WEBVTT 00:00:00.000 --> 00:00:02.465 align:middle line:90% [SQUEAKING] 00:00:02.465 --> 00:00:04.437 align:middle line:90% [RUSTLING] 00:00:04.437 --> 00:00:06.902 align:middle line:90% [CLICKING] 00:00:06.902 --> 00:00:17.570 align:middle line:90% 00:00:17.570 --> 00:00:21.260 align:middle line:84% GLENN ELLISON: OK, let me go ahead and get started. 00:00:21.260 --> 00:00:24.870 align:middle line:84% Today's topic is going to be entry. 00:00:24.870 --> 00:00:27.660 align:middle line:84% And I think entry is an incredibly important topic 00:00:27.660 --> 00:00:28.160 align:middle line:90% in IO. 00:00:28.160 --> 00:00:30.159 align:middle line:84% In fact, one of the messages I'm going 00:00:30.159 --> 00:00:32.659 align:middle line:84% to talk about today is, in some sense, just about everything 00:00:32.659 --> 00:00:34.190 align:middle line:84% we've done in this semester so far 00:00:34.190 --> 00:00:37.080 align:middle line:84% is kind of like rounding error compared to what we do now. 00:00:37.080 --> 00:00:42.410 align:middle line:90% So how do I think about entry? 00:00:42.410 --> 00:00:44.870 align:middle line:84% So far, we've talked about a lot of models that 00:00:44.870 --> 00:00:47.540 align:middle line:90% have the number of firms fixed. 00:00:47.540 --> 00:00:49.040 align:middle line:84% And I've talked about lots of things 00:00:49.040 --> 00:00:51.273 align:middle line:84% about factors that affect pricing 00:00:51.273 --> 00:00:52.565 align:middle line:90% with the number of firms fixed. 00:00:52.565 --> 00:00:54.773 align:middle line:84% You know, monopoly pricing, if you have one firm, how 00:00:54.773 --> 00:00:57.030 align:middle line:90% does that-- what do they do? 00:00:57.030 --> 00:01:00.920 align:middle line:84% And then static competition with vertical differentiation 00:01:00.920 --> 00:01:03.873 align:middle line:84% or horizontal differentiation or search costs or other things, 00:01:03.873 --> 00:01:05.540 align:middle line:84% and it's always the nature of the market 00:01:05.540 --> 00:01:07.940 align:middle line:84% is determining what's the level of markups 00:01:07.940 --> 00:01:11.710 align:middle line:84% and what inefficiencies there might be. 00:01:11.710 --> 00:01:14.540 align:middle line:84% But that's all taking market structure as fixed. 00:01:14.540 --> 00:01:16.390 align:middle line:84% And so starting today, I'm going to think 00:01:16.390 --> 00:01:20.298 align:middle line:84% about what happens if you allow the number of firms to change. 00:01:20.298 --> 00:01:22.090 align:middle line:84% And so the simplest way to think about this 00:01:22.090 --> 00:01:25.240 align:middle line:84% is let's look at a two-stage model. 00:01:25.240 --> 00:01:27.820 align:middle line:84% I'm going to start with the case of homogeneous goods. 00:01:27.820 --> 00:01:31.090 align:middle line:84% So you can think of this as old-fashioned steel 00:01:31.090 --> 00:01:34.000 align:middle line:84% plants entering in each-- producing cold-rolled steel 00:01:34.000 --> 00:01:37.180 align:middle line:84% or aluminum plants or some industry that 00:01:37.180 --> 00:01:39.700 align:middle line:84% has a small number of firms because they're 00:01:39.700 --> 00:01:42.010 align:middle line:84% big fixed costs of setting up plants 00:01:42.010 --> 00:01:43.780 align:middle line:84% and then they compete with each other. 00:01:43.780 --> 00:01:47.570 align:middle line:84% So stage one, we have a large number of potential entrants. 00:01:47.570 --> 00:01:49.880 align:middle line:84% The potential entrants choose in or out. 00:01:49.880 --> 00:01:54.490 align:middle line:84% If they decide to come in, they pay some fixed entry cost K. 00:01:54.490 --> 00:01:56.800 align:middle line:84% And I'm going to think about this, most of the lecture, 00:01:56.800 --> 00:01:57.803 align:middle line:90% as a sunk cost. 00:01:57.803 --> 00:02:00.220 align:middle line:84% That is, once you build a steel plant, it's a steel plant, 00:02:00.220 --> 00:02:01.940 align:middle line:84% you can't use it for anything else. 00:02:01.940 --> 00:02:04.148 align:middle line:84% You're not going be able to sell it to somebody else, 00:02:04.148 --> 00:02:06.340 align:middle line:90% do something else with it. 00:02:06.340 --> 00:02:08.830 align:middle line:84% Firms that choose to enter then play some game 00:02:08.830 --> 00:02:12.170 align:middle line:84% like Bertrand competition, Cournot competition, price 00:02:12.170 --> 00:02:14.220 align:middle line:84% competition with search, et cetera. 00:02:14.220 --> 00:02:18.370 align:middle line:84% And assume firms have some variable costs c of Q. 00:02:18.370 --> 00:02:20.370 align:middle line:84% And then, how are you going to solve this model? 00:02:20.370 --> 00:02:23.210 align:middle line:84% I'm going to solve this model by backward induction. 00:02:23.210 --> 00:02:25.410 align:middle line:84% I first start with the second stage. 00:02:25.410 --> 00:02:28.943 align:middle line:84% In the second stage, if there are N firms, 00:02:28.943 --> 00:02:30.860 align:middle line:84% there are going to be some equilibrium prices, 00:02:30.860 --> 00:02:36.870 align:middle line:84% p star of N. p star of N times Q star of N minus c of Q star of N 00:02:36.870 --> 00:02:38.870 align:middle line:84% is going to be the variable profits of the firms 00:02:38.870 --> 00:02:39.990 align:middle line:90% if they enter. 00:02:39.990 --> 00:02:42.440 align:middle line:84% And then you find the number of equilibrium entrants 00:02:42.440 --> 00:02:43.735 align:middle line:90% by looking at the first stage. 00:02:43.735 --> 00:02:46.604 align:middle line:90% 00:02:46.604 --> 00:02:49.970 align:middle line:90% And what's that going to be? 00:02:49.970 --> 00:02:52.700 align:middle line:84% OK, first comment, I guess these slides were made up 00:02:52.700 --> 00:02:57.980 align:middle line:84% in the COVID era, where I would write on them right on my iPad. 00:02:57.980 --> 00:03:00.180 align:middle line:84% But let me go ahead and do this on the board. 00:03:00.180 --> 00:03:09.020 align:middle line:84% So let me graph what our profits look like as a function 00:03:09.020 --> 00:03:10.170 align:middle line:90% of the number of firms. 00:03:10.170 --> 00:03:14.540 align:middle line:84% The easiest one to graph is Bertrand. 00:03:14.540 --> 00:03:20.030 align:middle line:90% So 1, 2, 3, 4, 5. 00:03:20.030 --> 00:03:27.200 align:middle line:84% Bertrand competition, you have this level of profits, pi M, 00:03:27.200 --> 00:03:29.300 align:middle line:90% if you have one firm. 00:03:29.300 --> 00:03:36.220 align:middle line:84% And then as soon as you have two firms, profits drop to 0. 00:03:36.220 --> 00:03:39.610 align:middle line:84% Another thing you could have is Cournot competition. 00:03:39.610 --> 00:03:43.060 align:middle line:84% If you have Cournot competition, you get exactly the same outcome 00:03:43.060 --> 00:03:46.060 align:middle line:90% when N equals 1. 00:03:46.060 --> 00:03:50.390 align:middle line:84% But then profits drop when you add 00:03:50.390 --> 00:03:55.490 align:middle line:90% 2, 3, 4, or 5, whatever firms. 00:03:55.490 --> 00:03:58.640 align:middle line:84% If you think about-- if we did Cournot with linear demand-- 00:03:58.640 --> 00:04:00.200 align:middle line:84% Cournot with linear demands, you were 00:04:00.200 --> 00:04:06.440 align:middle line:84% getting, like, P star is approximately c plus 1 over-- 00:04:06.440 --> 00:04:12.480 align:middle line:84% Or simplest case-- simplest case for Cournot 00:04:12.480 --> 00:04:17.550 align:middle line:84% was N firms demand P as 1 over P. 00:04:17.550 --> 00:04:20.730 align:middle line:84% And then I think in that model, it was P star was equal to 1 00:04:20.730 --> 00:04:22.110 align:middle line:90% over N plus 1. 00:04:22.110 --> 00:04:25.530 align:middle line:84% And q star was equal to 1 over N plus 1. 00:04:25.530 --> 00:04:28.850 align:middle line:84% So profits were like 1 over N squared. 00:04:28.850 --> 00:04:32.360 align:middle line:84% So Cournot profits, approximately 1 00:04:32.360 --> 00:04:35.545 align:middle line:84% over N squared or 1 over N plus 1 squared, whatever. 00:04:35.545 --> 00:04:38.810 align:middle line:90% 00:04:38.810 --> 00:04:44.390 align:middle line:84% Another model I did was a model with search. 00:04:44.390 --> 00:04:46.370 align:middle line:84% In a model with search, if you remember, 00:04:46.370 --> 00:04:48.230 align:middle line:84% there was the Stahl model, you would always 00:04:48.230 --> 00:04:50.150 align:middle line:84% have the upper bound of the distribution, 00:04:50.150 --> 00:04:52.420 align:middle line:84% always gave you the monopoly profits 00:04:52.420 --> 00:04:55.220 align:middle line:84% as long as the search costs were in an appropriate range. 00:04:55.220 --> 00:04:58.560 align:middle line:84% And so that one declined something-- 00:04:58.560 --> 00:05:00.110 align:middle line:84% if you think about that, that means 00:05:00.110 --> 00:05:03.750 align:middle line:84% it declines slower because the firms are 00:05:03.750 --> 00:05:06.870 align:middle line:90% serving the nonshoppers. 00:05:06.870 --> 00:05:09.420 align:middle line:84% So in the search model, you're serving the nonshoppers. 00:05:09.420 --> 00:05:11.860 align:middle line:84% You're always indifferent to charging the monopoly price. 00:05:11.860 --> 00:05:13.235 align:middle line:84% And so you get the monopoly price 00:05:13.235 --> 00:05:17.490 align:middle line:84% divided by N plus-- divided by N times 1 minus mu is the profits. 00:05:17.490 --> 00:05:23.100 align:middle line:84% And they go down like 1 over N. But whatever you have, 00:05:23.100 --> 00:05:26.140 align:middle line:84% what's going to happen in this model in the first stage-- 00:05:26.140 --> 00:05:28.830 align:middle line:84% so if you have some level of fixed-- 00:05:28.830 --> 00:05:31.020 align:middle line:90% let me focus on Cournot. 00:05:31.020 --> 00:05:36.450 align:middle line:84% Let's suppose you do Cournot, and you have some fixed level 00:05:36.450 --> 00:05:40.320 align:middle line:84% of entry cost K. Then, in equilibrium, you're 00:05:40.320 --> 00:05:42.840 align:middle line:84% going to have exactly two firms enter. 00:05:42.840 --> 00:05:45.810 align:middle line:84% Because when two firms enter, the firms' profits 00:05:45.810 --> 00:05:48.720 align:middle line:84% are above K. If you had three firms in the market, 00:05:48.720 --> 00:05:51.690 align:middle line:84% the profits would be below K, so N equals 2. 00:05:51.690 --> 00:05:56.070 align:middle line:84% And so the number of firms, it's locally invariant to K 00:05:56.070 --> 00:05:59.100 align:middle line:84% because you can raise or lower costs, 00:05:59.100 --> 00:06:00.340 align:middle line:90% and it doesn't affect things. 00:06:00.340 --> 00:06:04.792 align:middle line:84% Obviously, if K drops, then the third firm enters. 00:06:04.792 --> 00:06:10.500 align:middle line:84% (That's a terrible piece of chalk.) 00:06:10.500 --> 00:06:14.440 align:middle line:84% You could also think of a mixed strategy equilibrium solution. 00:06:14.440 --> 00:06:17.410 align:middle line:84% If there's some large but finite number-- 00:06:17.410 --> 00:06:24.200 align:middle line:84% if there's some number of M of potential entrants, 00:06:24.200 --> 00:06:28.010 align:middle line:84% where M is much bigger than N star-- 00:06:28.010 --> 00:06:31.940 align:middle line:84% you could also think of M firms each mixing in or out, 00:06:31.940 --> 00:06:34.400 align:middle line:84% and then you get a mixed strategy equilibrium. 00:06:34.400 --> 00:06:36.205 align:middle line:84% In the mixed strategy equilibrium, 00:06:36.205 --> 00:06:37.580 align:middle line:84% all the firms that are mixing are 00:06:37.580 --> 00:06:40.980 align:middle line:84% going to have to have expected profits exactly equal to K. 00:06:40.980 --> 00:06:44.090 align:middle line:84% And so in that model, all the firms that are mixing 00:06:44.090 --> 00:06:49.450 align:middle line:84% have expected profits exactly equal to K. Therefore, 00:06:49.450 --> 00:06:51.490 align:middle line:84% here you can think of it as you're 00:06:51.490 --> 00:06:54.570 align:middle line:84% going to expect to get two-plus firms, between two 00:06:54.570 --> 00:06:55.820 align:middle line:90% and three firms in the market. 00:06:55.820 --> 00:06:58.450 align:middle line:84% But if it's-- obviously, if it's like Poisson draws, 00:06:58.450 --> 00:07:03.370 align:middle line:84% sometimes you'll get one, two, three, four, five, or more. 00:07:03.370 --> 00:07:06.023 align:middle line:84% In models like a procurement auction, 00:07:06.023 --> 00:07:07.690 align:middle line:84% where there's one date on which everyone 00:07:07.690 --> 00:07:09.940 align:middle line:84% has to submit sealed bids and no one knows 00:07:09.940 --> 00:07:14.260 align:middle line:84% how many other bidders there are, this expected pi of N 00:07:14.260 --> 00:07:16.550 align:middle line:84% equals K is probably the right approach. 00:07:16.550 --> 00:07:19.960 align:middle line:84% If you have models like the steel plants 00:07:19.960 --> 00:07:22.390 align:middle line:84% where the firms are not entering simultaneously, 00:07:22.390 --> 00:07:24.130 align:middle line:84% they're entering sequentially, then 00:07:24.130 --> 00:07:26.320 align:middle line:84% it's probably like the pure strategy equilibrium 00:07:26.320 --> 00:07:28.570 align:middle line:84% is the one you want to focus on because no one's going 00:07:28.570 --> 00:07:30.820 align:middle line:84% to open a third steel plant if the third steel plant is going 00:07:30.820 --> 00:07:33.403 align:middle line:84% to drive prices below where you need to cover the fixed costs. 00:07:33.403 --> 00:07:39.240 align:middle line:90% 00:07:39.240 --> 00:07:44.310 align:middle line:84% So observations-- fixed costs and competition 00:07:44.310 --> 00:07:46.930 align:middle line:84% determine the number of entries, number of entrants. 