06.240 --> 00:47:08.040 align:middle line:90% plus epsilon ij. 00:47:08.040 --> 00:47:11.760 align:middle line:84% That's my uniform taste for how much I like iPhones 00:47:11.760 --> 00:47:13.950 align:middle line:84% or how much I like Samsung phones 00:47:13.950 --> 00:47:19.020 align:middle line:84% or how much I like Google Pixel phones, OK? 00:47:19.020 --> 00:47:21.270 align:middle line:84% And then people typically also actually with n firms 00:47:21.270 --> 00:47:24.420 align:middle line:84% will now typically go to n plus 1 dimensional uncertainty. 00:47:24.420 --> 00:47:26.250 align:middle line:84% And they'll add epsilon i0, which 00:47:26.250 --> 00:47:28.800 align:middle line:84% is how much do I like the outside good of not purchasing 00:47:28.800 --> 00:47:29.740 align:middle line:90% anything? 00:47:29.740 --> 00:47:32.940 align:middle line:84% So that could be how much sentimental value 00:47:32.940 --> 00:47:36.007 align:middle line:84% do I have for my current phone, which is often 00:47:36.007 --> 00:47:38.340 align:middle line:84% the outside good is just not buying anything and keeping 00:47:38.340 --> 00:47:40.290 align:middle line:90% the phone that I've already got. 00:47:40.290 --> 00:47:44.498 align:middle line:84% And people can have different-- so in some sense, 00:47:44.498 --> 00:47:47.040 align:middle line:84% in that phone example, I've got a four-dimensional preference 00:47:47.040 --> 00:47:47.410 align:middle line:90% space. 00:47:47.410 --> 00:47:48.790 align:middle line:90% How much do I like new iphones? 00:47:48.790 --> 00:47:50.710 align:middle line:84% How much do I like new Samsung phones? 00:47:50.710 --> 00:47:52.440 align:middle line:84% How much do I like new Pixel phones? 00:47:52.440 --> 00:47:54.090 align:middle line:84% And how much do I like the old phone 00:47:54.090 --> 00:47:55.740 align:middle line:90% that's already in my pocket? 00:47:55.740 --> 00:47:58.573 align:middle line:84% And people can have different views about these things, 00:47:58.573 --> 00:48:00.990 align:middle line:84% both for taste-based reasons and like the one in my pocket 00:48:00.990 --> 00:48:06.530 align:middle line:84% is broken or not broken or whatever condition it's in, OK? 00:48:06.530 --> 00:48:08.600 align:middle line:84% Demand in this model in general case is just 00:48:08.600 --> 00:48:11.510 align:middle line:84% an n-plus-1-dimensional integral to figure out. 00:48:11.510 --> 00:48:14.900 align:middle line:84% The demand for product j, when these are the prices, 00:48:14.900 --> 00:48:18.780 align:middle line:84% I just integrate over that n-plus-1-dimensional space. 00:48:18.780 --> 00:48:23.210 align:middle line:84% It's just the integral over the subset of that space, where 00:48:23.210 --> 00:48:26.090 align:middle line:84% product j gives higher utility than product 00:48:26.090 --> 00:48:28.440 align:middle line:90% k for all k different from j. 00:48:28.440 --> 00:48:30.770 align:middle line:84% And I'm just integrating the density 00:48:30.770 --> 00:48:33.540 align:middle line:84% of the joint distribution of types over that region. 00:48:33.540 --> 00:48:38.180 align:middle line:84% So it's like here I'm integrating the density of types 00:48:38.180 --> 00:48:41.190 align:middle line:84% to find demand for good 1 in this two-dimensional space. 00:48:41.190 --> 00:48:44.870 align:middle line:84% I just integrate the density over this particular region 00:48:44.870 --> 00:48:45.900 align:middle line:90% of space. 00:48:45.900 --> 00:48:49.640 align:middle line:84% And so I'm still integrating over these regions of space 00:48:49.640 --> 00:48:52.610 align:middle line:90% that look kind of like that. 00:48:52.610 --> 00:48:54.928 align:middle line:84% Actually, the two-dimensional model here-- 00:48:54.928 --> 00:48:56.720 align:middle line:84% let me do two products and no outside good. 00:48:56.720 --> 00:49:02.900 align:middle line:84% It would just be like I've got epsilon i1 on this axis, epsilon 00:49:02.900 --> 00:49:05.270 align:middle line:90% i2 on this axis. 00:49:05.270 --> 00:49:07.890 align:middle line:90% And I would just be this region. 00:49:07.890 --> 00:49:10.910 align:middle line:90% So these people buy from good 1. 00:49:10.910 --> 00:49:13.110 align:middle line:90% These people buy good 2. 00:49:13.110 --> 00:49:16.370 align:middle line:84% It's just entirely is epsilon i2 greater than epsilon i1? 00:49:16.370 --> 00:49:18.500 align:middle line:84% So it's an easier integral to do, typically, 00:49:18.500 --> 00:49:20.780 align:middle line:84% than those ones with the things stuck into a lower 00:49:20.780 --> 00:49:25.040 align:middle line:84% dimensional space because you're just integrating over quadrants 00:49:25.040 --> 00:49:25.990 align:middle line:90% or half spaces. 00:49:25.990 --> 00:49:34.753 align:middle line:90% 00:49:34.753 --> 00:49:37.170 align:middle line:84% Sometimes, in empirical papers, if people want to do this, 00:49:37.170 --> 00:49:40.172 align:middle line:84% they're just simulating a bunch of-- drawing a bunch of epsilons 00:49:40.172 --> 00:49:41.880 align:middle line:84% at random, figuring out how many of those 00:49:41.880 --> 00:49:43.530 align:middle line:90% consumers buy each product. 00:49:43.530 --> 00:49:45.965 align:middle line:84% That's how you do this, practically speaking. 00:49:45.965 --> 00:49:48.480 align:middle line:90% 00:49:48.480 --> 00:49:52.140 align:middle line:84% This model is tractable in the special case. 00:49:52.140 --> 00:49:56.370 align:middle line:84% When there's no outside goods, the v's are all equal, 00:49:56.370 --> 00:49:58.230 align:middle line:90% and the epsilons are i.i.d. 00:49:58.230 --> 00:50:00.240 align:middle line:90% with some density f. 00:50:00.240 --> 00:50:06.220 align:middle line:84% In general, you're trying to solve a game, an n player game, 00:50:06.220 --> 00:50:09.510 align:middle line:84% you have to solve an n equations and n unknowns problem. 00:50:09.510 --> 00:50:13.020 align:middle line:84% But if you have looking for a symmetric equilibrium, 00:50:13.020 --> 00:50:15.210 align:middle line:84% then you're back to a one equation 00:50:15.210 --> 00:50:16.642 align:middle line:90% and one unknown problem. 00:50:16.642 --> 00:50:18.600 align:middle line:84% Because you have a one unknown equation and one 00:50:18.600 --> 00:50:20.725 align:middle line:84% unknown problem, I'm just trying to max-- you know, 00:50:20.725 --> 00:50:24.780 align:middle line:84% I'm solving the fact that when is there 00:50:24.780 --> 00:50:27.000 align:middle line:84% an equilibrium of a symmetric model 00:50:27.000 --> 00:50:31.410 align:middle line:84% where all the firms set price p star. 00:50:31.410 --> 00:50:39.180 align:middle line:84% That's going to be if p star belongs to the arg max over p 00:50:39.180 --> 00:50:49.350 align:middle line:84% of profit of Firm J when it sets price pj and the other firms 00:50:49.350 --> 00:50:50.435 align:middle line:90% set price p star. 00:50:50.435 --> 00:50:54.100 align:middle line:90% 00:50:54.100 --> 00:50:56.120 align:middle line:84% So, sorry, if I make it symmetric 00:50:56.120 --> 00:50:59.240 align:middle line:84% so this profit doesn't depend on j, 00:50:59.240 --> 00:51:01.990 align:middle line:84% this is just one equation in one unknown 00:51:01.990 --> 00:51:03.720 align:middle line:90% that lets me find p star. 00:51:03.720 --> 00:51:06.910 align:middle line:84% It's just each firm is maximizing its profit, 00:51:06.910 --> 00:51:09.520 align:middle line:84% holding everybody else's profits at p star. 00:51:09.520 --> 00:51:15.520 align:middle line:84% And so, where asymmetric models are an n equation problem, 00:51:15.520 --> 00:51:17.220 align:middle line:90% one equation-- 00:51:17.220 --> 00:51:18.790 align:middle line:84% symmetric equilibria you can often 00:51:18.790 --> 00:51:21.080 align:middle line:84% find by just solving one equation and one unknown. 