00:07:46.930 --> 00:07:51.580 align:middle line:84% But with lower fixed costs, we get more entry. 00:07:51.580 --> 00:07:53.680 align:middle line:84% In many models, the number of firms 00:07:53.680 --> 00:07:57.260 align:middle line:84% goes to infinity as the fixed costs of entry go to 0. 00:07:57.260 --> 00:08:01.690 align:middle line:84% The only time that's not going to happen is if you had-- 00:08:01.690 --> 00:08:03.370 align:middle line:84% I talked about the low demand models, 00:08:03.370 --> 00:08:07.870 align:middle line:84% where price asymptotes to a positive-- 00:08:07.870 --> 00:08:09.820 align:middle line:90% no, it's still going to work. 00:08:09.820 --> 00:08:11.540 align:middle line:84% So where are you not going to N star-- 00:08:11.540 --> 00:08:16.118 align:middle line:90% 00:08:16.118 --> 00:08:18.410 align:middle line:84% You're not going to get N star goes to infinity-- like, 00:08:18.410 --> 00:08:20.000 align:middle line:84% in Cournot, you don't get N star goes 00:08:20.000 --> 00:08:22.590 align:middle line:84% to infinity because in Cournot, in fact, you get N star is 1. 00:08:22.590 --> 00:08:27.020 align:middle line:84% So if profits hit 0 at some point before, when N gets large, 00:08:27.020 --> 00:08:29.550 align:middle line:84% and even with no entry costs, you can still get-- 00:08:29.550 --> 00:08:34.280 align:middle line:84% or small positive entry costs, you can still get finite entry. 00:08:34.280 --> 00:08:37.830 align:middle line:84% Profits are, in this model, are a rounding error. 00:08:37.830 --> 00:08:39.960 align:middle line:84% And we spent all this time working on markups, 00:08:39.960 --> 00:08:46.580 align:middle line:84% but here, the profits are just-- if this 00:08:46.580 --> 00:08:49.980 align:middle line:84% happens to be the fixed cost, you get pretty big profits. 00:08:49.980 --> 00:08:52.800 align:middle line:84% If this was the fixed cost, you'd get very little profits. 00:08:52.800 --> 00:08:58.070 align:middle line:84% If the fixed costs dropped here, you'd get even higher profits. 00:08:58.070 --> 00:09:01.820 align:middle line:84% When then they drop more, you get hardly any profits at all. 00:09:01.820 --> 00:09:07.028 align:middle line:84% So equilibrium profits that we observed really 00:09:07.028 --> 00:09:09.320 align:middle line:84% don't have to be related to anything we've talked about 00:09:09.320 --> 00:09:11.960 align:middle line:84% so far because all that matters is how many firms 00:09:11.960 --> 00:09:12.980 align:middle line:90% fit in the market. 00:09:12.980 --> 00:09:15.370 align:middle line:84% And then everything else just determines 00:09:15.370 --> 00:09:17.870 align:middle line:84% where you are in between the profits with two firms or three 00:09:17.870 --> 00:09:19.920 align:middle line:84% firms or three firms and four firms. 00:09:19.920 --> 00:09:22.050 align:middle line:84% And so profits just become this rounding error 00:09:22.050 --> 00:09:24.830 align:middle line:84% that's just coincidence of where entry costs big enough 00:09:24.830 --> 00:09:27.330 align:middle line:84% that the last firm just barely gets in. 00:09:27.330 --> 00:09:34.260 align:middle line:84% Now, that's some-- that is equilibrium profits taking 00:09:34.260 --> 00:09:37.170 align:middle line:84% the fixed costs of entry into account. 00:09:37.170 --> 00:09:38.670 align:middle line:84% It's still the case that the markups 00:09:38.670 --> 00:09:40.818 align:middle line:84% are higher when you have smaller numbers of firms. 00:09:40.818 --> 00:09:42.360 align:middle line:84% The markups are higher, but it's just 00:09:42.360 --> 00:09:43.950 align:middle line:84% the markups just offset the fixed 00:09:43.950 --> 00:09:48.150 align:middle line:90% costs the firms are incurring. 00:09:48.150 --> 00:09:51.510 align:middle line:84% In many models, the equilibrium firm size 00:09:51.510 --> 00:09:53.680 align:middle line:84% increases when the market size increases. 00:09:53.680 --> 00:09:57.150 align:middle line:84% So I give the Cournot example here. 00:09:57.150 --> 00:09:59.010 align:middle line:84% In the Cournot example, suppose you 00:09:59.010 --> 00:10:01.800 align:middle line:84% have little m consumers in the market, 00:10:01.800 --> 00:10:05.040 align:middle line:84% and so demand becomes m times D of p. 00:10:05.040 --> 00:10:07.260 align:middle line:84% Let's suppose we double the market size. 00:10:07.260 --> 00:10:09.270 align:middle line:84% If you double the market size and you 00:10:09.270 --> 00:10:14.250 align:middle line:84% double the number of firms, then the number of customers per firm 00:10:14.250 --> 00:10:15.790 align:middle line:90% would be the same. 00:10:15.790 --> 00:10:19.570 align:middle line:84% But there's a second effect of the prices decreasing. 00:10:19.570 --> 00:10:22.920 align:middle line:90% And so if the prices decrease-- 00:10:22.920 --> 00:10:25.830 align:middle line:84% the prices decrease, then the firms are worse off. 00:10:25.830 --> 00:10:28.920 align:middle line:84% So Cournot, in some sense, it's like the profits are going down 00:10:28.920 --> 00:10:30.600 align:middle line:90% like 1 over N squared. 00:10:30.600 --> 00:10:33.870 align:middle line:84% With N firms, profits are going up proportional 00:10:33.870 --> 00:10:36.250 align:middle line:84% to m if the number of customers goes up. 00:10:36.250 --> 00:10:38.060 align:middle line:90% So you're going to get-- 00:10:38.060 --> 00:10:39.810 align:middle line:84% firm growth is going to be the square root 00:10:39.810 --> 00:10:41.440 align:middle line:90% of the number of customers. 00:10:41.440 --> 00:10:42.810 align:middle line:90% So as the firm-- 00:10:42.810 --> 00:10:45.420 align:middle line:84% as the market increases, firms go up 00:10:45.420 --> 00:10:47.500 align:middle line:84% square root of the number of customers goes up. 00:10:47.500 --> 00:10:50.650 align:middle line:84% So firm size goes up like square root of the number of customers. 00:10:50.650 --> 00:10:55.090 align:middle line:90% 00:10:55.090 --> 00:10:57.486 align:middle line:84% Any questions on these simple observations? 00:10:57.486 --> 00:11:01.510 align:middle line:90% 00:11:01.510 --> 00:11:04.120 align:middle line:84% First substantial topic I want to talk about today 00:11:04.120 --> 00:11:08.120 align:middle line:84% is, what's the efficiency of entry? 00:11:08.120 --> 00:11:10.520 align:middle line:84% Do we get more firms and markets than we want? 00:11:10.520 --> 00:11:12.770 align:middle line:84% Do we get fewer firms and markets than we want? 00:11:12.770 --> 00:11:15.010 align:middle line:84% And this is an important practical question. 00:11:15.010 --> 00:11:17.500 align:middle line:84% There are many, many industries and many, many countries 00:11:17.500 --> 00:11:19.000 align:middle line:84% where the firms have gotten together 00:11:19.000 --> 00:11:22.630 align:middle line:84% and have some kind of government-sanctioned entry 00:11:22.630 --> 00:11:24.940 align:middle line:90% limitations. 00:11:24.940 --> 00:11:27.370 align:middle line:84% There's a question on the Massachusetts ballot about 00:11:27.370 --> 00:11:30.520 align:middle line:90% should liquor stores-- 00:11:30.520 --> 00:11:34.960 align:middle line:84% or should firms be able to sell beer in more than nine stores 00:11:34.960 --> 00:11:36.225 align:middle line:90% in the state of Massachusetts? 00:11:36.225 --> 00:11:38.350 align:middle line:84% For many years, you were only allowed to sell beer, 00:11:38.350 --> 00:11:40.520 align:middle line:84% I think, in one store in the state of Massachusetts. 00:11:40.520 --> 00:11:42.790 align:middle line:84% So all the supermarkets, you notice-- 00:11:42.790 --> 00:11:43.810 align:middle line:90% I don't know if-- 00:11:43.810 --> 00:11:47.555 align:middle line:84% if you go to-- supermarkets in other states have beer. 00:11:47.555 --> 00:11:49.180 align:middle line:84% Supermarkets in Massachusetts typically 00:11:49.180 --> 00:11:50.597 align:middle line:84% didn't have beer because there was 00:11:50.597 --> 00:11:54.430 align:middle line:84% a law that said you could only sell beer in one of your stores 00:11:54.430 --> 00:11:56.000 align:middle line:84% in the entire state of Massachusetts. 00:11:56.000 --> 00:12:00.060 align:middle line:84% And so Star Market had to pick one Star Market to have beer. 00:12:00.060 --> 00:12:01.310 align:middle line:90% And now there are-- 00:12:01.310 --> 00:12:03.123 align:middle line:84% now you can sell beer in nine Star Markets, 00:12:03.123 --> 00:12:05.040 align:middle line:84% and they're thinking of increasing that level. 00:12:05.040 --> 00:12:10.217 align:middle line:84% But why do we get these entry laws? 00:12:10.217 --> 00:12:11.800 align:middle line:84% Well, the firms that are in the market 00:12:11.800 --> 00:12:15.610 align:middle line:84% always argue that competition entry is wasteful, 00:12:15.610 --> 00:12:17.298 align:middle line:84% and we need to save the mom and pop 00:12:17.298 --> 00:12:19.840 align:middle line:84% stores and the small businesses and protect them from, quote, 00:12:19.840 --> 00:12:21.090 align:middle line:90% excessive entry. 00:12:21.090 --> 00:12:25.390 align:middle line:84% So anyway, here's a discussion of do we think entry should 00:12:25.390 --> 00:12:29.320 align:middle line:84% or shouldn't, would or would not be excessive in markets? 00:12:29.320 --> 00:12:31.150 align:middle line:90% What's the first best? 00:12:31.150 --> 00:12:33.880 align:middle line:84% Here I'm going to do the homogeneous case first. 00:12:33.880 --> 00:12:37.880 align:middle line:84% Homogeneous goods, there's no idiosyncratic preferences. 00:12:37.880 --> 00:12:39.610 align:middle line:84% So the first best is just one firm-- 00:12:39.610 --> 00:12:42.760 align:middle line:84% have that one firm price at marginal cost. 00:12:42.760 --> 00:12:44.620 align:middle line:84% That's typically not feasible because you'd 00:12:44.620 --> 00:12:46.870 align:middle line:84% need price regulation to force the monopolist to price 00:12:46.870 --> 00:12:47.660 align:middle line:90% at marginal cost. 00:12:47.660 --> 00:12:50.140 align:middle line:84% So what we often compare it to is the second best, 00:12:50.140 --> 00:12:53.990 align:middle line:84% where the second best you take p star of N as given. 00:12:53.990 --> 00:12:56.277 align:middle line:84% You can't affect the nature of the competition, 00:12:56.277 --> 00:12:58.360 align:middle line:84% and you just say, what would be the optimal number 00:12:58.360 --> 00:13:02.470 align:middle line:84% of firms, given that p star of N can 00:13:02.470 --> 00:13:04.150 align:middle line:90% be determined in equilibrium? 00:13:04.150 --> 00:13:08.830 align:middle line:84% And so this would be our welfare calculation. 00:13:08.830 --> 00:13:15.700 align:middle line:84% The welfare with N firms is equal to the integral 0 to N-- 00:13:15.700 --> 00:13:17.350 align:middle line:90% did we do big Q or little q? 00:13:17.350 --> 00:13:17.895 align:middle line:90% Little q. 00:13:17.895 --> 00:13:33.250 align:middle line:90% 00:13:33.250 --> 00:13:37.450 align:middle line:84% So if you have N firms, this is the gross surplus produced 00:13:37.450 --> 00:13:43.390 align:middle line:84% by firms producing total quantity N q star of N. This 00:13:43.390 --> 00:13:46.330 align:middle line:84% is the total production costs incurred when each of N firms 00:13:46.330 --> 00:13:50.620 align:middle line:84% produces quantity q star of N. And these are the fixed costs. 00:13:50.620 --> 00:13:53.080 align:middle line:90% So we want to maximize that. 00:13:53.080 --> 00:13:56.410 align:middle line:84% So the first theorem is that in this model 00:13:56.410 --> 00:13:59.510 align:middle line:84% with homogeneous goods, entry is always excessive. 00:13:59.510 --> 00:14:01.900 align:middle line:84% So we do get too many firms and markets. 00:14:01.900 --> 00:14:03.200 align:middle line:90% We would like to restrict it. 00:14:03.200 --> 00:14:03.880 align:middle line:90% Why? 00:14:03.880 --> 00:14:05.320 align:middle line:90% Here's a theorem. 00:14:05.320 --> 00:14:09.423 align:middle line:84% So suppose that this welfare function is concave. 00:14:09.423 --> 00:14:11.840 align:middle line:84% I know I've talked about how things are often not concave. 00:14:11.840 --> 00:14:13.540 align:middle line:84% Welfare functions here would be concave 00:14:13.540 --> 00:14:17.110 align:middle line:84% because as you get lots of firms, 00:14:17.110 --> 00:14:20.983 align:middle line:84% you just asymptote to line of slope K. It's 00:14:20.983 --> 00:14:23.650 align:middle line:84% inefficient to keep paying these fixed entry costs over and over 00:14:23.650 --> 00:14:25.360 align:middle line:90% and over again. 00:14:25.360 --> 00:14:28.280 align:middle line:84% So suppose the welfare function is concave. 00:14:28.280 --> 00:14:30.700 align:middle line:84% Suppose the variable profits are decreasing 00:14:30.700 --> 00:14:34.500 align:middle line:84% in number of firms N. And suppose 00:14:34.500 --> 00:14:38.070 align:middle line:84% that the equilibrium price per firm quantities 00:14:38.070 --> 00:14:40.380 align:middle line:84% can be extended to differentiable functions that 00:14:40.380 --> 00:14:42.660 align:middle line:90% have these natural properties. 00:14:42.660 --> 00:14:47.890 align:middle line:84% As the number of firms increases, total output goes up. 00:14:47.890 --> 00:14:51.250 align:middle line:84% As the number of firms goes up, each individual firm's output 00:14:51.250 --> 00:14:53.070 align:middle line:90% goes down. 00:14:53.070 --> 00:15:01.060 align:middle line:84% And at the equilibrium number of firms, price minus marginal cost 00:15:01.060 --> 00:15:05.310 align:middle line:84% is positive, which it always should be. 00:15:05.310 --> 00:15:07.060 align:middle line:84% Sorry, this is given any number of firms-- 00:15:07.060 --> 00:15:09.970 align:middle line:84% given any number of firms N, the resulting price 00:15:09.970 --> 00:15:12.130 align:middle line:90% would be above marginal cost. 00:15:12.130 --> 00:15:16.880 align:middle line:84% The theorem is that then N is at least N second best minus 1. 00:15:16.880 --> 00:15:18.970 align:middle line:84% So it's entries excessive, although it 00:15:18.970 --> 00:15:21.700 align:middle line:84% can, due to rounding errors, be one too few. 00:15:21.700 --> 00:15:24.110 align:middle line:84% Bertrand is a case where it's one too few. 00:15:24.110 --> 00:15:27.430 align:middle line:84% Sometimes you'd like two firms, you only get one. 00:15:27.430 --> 00:15:29.650 align:middle line:84% But the general result is that you 00:15:29.650 --> 00:15:32.965 align:middle line:84% get too many firms, other than this possible rounding error 00:15:32.965 --> 00:15:33.465 align:middle line:90% issue. 00:15:33.465 --> 00:15:36.960 align:middle line:90% 00:15:36.960 --> 00:15:39.030 align:middle line:90% So proof. 00:15:39.030 --> 00:15:42.360 align:middle line:84% So first, we've got this welfare function. 00:15:42.360 --> 00:15:44.910 align:middle line:84% The welfare function is naturally described only 00:15:44.910 --> 00:15:46.400 align:middle line:90% at a set of integer points. 00:15:46.400 --> 00:15:51.680 align:middle line:90% 00:15:51.680 --> 00:15:55.960 align:middle line:84% But in many of these models, like Cournot over there, 00:15:55.960 --> 00:16:05.500 align:middle line:84% you have p star of N equals 1 over N plus 1, Q star of N 00:16:05.500 --> 00:16:07.710 align:middle line:90% equals 1 over N plus 1. 00:16:07.710 --> 00:16:11.080 align:middle line:84% So you can just naturally treat this as a continuous function 00:16:11.080 --> 00:16:15.310 align:middle line:84% when N is a continuous variable, like use a function Q star of x 00:16:15.310 --> 00:16:17.240 align:middle line:90% equals 1 over x plus 1. 00:16:17.240 --> 00:16:19.900 align:middle line:84% And by doing that, you extend the-- 00:16:19.900 --> 00:16:24.150 align:middle line:84% you just draw a smooth curve through those welfare points. 00:16:24.150 --> 00:16:27.800 align:middle line:90% 00:16:27.800 --> 00:16:29.750 align:middle line:84% I'm going to let N hat second best 00:16:29.750 --> 00:16:32.480 align:middle line:84% be the solution to where this thing's first order condition is 00:16:32.480 --> 00:16:33.740 align:middle line:90% 0. 00:16:33.740 --> 00:16:35.175 align:middle line:90% So that would be right here. 00:16:35.175 --> 00:16:39.062 align:middle line:90% 00:16:39.062 --> 00:16:40.860 align:middle line:90% N hat second best. 00:16:40.860 --> 00:16:44.150 align:middle line:84% So I define N hat second best to be the maximizer 00:16:44.150 --> 00:16:45.115 align:middle line:90% of this smooth curve. 00:16:45.115 --> 00:16:48.470 align:middle line:90% 00:16:48.470 --> 00:16:53.155 align:middle line:84% The second best is always going to be either-- 00:16:53.155 --> 00:16:56.450 align:middle line:84% if W is a concave function, it's either 00:16:56.450 --> 00:16:58.900 align:middle line:84% going to be this point or this point. 00:16:58.900 --> 00:17:04.780 align:middle line:84% So the optimal number of firms is always at most what you get-- 00:17:04.780 --> 00:17:06.940 align:middle line:84% optimal number first is always at most 00:17:06.940 --> 00:17:12.010 align:middle line:84% what you get by just rounding up this point, N hat second best. 00:17:12.010 --> 00:17:14.319 align:middle line:84% So what is the first order condition 00:17:14.319 --> 00:17:16.060 align:middle line:90% defining N hat second best? 00:17:16.060 --> 00:17:18.640 align:middle line:84% Well, it's just-- the first order condition 00:17:18.640 --> 00:17:31.290 align:middle line:84% is d W of N dN equals evaluated at N hat second best equals 0. 00:17:31.290 --> 00:17:35.410 align:middle line:84% That's what determines this point here. 00:17:35.410 --> 00:17:37.220 align:middle line:84% What does that derivative look like? 00:17:37.220 --> 00:17:39.940 align:middle line:84% So I differentiate this expression with respect 00:17:39.940 --> 00:17:42.640 align:middle line:84% to N. The first term only depends 00:17:42.640 --> 00:17:46.300 align:middle line:84% on N through the upper limit of integration. 00:17:46.300 --> 00:17:49.360 align:middle line:84% So the derivative of this with respect to N 00:17:49.360 --> 00:17:53.080 align:middle line:84% is just the value of this evaluated 00:17:53.080 --> 00:17:56.890 align:middle line:84% at N q star of N, P of N q star of N 00:17:56.890 --> 00:17:59.830 align:middle line:84% times the amount by which the upper limit moves 00:17:59.830 --> 00:18:00.920 align:middle line:90% when N changes. 00:18:00.920 --> 00:18:03.610 align:middle line:84% So the derivative of this with respect to N 00:18:03.610 --> 00:18:05.100 align:middle line:90% is what I wrote down here. 00:18:05.100 --> 00:18:08.610 align:middle line:90% 00:18:08.610 --> 00:18:12.180 align:middle line:84% The second effect of N on welfare 00:18:12.180 --> 00:18:16.030 align:middle line:84% is this term changes, Nc of q star of N. 00:18:16.030 --> 00:18:18.690 align:middle line:84% So the derivative of that with respect to N 00:18:18.690 --> 00:18:25.080 align:middle line:84% is c of q star of N plus Nc prime of q star of N, 00:18:25.080 --> 00:18:31.252 align:middle line:84% q star prime at N. So that's a derivative of the second term. 00:18:31.252 --> 00:18:33.710 align:middle line:84% And then the derivative of the third term with respect to N 00:18:33.710 --> 00:18:36.330 align:middle line:90% is just K. 00:18:36.330 --> 00:18:39.180 align:middle line:84% So I just differentiate this expression with respect 00:18:39.180 --> 00:18:44.070 align:middle line:84% to N. I say that evaluated at N hat second best 00:18:44.070 --> 00:18:47.760 align:middle line:90% is going to be equal to 0. 00:18:47.760 --> 00:18:50.465 align:middle line:84% And then I'm going to start grouping terms. 00:18:50.465 --> 00:18:58.200 align:middle line:84% The first term I pull together are P times q minus c of q. 00:18:58.200 --> 00:19:02.250 align:middle line:84% And so I'm going to take this term times this minus this 00:19:02.250 --> 00:19:04.770 align:middle line:84% and call that the variable profit. 00:19:04.770 --> 00:19:08.670 align:middle line:90% So that's pi v star of N. 00:19:08.670 --> 00:19:10.570 align:middle line:90% What's left over? 00:19:10.570 --> 00:19:15.390 align:middle line:84% Everything that's left over has an Nq star prime of N. Well, 00:19:15.390 --> 00:19:16.690 align:middle line:90% there are two terms left over. 00:19:16.690 --> 00:19:21.810 align:middle line:84% This times this and this that have an Nq star prime at N. 00:19:21.810 --> 00:19:25.200 align:middle line:84% And those become Nq star prime at N times 00:19:25.200 --> 00:19:28.300 align:middle line:90% price minus marginal cost. 00:19:28.300 --> 00:19:31.110 align:middle line:84% And then the third thing that's left over is the K at the end. 00:19:31.110 --> 00:19:33.760 align:middle line:90% 00:19:33.760 --> 00:19:35.890 align:middle line:84% And then under this assumption that I 00:19:35.890 --> 00:19:40.390 align:middle line:84% made that price minus marginal cost 00:19:40.390 --> 00:19:43.020 align:middle line:84% is always positive at the equilibrium prices, 00:19:43.020 --> 00:19:45.540 align:middle line:90% this is a positive number. 00:19:45.540 --> 00:19:52.400 align:middle line:84% And so what that means is that if you evaluate this at N hat 00:19:52.400 --> 00:20:03.580 align:middle line:84% second best, I get variable profit minus K plus this equals 00:20:03.580 --> 00:20:04.080 align:middle line:90% 0. 00:20:04.080 --> 00:20:07.340 align:middle line:84% That tells me that the variable profit evaluated at N second 00:20:07.340 --> 00:20:12.380 align:middle line:84% best minus K is strictly positive, which means that 1x-- 00:20:12.380 --> 00:20:16.560 align:middle line:84% at N hat second best, variable profit 00:20:16.560 --> 00:20:19.710 align:middle line:84% is bigger than K. So that means other firms would 00:20:19.710 --> 00:20:21.270 align:middle line:90% like to come in. 00:20:21.270 --> 00:20:24.000 align:middle line:84% So if we had exactly this many firms, 00:20:24.000 --> 00:20:26.040 align:middle line:84% not that this is an integer, the next firm 00:20:26.040 --> 00:20:27.081 align:middle line:90% always wants to come in. 00:20:27.081 --> 00:20:28.623 align:middle line:84% So that means the equilibrium entry-- 00:20:28.623 --> 00:20:32.160 align:middle line:90% 00:20:32.160 --> 00:20:34.290 align:middle line:90% oops. 00:20:34.290 --> 00:20:40.260 align:middle line:84% So equilibrium entry is at least here. 00:20:40.260 --> 00:20:43.200 align:middle line:84% Because at this point, we know a firm wants to come in. 00:20:43.200 --> 00:20:44.410 align:middle line:90% At this point, we don't know. 00:20:44.410 --> 00:20:46.140 align:middle line:84% But if you're less, then you definitely 00:20:46.140 --> 00:20:49.390 align:middle line:84% want to come in because pi v star is a decreasing function. 00:20:49.390 --> 00:20:53.020 align:middle line:84% So pi v star is bigger than K at this point. 00:20:53.020 --> 00:20:55.870 align:middle line:84% So pi v star is also bigger than K at this point. 00:20:55.870 --> 00:20:59.765 align:middle line:90% So N star is somewhere out here. 00:20:59.765 --> 00:21:02.480 align:middle line:90% 00:21:02.480 --> 00:21:04.760 align:middle line:84% So N star is at least what you get-- 00:21:04.760 --> 00:21:06.650 align:middle line:90% is at least here. 00:21:06.650 --> 00:21:07.610 align:middle line:90% And what did I say? 00:21:07.610 --> 00:21:14.850 align:middle line:84% I said that the first best and second best is one of these. 00:21:14.850 --> 00:21:17.780 align:middle line:84% So if N second best is either this point or this point, 00:21:17.780 --> 00:21:21.450 align:middle line:84% the equilibrium number is somewhere this point or higher, 00:21:21.450 --> 00:21:23.215 align:middle line:84% we're always getting too many firms in. 00:21:23.215 --> 00:21:27.830 align:middle line:90% 00:21:27.830 --> 00:21:30.590 align:middle line:90% Is that OK? 00:21:30.590 --> 00:21:35.710 align:middle line:84% I have on the next page easier, maybe simpler intuition. 00:21:35.710 --> 00:21:39.850 align:middle line:84% In a homogeneous good model, the only benefit 00:21:39.850 --> 00:21:42.490 align:middle line:84% that anyone gets from entry is that we 00:21:42.490 --> 00:21:44.270 align:middle line:90% reduce the deadweight loss. 00:21:44.270 --> 00:21:46.930 align:middle line:90% We get quantity increases. 00:21:46.930 --> 00:21:54.220 align:middle line:84% So what are the total gross surplus, total consumer and firm 00:21:54.220 --> 00:21:55.970 align:middle line:90% benefits from the extra entry? 00:21:55.970 --> 00:21:57.910 align:middle line:84% It's just the extra quantity that 00:21:57.910 --> 00:22:00.130 align:middle line:84% gets produced times p star minus c, 00:22:00.130 --> 00:22:01.930 align:middle line:84% where p star is like the equilibrium 00:22:01.930 --> 00:22:04.770 align:middle line:84% profit you get at the equilibrium number of firms. 00:22:04.770 --> 00:22:08.380 align:middle line:84% So when we let in more firms, the welfare benefit is just, 00:22:08.380 --> 00:22:11.160 align:middle line:84% how much did quantity go up times p star minus c? 00:22:11.160 --> 00:22:15.390 align:middle line:90% 00:22:15.390 --> 00:22:18.010 align:middle line:90% What does the entering firm get? 00:22:18.010 --> 00:22:21.850 align:middle line:84% The entering firm gets much more than this because it's not-- 00:22:21.850 --> 00:22:24.270 align:middle line:84% the entering firm is not just selling the amount 00:22:24.270 --> 00:22:26.580 align:middle line:90% by which quantity has gone up. 00:22:26.580 --> 00:22:29.450 align:middle line:84% The entering firm is getting that quantity-- 00:22:29.450 --> 00:22:32.520 align:middle line:84% it's getting the extra quantity, but it's also 00:22:32.520 --> 00:22:35.100 align:middle line:84% stealing some quantity away from all the other firms that 00:22:35.100 --> 00:22:36.660 align:middle line:90% were there before. 00:22:36.660 --> 00:22:39.720 align:middle line:84% And so people call that the business stealing effect, 00:22:39.720 --> 00:22:41.730 align:middle line:84% that the amount by which quantity 00:22:41.730 --> 00:22:43.560 align:middle line:84% goes up, which is the welfare gain, 00:22:43.560 --> 00:22:46.680 align:middle line:84% is much smaller than the amount by which sales go up 00:22:46.680 --> 00:22:48.740 align:middle line:90% for the last firm that comes in. 00:22:48.740 --> 00:22:51.960 align:middle line:90% So the last firm's profits-- 00:22:51.960 --> 00:22:54.600 align:middle line:84% the social cost of it coming in is 00:22:54.600 --> 00:22:59.610 align:middle line:84% K. The social benefit of it coming in is like delta q times 00:22:59.610 --> 00:23:00.840 align:middle line:90% p minus c. 00:23:00.840 --> 00:23:03.697 align:middle line:84% But its profits are much bigger than-- its variable profits are 00:23:03.697 --> 00:23:05.280 align:middle line:84% much bigger than delta q times p minus 00:23:05.280 --> 00:23:07.197 align:middle line:84% c because it's getting all the profits and all 00:23:07.197 --> 00:23:09.870 align:middle line:84% the other units it's taking away from other firms instead. 00:23:09.870 --> 00:23:12.010 align:middle line:84% And so that's the business stealing effect. 00:23:12.010 --> 00:23:15.900 align:middle line:84% And in this homogeneous good model, 00:23:15.900 --> 00:23:17.650 align:middle line:84% that business stealing effect is positive. 00:23:17.650 --> 00:23:19.025 align:middle line:84% Therefore, you get too much entry 00:23:19.025 --> 00:23:21.245 align:middle line:84% other than this possible rounding error question. 