00:51:21.080 --> 00:51:24.790 align:middle line:84% And so people often do that to give insights. 00:51:24.790 --> 00:51:26.560 align:middle line:90% So let's look at what is the-- 00:51:26.560 --> 00:51:32.740 align:middle line:84% and obviously, the pi of pj comma p star 00:51:32.740 --> 00:51:47.070 align:middle line:84% is going to be xj of pj comma p star times pj minus c. 00:51:47.070 --> 00:51:52.460 align:middle line:84% So your demand is just price minus cost times demand, 00:51:52.460 --> 00:51:54.890 align:middle line:84% like it was in all the other models. 00:51:54.890 --> 00:51:57.355 align:middle line:90% OK, what does demand look like? 00:51:57.355 --> 00:52:00.450 align:middle line:90% 00:52:00.450 --> 00:52:04.050 align:middle line:84% So if I'm thinking about every other firm is charging 00:52:04.050 --> 00:52:06.780 align:middle line:84% price p or p star and I'm considering 00:52:06.780 --> 00:52:13.240 align:middle line:84% charging my price pj, when is someone going to buy from me? 00:52:13.240 --> 00:52:18.200 align:middle line:84% They're going to buy from me if their preference for me-- 00:52:18.200 --> 00:52:23.750 align:middle line:84% so they're going to buy from me if epsilon ij is 00:52:23.750 --> 00:52:32.180 align:middle line:84% at least the maximum k different from j epsilon ik 00:52:32.180 --> 00:52:38.420 align:middle line:90% plus pj minus p star. 00:52:38.420 --> 00:52:40.940 align:middle line:84% If everyone else is charging p star 00:52:40.940 --> 00:52:44.300 align:middle line:84% and I charge pj, which is greater than p star, 00:52:44.300 --> 00:52:46.762 align:middle line:90% I have to be that much-- 00:52:46.762 --> 00:52:49.220 align:middle line:84% they have to have that much higher idiosyncratic preference 00:52:49.220 --> 00:52:52.280 align:middle line:84% for me than they have for anybody else. 00:52:52.280 --> 00:52:54.050 align:middle line:84% And if I charge a lower price, they 00:52:54.050 --> 00:52:55.760 align:middle line:84% can be this much lower than their best 00:52:55.760 --> 00:52:58.760 align:middle line:84% preference for everybody else and still buy from me. 00:52:58.760 --> 00:53:04.010 align:middle line:84% So what you get is the demand for me is this is-- 00:53:04.010 --> 00:53:06.440 align:middle line:90% let's suppose that there-- 00:53:06.440 --> 00:53:11.540 align:middle line:84% suppose that this, I'm going to call theta, their greatest 00:53:11.540 --> 00:53:14.960 align:middle line:84% utility they get from buying from any other firm or greatest 00:53:14.960 --> 00:53:17.900 align:middle line:84% idiosyncratic taste for any other firm, 00:53:17.900 --> 00:53:20.810 align:middle line:84% then they're going to buy from me-- 00:53:20.810 --> 00:53:23.690 align:middle line:84% this is the probability that their type is bigger 00:53:23.690 --> 00:53:26.840 align:middle line:90% than theta plus pj minus p. 00:53:26.840 --> 00:53:28.430 align:middle line:90% So that's a probability that-- 00:53:28.430 --> 00:53:30.830 align:middle line:84% this is the probability that epsilon ij 00:53:30.830 --> 00:53:34.220 align:middle line:90% is bigger than theta plus this. 00:53:34.220 --> 00:53:42.060 align:middle line:84% And then, this is the density of theta. 00:53:42.060 --> 00:53:43.456 align:middle line:90% So if you're choosing-- 00:53:43.456 --> 00:53:46.980 align:middle line:90% 00:53:46.980 --> 00:53:52.360 align:middle line:84% there are n other draws or n minus 1 other draws, 00:53:52.360 --> 00:53:56.110 align:middle line:84% there are n minus 1 draws from some distribution f, 00:53:56.110 --> 00:53:58.900 align:middle line:84% what's the probability that the largest of n minus 1 00:53:58.900 --> 00:54:05.200 align:middle line:84% draws from f is in some tiny interval theta plus d theta? 00:54:05.200 --> 00:54:07.540 align:middle line:84% And the probability that this is-- it's 00:54:07.540 --> 00:54:09.083 align:middle line:90% an order statistic calculation. 00:54:09.083 --> 00:54:11.500 align:middle line:84% I don't know if the order statistics have disappeared from 00:54:11.500 --> 00:54:12.550 align:middle line:90% [14.]380. 00:54:12.550 --> 00:54:17.980 align:middle line:84% But so, the density of the highest of n draws-- 00:54:17.980 --> 00:54:21.580 align:middle line:84% so the probability that someone is in the highest of n minus 1 00:54:21.580 --> 00:54:25.120 align:middle line:84% draws in that interval is you pick some firm 00:54:25.120 --> 00:54:27.810 align:middle line:90% to be the highest, their value-- 00:54:27.810 --> 00:54:31.090 align:middle line:84% the epsilon for them has to be in this interval, which 00:54:31.090 --> 00:54:33.610 align:middle line:84% happens with probability f of theta 00:54:33.610 --> 00:54:37.570 align:middle line:84% and all other epsilons have to be less than that theta, which 00:54:37.570 --> 00:54:40.600 align:middle line:84% happens with probability capital F of theta to the n minus 2. 00:54:40.600 --> 00:54:43.060 align:middle line:84% So this is the density for the highest 00:54:43.060 --> 00:54:45.650 align:middle line:90% of the n minus 1 rival draws. 00:54:45.650 --> 00:54:53.228 align:middle line:84% But so anyway, that's what my demand looks like, OK? 00:54:53.228 --> 00:54:55.270 align:middle line:84% If this is what my demand looks like, then again, 00:54:55.270 --> 00:54:57.270 align:middle line:84% I'm just going to have the first-order condition 00:54:57.270 --> 00:55:00.810 align:middle line:90% that I'm going to have to have. 00:55:00.810 --> 00:55:06.850 align:middle line:84% p star satisfies the first-order condition 00:55:06.850 --> 00:55:16.693 align:middle line:84% d pi j, dpj evaluated at pj equals p star equals 0. 00:55:16.693 --> 00:55:18.610 align:middle line:84% And so I'm going to get first-order condition. 00:55:18.610 --> 00:55:19.985 align:middle line:84% The first-order condition is just 00:55:19.985 --> 00:55:25.985 align:middle line:84% going to look like pj minus c times dxj dpj plus xj equals 0. 00:55:25.985 --> 00:55:29.280 align:middle line:90% 00:55:29.280 --> 00:55:31.240 align:middle line:84% And so it turns out you can just-- 00:55:31.240 --> 00:55:32.910 align:middle line:90% maybe I should do that right. 00:55:32.910 --> 00:55:35.430 align:middle line:84% Again, so I have this first-order condition. 00:55:35.430 --> 00:55:41.210 align:middle line:84% It's going to look like p star minus c 00:55:41.210 --> 00:55:54.310 align:middle line:84% times dxj dpj evaluated at p star plus xj of p star equals 0. 00:55:54.310 --> 00:55:56.080 align:middle line:84% So that's what the first-order condition 00:55:56.080 --> 00:55:59.590 align:middle line:84% is going to look like, as it has always looked in this class. 00:55:59.590 --> 00:56:03.580 align:middle line:84% And then the xj of p star is going 00:56:03.580 --> 00:56:08.140 align:middle line:84% to be 1 over n in equilibrium with n symmetric firms. 00:56:08.140 --> 00:56:14.350 align:middle line:84% So you just get p star minus c is just equal to minus 1 00:56:14.350 --> 00:56:17.710 align:middle line:90% over n dxj dpj. 00:56:17.710 --> 00:56:21.760 align:middle line:90% 00:56:21.760 --> 00:56:23.920 align:middle line:84% One other thing I meant to mention before 00:56:23.920 --> 00:56:30.220 align:middle line:84% is look at this utility function, v minus alpha times p 00:56:30.220 --> 00:56:31.640 align:middle line:90% plus epsilon. 00:56:31.640 --> 00:56:35.980 align:middle line:84% Utilities are only defined up to an affine transformation. 00:56:35.980 --> 00:56:38.860 align:middle line:84% I think probably hear that in [14.]121 a lot. 00:56:38.860 --> 00:56:45.640 align:middle line:84% So you can also think of this as like v over alpha minus p plus 1 00:56:45.640 --> 00:56:49.120 align:middle line:90% over alpha times epsilon ij. 00:56:49.120 --> 00:56:53.470 align:middle line:84% So this model, when people put in a price coefficient alpha, 00:56:53.470 --> 00:56:57.340 align:middle line:84% is a lot like the Hotelling model, where one puts 1 00:56:57.340 --> 00:57:01.490 align:middle line:84% over alpha where the t used to be because 1 over alpha 00:57:01.490 --> 00:57:06.050 align:middle line:84% is like the size of the transportation cost, size 00:57:06.050 --> 00:57:08.810 align:middle line:84% of the heterogeneity relative to having a unit 00:57:08.810 --> 00:57:10.610 align:middle line:90% coefficient on the price. 00:57:10.610 --> 00:57:14.360 align:middle line:84% So when people do empirical IO, they always put an alpha here. 00:57:14.360 --> 00:57:16.850 align:middle line:84% But you can think of it as fixing this as 1 00:57:16.850 --> 00:57:21.140 align:middle line:84% and putting 1 over alpha in front of the epsilons. 00:57:21.140 --> 00:57:25.580 align:middle line:84% So anyway, so what do you get as the markup when you do this? 00:57:25.580 --> 00:57:28.590 align:middle line:84% What you get as a markup is price. 00:57:28.590 --> 00:57:35.410 align:middle line:84% So this is price equals cost plus negative 1 00:57:35.410 --> 00:57:37.790 align:middle line:90% over n 1 over dxj dpj. 00:57:37.790 --> 00:57:40.540 align:middle line:90% 00:57:40.540 --> 00:57:42.850 align:middle line:84% So anyway, the equilibrium formula 00:57:42.850 --> 00:57:47.770 align:middle line:84% is price equals c plus t times something. 00:57:47.770 --> 00:57:52.540 align:middle line:84% So it's c plus t times 1 over m of n, and the 1 over m of n 00:57:52.540 --> 00:57:54.646 align:middle line:84% is just what you get differentiating-- 00:57:54.646 --> 00:57:58.790 align:middle line:90% 00:57:58.790 --> 00:58:00.680 align:middle line:84% m of n is like what you get differentiating 00:58:00.680 --> 00:58:02.480 align:middle line:90% this thing with respect to pj. 00:58:02.480 --> 00:58:05.120 align:middle line:90% 00:58:05.120 --> 00:58:08.210 align:middle line:84% And you can see it's got things like f to the n minus 2 00:58:08.210 --> 00:58:11.340 align:middle line:90% and F and n's in it and stuff. 00:58:11.340 --> 00:58:13.110 align:middle line:84% But anyway, if you do the calculation, 00:58:13.110 --> 00:58:15.750 align:middle line:84% you differentiate on the integral sign, 00:58:15.750 --> 00:58:17.170 align:middle line:90% this is what you get. 00:58:17.170 --> 00:58:22.440 align:middle line:84% So price equals c plus 1 over m of n times 1 over alpha, where 00:58:22.440 --> 00:58:28.290 align:middle line:84% m of n depends on the assumed density of the distribution 00:58:28.290 --> 00:58:31.370 align:middle line:90% of the epsilons, OK? 00:58:31.370 --> 00:58:32.766 align:middle line:90% So some corollaries. 00:58:32.766 --> 00:58:35.650 align:middle line:90% 00:58:35.650 --> 00:58:37.930 align:middle line:90% Suppose F is uniform 0, 1. 00:58:37.930 --> 00:58:43.240 align:middle line:84% So certainly, Hotelling could have done, instead of the beach, 00:58:43.240 --> 00:58:45.790 align:middle line:84% he could have done the people living on a square, 00:58:45.790 --> 00:58:49.510 align:middle line:84% where this was utility epsilon i1. 00:58:49.510 --> 00:58:52.930 align:middle line:90% This is epsilon i2, OK? 00:58:52.930 --> 00:58:56.320 align:middle line:84% It turns out that if Hotelling had done his model on a square, 00:58:56.320 --> 00:59:00.370 align:middle line:84% he would have found the neat result that price equals c plus 00:59:00.370 --> 00:59:01.602 align:middle line:90% 1/2t. 00:59:01.602 --> 00:59:04.060 align:middle line:84% He would have gotten exactly the same thing except with 1/2 00:59:04.060 --> 00:59:06.040 align:middle line:90% in it. 00:59:06.040 --> 00:59:08.020 align:middle line:84% So with the linear model, you can 00:59:08.020 --> 00:59:11.080 align:middle line:84% extend this to people living on a hypercube-- or cube 00:59:11.080 --> 00:59:12.830 align:middle line:90% or a hypercube or whatever. 00:59:12.830 --> 00:59:15.590 align:middle line:84% And the formula is exactly correct, 00:59:15.590 --> 00:59:19.100 align:middle line:84% that price equals c plus 1 over n times t. 00:59:19.100 --> 00:59:21.760 align:middle line:84% So the thing that everyone loved about Cournot 00:59:21.760 --> 00:59:27.130 align:middle line:84% is true of this hypercube model of product differentiation. 00:59:27.130 --> 00:59:30.850 align:middle line:84% Price is just c plus t, where t is the length 00:59:30.850 --> 00:59:31.880 align:middle line:90% of a side of the cube. 00:59:31.880 --> 00:59:33.850 align:middle line:84% How intense is your preference for Coke 00:59:33.850 --> 00:59:36.450 align:middle line:90% versus non-Coke or whatever? 00:59:36.450 --> 00:59:40.310 align:middle line:84% And things decline like 1 over n if there 00:59:40.310 --> 00:59:41.440 align:middle line:90% are n firms in the model. 00:59:41.440 --> 00:59:45.720 align:middle line:90% 00:59:45.720 --> 00:59:47.460 align:middle line:84% What can we say more generally going 00:59:47.460 --> 00:59:50.010 align:middle line:84% outside the uniform distribution? 00:59:50.010 --> 00:59:53.450 align:middle line:84% Suppose that uniform distribution is bounded above. 00:59:53.450 --> 00:59:55.980 align:middle line:84% Suppose that the epsilon is bounded above 00:59:55.980 --> 00:59:57.960 align:middle line:90% or that the tails are thin. 00:59:57.960 --> 01:00:00.240 align:middle line:84% Tails are thin like the normal distribution 01:00:00.240 --> 01:00:02.310 align:middle line:84% in this sense of limit as epsilon 01:00:02.310 --> 01:00:07.020 align:middle line:84% goes to infinity F prime over F goes to negative infinity. 01:00:07.020 --> 01:00:12.350 align:middle line:84% Then, as the number of firms goes up, prices drop to cost. 01:00:12.350 --> 01:00:15.420 align:middle line:84% So if we take bounded distributions 01:00:15.420 --> 01:00:18.540 align:middle line:84% or we take distributions that are not bounded but have 01:00:18.540 --> 01:00:21.210 align:middle line:84% very thin tails, then you do get the result 01:00:21.210 --> 01:00:24.630 align:middle line:84% that competition drives prices to 0. 01:00:24.630 --> 01:00:26.890 align:middle line:84% Does that happen for all distributions? 01:00:26.890 --> 01:00:28.270 align:middle line:90% The answer is no. 01:00:28.270 --> 01:00:30.900 align:middle line:84% Most important example where that doesn't happen 01:00:30.900 --> 01:00:33.210 align:middle line:84% is the logit error distribution, which people 01:00:33.210 --> 01:00:36.310 align:middle line:84% often assume because it makes algebra easier. 01:00:36.310 --> 01:00:38.590 align:middle line:84% But it turns out for the logit model-- 01:00:38.590 --> 01:00:42.690 align:middle line:84% so this is the logit cdf, where gamma 01:00:42.690 --> 01:00:46.520 align:middle line:84% is the Euler-Mascheroni constant, like 0.577. 01:00:46.520 --> 01:00:49.600 align:middle line:84% So in the logit model, what you actually get 01:00:49.600 --> 01:00:55.480 align:middle line:84% is price equals cost plus some constant times 1 01:00:55.480 --> 01:00:59.050 align:middle line:84% plus 1 over n minus 1 times 1 over alpha. 