00:23:21.245 --> 00:23:24.070 align:middle line:90% 00:23:24.070 --> 00:23:26.500 align:middle line:84% As I said, it's true up to a rounding error, 00:23:26.500 --> 00:23:28.240 align:middle line:84% but if you do numerical examples, 00:23:28.240 --> 00:23:30.430 align:middle line:84% you find that you often get many, many more 00:23:30.430 --> 00:23:34.780 align:middle line:90% firms than you'd want socially. 00:23:34.780 --> 00:23:38.650 align:middle line:84% And the reason is that it's not just some of the demand 00:23:38.650 --> 00:23:40.083 align:middle line:90% is business stealing. 00:23:40.083 --> 00:23:41.750 align:middle line:84% Most of the demand is business stealing. 00:23:41.750 --> 00:23:45.090 align:middle line:84% So in this Cournot example, D of p is 1 minus p. 00:23:45.090 --> 00:23:48.940 align:middle line:90% q star of N is 1 over N plus 1. 00:23:48.940 --> 00:23:53.530 align:middle line:84% So what do you get from adding an Nth firm? 00:23:53.530 --> 00:23:56.560 align:middle line:84% When you have N firms production goes up to N over plus 1 00:23:56.560 --> 00:23:59.840 align:middle line:84% where it used to be N minus 1 over N, 00:23:59.840 --> 00:24:04.285 align:middle line:84% so that difference is 1 over N times N plus 1. 00:24:04.285 --> 00:24:07.470 align:middle line:90% 00:24:07.470 --> 00:24:10.800 align:middle line:84% The Nth firm is producing 1 over N plus 1. 00:24:10.800 --> 00:24:16.260 align:middle line:84% So 1 over N fraction of its output is actual added output. 00:24:16.260 --> 00:24:21.220 align:middle line:84% N minus 1 over N of its output is business stealing output. 00:24:21.220 --> 00:24:24.660 align:middle line:84% And so in some sense, the incentive that it has to enter 00:24:24.660 --> 00:24:31.350 align:middle line:84% is N times too large because it's treating 1 over N plus 1 00:24:31.350 --> 00:24:34.500 align:middle line:84% as the benefit it's getting, whereas 1 over N times that 00:24:34.500 --> 00:24:37.770 align:middle line:84% is actually the social benefit that it's producing. 00:24:37.770 --> 00:24:43.865 align:middle line:84% And so because private benefit is N times the social benefit-- 00:24:43.865 --> 00:24:45.990 align:middle line:84% when private benefit is N times the social benefit, 00:24:45.990 --> 00:24:48.157 align:middle line:84% you can get way, way too many firms into the market. 00:24:48.157 --> 00:24:51.650 align:middle line:90% 00:24:51.650 --> 00:24:53.540 align:middle line:90% OK, so now let me think of it-- 00:24:53.540 --> 00:24:56.410 align:middle line:84% that was entry when you have homogeneous goods. 00:24:56.410 --> 00:24:58.980 align:middle line:84% What happens when you get away from homogeneous goods? 00:24:58.980 --> 00:25:00.920 align:middle line:84% When you get away from homogeneous goods, 00:25:00.920 --> 00:25:04.380 align:middle line:84% entry can be too high or too low. 00:25:04.380 --> 00:25:05.430 align:middle line:90% And why is that? 00:25:05.430 --> 00:25:07.750 align:middle line:90% Well, the general setup-- 00:25:07.750 --> 00:25:09.657 align:middle line:84% welfare when you have N firms, it's 00:25:09.657 --> 00:25:11.740 align:middle line:84% going to be the sum of all the firms in the market 00:25:11.740 --> 00:25:16.030 align:middle line:84% of their variable profits plus the total consumer 00:25:16.030 --> 00:25:18.375 align:middle line:84% surplus in the market minus the fixed costs. 00:25:18.375 --> 00:25:20.890 align:middle line:90% 00:25:20.890 --> 00:25:26.380 align:middle line:84% If I add an N plus first firm, I get the sum over N 00:25:26.380 --> 00:25:29.590 align:middle line:84% plus 1 firms instead of N firms of the variable profits. 00:25:29.590 --> 00:25:33.000 align:middle line:84% I now get consumer surplus when you have N plus 1 firms, 00:25:33.000 --> 00:25:36.090 align:middle line:90% but I pay higher fixed costs. 00:25:36.090 --> 00:25:40.560 align:middle line:84% So what's the change in welfare from the last entrant? 00:25:40.560 --> 00:25:42.570 align:middle line:84% First, let me group together the firm 00:25:42.570 --> 00:25:46.440 align:middle line:84% that's here that wasn't in this sum, the firm N plus 1. 00:25:46.440 --> 00:25:48.870 align:middle line:84% I get the variable profit of firm N 00:25:48.870 --> 00:25:52.050 align:middle line:90% plus 1 minus its fixed cost. 00:25:52.050 --> 00:25:54.450 align:middle line:90% That's a difference here. 00:25:54.450 --> 00:25:56.650 align:middle line:90% And then I get two other terms. 00:25:56.650 --> 00:26:01.200 align:middle line:84% The first is subtracting the corresponding i's here, 00:26:01.200 --> 00:26:05.280 align:middle line:84% I get sum i equals 1 to N variable profits of firm i 00:26:05.280 --> 00:26:07.860 align:middle line:90% with N plus 1 versus N firms. 00:26:07.860 --> 00:26:10.200 align:middle line:84% And then I get the consumer surplus with N 00:26:10.200 --> 00:26:11.525 align:middle line:90% plus 1 minus N firms. 00:26:11.525 --> 00:26:14.860 align:middle line:90% 00:26:14.860 --> 00:26:17.860 align:middle line:84% So when I wrote here "entry is socially optimal," 00:26:17.860 --> 00:26:20.680 align:middle line:84% I probably should have said entry of firm N plus 1 is 00:26:20.680 --> 00:26:24.890 align:middle line:84% socially optimal if this delta W is positive. 00:26:24.890 --> 00:26:28.550 align:middle line:90% 00:26:28.550 --> 00:26:30.440 align:middle line:90% Why might free entry-- 00:26:30.440 --> 00:26:35.060 align:middle line:84% so what we want is if this is positive, we want firm N plus 1 00:26:35.060 --> 00:26:36.060 align:middle line:90% to come in. 00:26:36.060 --> 00:26:38.900 align:middle line:84% And if firm-- if delta W was negative, 00:26:38.900 --> 00:26:42.350 align:middle line:84% we don't want firm N plus 1 to come in. 00:26:42.350 --> 00:26:46.170 align:middle line:84% So first of all, why might entry be excessive? 00:26:46.170 --> 00:26:49.250 align:middle line:84% So entry would be excessive if this was positive 00:26:49.250 --> 00:26:50.930 align:middle line:90% but this was negative. 00:26:50.930 --> 00:26:53.550 align:middle line:84% Why could this be positive and this be negative? 00:26:53.550 --> 00:26:56.270 align:middle line:84% Well, if this is positive but small 00:26:56.270 --> 00:27:00.690 align:middle line:84% to make a firm want to come in but this 00:27:00.690 --> 00:27:02.610 align:middle line:90% is a big negative number-- 00:27:02.610 --> 00:27:04.500 align:middle line:84% and why could this be a big negative number? 00:27:04.500 --> 00:27:06.960 align:middle line:84% This is how every other firm's profits 00:27:06.960 --> 00:27:09.020 align:middle line:90% are affected by me coming in. 00:27:09.020 --> 00:27:12.210 align:middle line:84% If I drive down prices and I take quantity away 00:27:12.210 --> 00:27:16.410 align:middle line:84% from the other firms, they suffer both because the profits 00:27:16.410 --> 00:27:19.090 align:middle line:84% they earn on the units they still sell go down 00:27:19.090 --> 00:27:21.360 align:middle line:84% and because they don't sell some units 00:27:21.360 --> 00:27:23.480 align:middle line:84% and they don't earn p star minus c. 00:27:23.480 --> 00:27:25.470 align:middle line:84% So this is what we call-- again, this is 00:27:25.470 --> 00:27:26.700 align:middle line:90% the business stealing effect. 00:27:26.700 --> 00:27:29.680 align:middle line:84% If this business stealing number is always negative-- 00:27:29.680 --> 00:27:31.740 align:middle line:84% if it's a big negative number and this 00:27:31.740 --> 00:27:35.220 align:middle line:84% is a small positive number, we can get the entrant coming in, 00:27:35.220 --> 00:27:37.510 align:middle line:84% even though this business stealing term is negative. 00:27:37.510 --> 00:27:40.040 align:middle line:90% 00:27:40.040 --> 00:27:43.130 align:middle line:84% But then the second effect is that we 00:27:43.130 --> 00:27:48.750 align:middle line:84% could have firm N doesn't come in because this is negative. 00:27:48.750 --> 00:27:52.350 align:middle line:84% And this is negative but delta W is positive 00:27:52.350 --> 00:27:58.660 align:middle line:84% because there's a big increase in consumer surplus. 00:27:58.660 --> 00:28:01.220 align:middle line:84% And I showed the homogeneous good model 00:28:01.220 --> 00:28:05.310 align:middle line:84% this doesn't happen except with that rounding error effect. 00:28:05.310 --> 00:28:08.410 align:middle line:84% But once you get to heterogeneous goods, 00:28:08.410 --> 00:28:10.960 align:middle line:84% it could be that when you get more goods in the market, 00:28:10.960 --> 00:28:13.510 align:middle line:84% consumer surplus goes up by more than prices 00:28:13.510 --> 00:28:16.150 align:middle line:84% go down because consumers get a good that's 00:28:16.150 --> 00:28:18.160 align:middle line:90% better matched to their tastes. 00:28:18.160 --> 00:28:21.230 align:middle line:84% And because the new good is better matched to their tastes, 00:28:21.230 --> 00:28:23.590 align:middle line:84% there's a big increase in consumer surplus 00:28:23.590 --> 00:28:26.320 align:middle line:84% that isn't just the loss and profits. 00:28:26.320 --> 00:28:28.120 align:middle line:84% And so if the increase in consumer surplus 00:28:28.120 --> 00:28:31.150 align:middle line:84% is coming from other channels like match quality 00:28:31.150 --> 00:28:34.000 align:middle line:84% rather than just from prices going down, 00:28:34.000 --> 00:28:38.840 align:middle line:84% then this term can outweigh the business stealing effect 00:28:38.840 --> 00:28:42.730 align:middle line:84% and you could have too few firms in a market because firms-- 00:28:42.730 --> 00:28:44.300 align:middle line:90% firms don't like-- 00:28:44.300 --> 00:28:47.020 align:middle line:84% I mean, firms not internalizing consumer surplus 00:28:47.020 --> 00:28:49.510 align:middle line:84% is why you get too few firms in the Bertrand model. 00:28:49.510 --> 00:28:52.960 align:middle line:84% In the Bertrand model, firms don't realize I come in, yes, I 00:28:52.960 --> 00:28:55.090 align:middle line:84% lose some money, but all those consumers 00:28:55.090 --> 00:28:59.840 align:middle line:84% are way better off because the price drops so much. 00:28:59.840 --> 00:29:02.490 align:middle line:84% But in another model, it's the consumers don't realize-- 00:29:02.490 --> 00:29:04.468 align:middle line:84% the firms don't realize that, like, I come in, 00:29:04.468 --> 00:29:06.260 align:middle line:84% I don't make that much money, but consumers 00:29:06.260 --> 00:29:10.780 align:middle line:84% are so happy to have my product that social welfare is better. 00:29:10.780 --> 00:29:16.360 align:middle line:90% 00:29:16.360 --> 00:29:18.250 align:middle line:90% OK, any questions? 00:29:18.250 --> 00:29:20.800 align:middle line:84% So in a general model, the most general conclusion 00:29:20.800 --> 00:29:23.150 align:middle line:84% is that entry can be too high or too low socially. 00:29:23.150 --> 00:29:26.430 align:middle line:84% And it depends on which of these effects is more important, 00:29:26.430 --> 00:29:30.070 align:middle line:84% the social welfare effect or the business stealing effect. 00:29:30.070 --> 00:29:34.490 align:middle line:84% Prices going down alone is not enough to do it. 00:29:34.490 --> 00:29:36.760 align:middle line:84% You've got to have other channels of the consumer 00:29:36.760 --> 00:29:37.830 align:middle line:90% surplus going up. 00:29:37.830 --> 00:29:44.630 align:middle line:90% 00:29:44.630 --> 00:29:47.870 align:middle line:84% I just figured I'd put in one slide of what happens if I 00:29:47.870 --> 00:29:49.760 align:middle line:90% actually compute these things. 00:29:49.760 --> 00:29:53.670 align:middle line:84% I would say that if you write down the most obvious models 00:29:53.670 --> 00:29:56.460 align:middle line:84% you're going to write down to try to compute these things. 00:29:56.460 --> 00:30:00.420 align:middle line:84% While this consumer surplus effect means that welfare can-- 00:30:00.420 --> 00:30:04.385 align:middle line:84% we can get too few firms, most models you write down, 00:30:04.385 --> 00:30:06.510 align:middle line:84% if you're not thinking about writing down something 00:30:06.510 --> 00:30:07.800 align:middle line:84% to get it to happen, you're going 00:30:07.800 --> 00:30:09.258 align:middle line:84% to also conclude that there's still 00:30:09.258 --> 00:30:10.960 align:middle line:90% way too many firms in markets. 00:30:10.960 --> 00:30:13.240 align:middle line:90% So I do an example here. 00:30:13.240 --> 00:30:16.320 align:middle line:84% So consider a Hotelling-like model, where 00:30:16.320 --> 00:30:18.570 align:middle line:90% you have a mass m of consumers. 00:30:18.570 --> 00:30:21.210 align:middle line:90% And I'll write over here. 00:30:21.210 --> 00:30:25.540 align:middle line:84% So let's think about a Hotelling circle. 00:30:25.540 --> 00:30:27.030 align:middle line:90% So this is, ah-- 00:30:27.030 --> 00:30:31.080 align:middle line:84% ice cream stands locating around like a Hawaiian island that 00:30:31.080 --> 00:30:33.660 align:middle line:84% has just beaches around the entire perimeter. 00:30:33.660 --> 00:30:35.253 align:middle line:90% And so if you get N firms-- 00:30:35.253 --> 00:30:38.950 align:middle line:90% 00:30:38.950 --> 00:30:41.040 align:middle line:84% suppose you get N firms; they locate themselves 00:30:41.040 --> 00:30:42.245 align:middle line:90% evenly around the circle. 00:30:42.245 --> 00:30:47.880 align:middle line:90% 00:30:47.880 --> 00:30:50.880 align:middle line:90% In the c plus t model-- 00:30:50.880 --> 00:30:55.560 align:middle line:84% if you have N firms, the transportation cost distance 00:30:55.560 --> 00:30:57.780 align:middle line:84% between here and here is only going 00:30:57.780 --> 00:30:59.970 align:middle line:84% to be t over N when you have N firms. 00:30:59.970 --> 00:31:03.690 align:middle line:84% So if it's t to walk the whole perimeter of the island, 00:31:03.690 --> 00:31:07.360 align:middle line:84% it's t over N when you put N firms around the perimeter. 