01:00:59.050 --> 01:01:08.210 align:middle line:84% So as n goes to infinity, p star is going to c plus 1 over alpha. 01:01:08.210 --> 01:01:11.085 align:middle line:90% So in the logit model, prices-- 01:01:11.085 --> 01:01:11.960 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:01:11.960 --> 01:01:13.642 align:middle line:90% GLENN ELLISON: What? 01:01:13.642 --> 01:01:14.600 align:middle line:90% AUDIENCE: k over alpha? 01:01:14.600 --> 01:01:16.142 align:middle line:84% GLENN ELLISON: Oh, yes, k over alpha. 01:01:16.142 --> 01:01:21.165 align:middle line:90% Thank you, where k is some-- 01:01:21.165 --> 01:01:22.040 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:01:22.040 --> 01:01:22.940 align:middle line:90% GLENN ELLISON: k, it's-- 01:01:22.940 --> 01:01:23.195 align:middle line:90% AUDIENCE: It's some arbitrary-- 01:01:23.195 --> 01:01:24.612 align:middle line:84% GLENN ELLISON: It's some constant. 01:01:24.612 --> 01:01:25.790 align:middle line:90% I forget exactly. 01:01:25.790 --> 01:01:27.660 align:middle line:84% You can think of it as like 0.2378. 01:01:27.660 --> 01:01:30.300 align:middle line:84% I forget what the number is, but it's just a number. 01:01:30.300 --> 01:01:31.040 align:middle line:90% [LAUGHTER] 01:01:31.040 --> 01:01:35.900 align:middle line:84% So in the logit model, you can compute what it is. 01:01:35.900 --> 01:01:39.020 align:middle line:90% Prices are just like c plus-- 01:01:39.020 --> 01:01:40.740 align:middle line:84% as the number of firms goes to infinity, 01:01:40.740 --> 01:01:44.210 align:middle line:84% competition doesn't eliminate markups. 01:01:44.210 --> 01:01:47.240 align:middle line:90% And how is this plausible? 01:01:47.240 --> 01:01:51.920 align:middle line:84% The idea is that these models have a somewhat unreasonable 01:01:51.920 --> 01:01:57.500 align:middle line:84% assumption that I snuck over on you, which was that, 01:01:57.500 --> 01:01:59.840 align:middle line:84% as I said, in two dimensions, it's 01:01:59.840 --> 01:02:03.917 align:middle line:84% like, how much do I like iphones versus do I like Samsung phones? 01:02:03.917 --> 01:02:05.750 align:middle line:84% It seems like, OK, it's reasonable to assume 01:02:05.750 --> 01:02:07.917 align:middle line:84% there are people with those two separate differences 01:02:07.917 --> 01:02:08.660 align:middle line:90% of preferences. 01:02:08.660 --> 01:02:11.720 align:middle line:84% But what I snuck over on you is that-- 01:02:11.720 --> 01:02:14.870 align:middle line:84% here I said it-- epsilons are i.i.d., independent 01:02:14.870 --> 01:02:16.520 align:middle line:90% and identically distributed. 01:02:16.520 --> 01:02:20.030 align:middle line:84% The more products you have, it gets harder and harder 01:02:20.030 --> 01:02:23.330 align:middle line:84% to say it's really plausible that my taste for a BMW 01:02:23.330 --> 01:02:25.970 align:middle line:84% and a Mercedes and a whatever are all completely 01:02:25.970 --> 01:02:27.650 align:middle line:90% independent of each other. 01:02:27.650 --> 01:02:29.480 align:middle line:84% As the number of firms gets large, 01:02:29.480 --> 01:02:31.500 align:middle line:84% the products get awfully similar to each other. 01:02:31.500 --> 01:02:34.100 align:middle line:84% So if you're a person who likes Mercedes styling, 01:02:34.100 --> 01:02:36.230 align:middle line:84% you probably also like BMW styling. 01:02:36.230 --> 01:02:40.010 align:middle line:84% And if you're one who likes Toyota Lexus styling, 01:02:40.010 --> 01:02:43.800 align:middle line:84% maybe you also like Acura styling, or whatever. 01:02:43.800 --> 01:02:46.640 align:middle line:84% So, in some sense, what the logit model is assuming, 01:02:46.640 --> 01:02:49.250 align:middle line:84% if you assume we keep having this-- every new product has 01:02:49.250 --> 01:02:53.810 align:middle line:84% this completely new idiosyncratic reaction to it, 01:02:53.810 --> 01:02:55.800 align:middle line:84% suppose there are a million products out there 01:02:55.800 --> 01:02:57.330 align:middle line:84% and you tell me, OK, yeah, you're 01:02:57.330 --> 01:02:59.400 align:middle line:84% one of a million products in the market. 01:02:59.400 --> 01:03:01.680 align:middle line:84% But this person likes your product better 01:03:01.680 --> 01:03:03.850 align:middle line:90% than every other product. 01:03:03.850 --> 01:03:05.620 align:middle line:90% Well, to think about-- 01:03:05.620 --> 01:03:08.470 align:middle line:84% the markups depend on what this dxj dpj. 01:03:08.470 --> 01:03:12.112 align:middle line:84% What do I conclude when I've just 01:03:12.112 --> 01:03:13.570 align:middle line:84% been told they like my product more 01:03:13.570 --> 01:03:15.200 align:middle line:90% than everybody else's product? 01:03:15.200 --> 01:03:16.040 align:middle line:90% I'm like, wow. 01:03:16.040 --> 01:03:18.190 align:middle line:90% They like my product a lot, OK? 01:03:18.190 --> 01:03:24.850 align:middle line:84% Now, in the hypercube model, if the epsilon ij 01:03:24.850 --> 01:03:29.940 align:middle line:84% is distributed uniform 0, 1, I'm like, 01:03:29.940 --> 01:03:31.690 align:middle line:84% they like me best out of a million things. 01:03:31.690 --> 01:03:32.800 align:middle line:90% It must be my-- 01:03:32.800 --> 01:03:37.480 align:middle line:84% utility for me is like 0.999999 something or other, 01:03:37.480 --> 01:03:39.280 align:middle line:84% or they wouldn't have been buying from me. 01:03:39.280 --> 01:03:41.020 align:middle line:84% But while they like me this much, 01:03:41.020 --> 01:03:46.400 align:middle line:84% there's also somebody else who they like 0.999998 or something. 01:03:46.400 --> 01:03:48.340 align:middle line:84% And so I think the amount by which 01:03:48.340 --> 01:03:51.530 align:middle line:84% they like my product over anybody else's product is tiny. 01:03:51.530 --> 01:03:54.550 align:middle line:84% Therefore, my demand is very price sensitive. 01:03:54.550 --> 01:03:57.760 align:middle line:84% And if I don't price really low, they're going to switch. 01:03:57.760 --> 01:04:00.440 align:middle line:84% So I have this incredibly price-sensitive demand. 01:04:00.440 --> 01:04:02.357 align:middle line:90% But if you have a-- 01:04:02.357 --> 01:04:03.190 align:middle line:90% maybe you know this. 01:04:03.190 --> 01:04:06.190 align:middle line:84% If you have an exponential distribution 01:04:06.190 --> 01:04:09.470 align:middle line:84% and you're told that you're the largest of n exponentials, 01:04:09.470 --> 01:04:12.400 align:middle line:84% how far are you above the next highest draw? 01:04:12.400 --> 01:04:13.600 align:middle line:90% The answer is 1. 01:04:13.600 --> 01:04:15.940 align:middle line:84% That's a property of the exponential distribution, 01:04:15.940 --> 01:04:18.370 align:middle line:84% that if you're the highest of n draws 01:04:18.370 --> 01:04:23.350 align:middle line:84% from a standard exponential, your posterior for their value 01:04:23.350 --> 01:04:24.280 align:middle line:90% for you is n. 01:04:24.280 --> 01:04:25.780 align:middle line:84% And your posterior for the product-- 01:04:25.780 --> 01:04:27.280 align:middle line:84% their value for the next highest one 01:04:27.280 --> 01:04:29.550 align:middle line:90% has high expectation n minus 1. 01:04:29.550 --> 01:04:33.670 align:middle line:84% So you think you have one of space 01:04:33.670 --> 01:04:35.950 align:middle line:90% to price relative to your rival. 