00:31:07.360 --> 00:31:11.640 align:middle line:84% So if you get N firms that are arranged evenly, 00:31:11.640 --> 00:31:13.650 align:middle line:84% what you basically get is each firm here 00:31:13.650 --> 00:31:15.570 align:middle line:84% is just competing with the firm on its right 00:31:15.570 --> 00:31:17.250 align:middle line:90% and the firm on its left. 00:31:17.250 --> 00:31:20.430 align:middle line:84% I didn't draw those so evenly, but let's assume 00:31:20.430 --> 00:31:23.160 align:middle line:84% this distance is t over N, this distance is t over N. 00:31:23.160 --> 00:31:25.650 align:middle line:84% So it's just like I'm playing two simultaneous Hotelling 00:31:25.650 --> 00:31:28.590 align:middle line:84% games, one against this firm, one against this firm. 00:31:28.590 --> 00:31:35.740 align:middle line:84% So the equilibrium becomes p star equals c plus t over N. 00:31:35.740 --> 00:31:38.020 align:middle line:90% What's the variable profit? 00:31:38.020 --> 00:31:41.620 align:middle line:84% If there are m consumers on the beach, 00:31:41.620 --> 00:31:44.440 align:middle line:84% I get a fraction 1 over N of them in equilibrium, 00:31:44.440 --> 00:31:56.500 align:middle line:84% and my markup is t over N. So my profits are mt over N squared. 00:31:56.500 --> 00:31:58.990 align:middle line:84% I set that equal to K, and then it 00:31:58.990 --> 00:32:03.220 align:middle line:84% just becomes N equals square root of m times t over K. 00:32:03.220 --> 00:32:06.790 align:middle line:84% So again, as I said, this is, again, 00:32:06.790 --> 00:32:12.180 align:middle line:84% a larger firms theorem that says as the market size goes up, 00:32:12.180 --> 00:32:13.930 align:middle line:84% the number of firms goes up in this model, 00:32:13.930 --> 00:32:16.446 align:middle line:84% also like the square root of the number of customers. 00:32:16.446 --> 00:32:20.180 align:middle line:90% 00:32:20.180 --> 00:32:22.670 align:middle line:90% What's the social welfare? 00:32:22.670 --> 00:32:24.066 align:middle line:90% There are m consumers. 00:32:24.066 --> 00:32:29.165 align:middle line:90% 00:32:29.165 --> 00:32:31.290 align:middle line:84% So suppose we're in this model and these things are 00:32:31.290 --> 00:32:38.550 align:middle line:84% both t over N. Social welfare is just total gross surplus 00:32:38.550 --> 00:32:42.330 align:middle line:84% received minus costs of production 00:32:42.330 --> 00:32:46.980 align:middle line:84% minus average mismatch disutility or transportation 00:32:46.980 --> 00:32:50.730 align:middle line:90% cost disutility. 00:32:50.730 --> 00:32:55.470 align:middle line:84% This guy here sells to customers who are within distance t over 00:32:55.470 --> 00:33:03.990 align:middle line:84% 2N to the left and customers within t over 2N to the right. 00:33:03.990 --> 00:33:07.030 align:middle line:84% So he's selling to customers who are-- t over N is this distance. 00:33:07.030 --> 00:33:09.960 align:middle line:84% So everybody equidistant between him and the next firm 00:33:09.960 --> 00:33:11.490 align:middle line:90% over buys from him. 00:33:11.490 --> 00:33:15.120 align:middle line:84% If you sell to customers whose distance ranges from 0 to t over 00:33:15.120 --> 00:33:19.950 align:middle line:84% 2N, the average distance that people have to travel is t over 00:33:19.950 --> 00:33:21.030 align:middle line:90% 4N. 00:33:21.030 --> 00:33:24.180 align:middle line:84% So this is the extra welfare increase that I mentioned, 00:33:24.180 --> 00:33:28.570 align:middle line:84% that as N increases, the distance traveled goes down. 00:33:28.570 --> 00:33:30.690 align:middle line:84% That causes a consumer surplus increase 00:33:30.690 --> 00:33:32.070 align:middle line:84% that's separate from the one that 00:33:32.070 --> 00:33:35.400 align:middle line:90% comes from the prices dropping. 00:33:35.400 --> 00:33:39.630 align:middle line:84% Anyway, so in this model, total social welfare is m times v 00:33:39.630 --> 00:33:45.820 align:middle line:84% minus m times c minus m times t over 4N minus NK. 00:33:45.820 --> 00:33:49.420 align:middle line:84% Notice that m times v minus c is completely independent of N. 00:33:49.420 --> 00:33:52.390 align:middle line:84% And the Hotelling model, assuming v is large, 00:33:52.390 --> 00:33:54.490 align:middle line:90% everybody buys all the time. 00:33:54.490 --> 00:33:57.640 align:middle line:90% So what we get is-- 00:33:57.640 --> 00:34:00.100 align:middle line:84% differentiating this with respect to N, 00:34:00.100 --> 00:34:03.670 align:middle line:84% derivative of this with respect to N is mt over 4 times 1 00:34:03.670 --> 00:34:05.320 align:middle line:90% over N squared. 00:34:05.320 --> 00:34:09.280 align:middle line:84% Derivative of this with respect to N is just K. 00:34:09.280 --> 00:34:13.030 align:middle line:84% And so what I get is that m over 4 times 1 over N squared minus 00:34:13.030 --> 00:34:16.330 align:middle line:84% K, if I add N second best equals 0, 00:34:16.330 --> 00:34:20.020 align:middle line:84% N second best is square root of mt over 4K, 00:34:20.020 --> 00:34:25.659 align:middle line:90% which is exactly half of N star. 00:34:25.659 --> 00:34:27.790 align:middle line:84% So this is saying, in some sense, in equilibrium, 00:34:27.790 --> 00:34:32.900 align:middle line:84% you get exactly twice as many firms as you would like. 00:34:32.900 --> 00:34:34.130 align:middle line:90% And this is just-- 00:34:34.130 --> 00:34:35.975 align:middle line:84% it's another case that in this model-- 00:34:35.975 --> 00:34:38.719 align:middle line:90% 00:34:38.719 --> 00:34:40.760 align:middle line:84% so this model has the welfare benefit 00:34:40.760 --> 00:34:43.040 align:middle line:84% of people getting better matches. 00:34:43.040 --> 00:34:46.260 align:middle line:84% This model has no market expansion effect whatsoever. 00:34:46.260 --> 00:34:49.850 align:middle line:84% When you put in an Nth firm, it's 100% business stealing. 00:34:49.850 --> 00:34:53.060 align:middle line:84% And so it turns out that because the market expansion is 00:34:53.060 --> 00:34:56.870 align:middle line:84% 100% business stealing, so business stealing is a big deal, 00:34:56.870 --> 00:35:00.410 align:middle line:84% this extra benefit that you get from extra match quality 00:35:00.410 --> 00:35:03.650 align:middle line:84% isn't nearly large enough to overcome the business stealing 00:35:03.650 --> 00:35:06.860 align:middle line:84% negative, and you're getting twice as many firms. 00:35:06.860 --> 00:35:09.980 align:middle line:84% And I think, in some sense, I view 00:35:09.980 --> 00:35:12.280 align:middle line:84% this as an important cautionary tale. 00:35:12.280 --> 00:35:14.702 align:middle line:84% You're going to write down models with logit demand 00:35:14.702 --> 00:35:16.660 align:middle line:84% and estimate how many firms you're going to get 00:35:16.660 --> 00:35:19.750 align:middle line:84% and how many firms you think are optimal or whatever. 00:35:19.750 --> 00:35:22.162 align:middle line:84% A lot of models like this are set up-- again, 00:35:22.162 --> 00:35:23.620 align:middle line:84% I could have done this model, and I 00:35:23.620 --> 00:35:26.230 align:middle line:84% could have said I'm estimating demand 00:35:26.230 --> 00:35:29.350 align:middle line:90% elasticities by estimating t. 00:35:29.350 --> 00:35:33.250 align:middle line:84% But whatever value of t I estimated when I estimated 00:35:33.250 --> 00:35:34.865 align:middle line:90% this model, my model-- 00:35:34.865 --> 00:35:36.490 align:middle line:84% I do my counterfactual and say how many 00:35:36.490 --> 00:35:38.365 align:middle line:84% firms would be socially optimal, and socially 00:35:38.365 --> 00:35:41.140 align:middle line:84% optimal would be exactly half the number that are observed. 00:35:41.140 --> 00:35:44.030 align:middle line:84% So it's just important to be aware of. 00:35:44.030 --> 00:35:48.065 align:middle line:84% Do models have built-in answers as to whether the consumer 00:35:48.065 --> 00:35:50.440 align:middle line:84% surplus effect is going to outweigh the business stealing 00:35:50.440 --> 00:35:51.230 align:middle line:90% effect or not? 00:35:51.230 --> 00:35:52.730 align:middle line:84% And this one, it's totally built in. 00:35:52.730 --> 00:35:55.510 align:middle line:84% And the answer is it's a factor of 2. 00:35:55.510 --> 00:35:58.420 align:middle line:90% But I think it's generally true. 00:35:58.420 --> 00:36:03.087 align:middle line:84% Most models you write down, you are going to get a factor-- 00:36:03.087 --> 00:36:05.420 align:middle line:84% you are going to find that there are way too many firms. 00:36:05.420 --> 00:36:07.240 align:middle line:90% And I don't know if I-- 00:36:07.240 --> 00:36:08.860 align:middle line:90% maybe I believe that. 00:36:08.860 --> 00:36:09.813 align:middle line:90% How would you get-- 00:36:09.813 --> 00:36:13.450 align:middle line:90% 00:36:13.450 --> 00:36:19.650 align:middle line:84% how would you get bigger social welfare benefits? 00:36:19.650 --> 00:36:22.690 align:middle line:84% There's two ways you would get bigger social welfare benefits. 00:36:22.690 --> 00:36:25.950 align:middle line:84% The first is-- in this model, people's utility 00:36:25.950 --> 00:36:30.150 align:middle line:84% for getting a product that's not ideal just goes down linearly. 00:36:30.150 --> 00:36:34.350 align:middle line:84% If you imagine people's utility looked more like this, 00:36:34.350 --> 00:36:38.280 align:middle line:84% so there are people who really, really like 00:36:38.280 --> 00:36:42.630 align:middle line:84% having a product that's very close to their-- 00:36:42.630 --> 00:36:44.440 align:middle line:90% very close to their ideal point. 00:36:44.440 --> 00:36:47.160 align:middle line:84% So when you add an extra and have three ideal points instead 00:36:47.160 --> 00:36:49.950 align:middle line:84% of two, you're giving some people lots and lots 00:36:49.950 --> 00:36:51.340 align:middle line:90% of extra utility. 00:36:51.340 --> 00:36:54.840 align:middle line:84% So having something like this, people 00:36:54.840 --> 00:36:57.120 align:middle line:84% who like things very close to their ideal point, 00:36:57.120 --> 00:37:03.240 align:middle line:84% would be one way to get entry to be not too high. 00:37:03.240 --> 00:37:05.028 align:middle line:84% Obviously, you can only go so high here 00:37:05.028 --> 00:37:07.320 align:middle line:84% before the firm is going to give up on serving everyone 00:37:07.320 --> 00:37:09.487 align:middle line:84% and just serve the people who like its product a lot 00:37:09.487 --> 00:37:10.862 align:middle line:90% at a really high price. 00:37:10.862 --> 00:37:13.320 align:middle line:84% So that's going to be kind of like those information design 00:37:13.320 --> 00:37:16.010 align:middle line:84% things where you can only make the curve go up so much 00:37:16.010 --> 00:37:18.220 align:middle line:84% and have the firm still sell to everybody. 00:37:18.220 --> 00:37:22.300 align:middle line:84% And then the other effect is here, again, 100% of your demand 00:37:22.300 --> 00:37:23.300 align:middle line:90% is business stealing. 00:37:23.300 --> 00:37:25.600 align:middle line:84% If you think of an infinite dimensional space, where 00:37:25.600 --> 00:37:28.420 align:middle line:84% most people are not buying any product at all, 00:37:28.420 --> 00:37:32.620 align:middle line:84% so every new firm that comes in is mostly serving new customers. 00:37:32.620 --> 00:37:36.280 align:middle line:84% So if you can make the business stealing effect small 00:37:36.280 --> 00:37:39.408 align:middle line:84% and make this consumer surplus large for people 00:37:39.408 --> 00:37:41.200 align:middle line:84% who get close matches, those are the things 00:37:41.200 --> 00:37:45.390 align:middle line:84% that are going to make entry be insufficient in practice. 00:37:45.390 --> 00:37:49.000 align:middle line:84% And I think if you want to do an empirical study, 00:37:49.000 --> 00:37:50.590 align:middle line:84% you'd really want to think about, 00:37:50.590 --> 00:37:53.170 align:middle line:84% do I have free parameters to capture 00:37:53.170 --> 00:37:54.560 align:middle line:90% what this surplus looks like? 00:37:54.560 --> 00:37:56.750 align:middle line:84% And do I have a free parameter to capture 00:37:56.750 --> 00:37:59.590 align:middle line:84% how much of the people are being added 00:37:59.590 --> 00:38:03.370 align:middle line:84% to the model versus how many people are just business stolen 00:38:03.370 --> 00:38:04.125 align:middle line:90% from another firm? 00:38:04.125 --> 00:38:08.040 align:middle line:90% 00:38:08.040 --> 00:38:10.900 align:middle line:84% For instance, I read that nested logit has that extra parameter 00:38:10.900 --> 00:38:12.900 align:middle line:84% that substitution to the outside good 00:38:12.900 --> 00:38:15.660 align:middle line:84% is different from substitution to the inside goods. 00:38:15.660 --> 00:38:18.150 align:middle line:84% And a pure logit with no outside good 00:38:18.150 --> 00:38:19.895 align:middle line:90% is 100% business stealing model. 00:38:19.895 --> 00:38:22.420 align:middle line:90% 00:38:22.420 --> 00:38:23.050 align:middle line:90% Questions? 00:38:23.050 --> 00:38:25.640 align:middle line:90% 00:38:25.640 --> 00:38:29.390 align:middle line:84% Entry with vertical differentiation. 00:38:29.390 --> 00:38:32.660 align:middle line:84% OK, so let's go back again and review 00:38:32.660 --> 00:38:35.540 align:middle line:84% our classic vertical differentiation model. 00:38:35.540 --> 00:38:38.960 align:middle line:84% You have consumers that have these vertical types theta. 00:38:38.960 --> 00:38:41.330 align:middle line:84% They have unit demands where your utility 00:38:41.330 --> 00:38:45.560 align:middle line:84% is theta times the quality of the good minus p. 00:38:45.560 --> 00:38:49.280 align:middle line:84% Let's assume that firms have fixed entry costs K. 00:38:49.280 --> 00:38:51.950 align:middle line:84% And then they have constant marginal cost c of s, 00:38:51.950 --> 00:38:53.810 align:middle line:84% where the higher quality products 00:38:53.810 --> 00:38:56.750 align:middle line:90% are more expensive to produce. 