01:04:35.950 --> 01:04:38.200 align:middle line:84% And so with an exponential distribution, we actually-- 01:04:38.200 --> 01:04:39.640 align:middle line:90% you get-- 01:04:39.640 --> 01:04:42.490 align:middle line:84% exponential distribution, you're going to get like p star 01:04:42.490 --> 01:04:45.430 align:middle line:84% equals c plus t doesn't depend on n at all. 01:04:45.430 --> 01:04:47.800 align:middle line:84% The more exponential draws that are out there, 01:04:47.800 --> 01:04:49.180 align:middle line:84% they're just, yeah, they probably 01:04:49.180 --> 01:04:51.460 align:middle line:84% like me a lot more than somebody else. 01:04:51.460 --> 01:04:52.610 align:middle line:90% They like me a million. 01:04:52.610 --> 01:04:55.810 align:middle line:90% They like the next guy 999,999. 01:04:55.810 --> 01:04:58.060 align:middle line:84% Logit isn't quite like the exponential, 01:04:58.060 --> 01:05:01.150 align:middle line:84% but it turns out to be just very similar to the exponential 01:05:01.150 --> 01:05:03.910 align:middle line:90% and that approximately-- 01:05:03.910 --> 01:05:08.400 align:middle line:84% it ends up with an approximately constant markup. 01:05:08.400 --> 01:05:10.590 align:middle line:84% And then markup depends on what weight 01:05:10.590 --> 01:05:12.810 align:middle line:84% you stick in front of the epsilon ij 01:05:12.810 --> 01:05:14.960 align:middle line:84% in the logit model, the 1 over alpha. 01:05:14.960 --> 01:05:17.640 align:middle line:90% 01:05:17.640 --> 01:05:19.597 align:middle line:84% And there are distributions for which-- 01:05:19.597 --> 01:05:21.930 align:middle line:84% if you take a really fat-tailed distribution, one that's 01:05:21.930 --> 01:05:23.850 align:middle line:84% fatter tailed than the exponential, 01:05:23.850 --> 01:05:26.950 align:middle line:84% prices can go up as n goes to infinity. 01:05:26.950 --> 01:05:31.270 align:middle line:84% And I don't know that we think that's often realistic. 01:05:31.270 --> 01:05:34.000 align:middle line:84% Where do these-- you keep getting these independent tastes 01:05:34.000 --> 01:05:34.900 align:middle line:90% from? 01:05:34.900 --> 01:05:38.410 align:middle line:84% But in these models, it's there, and you 01:05:38.410 --> 01:05:40.690 align:middle line:90% should be aware of it, OK? 01:05:40.690 --> 01:05:43.340 align:middle line:90% 01:05:43.340 --> 01:05:45.060 align:middle line:90% Questions on that? 01:05:45.060 --> 01:05:47.800 align:middle line:84% So, OK, I think that's what I had to say. 01:05:47.800 --> 01:05:51.890 align:middle line:84% Yeah, so I think I'm going to skip this slide. 01:05:51.890 --> 01:05:54.230 align:middle line:84% One thing I wanted to say in this slide is 01:05:54.230 --> 01:05:56.330 align:middle line:84% suppose a student comes to me and says, 01:05:56.330 --> 01:05:58.430 align:middle line:84% I want to write a paper about mergers 01:05:58.430 --> 01:06:03.650 align:middle line:84% and the effect mergers are having on markups in industry x. 01:06:03.650 --> 01:06:07.350 align:middle line:84% This is a know-your-theory cautionary tale. 01:06:07.350 --> 01:06:10.070 align:middle line:84% If a student says, OK, I'm going to estimate logit demand 01:06:10.070 --> 01:06:12.560 align:middle line:84% in this model and see what's happened when you merge 01:06:12.560 --> 01:06:14.550 align:middle line:84% from five firms down to four firms 01:06:14.550 --> 01:06:18.025 align:middle line:84% if phone maker A buys phone maker B, or whatever. 01:06:18.025 --> 01:06:20.345 align:middle line:90% 01:06:20.345 --> 01:06:22.220 align:middle line:84% So you can estimate your logit model and say, 01:06:22.220 --> 01:06:23.887 align:middle line:84% I'm going to allow the price sensitivity 01:06:23.887 --> 01:06:30.092 align:middle line:84% to vary and have it be v minus alpha p plus epsilon ij utility. 01:06:30.092 --> 01:06:31.550 align:middle line:84% And I'm going to estimate the alpha 01:06:31.550 --> 01:06:33.720 align:middle line:84% and see how price sensitive things are. 01:06:33.720 --> 01:06:35.150 align:middle line:84% And then when I find out how price sensitive things are, 01:06:35.150 --> 01:06:36.608 align:middle line:84% see what the merger is going to do. 01:06:36.608 --> 01:06:39.510 align:middle line:90% 01:06:39.510 --> 01:06:40.920 align:middle line:84% If you then use that model to say 01:06:40.920 --> 01:06:44.010 align:middle line:84% when you go from five to four firms, how do markups go up? 01:06:44.010 --> 01:06:46.980 align:middle line:84% The answer is markups go up by 1.067. 01:06:46.980 --> 01:06:51.990 align:middle line:84% With five symmetric firms, the markup is c plus k over thing 01:06:51.990 --> 01:06:53.230 align:middle line:90% times 5/4. 01:06:53.230 --> 01:06:58.300 align:middle line:84% When you go to four firms, it's c plus k over alpha times 4/3. 01:06:58.300 --> 01:07:01.410 align:middle line:84% So on the question of how do markups change when 01:07:01.410 --> 01:07:03.510 align:middle line:84% you go from four firms to three firms-- 01:07:03.510 --> 01:07:07.200 align:middle line:84% five firms to four firms, the answer 01:07:07.200 --> 01:07:09.873 align:middle line:84% is-- that question has an answer that's 01:07:09.873 --> 01:07:11.790 align:middle line:84% independent of all the parameters you estimate 01:07:11.790 --> 01:07:12.760 align:middle line:90% in the model. 01:07:12.760 --> 01:07:14.650 align:middle line:90% And the answer is just this. 01:07:14.650 --> 01:07:20.160 align:middle line:84% And so if you do want to estimate how mergers would 01:07:20.160 --> 01:07:24.420 align:middle line:84% affect markups in models with horizontal differentiation, 01:07:24.420 --> 01:07:30.340 align:middle line:84% you have to make sure you're correctly estimating this object 01:07:30.340 --> 01:07:34.470 align:middle line:90% dxj dpi versus dxi dpi. 01:07:34.470 --> 01:07:38.400 align:middle line:84% And the models, like the logit model, 01:07:38.400 --> 01:07:40.900 align:middle line:84% can have built-in assumptions about what those things are. 01:07:40.900 --> 01:07:42.960 align:middle line:84% And if these things both just have 01:07:42.960 --> 01:07:45.690 align:middle line:84% an alpha in them and those alphas cancel, 01:07:45.690 --> 01:07:47.790 align:middle line:84% you're not actually estimating what 01:07:47.790 --> 01:07:51.035 align:middle line:90% you think you're estimating. 01:07:51.035 --> 01:07:52.660 align:middle line:84% But I didn't want to take time on that. 01:07:52.660 --> 01:07:58.210 align:middle line:84% So going to more modern pictures, 01:07:58.210 --> 01:08:00.580 align:middle line:84% I stuck Jidong's picture on this slide. 01:08:00.580 --> 01:08:07.200 align:middle line:84% So discuss a recent paper discussing the effects 01:08:07.200 --> 01:08:10.080 align:middle line:90% of bundling on competition. 01:08:10.080 --> 01:08:16.890 align:middle line:84% So the motivation for this paper is 01:08:16.890 --> 01:08:21.569 align:middle line:84% there are many firms where there is this antitrust concern 01:08:21.569 --> 01:08:25.590 align:middle line:84% about firms bundling and selling their products together instead 01:08:25.590 --> 01:08:27.870 align:middle line:84% of selling their products separately. 01:08:27.870 --> 01:08:30.912 align:middle line:84% So firms, for instance, if you're-- 01:08:30.912 --> 01:08:32.620 align:middle line:84% maybe you think they don't really matter. 01:08:32.620 --> 01:08:37.590 align:middle line:84% But Apple is selling phones and they're selling earbuds. 01:08:37.590 --> 01:08:39.282 align:middle line:84% And you can think of, I can design 01:08:39.282 --> 01:08:41.490 align:middle line:84% the phones and the earbuds so they only work together 01:08:41.490 --> 01:08:43.120 align:middle line:84% and have to be bought as a bundle. 