00:38:56.750 --> 00:38:59.400 align:middle line:90% So consider a two-stage game. 00:38:59.400 --> 00:39:01.220 align:middle line:84% The first, the firms are simultaneously 00:39:01.220 --> 00:39:02.960 align:middle line:90% choosing whether to enter. 00:39:02.960 --> 00:39:04.940 align:middle line:84% And if they enter, they're going to choose 00:39:04.940 --> 00:39:07.850 align:middle line:90% which quality level to produce. 00:39:07.850 --> 00:39:09.713 align:middle line:84% And then, once they've done that, 00:39:09.713 --> 00:39:12.380 align:middle line:84% they compete in prices according to the vertical differentiation 00:39:12.380 --> 00:39:14.770 align:middle line:90% model. 00:39:14.770 --> 00:39:17.620 align:middle line:84% And Shaked and Sutton have this classic paper 00:39:17.620 --> 00:39:22.330 align:middle line:84% that shows that you can get two different types of outcomes 00:39:22.330 --> 00:39:24.400 align:middle line:90% in this. 00:39:24.400 --> 00:39:28.485 align:middle line:84% First one is what they call the natural oligopoly case. 00:39:28.485 --> 00:39:31.670 align:middle line:90% 00:39:31.670 --> 00:39:40.482 align:middle line:84% So imagine that if I put s on this axis and I put-- 00:39:40.482 --> 00:39:42.115 align:middle line:90% what am I going to do?-- 00:39:42.115 --> 00:39:45.320 align:middle line:90% 00:39:45.320 --> 00:39:48.770 align:middle line:84% either the value that they get from s, theta s minus p, 00:39:48.770 --> 00:39:51.610 align:middle line:84% on this axis or I put c of s on this axis. 00:39:51.610 --> 00:39:54.600 align:middle line:90% 00:39:54.600 --> 00:40:03.180 align:middle line:84% So imagine that-- imagine that you have relatively 00:40:03.180 --> 00:40:05.610 align:middle line:90% flat marginal cost curves. 00:40:05.610 --> 00:40:09.360 align:middle line:84% So imagine that marginal cost c of s 00:40:09.360 --> 00:40:12.260 align:middle line:84% looks like this, that there's just not 00:40:12.260 --> 00:40:15.650 align:middle line:84% that much cost to producing high-quality goods. 00:40:15.650 --> 00:40:21.230 align:middle line:84% And suppose that you have like theta lower bar 00:40:21.230 --> 00:40:23.570 align:middle line:90% times s looks like this. 00:40:23.570 --> 00:40:32.230 align:middle line:84% And theta upper bar s minus p looks like that. 00:40:32.230 --> 00:40:35.260 align:middle line:84% So we have a model where everybody, even the lowest 00:40:35.260 --> 00:40:39.280 align:middle line:84% possible types, value quality more than it costs to produce 00:40:39.280 --> 00:40:41.980 align:middle line:90% the extra units of quality. 00:40:41.980 --> 00:40:47.230 align:middle line:84% And there's some range here, s lower bar, 00:40:47.230 --> 00:40:48.850 align:middle line:84% s upper bar of the qualities that 00:40:48.850 --> 00:40:50.070 align:middle line:90% are available to be produced. 00:40:50.070 --> 00:40:52.828 align:middle line:90% 00:40:52.828 --> 00:40:57.390 align:middle line:84% In a model like this, what they call the natural oligopoly case, 00:40:57.390 --> 00:40:59.888 align:middle line:90% everybody should-- 00:40:59.888 --> 00:41:02.430 align:middle line:84% in an efficient market, everyone should be buying the highest 00:41:02.430 --> 00:41:05.080 align:middle line:90% possible quality. 00:41:05.080 --> 00:41:09.220 align:middle line:84% And so if you imagine what happens-- 00:41:09.220 --> 00:41:16.670 align:middle line:84% suppose you have lots of firms entering and producing 00:41:16.670 --> 00:41:18.330 align:middle line:90% different qualities. 00:41:18.330 --> 00:41:22.610 align:middle line:84% And then what are they going to set their prices at? 00:41:22.610 --> 00:41:25.190 align:middle line:84% Well, if you have lots of firms in the market, 00:41:25.190 --> 00:41:27.860 align:middle line:90% the prices are going to fall-- 00:41:27.860 --> 00:41:30.680 align:middle line:84% these are prices; I'm putting dots in here-- 00:41:30.680 --> 00:41:33.140 align:middle line:84% the prices are going to have to fall towards cost as N goes 00:41:33.140 --> 00:41:35.720 align:middle line:84% to-- as the number of firms into this finite product space 00:41:35.720 --> 00:41:37.310 align:middle line:90% goes to infinity. 00:41:37.310 --> 00:41:40.400 align:middle line:84% But then if the prices fall towards cost, 00:41:40.400 --> 00:41:43.720 align:middle line:84% everyone is going to buy from the highest quality firm. 00:41:43.720 --> 00:41:47.590 align:middle line:84% And so you just can't have prices falling to cost, 00:41:47.590 --> 00:41:51.322 align:middle line:84% because if prices fall to cost, all these firms make zero sales, 00:41:51.322 --> 00:41:52.780 align:middle line:84% and then they earn negative profits 00:41:52.780 --> 00:41:56.135 align:middle line:90% after paying their fixed cost K. 00:41:56.135 --> 00:41:58.900 align:middle line:84% So if you have this case where everybody should 00:41:58.900 --> 00:42:01.870 align:middle line:84% buy the same product, there's only a finite number 00:42:01.870 --> 00:42:02.870 align:middle line:90% of firms in the market. 00:42:02.870 --> 00:42:06.940 align:middle line:84% Again, this isn't an N goes to infinity as K goes to 0. 00:42:06.940 --> 00:42:10.610 align:middle line:84% As K goes to 0, you still get a finite number of firms. 00:42:10.610 --> 00:42:13.390 align:middle line:84% It may be this market can fit three firms or five or six 00:42:13.390 --> 00:42:15.790 align:middle line:84% or whatever, but there's a finite amount of entry 00:42:15.790 --> 00:42:19.810 align:middle line:84% that can ever occur if the same product is 00:42:19.810 --> 00:42:21.225 align:middle line:90% efficient for everyone to buy. 00:42:21.225 --> 00:42:24.490 align:middle line:90% 00:42:24.490 --> 00:42:28.210 align:middle line:84% And then the second case they talk about is the specialization 00:42:28.210 --> 00:42:29.440 align:middle line:90% case. 00:42:29.440 --> 00:42:36.010 align:middle line:84% The specialization case would be if you have marginal costs that 00:42:36.010 --> 00:42:37.600 align:middle line:90% work like this. 00:42:37.600 --> 00:42:43.370 align:middle line:84% Marginal costs are initially low, 00:42:43.370 --> 00:42:45.160 align:middle line:84% but then they shoot up like that. 00:42:45.160 --> 00:42:49.890 align:middle line:90% 00:42:49.890 --> 00:42:52.710 align:middle line:84% If the marginal costs look like this, 00:42:52.710 --> 00:42:55.210 align:middle line:84% what's efficient for the theta lower bar types? 00:42:55.210 --> 00:43:00.673 align:middle line:84% The theta lower bar types would pick the point-- 00:43:00.673 --> 00:43:02.090 align:middle line:84% what's efficient for them to do is 00:43:02.090 --> 00:43:05.385 align:middle line:84% where the marginal cost of producing extra quality 00:43:05.385 --> 00:43:07.510 align:middle line:84% is equal to the marginal benefit that they receive. 00:43:07.510 --> 00:43:10.380 align:middle line:90% So the theta lower bar types-- 00:43:10.380 --> 00:43:16.410 align:middle line:84% so this would be s star optimal for the theta lower bar types. 00:43:16.410 --> 00:43:18.150 align:middle line:84% They want to produce where-- they 00:43:18.150 --> 00:43:20.970 align:middle line:84% should be buying the good where the marginal value of increasing 00:43:20.970 --> 00:43:23.670 align:middle line:84% quality is exactly equal to their willingness to pay. 00:43:23.670 --> 00:43:25.572 align:middle line:90% And the theta upper bar types-- 00:43:25.572 --> 00:43:27.155 align:middle line:84% maybe I should have made this steeper. 00:43:27.155 --> 00:43:31.200 align:middle line:84% [CHUCKLES] Let me make theta upper bar even steeper. 00:43:31.200 --> 00:43:33.300 align:middle line:84% The theta upper bar types are going 00:43:33.300 --> 00:43:37.080 align:middle line:84% to have a point where, again, they're going to buy up here, 00:43:37.080 --> 00:43:39.240 align:middle line:90% where it has this greater slope. 00:43:39.240 --> 00:43:42.750 align:middle line:84% So the s star theta upper bar, they 00:43:42.750 --> 00:43:45.090 align:middle line:90% should be buying this product. 00:43:45.090 --> 00:43:48.570 align:middle line:84% And everybody with a theta in between 00:43:48.570 --> 00:43:50.650 align:middle line:84% should be buying something in between. 00:43:50.650 --> 00:43:51.930 align:middle line:90% Everybody should be picking-- 00:43:51.930 --> 00:43:53.580 align:middle line:84% the optimal product for everybody 00:43:53.580 --> 00:43:57.930 align:middle line:84% is the point on that curve where it's 00:43:57.930 --> 00:44:00.240 align:middle line:90% an efficient quality for them. 00:44:00.240 --> 00:44:03.340 align:middle line:84% So if you have a model like this where efficient quality-- 00:44:03.340 --> 00:44:06.060 align:middle line:90% 00:44:06.060 --> 00:44:08.100 align:middle line:84% everybody has a different efficient quality, 00:44:08.100 --> 00:44:09.810 align:middle line:84% then as N goes to infinity, you are 00:44:09.810 --> 00:44:11.840 align:middle line:84% going to get an infinitely divided model. 00:44:11.840 --> 00:44:14.470 align:middle line:84% So every product is efficient for someone. 00:44:14.470 --> 00:44:16.480 align:middle line:84% So if the number of customers is large, 00:44:16.480 --> 00:44:17.990 align:middle line:90% all those products get produced. 00:44:17.990 --> 00:44:20.210 align:middle line:84% They all sell to 1 over N of the people. 00:44:20.210 --> 00:44:22.510 align:middle line:84% They sell to the people whose prices are-- 00:44:22.510 --> 00:44:27.130 align:middle line:84% whose marginal values are close to their marginal-- 00:44:27.130 --> 00:44:31.100 align:middle line:84% whose optimal qualities are close to their quality 00:44:31.100 --> 00:44:34.010 align:middle line:84% and prices do fall towards marginal cost. 00:44:34.010 --> 00:44:36.250 align:middle line:84% But even though prices fall to marginal cost, 00:44:36.250 --> 00:44:40.750 align:middle line:84% everybody still buys it from a different firm. 00:44:40.750 --> 00:44:44.290 align:middle line:84% So what happens with vertical differentiation is sometimes 00:44:44.290 --> 00:44:46.930 align:middle line:84% you can't get a lot of firms, but sometimes you 00:44:46.930 --> 00:44:48.080 align:middle line:90% get the specialization. 00:44:48.080 --> 00:44:51.160 align:middle line:84% And it all depends on whether different products are 00:44:51.160 --> 00:44:52.380 align:middle line:90% optimal for different people. 00:44:52.380 --> 00:44:57.140 align:middle line:90% 00:44:57.140 --> 00:44:58.060 align:middle line:90% Questions? 00:44:58.060 --> 00:45:03.540 align:middle line:90% 00:45:03.540 --> 00:45:08.040 align:middle line:84% OK, so next thing-- next set of papers I want-- 00:45:08.040 --> 00:45:09.930 align:middle line:84% next paper I want to discuss is-- 00:45:09.930 --> 00:45:12.450 align:middle line:90% this paper is motivated by-- 00:45:12.450 --> 00:45:17.700 align:middle line:84% there's a large literature on firm dynamics 00:45:17.700 --> 00:45:21.480 align:middle line:84% and entry and exit that's generated by people 00:45:21.480 --> 00:45:23.970 align:middle line:90% looking at census data. 00:45:23.970 --> 00:45:26.468 align:middle line:90% So I don't know if I mentioned-- 00:45:26.468 --> 00:45:28.510 align:middle line:84% I think I mentioned this earlier in the semester. 00:45:28.510 --> 00:45:32.930 align:middle line:84% So there's this great resource for IO economists 00:45:32.930 --> 00:45:37.710 align:middle line:84% which is called the Census of Manufacturers. 00:45:37.710 --> 00:45:51.980 align:middle line:84% So the Census of Manufacturers is conducted by the US Census 00:45:51.980 --> 00:45:55.520 align:middle line:84% Bureau every five years, all the years 00:45:55.520 --> 00:45:58.310 align:middle line:90% that end in twos and sevens. 00:45:58.310 --> 00:46:00.920 align:middle line:84% Census of Manufacturers, it's a complete census 00:46:00.920 --> 00:46:05.240 align:middle line:84% of every manufacturing firm in the United States. 00:46:05.240 --> 00:46:06.950 align:middle line:84% In addition, the census does something 00:46:06.950 --> 00:46:08.888 align:middle line:84% called the Annual Survey of Manufacturers. 00:46:08.888 --> 00:46:10.430 align:middle line:84% It takes a subset of this and samples 00:46:10.430 --> 00:46:14.480 align:middle line:84% them to produce annual data instead of every-five-year data. 00:46:14.480 --> 00:46:18.610 align:middle line:84% But anyway, they send out census forms 00:46:18.610 --> 00:46:21.040 align:middle line:84% to all manufacturing firms every five years, 00:46:21.040 --> 00:46:24.430 align:middle line:84% asking them lots and lots of questions. 00:46:24.430 --> 00:46:25.850 align:middle line:90% What do they produce? 00:46:25.850 --> 00:46:30.670 align:middle line:84% How much do they sell of every different, narrowly defined 00:46:30.670 --> 00:46:31.700 align:middle line:90% product? 00:46:31.700 --> 00:46:33.710 align:middle line:90% How many employees do you have? 00:46:33.710 --> 00:46:35.810 align:middle line:84% What's the value of your plant and equipment? 00:46:35.810 --> 00:46:38.710 align:middle line:90% How much electricity do you use? 00:46:38.710 --> 00:46:42.610 align:middle line:84% So you get lots of data on these firms. 00:46:42.610 --> 00:46:45.557 align:middle line:84% Sometimes the accounting data of what are all their costs 00:46:45.557 --> 00:46:46.390 align:middle line:90% are hard to believe. 00:46:46.390 --> 00:46:49.120 align:middle line:84% But one thing that's very good in that data is, do you exist? 00:46:49.120 --> 00:46:50.620 align:middle line:90% What's your address? 