01:08:43.120 --> 01:08:46.540 align:middle line:84% Or I can design the phones and earbuds so they work separately. 01:08:46.540 --> 01:08:49.080 align:middle line:84% And I can be competing with Samsung separately 01:08:49.080 --> 01:08:52.200 align:middle line:84% in the phone market and separately in the earbud market. 01:08:52.200 --> 01:08:53.819 align:middle line:84% With operating systems, this often 01:08:53.819 --> 01:08:57.450 align:middle line:84% comes up as what features do I build into an operating system 01:08:57.450 --> 01:09:00.060 align:middle line:84% so that people have to buy the bundle of the operating 01:09:00.060 --> 01:09:02.460 align:middle line:84% system containing these 37 different components, all 01:09:02.460 --> 01:09:03.240 align:middle line:90% from me? 01:09:03.240 --> 01:09:05.490 align:middle line:84% Or do I allow plug-and-play compatibility 01:09:05.490 --> 01:09:09.200 align:middle line:84% so we have separate competition product by product? 01:09:09.200 --> 01:09:10.439 align:middle line:90% OK? 01:09:10.439 --> 01:09:14.490 align:middle line:84% OK, and so this is a potential antitrust remedy 01:09:14.490 --> 01:09:16.500 align:middle line:84% and industries with large market power 01:09:16.500 --> 01:09:20.100 align:middle line:84% is forcing them to be compatible and not 01:09:20.100 --> 01:09:23.580 align:middle line:84% use proprietary connectors or whatever 01:09:23.580 --> 01:09:25.090 align:middle line:90% to extend their monopolies. 01:09:25.090 --> 01:09:31.010 align:middle line:84% And so Joe's paper is about this question of, when will markups-- 01:09:31.010 --> 01:09:33.899 align:middle line:84% will bundling products together make markups higher? 01:09:33.899 --> 01:09:35.160 align:middle line:90% Will it make markups lower? 01:09:35.160 --> 01:09:37.790 align:middle line:84% How will it affect consumer utility? 01:09:37.790 --> 01:09:43.460 align:middle line:84% So in his model, you have these n firms, 01:09:43.460 --> 01:09:47.810 align:middle line:84% and the n firms all sell m distinct products. 01:09:47.810 --> 01:09:50.529 align:middle line:84% And he looks at utilities of the following form. 01:09:50.529 --> 01:09:56.120 align:middle line:84% You get utility v minus pjm plus epsilon ijm 01:09:56.120 --> 01:10:00.740 align:middle line:90% if you buy product j-- 01:10:00.740 --> 01:10:05.050 align:middle line:84% if you buy-- sorry-- product m from Firm J. 01:10:05.050 --> 01:10:08.910 align:middle line:84% And he compares two separate models. 01:10:08.910 --> 01:10:13.580 align:middle line:84% One model is where the firms compete separately 01:10:13.580 --> 01:10:15.810 align:middle line:90% in this whole matrix of prices. 01:10:15.810 --> 01:10:22.610 align:middle line:84% So Firm 1 sets prices p11, p12, up to p1m. 01:10:22.610 --> 01:10:27.200 align:middle line:84% And then Firm 2 sets prices p21 up to p2m. 01:10:27.200 --> 01:10:28.760 align:middle line:90% And then Firm 3-- 01:10:28.760 --> 01:10:32.330 align:middle line:84% I'll just have three firms-- post its bundle of prices p3m. 01:10:32.330 --> 01:10:36.680 align:middle line:84% He compares that to a bundled system where the firms just 01:10:36.680 --> 01:10:39.570 align:middle line:84% design their products to be all mutually incompatible. 01:10:39.570 --> 01:10:46.050 align:middle line:84% So Firm 1 just sets a price capital p1. 01:10:46.050 --> 01:10:48.390 align:middle line:84% Firm 2 sets of price, capital P2. 01:10:48.390 --> 01:10:51.580 align:middle line:84% And Firm 3 sets of price capital P3 for the bundle. 01:10:51.580 --> 01:10:54.537 align:middle line:84% So this is the bundle of getting all of these goods from me. 01:10:54.537 --> 01:10:57.120 align:middle line:84% This is the bundle of getting all of these things from Firm 2. 01:10:57.120 --> 01:10:58.620 align:middle line:84% And this is the bundle of getting all of these things 01:10:58.620 --> 01:10:59.770 align:middle line:90% from Firm 3. 01:10:59.770 --> 01:11:03.060 align:middle line:84% And he thinks about which results in greater consumer 01:11:03.060 --> 01:11:07.620 align:middle line:84% welfare and greater profits, having unbundled pricing 01:11:07.620 --> 01:11:09.125 align:middle line:90% or having bundled pricing? 01:11:09.125 --> 01:11:12.210 align:middle line:90% 01:11:12.210 --> 01:11:19.770 align:middle line:84% OK, first observation is when do consumers prefer buying bundle 1 01:11:19.770 --> 01:11:21.300 align:middle line:90% from bundle 2? 01:11:21.300 --> 01:11:25.960 align:middle line:84% Well, that's if m times v minus the price 01:11:25.960 --> 01:11:28.750 align:middle line:84% of the bundle plus the sum across all products 01:11:28.750 --> 01:11:31.600 align:middle line:84% within the bundle of epsilon ijm is 01:11:31.600 --> 01:11:35.980 align:middle line:84% better than buying mv minus the price of bundle k times 01:11:35.980 --> 01:11:39.940 align:middle line:84% the sum over all things in the bundle of epsilon ikm. 01:11:39.940 --> 01:11:42.850 align:middle line:84% And again, normalizing this by dividing 01:11:42.850 --> 01:11:44.560 align:middle line:90% by the number of firms-- 01:11:44.560 --> 01:11:46.900 align:middle line:90% so if I convert this to-- 01:11:46.900 --> 01:11:48.700 align:middle line:90% this is m products. 01:11:48.700 --> 01:11:52.515 align:middle line:84% So p1 over m I'm going to think of as the per product price. 01:11:52.515 --> 01:11:55.810 align:middle line:90% 01:11:55.810 --> 01:11:59.770 align:middle line:84% This is what's going to be equivalent to p11 or something. 01:11:59.770 --> 01:12:02.650 align:middle line:84% How much are we charging per product in the bundle? 01:12:02.650 --> 01:12:11.700 align:middle line:84% So I like this one better if and only if v minus 1 over mpj 01:12:11.700 --> 01:12:16.870 align:middle line:84% plus 1 over m the sum of epsilon ijm is bigger than this. 01:12:16.870 --> 01:12:20.890 align:middle line:84% So basically, bundling is like converting the model where 01:12:20.890 --> 01:12:29.960 align:middle line:84% you have utilities epsilon i1 up to epsilon n1 01:12:29.960 --> 01:12:35.950 align:middle line:84% into a model where you have 1 over m sum of epsilon i1 01:12:35.950 --> 01:12:40.250 align:middle line:84% and 1 over m sum of epsilon im, right? 01:12:40.250 --> 01:12:42.700 align:middle line:84% You're just basically comparing the model 01:12:42.700 --> 01:12:45.610 align:middle line:84% with utilities from the original-- 01:12:45.610 --> 01:12:47.890 align:middle line:84% random draws from the original distribution 01:12:47.890 --> 01:12:50.290 align:middle line:84% to the model with utilities that are random 01:12:50.290 --> 01:12:52.563 align:middle line:90% draws from this distribution. 01:12:52.563 --> 01:12:53.980 align:middle line:84% So that's what I do when I bundle, 01:12:53.980 --> 01:12:55.360 align:middle line:84% is I just change the distribution 01:12:55.360 --> 01:12:57.490 align:middle line:84% of idiosyncratic consumer preferences 01:12:57.490 --> 01:13:00.300 align:middle line:90% and make it an average of these. 01:13:00.300 --> 01:13:04.620 align:middle line:84% And obviously, the central limit theorem 01:13:04.620 --> 01:13:06.930 align:middle line:84% is going to tell us that as m goes to infinity, 01:13:06.930 --> 01:13:09.328 align:middle line:84% these things are going to have smaller-- 01:13:09.328 --> 01:13:11.370 align:middle line:84% this is going to have smaller variance than that. 01:13:11.370 --> 01:13:13.920 align:middle line:84% And it's going to look approximately normal as m goes 01:13:13.920 --> 01:13:16.830 align:middle line:84% to infinity, but normal with a smaller variance 01:13:16.830 --> 01:13:17.810 align:middle line:90% than the first one had. 01:13:17.810 --> 01:13:21.430 align:middle line:90% 01:13:21.430 --> 01:13:24.610 align:middle line:84% OK, so let's think about whether prices are higher. 01:13:24.610 --> 01:13:27.880 align:middle line:84% Again, same price, first-order condition I've 01:13:27.880 --> 01:13:29.330 align:middle line:90% done over and over again. 01:13:29.330 --> 01:13:32.500 align:middle line:84% So the first-order condition for price competition 01:13:32.500 --> 01:13:38.530 align:middle line:84% is pj minus c times minus dxj dpj equals xj. 01:13:38.530 --> 01:13:41.140 align:middle line:84% And again, if I'm looking for a symmetric equilibrium 01:13:41.140 --> 01:13:43.090 align:middle line:84% of this model, this is going to be 01:13:43.090 --> 01:13:48.825 align:middle line:84% p star minus c times minus dxj dpj equals 1 over n. 01:13:48.825 --> 01:13:51.860 align:middle line:90% 01:13:51.860 --> 01:13:55.970 align:middle line:90% And what is dxj dpj going to be? 01:13:55.970 --> 01:13:59.960 align:middle line:84% dxj dpj is just the density of consumers 01:13:59.960 --> 01:14:04.160 align:middle line:84% who have utility for me equal to the maximum 01:14:04.160 --> 01:14:07.243 align:middle line:84% of their idiosyncratic reaction to me 01:14:07.243 --> 01:14:09.410 align:middle line:84% equal to the maximum of their idiosyncratic reaction 01:14:09.410 --> 01:14:11.740 align:middle line:90% to everybody else. 01:14:11.740 --> 01:14:21.680 align:middle line:84% And so, fixing n, this first-order condition-- where-- 01:14:21.680 --> 01:14:23.900 align:middle line:84% I don't have it written down anymore. 01:14:23.900 --> 01:14:29.090 align:middle line:84% So my first-order condition was p star 01:14:29.090 --> 01:14:36.000 align:middle line:84% equals c minus 1 over n times 1 over dxj dpj. 01:14:36.000 --> 01:14:39.650 align:middle line:90% All right, let me do this, OK? 01:14:39.650 --> 01:14:41.510 align:middle line:84% That's what my first-order conditions always 01:14:41.510 --> 01:14:42.750 align:middle line:90% keep looking like. 01:14:42.750 --> 01:14:47.870 align:middle line:84% So equilibrium prices are low if this density is high. 01:14:47.870 --> 01:14:51.290 align:middle line:84% And equilibrium prices are high, if this density is low. 01:14:51.290 --> 01:14:54.260 align:middle line:84% So in this dxj dpj is the density 01:14:54.260 --> 01:14:58.930 align:middle line:84% of the set of consumers who have my epsilon just 01:14:58.930 --> 01:15:01.990 align:middle line:90% about everybody else's epsilon. 01:15:01.990 --> 01:15:05.710 align:middle line:84% Notice that the distribution of sum of the epsilons, 01:15:05.710 --> 01:15:07.390 align:middle line:84% it's more concentrated about its mean. 01:15:07.390 --> 01:15:08.550 align:middle line:90% It's thinner in the tails. 01:15:08.550 --> 01:15:15.150 align:middle line:90% 01:15:15.150 --> 01:15:17.580 align:middle line:84% OK, so consumer surplus in this model 01:15:17.580 --> 01:15:20.920 align:middle line:84% depends on two main welfare effects for consumers. 01:15:20.920 --> 01:15:22.510 align:middle line:90% One is price levels. 01:15:22.510 --> 01:15:25.680 align:middle line:90% Consumers like low prices. 01:15:25.680 --> 01:15:28.980 align:middle line:84% And there's less deadweight loss when prices are low. 01:15:28.980 --> 01:15:32.500 align:middle line:84% The other thing that welfare depends on is match quality. 01:15:32.500 --> 01:15:35.340 align:middle line:84% Consumers are better if they're getting their favorite phone 01:15:35.340 --> 01:15:38.190 align:middle line:84% and their favorite earbuds and their favorite charger 01:15:38.190 --> 01:15:41.437 align:middle line:84% than if they're getting their favorite of one 01:15:41.437 --> 01:15:43.020 align:middle line:84% and their second favorite of the other 01:15:43.020 --> 01:15:44.970 align:middle line:84% and their third favorite of another. 01:15:44.970 --> 01:15:47.040 align:middle line:84% So the match quality is are consumers 01:15:47.040 --> 01:15:51.540 align:middle line:84% getting what's the best product for them on every subcomponent? 01:15:51.540 --> 01:15:55.610 align:middle line:84% And then there's the price level thing that they care about. 01:15:55.610 --> 01:15:57.180 align:middle line:90% OK, so what's the result? 01:15:57.180 --> 01:16:00.620 align:middle line:84% So first result in the paper is that bundling 01:16:00.620 --> 01:16:04.130 align:middle line:84% reduces per good prices when n equals 2. 01:16:04.130 --> 01:16:08.810 align:middle line:84% So if you have two firms and they bundle their goods 01:16:08.810 --> 01:16:12.565 align:middle line:84% together, equilibrium per product prices go down. 01:16:12.565 --> 01:16:16.300 align:middle line:90% 01:16:16.300 --> 01:16:21.360 align:middle line:84% Noting prices go down, meaning that the firms make less profit. 01:16:21.360 --> 01:16:24.680 align:middle line:90% And why is that? 01:16:24.680 --> 01:16:31.000 align:middle line:84% The answer is that density of 1 over m epsilon im 01:16:31.000 --> 01:16:33.130 align:middle line:90% becomes more concentrated. 01:16:33.130 --> 01:16:36.040 align:middle line:84% When n equals 2, what we have is just 01:16:36.040 --> 01:16:40.040 align:middle line:84% what's the probability that ui1 minus ui2 is less than delta? 01:16:40.040 --> 01:16:42.940 align:middle line:84% And that's just the probability that we're close 01:16:42.940 --> 01:16:44.760 align:middle line:90% to the 45-degree line. 01:16:44.760 --> 01:16:50.400 align:middle line:84% That is that my epsilon for Firm 1 is within epsilon of my-- 01:16:50.400 --> 01:16:53.420 align:middle line:84% I'm sorry, within, let's say, this small delta. 01:16:53.420 --> 01:16:55.810 align:middle line:84% What's the probability that my preference for Firm 1 01:16:55.810 --> 01:16:58.070 align:middle line:84% and my preference for Firm 2 are within delta? 01:16:58.070 --> 01:17:00.610 align:middle line:84% Well, if you take the distribution of tastes that used 01:17:00.610 --> 01:17:04.210 align:middle line:90% to be uniform and you sort of-- 01:17:04.210 --> 01:17:05.710 align:middle line:84% like in the uniform distribution, 01:17:05.710 --> 01:17:07.100 align:middle line:90% this thing is not all that big. 01:17:07.100 --> 01:17:08.770 align:middle line:84% But then you add n goods, and you 01:17:08.770 --> 01:17:11.880 align:middle line:84% make this distribution look like this. 01:17:11.880 --> 01:17:14.110 align:middle line:84% Almost everybody has a preference of exactly 1/2 01:17:14.110 --> 01:17:15.480 align:middle line:90% for both products. 01:17:15.480 --> 01:17:17.800 align:middle line:84% Then, once they have a utility of exactly 1/2 for both 01:17:17.800 --> 01:17:20.770 align:middle line:84% products, they have a huge probability they're within some 01:17:20.770 --> 01:17:22.310 align:middle line:90% tiny delta of each other. 01:17:22.310 --> 01:17:25.060 align:middle line:84% Therefore, price competition becomes very intense. 01:17:25.060 --> 01:17:31.360 align:middle line:84% So when n equals two, it turns out that whatever m is, 01:17:31.360 --> 01:17:35.220 align:middle line:84% bundling just always makes the prices lower. 01:17:35.220 --> 01:17:37.350 align:middle line:84% So, in some sense, firms should not 01:17:37.350 --> 01:17:40.550 align:middle line:84% want to bundle in a two-firm model. 01:17:40.550 --> 01:17:43.680 align:middle line:90% 01:17:43.680 --> 01:17:45.960 align:middle line:84% What's noteworthy, though, is while the firms don't 01:17:45.960 --> 01:17:47.970 align:middle line:84% want to bundle, the consumers also 01:17:47.970 --> 01:17:49.410 align:middle line:90% don't want the firms to bundle. 