00:46:50.620 --> 00:46:53.410 align:middle line:90% How many employees do you have? 00:46:53.410 --> 00:46:57.430 align:middle line:84% And so this lets you-- if you want to study entry and exit, 00:46:57.430 --> 00:47:01.000 align:middle line:84% you can just-- there's a windowless room at the NBER 00:47:01.000 --> 00:47:02.840 align:middle line:84% where one can access census data. 00:47:02.840 --> 00:47:05.260 align:middle line:84% Now, as a graduate student, one of the difficulties 00:47:05.260 --> 00:47:08.890 align:middle line:84% is that you try to access it through the NBER, 00:47:08.890 --> 00:47:11.470 align:middle line:84% and there's a two-year application process 00:47:11.470 --> 00:47:14.840 align:middle line:84% to be approved as a special sworn employee of the census. 00:47:14.840 --> 00:47:18.232 align:middle line:84% And two years is a long time for a graduate student. 00:47:18.232 --> 00:47:20.440 align:middle line:84% I don't know if I should say this on camera, I think, 00:47:20.440 --> 00:47:22.120 align:middle line:84% but what people often do if they want 00:47:22.120 --> 00:47:24.700 align:middle line:84% to access census data is they get a RA job working 00:47:24.700 --> 00:47:27.100 align:middle line:84% with someone who has access to the census data, 00:47:27.100 --> 00:47:30.070 align:middle line:84% learn the census data well enough that they can describe 00:47:30.070 --> 00:47:33.130 align:middle line:84% all of the regressions and code that they will run when they get 00:47:33.130 --> 00:47:35.920 align:middle line:84% access to the census data, and then they have all the programs 00:47:35.920 --> 00:47:38.680 align:middle line:84% entirely written to just push the run 00:47:38.680 --> 00:47:40.540 align:middle line:84% button when their access is eventually 00:47:40.540 --> 00:47:41.740 align:middle line:90% approved two years later. 00:47:41.740 --> 00:47:43.690 align:middle line:84% And then they can write their paper 00:47:43.690 --> 00:47:45.730 align:middle line:84% using the Census of Manufacturers data. 00:47:45.730 --> 00:47:49.990 align:middle line:84% But anyway, one thing that's very good to do with census data 00:47:49.990 --> 00:47:56.840 align:middle line:84% is you can get very good statistics on, how many firms 00:47:56.840 --> 00:47:58.440 align:middle line:90% enter every five years? 00:47:58.440 --> 00:48:00.320 align:middle line:90% How many firms grow? 00:48:00.320 --> 00:48:02.730 align:middle line:84% Of firms that enter in a five-year period, 00:48:02.730 --> 00:48:05.747 align:middle line:84% how many of them are still there five years later? 00:48:05.747 --> 00:48:07.830 align:middle line:84% Of the ones that are still there five years later, 00:48:07.830 --> 00:48:08.997 align:middle line:90% how many of them have grown? 00:48:08.997 --> 00:48:10.520 align:middle line:90% How many of them have shrunk? 00:48:10.520 --> 00:48:13.100 align:middle line:84% What's the relative profitability 00:48:13.100 --> 00:48:15.530 align:middle line:84% of the new firms versus the old firms? 00:48:15.530 --> 00:48:22.370 align:middle line:84% So there's a set of old papers I used to teach here. 00:48:22.370 --> 00:48:27.080 align:middle line:84% Obviously, the classic one that's still on my syllabus is 00:48:27.080 --> 00:48:34.670 align:middle line:84% Dunne, Roberts, and Samuelson from the 1970s that first just 00:48:34.670 --> 00:48:37.610 align:middle line:84% wrote lots and lots of statistics on what entry 00:48:37.610 --> 00:48:39.480 align:middle line:84% and exit looked like in the census data. 00:48:39.480 --> 00:48:41.000 align:middle line:84% But you could search for things that 00:48:41.000 --> 00:48:43.320 align:middle line:84% have cited it to find many updates since then. 00:48:43.320 --> 00:48:45.740 align:middle line:84% But let me say, some of the stylized facts 00:48:45.740 --> 00:48:49.550 align:middle line:84% here is that according to the census data, at least, 00:48:49.550 --> 00:48:52.550 align:middle line:90% there's a lot of entry and exit. 00:48:52.550 --> 00:48:57.330 align:middle line:84% And I think in some industries, we know this. 00:48:57.330 --> 00:48:59.580 align:middle line:84% If you watch restaurants or something like that, 00:48:59.580 --> 00:49:01.860 align:middle line:84% you're aware that new restaurants are 00:49:01.860 --> 00:49:05.440 align:middle line:84% born all the time, restaurants die all the time. 00:49:05.440 --> 00:49:08.010 align:middle line:84% There's a tremendous amount of entry and exit 00:49:08.010 --> 00:49:09.780 align:middle line:90% into the restaurant business. 00:49:09.780 --> 00:49:12.840 align:middle line:84% Well, the surprising result from Dunne, Robertson, and Samuelson 00:49:12.840 --> 00:49:17.580 align:middle line:84% is that lots of other businesses seem to look like that too. 00:49:17.580 --> 00:49:20.340 align:middle line:84% Now, it's not the case that there's 00:49:20.340 --> 00:49:21.930 align:middle line:84% a tremendous number of new Apples 00:49:21.930 --> 00:49:24.395 align:middle line:90% and Samsungs every five years. 00:49:24.395 --> 00:49:25.770 align:middle line:84% But if you look at the firms that 00:49:25.770 --> 00:49:28.770 align:middle line:84% are classified into many narrowly defined businesses, 00:49:28.770 --> 00:49:32.220 align:middle line:84% it seems like many more are like the-- 00:49:32.220 --> 00:49:36.030 align:middle line:84% many more are like the restaurants than the Apple 00:49:36.030 --> 00:49:39.870 align:middle line:90% and Samsung phone producers. 00:49:39.870 --> 00:49:43.410 align:middle line:84% Anyway, so what Jovanovic's paper is about, 00:49:43.410 --> 00:49:46.860 align:middle line:84% trying to discuss basic framework for how 00:49:46.860 --> 00:49:51.990 align:middle line:84% do we think about entry and exit in a way that would explain 00:49:51.990 --> 00:49:53.970 align:middle line:84% what's going on in the census data, 00:49:53.970 --> 00:49:55.620 align:middle line:84% when all these new firms are coming in, 00:49:55.620 --> 00:49:59.195 align:middle line:84% all these firms are exiting, and growth patterns, and so on. 00:49:59.195 --> 00:50:02.760 align:middle line:90% 00:50:02.760 --> 00:50:07.210 align:middle line:84% So classic model Jovanovic is a macro-ish paper. 00:50:07.210 --> 00:50:10.110 align:middle line:84% So there's a lot of this assuming continuum of firms 00:50:10.110 --> 00:50:14.140 align:middle line:84% and whatever and assuming that everything works out evenly. 00:50:14.140 --> 00:50:16.320 align:middle line:84% So it looks a little different from I/O, 00:50:16.320 --> 00:50:18.720 align:middle line:90% but I wanted to cover it. 00:50:18.720 --> 00:50:20.910 align:middle line:90% So we start in this model-- 00:50:20.910 --> 00:50:24.240 align:middle line:84% imagine we have a continuum of small potential entrants 00:50:24.240 --> 00:50:26.180 align:middle line:90% that are out there. 00:50:26.180 --> 00:50:28.990 align:middle line:84% And these firms are going to have some fixed cost 00:50:28.990 --> 00:50:31.310 align:middle line:90% K of entering the industry. 00:50:31.310 --> 00:50:33.447 align:middle line:84% And then if they enter the industry 00:50:33.447 --> 00:50:35.030 align:middle line:84% and then they decide to leave, they're 00:50:35.030 --> 00:50:38.730 align:middle line:84% going to have some liquidation value w that's less than K. 00:50:38.730 --> 00:50:40.670 align:middle line:84% So you're a restaurant, you enter, 00:50:40.670 --> 00:50:42.780 align:middle line:84% you pay K to set up your restaurant. 00:50:42.780 --> 00:50:46.670 align:middle line:84% When you're done, you can sell all 00:50:46.670 --> 00:50:48.460 align:middle line:84% your tables and your cooking equipment 00:50:48.460 --> 00:50:50.210 align:middle line:84% and the leases and whatever, all the money 00:50:50.210 --> 00:50:53.100 align:middle line:84% you spent on advertising and other things, that's sunk. 00:50:53.100 --> 00:50:55.730 align:middle line:84% But there's some fraction of-- there's some amount w that you 00:50:55.730 --> 00:50:57.280 align:middle line:90% can get back when you close up. 00:50:57.280 --> 00:51:00.550 align:middle line:90% 00:51:00.550 --> 00:51:03.140 align:middle line:84% Jovanovic assumed that these firms have unknown types 00:51:03.140 --> 00:51:04.160 align:middle line:90% theta i. 00:51:04.160 --> 00:51:06.370 align:middle line:90% You can think of theta i as-- 00:51:06.370 --> 00:51:10.330 align:middle line:84% well, it's like the inverse of their productivity. 00:51:10.330 --> 00:51:16.370 align:middle line:84% So theta i is distributed normal 0 sigma theta squared. 00:51:16.370 --> 00:51:18.890 align:middle line:84% This is how good of a firm you are. 00:51:18.890 --> 00:51:21.610 align:middle line:84% You could think of it as, like in the restaurant case, 00:51:21.610 --> 00:51:24.340 align:middle line:84% everybody thinks they have food that people 00:51:24.340 --> 00:51:25.910 align:middle line:90% are going to like the taste of. 00:51:25.910 --> 00:51:28.560 align:middle line:84% But you never know until you open your restaurant 00:51:28.560 --> 00:51:30.220 align:middle line:90% and you see how popular it is. 00:51:30.220 --> 00:51:34.240 align:middle line:84% So all these firms, they all have some d well, in fact, 00:51:34.240 --> 00:51:35.080 align:middle line:90% they all have-- 00:51:35.080 --> 00:51:37.520 align:middle line:84% in this model, they all have exactly the same prior. 00:51:37.520 --> 00:51:39.850 align:middle line:84% They all have the prior that my theta i is 00:51:39.850 --> 00:51:41.870 align:middle line:90% drawn from this distribution. 00:51:41.870 --> 00:51:43.930 align:middle line:84% But the only way to learn whether my theta 00:51:43.930 --> 00:51:46.600 align:middle line:84% i is low, in which I'm going to be a very profitable firm, 00:51:46.600 --> 00:51:49.240 align:middle line:84% or high, in which I'm going to be a very unprofitable firm, 00:51:49.240 --> 00:51:53.290 align:middle line:84% is to enter, start selling some-- open my restaurant, 00:51:53.290 --> 00:51:55.030 align:middle line:84% start selling to customers, see if people 00:51:55.030 --> 00:51:58.335 align:middle line:84% come and are willing to pay my prices, and I sell out or not. 00:51:58.335 --> 00:52:01.150 align:middle line:90% 00:52:01.150 --> 00:52:03.772 align:middle line:90% So he does this with the thetas. 00:52:03.772 --> 00:52:05.230 align:middle line:84% Rather than quality of the food, he 00:52:05.230 --> 00:52:08.380 align:middle line:84% does this by your cost of producing as if it's your-- 00:52:08.380 --> 00:52:09.740 align:middle line:90% everyone's trying to come in. 00:52:09.740 --> 00:52:14.620 align:middle line:84% They're all going to try to produce some kind of steel. 00:52:14.620 --> 00:52:17.350 align:middle line:84% And then some of them end up being high-cost producers, 00:52:17.350 --> 00:52:19.060 align:middle line:84% some end up being low-cost producers, 00:52:19.060 --> 00:52:21.950 align:middle line:84% and that's what determines their profitability. 00:52:21.950 --> 00:52:24.910 align:middle line:84% So firm i's period t cost, there's 00:52:24.910 --> 00:52:30.280 align:middle line:84% this some common function c of qit that applies to everyone. 00:52:30.280 --> 00:52:35.200 align:middle line:84% But then it's multiplied by f of theta i plus epsilon "it", 00:52:35.200 --> 00:52:38.950 align:middle line:84% where theta i is your permanent type and epsilon "it" 00:52:38.950 --> 00:52:41.860 align:middle line:90% is a shock. 00:52:41.860 --> 00:52:46.720 align:middle line:84% And what he's imagining is that f might be some function that 00:52:46.720 --> 00:52:47.655 align:middle line:90% looks like this. 00:52:47.655 --> 00:52:57.720 align:middle line:90% 00:52:57.720 --> 00:53:00.610 align:middle line:90% And so we'll make this 1. 00:53:00.610 --> 00:53:06.250 align:middle line:84% So if my type is exactly 0, then-- 00:53:06.250 --> 00:53:08.090 align:middle line:90% or when I make this-- 00:53:08.090 --> 00:53:16.325 align:middle line:90% 00:53:16.325 --> 00:53:18.200 align:middle line:84% There are extra parameters in this model that 00:53:18.200 --> 00:53:19.570 align:middle line:90% probably shouldn't be there. 00:53:19.570 --> 00:53:23.250 align:middle line:90% So let's call this theta 0. 00:53:23.250 --> 00:53:32.660 align:middle line:84% So if my type is exactly theta 0, my cost is c of q. 00:53:32.660 --> 00:53:36.320 align:middle line:84% If my theta is negative infinity, 00:53:36.320 --> 00:53:40.680 align:middle line:90% then my cost is like 1/2 c of q. 00:53:40.680 --> 00:53:45.180 align:middle line:84% And if my theta is like positive infinity-- 00:53:45.180 --> 00:53:49.010 align:middle line:90% so I'm graphing f of x-- 00:53:49.010 --> 00:53:52.550 align:middle line:90% maybe my cost is twice c of q. 00:53:52.550 --> 00:53:55.160 align:middle line:84% And so with these firms that are entering, 00:53:55.160 --> 00:53:59.050 align:middle line:84% if their costs are low, they're going to earn positive profits, 00:53:59.050 --> 00:53:59.820 align:middle line:90% high profits. 00:53:59.820 --> 00:54:03.680 align:middle line:84% If their costs are high, they're going to earn negative profits. 00:54:03.680 --> 00:54:06.740 align:middle line:84% But he adds this random shock in. 00:54:06.740 --> 00:54:09.000 align:middle line:84% So there's this random period-by-period shock. 00:54:09.000 --> 00:54:12.210 align:middle line:84% So I enter, I try to produce, this period 00:54:12.210 --> 00:54:14.430 align:middle line:84% I turn out that I had high costs. 00:54:14.430 --> 00:54:16.580 align:middle line:84% I don't know, am I a high theta type? 00:54:16.580 --> 00:54:18.260 align:middle line:90% Or was I just unlucky? 00:54:18.260 --> 00:54:22.100 align:middle line:84% So again, if you think about it on the quality side, 00:54:22.100 --> 00:54:25.400 align:middle line:90% I enter, I start selling-- 00:54:25.400 --> 00:54:28.520 align:middle line:84% either this week, there's nobody at my restaurant; is it 00:54:28.520 --> 00:54:29.570 align:middle line:90% that my quality is low? 00:54:29.570 --> 00:54:34.610 align:middle line:84% Or did I just have a bad shock, a bad random draw that week? 00:54:34.610 --> 00:54:39.050 align:middle line:90% And so firms are-- 00:54:39.050 --> 00:54:42.200 align:middle line:84% symmetric information model firms don't know their types. 