01:17:49.410 --> 01:17:53.320 align:middle line:84% So the prices go down, but the consumers are worse off. 01:17:53.320 --> 01:17:57.060 align:middle line:84% And that's because the worst match quality 01:17:57.060 --> 01:17:58.750 align:middle line:90% overwhelms the price drop. 01:17:58.750 --> 01:18:01.483 align:middle line:84% So there's a price drop, but it also 01:18:01.483 --> 01:18:03.900 align:middle line:84% makes the consumers worse off because they get worse match 01:18:03.900 --> 01:18:04.400 align:middle line:90% quality. 01:18:04.400 --> 01:18:06.317 align:middle line:84% And it doesn't compensate-- and the price drop 01:18:06.317 --> 01:18:07.775 align:middle line:84% isn't big enough to compensate them 01:18:07.775 --> 01:18:09.050 align:middle line:90% for the drop in match quality. 01:18:09.050 --> 01:18:11.750 align:middle line:90% 01:18:11.750 --> 01:18:14.680 align:middle line:90% Now, when n equals 2, That's. 01:18:14.680 --> 01:18:15.180 align:middle line:90% True. 01:18:15.180 --> 01:18:19.010 align:middle line:84% When n is large, when n is above some threshold, 01:18:19.010 --> 01:18:22.100 align:middle line:84% bundling starts to increase profits. 01:18:22.100 --> 01:18:23.640 align:middle line:90% And why is that? 01:18:23.640 --> 01:18:26.030 align:middle line:90% Well, again, the value-- 01:18:26.030 --> 01:18:28.850 align:middle line:84% this sum of epsilon ijm starts getting 01:18:28.850 --> 01:18:32.630 align:middle line:90% to be a very tight distribution. 01:18:32.630 --> 01:18:36.260 align:middle line:84% And so, what's the density of consumers 01:18:36.260 --> 01:18:41.840 align:middle line:84% who have very close values for the best and second best thing? 01:18:41.840 --> 01:18:45.560 align:middle line:84% That's a density measured out here. 01:18:45.560 --> 01:18:47.360 align:middle line:84% If you like me best, what's the probability 01:18:47.360 --> 01:18:48.277 align:middle line:90% you like someone else? 01:18:48.277 --> 01:18:51.335 align:middle line:84% What's the probability the other person is close to you? 01:18:51.335 --> 01:18:55.740 align:middle line:90% 01:18:55.740 --> 01:19:01.232 align:middle line:84% When n gets large, holding m fixed, letting n go large, 01:19:01.232 --> 01:19:02.940 align:middle line:84% looking further out in that distribution, 01:19:02.940 --> 01:19:04.620 align:middle line:90% it gets thinner tailed. 01:19:04.620 --> 01:19:08.100 align:middle line:90% And the dxj dpj is small. 01:19:08.100 --> 01:19:10.260 align:middle line:84% And therefore, the p star is high. 01:19:10.260 --> 01:19:15.120 align:middle line:84% So bundling is good when the number of firms is large. 01:19:15.120 --> 01:19:17.550 align:middle line:84% And a third result is when you fix the number of firms 01:19:17.550 --> 01:19:22.140 align:middle line:84% and the number of goods goes to infinity, 01:19:22.140 --> 01:19:25.560 align:middle line:84% then eventually bundling drives prices to 0 01:19:25.560 --> 01:19:27.160 align:middle line:90% as m is going to infinity. 01:19:27.160 --> 01:19:31.180 align:middle line:90% 01:19:31.180 --> 01:19:35.470 align:middle line:84% So I think in some ways I wanted to do it because I wanted 01:19:35.470 --> 01:19:36.600 align:middle line:90% to cover some recent paper. 01:19:36.600 --> 01:19:40.850 align:middle line:84% And it's a nice example of how that basic Perloff-Salop 01:19:40.850 --> 01:19:43.550 align:middle line:84% intuition of price is about differentiation. 01:19:43.550 --> 01:19:49.122 align:middle line:84% And it's about dxj dpj is a very good way to think about a lot-- 01:19:49.122 --> 01:19:51.080 align:middle line:84% it's a good way to think about a lot of issues, 01:19:51.080 --> 01:19:52.225 align:middle line:90% bundling included. 01:19:52.225 --> 01:19:55.880 align:middle line:90% 01:19:55.880 --> 01:20:03.750 align:middle line:84% AUDIENCE: I don't understand why 4 is a result. 01:20:03.750 --> 01:20:05.490 align:middle line:90% GLENN ELLISON: So-- 01:20:05.490 --> 01:20:09.030 align:middle line:84% AUDIENCE: Because we're just putting infinity 01:20:09.030 --> 01:20:11.370 align:middle line:90% in the denominator. 01:20:11.370 --> 01:20:13.700 align:middle line:84% Would they ever charge an infinite price? 01:20:13.700 --> 01:20:16.060 align:middle line:84% GLENN ELLISON: Sorry, I should have said-- sorry, 01:20:16.060 --> 01:20:19.860 align:middle line:90% I should have said this is-- 01:20:19.860 --> 01:20:22.360 align:middle line:90% that's with c equals 0. 01:20:22.360 --> 01:20:24.060 align:middle line:90% So it's going to be that-- 01:20:24.060 --> 01:20:26.440 align:middle line:84% I think I had a c equals 0 assumption. 01:20:26.440 --> 01:20:29.370 align:middle line:84% So it's the limit as-- it probably 01:20:29.370 --> 01:20:36.450 align:middle line:84% should have written the limit as n goes to infinity pb over 01:20:36.450 --> 01:20:39.185 align:middle line:90% m minus c goes to 0. 01:20:39.185 --> 01:20:42.780 align:middle line:90% 01:20:42.780 --> 01:20:47.762 align:middle line:84% I think maybe I had c equals 0 throughout the paper. 01:20:47.762 --> 01:20:50.540 align:middle line:90% Yeah. 01:20:50.540 --> 01:20:51.940 align:middle line:90% OK? 01:20:51.940 --> 01:20:54.860 align:middle line:90% OK, let me end there then. 01:20:54.860 --> 01:20:57.400 align:middle line:84% I didn't think I would get to these last slides, but-- 01:20:57.400 --> 01:20:58.900 align:middle line:84% so anyway, on Monday, what I'm going 01:20:58.900 --> 01:21:04.600 align:middle line:84% to do is discuss oligopoly price discrimination, where you have 01:21:04.600 --> 01:21:07.210 align:middle line:84% oligopolies who are competing to sell multiple products, 01:21:07.210 --> 01:21:08.920 align:middle line:84% and therefore, are going to be price discriminating 01:21:08.920 --> 01:21:10.003 align:middle line:90% selling multiple products. 01:21:10.003 --> 01:21:12.670 align:middle line:84% And then I'm going to do two empirical papers, Bresnahan 01:21:12.670 --> 01:21:14.320 align:middle line:90% and Miller-Weinberg. 01:21:14.320 --> 01:21:19.090 align:middle line:84% Bresnahan, I took the star off it this year because Bresnahan, 01:21:19.090 --> 01:21:20.270 align:middle line:90% it's original. 01:21:20.270 --> 01:21:22.480 align:middle line:90% It's a real classic. 01:21:22.480 --> 01:21:25.120 align:middle line:84% It really looks 40 years old when you read it. 01:21:25.120 --> 01:21:28.180 align:middle line:84% And you're like, wow, I can't believe you do things that way. 01:21:28.180 --> 01:21:30.460 align:middle line:84% So I'll discuss the ideas in Bresnahan 01:21:30.460 --> 01:21:33.580 align:middle line:84% not going into the details, which now look very old 01:21:33.580 --> 01:21:34.120 align:middle line:90% fashioned. 01:21:34.120 --> 01:21:36.040 align:middle line:84% And then I'll discuss Miller-Weinberg. 01:21:36.040 --> 01:21:38.410 align:middle line:84% And I'm doing less empirical work 01:21:38.410 --> 01:21:41.488 align:middle line:84% here because Tobias is talking about demand estimation here. 01:21:41.488 --> 01:21:43.030 align:middle line:84% And an awful lot of demand estimation 01:21:43.030 --> 01:21:45.850 align:middle line:84% is really about estimating static models of product 01:21:45.850 --> 01:21:48.880 align:middle line:84% competition with those epsilon ij kinds of models 01:21:48.880 --> 01:21:51.780 align:middle line:90% that I talked about. 01:21:51.780 --> 01:22:11.000 align:middle line:90%