00:54:42.200 --> 00:54:45.530 align:middle line:84% But every time they produce, they get a signal 00:54:45.530 --> 00:54:47.400 align:middle line:90% about what their type is. 00:54:47.400 --> 00:54:49.010 align:middle line:90% They update their beliefs. 00:54:49.010 --> 00:54:51.440 align:middle line:84% And then by updating their beliefs, 00:54:51.440 --> 00:54:56.720 align:middle line:84% they're going to change two things. 00:54:56.720 --> 00:54:59.520 align:middle line:90% c is convex in this model. 00:54:59.520 --> 00:55:04.890 align:middle line:84% So if I think my cost is low, I'm going to produce a lot 00:55:04.890 --> 00:55:07.950 align:middle line:84% and continue going because I'm like, I can produce a lot 00:55:07.950 --> 00:55:11.010 align:middle line:84% and earn positive profits at the equilibrium level p star. 00:55:11.010 --> 00:55:12.953 align:middle line:84% If my cost is high, I'm only going 00:55:12.953 --> 00:55:15.120 align:middle line:84% to produce a little because I want to get the signal 00:55:15.120 --> 00:55:16.453 align:middle line:90% and find out if I'm good or not. 00:55:16.453 --> 00:55:19.170 align:middle line:84% But I'm only going to produce a little bit because I'm probably 00:55:19.170 --> 00:55:21.003 align:middle line:84% going to lose money on everything I produce. 00:55:21.003 --> 00:55:23.362 align:middle line:90% 00:55:23.362 --> 00:55:25.460 align:middle line:84% So anyway, he treats the entrance 00:55:25.460 --> 00:55:27.540 align:middle line:90% as a continuum per period. 00:55:27.540 --> 00:55:30.600 align:middle line:84% And so with this continuum of entrance, 00:55:30.600 --> 00:55:34.870 align:middle line:84% you get a deterministic price sequence, p1, p2, p3. 00:55:34.870 --> 00:55:37.320 align:middle line:84% And he also assumes that the firms are all price takers, 00:55:37.320 --> 00:55:42.150 align:middle line:84% and they're just choosing q to maximize the expectation over 00:55:42.150 --> 00:55:47.400 align:middle line:84% theta i of the profits I'm going to get this period, which is pt, 00:55:47.400 --> 00:55:53.010 align:middle line:84% which I know, times q minus my cost of production, c of q, 00:55:53.010 --> 00:55:54.570 align:middle line:90% f of theta i plus epsilon "it". 00:55:54.570 --> 00:55:57.112 align:middle line:84% And again, there's an expectation here 00:55:57.112 --> 00:55:58.320 align:middle line:90% because I don't know theta i. 00:55:58.320 --> 00:56:00.570 align:middle line:84% And actually, also there's going to be an epsilon "it" 00:56:00.570 --> 00:56:02.185 align:middle line:84% is also going to be random shock. 00:56:02.185 --> 00:56:04.560 align:middle line:84% So I guess this really should be expectation over theta i 00:56:04.560 --> 00:56:05.280 align:middle line:90% and epsilon "it". 00:56:05.280 --> 00:56:13.650 align:middle line:90% 00:56:13.650 --> 00:56:18.395 align:middle line:84% So then what's the optimal behavior for a firm? 00:56:18.395 --> 00:56:21.020 align:middle line:90% 00:56:21.020 --> 00:56:24.150 align:middle line:84% Suppose that you think theta is very low. 00:56:24.150 --> 00:56:26.685 align:middle line:84% If you think theta is very low, then you 00:56:26.685 --> 00:56:28.435 align:middle line:84% think your costs are going to be very low. 00:56:28.435 --> 00:56:30.300 align:middle line:90% You know that the prices are. 00:56:30.300 --> 00:56:32.177 align:middle line:84% So you produce a very high quantity-- 00:56:32.177 --> 00:56:34.010 align:middle line:84% because you can produce a very high quantity 00:56:34.010 --> 00:56:37.160 align:middle line:84% with the increasing costs and still make a profit. 00:56:37.160 --> 00:56:40.440 align:middle line:84% So this is not a constant marginal cost model. 00:56:40.440 --> 00:56:42.650 align:middle line:90% This is a marginal cost-- 00:56:42.650 --> 00:56:45.160 align:middle line:84% this is c of q that's increasing in q. 00:56:45.160 --> 00:56:47.920 align:middle line:90% 00:56:47.920 --> 00:56:53.260 align:middle line:84% If I have a medium expectation of theta, 00:56:53.260 --> 00:56:55.920 align:middle line:84% then I'm going to produce some low quantity. 00:56:55.920 --> 00:56:58.392 align:middle line:84% I'm going to hope that I'm better than I think I am, 00:56:58.392 --> 00:57:00.100 align:middle line:84% but I'm just going to produce the units I 00:57:00.100 --> 00:57:03.940 align:middle line:84% can produce cheaply, produce my initial cheap units, 00:57:03.940 --> 00:57:06.417 align:middle line:84% and then leave it at that and then hope that I find out 00:57:06.417 --> 00:57:08.500 align:middle line:84% I'm better, but at least make a profit on the ones 00:57:08.500 --> 00:57:09.125 align:middle line:90% that I produce. 00:57:09.125 --> 00:57:11.760 align:middle line:90% 00:57:11.760 --> 00:57:14.910 align:middle line:90% If I have a high theta-- 00:57:14.910 --> 00:57:20.070 align:middle line:84% if I have a high expectation of theta, I think I'm a bad firm, 00:57:20.070 --> 00:57:23.010 align:middle line:84% but I'm uncertain about how bad I am, 00:57:23.010 --> 00:57:25.800 align:middle line:84% then I'm going to produce a low qit and stay in the market. 00:57:25.800 --> 00:57:28.770 align:middle line:84% And I'm just going to produce these very few units 00:57:28.770 --> 00:57:30.900 align:middle line:84% and try to sell those and hope that I'm 00:57:30.900 --> 00:57:32.940 align:middle line:90% better than I think I am. 00:57:32.940 --> 00:57:38.130 align:middle line:84% But if I'm high theta and I have low uncertainty, 00:57:38.130 --> 00:57:40.320 align:middle line:84% then I'm just going to take the liquidation value w 00:57:40.320 --> 00:57:42.430 align:middle line:90% and get out of the market. 00:57:42.430 --> 00:57:45.440 align:middle line:90% OK, so firms are making this-- 00:57:45.440 --> 00:57:51.215 align:middle line:84% endogenously choosing both, What quantity do I produce? 00:57:51.215 --> 00:57:52.340 align:middle line:90% What quantity do I produce? 00:57:52.340 --> 00:57:55.770 align:middle line:90% And do I exit or not? 00:57:55.770 --> 00:57:59.370 align:middle line:84% And he separates these things where the amount I'll earn 00:57:59.370 --> 00:58:02.102 align:middle line:84% doesn't depend on the amount that I produced. 00:58:02.102 --> 00:58:03.810 align:middle line:84% And so if I produce, I'm going to produce 00:58:03.810 --> 00:58:05.405 align:middle line:90% the static optimal quantity. 00:58:05.405 --> 00:58:09.260 align:middle line:90% 00:58:09.260 --> 00:58:09.920 align:middle line:90% Yes. 00:58:09.920 --> 00:58:12.560 align:middle line:84% AUDIENCE: So someone's belief or their expectation of theta i 00:58:12.560 --> 00:58:15.245 align:middle line:84% is just based off their previous observations of theta i? 00:58:15.245 --> 00:58:17.120 align:middle line:84% GLENN ELLISON: It's based on their previous-- 00:58:17.120 --> 00:58:20.210 align:middle line:84% like, every period you get an observation of theta i plus 00:58:20.210 --> 00:58:21.170 align:middle line:90% epsilon "it". 00:58:21.170 --> 00:58:24.330 align:middle line:84% So you have a-- it's a normal learning model. 00:58:24.330 --> 00:58:28.280 align:middle line:84% I have a prior that it's normal 0 theta. 00:58:28.280 --> 00:58:30.450 align:middle line:90% These epsilons are also normal. 00:58:30.450 --> 00:58:32.480 align:middle line:84% So every time I enter, I get a normal signal, 00:58:32.480 --> 00:58:34.520 align:middle line:84% and then I just Bayesian update up and down. 00:58:34.520 --> 00:58:36.470 align:middle line:84% And the number of signals that I get 00:58:36.470 --> 00:58:41.650 align:middle line:84% determines whether my posterior is diffuse or narrow or tight. 00:58:41.650 --> 00:58:45.130 align:middle line:84% So sometimes the older I am, the less uncertainty I have. 00:58:45.130 --> 00:58:49.645 align:middle line:84% Like, with normal distributions, it's just purely 1 over N. 00:58:49.645 --> 00:58:51.730 align:middle line:84% The uncertainty diminishes like 1 over N 00:58:51.730 --> 00:58:53.330 align:middle line:90% as I get N observations. 00:58:53.330 --> 00:58:58.280 align:middle line:90% 00:58:58.280 --> 00:59:03.350 align:middle line:84% And so we notice that a basic model like this 00:59:03.350 --> 00:59:07.460 align:middle line:84% makes a number of predictions about firm dynamics 00:59:07.460 --> 00:59:10.610 align:middle line:84% that seem to fit with what the basic census data on firm 00:59:10.610 --> 00:59:12.110 align:middle line:90% dynamics look like. 00:59:12.110 --> 00:59:16.640 align:middle line:84% So some observations, small firms 00:59:16.640 --> 00:59:20.570 align:middle line:90% grow faster and fail more often. 00:59:20.570 --> 00:59:21.600 align:middle line:90% Why is that? 00:59:21.600 --> 00:59:24.770 align:middle line:84% Well, a lot of the small firms are-- 00:59:24.770 --> 00:59:28.220 align:middle line:90% 00:59:28.220 --> 00:59:30.560 align:middle line:84% a lot of the small firms are these people 00:59:30.560 --> 00:59:32.750 align:middle line:90% with high uncertainty. 00:59:32.750 --> 00:59:35.090 align:middle line:84% The small firms are new firms that come in 00:59:35.090 --> 00:59:38.550 align:middle line:84% or firms that have come in and gotten one bad draw. 00:59:38.550 --> 00:59:40.530 align:middle line:84% They think their theta is high, but they're 00:59:40.530 --> 00:59:42.480 align:middle line:84% very uncertain about their theta. 00:59:42.480 --> 00:59:46.140 align:middle line:84% So they're producing small quantities. 00:59:46.140 --> 00:59:48.210 align:middle line:84% If they find out that they're better firms, 00:59:48.210 --> 00:59:50.740 align:middle line:90% they grow very quickly. 00:59:50.740 --> 00:59:54.880 align:middle line:84% These guys, the only way you can have a low expectation of theta 00:59:54.880 --> 00:59:56.540 align:middle line:84% is if you've gotten a lot of data 00:59:56.540 --> 00:59:59.620 align:middle line:84% and all the data says that your quantity is low-- 00:59:59.620 --> 01:00:00.918 align:middle line:90% your costs are low. 01:00:00.918 --> 01:00:03.460 align:middle line:84% Therefore, you're not going to grow very fast, because you've 01:00:03.460 --> 01:00:05.030 align:middle line:90% already got a lot of data. 01:00:05.030 --> 01:00:07.447 align:middle line:84% You're going to continue to think that your costs are low, 01:00:07.447 --> 01:00:09.850 align:middle line:84% and you're going to have roughly the same output. 01:00:09.850 --> 01:00:15.070 align:middle line:84% So the small firms are firms who have a lot of uncertainty 01:00:15.070 --> 01:00:17.570 align:middle line:84% but think their costs are relatively high. 01:00:17.570 --> 01:00:21.290 align:middle line:84% Therefore, they grow fast if they stay in the market. 01:00:21.290 --> 01:00:24.105 align:middle line:84% But they also just exit and fail much more often. 01:00:24.105 --> 01:00:27.520 align:middle line:90% 01:00:27.520 --> 01:00:29.840 align:middle line:84% Bigger firms have higher profits. 01:00:29.840 --> 01:00:33.970 align:middle line:84% So profits are quite different across firms. 01:00:33.970 --> 01:00:35.920 align:middle line:84% The high-profit firms are the people 01:00:35.920 --> 01:00:37.370 align:middle line:90% who've been around for a while. 01:00:37.370 --> 01:00:39.400 align:middle line:84% They've learned that their theta is very low. 01:00:39.400 --> 01:00:43.870 align:middle line:84% Therefore, they can produce way out here on their cost curve 01:00:43.870 --> 01:00:45.500 align:middle line:90% and still make a profit. 01:00:45.500 --> 01:00:47.170 align:middle line:84% And they're making all these profits 01:00:47.170 --> 01:00:49.030 align:middle line:90% on the inframarginal units. 01:00:49.030 --> 01:00:54.280 align:middle line:84% So the big firms are the-- big firms are the profitable firms, 01:00:54.280 --> 01:00:56.222 align:middle line:84% and they're profitable because they just 01:00:56.222 --> 01:00:58.305 align:middle line:84% are more efficient cost-wise than the other firms. 01:00:58.305 --> 01:01:01.460 align:middle line:90% 01:01:01.460 --> 01:01:08.750 align:middle line:84% If you think about how our industry concentration 01:01:08.750 --> 01:01:11.090 align:middle line:90% and profits related-- 01:01:11.090 --> 01:01:12.740 align:middle line:84% and we have this sort of standard view 01:01:12.740 --> 01:01:14.740 align:middle line:84% that industry concentration and profits are related because we 01:01:14.740 --> 01:01:17.120 align:middle line:84% can put more firms into a Cournot model or more firms 01:01:17.120 --> 01:01:22.800 align:middle line:84% into a Hotelling circle model, markups drop. 01:01:22.800 --> 01:01:31.290 align:middle line:84% Here, this is like a perfect competition model. 01:01:31.290 --> 01:01:34.740 align:middle line:84% But in equilibrium, industry concentration 01:01:34.740 --> 01:01:37.350 align:middle line:84% is correlated in the cross-section with high profits 01:01:37.350 --> 01:01:40.080 align:middle line:84% because an industry that happens to have 01:01:40.080 --> 01:01:43.350 align:middle line:84% a few very low-cost firms in it, those firms 01:01:43.350 --> 01:01:44.860 align:middle line:90% will earn very high profits. 01:01:44.860 --> 01:01:47.010 align:middle line:84% Whereas with another industry, all the firms 01:01:47.010 --> 01:01:49.237 align:middle line:84% have very similar costs, then you're 01:01:49.237 --> 01:01:51.570 align:middle line:84% just going to have a large number of firms, each earning 01:01:51.570 --> 01:01:53.470 align:middle line:90% individually low profits. 01:01:53.470 --> 01:01:55.230 align:middle line:84% And so the firms that are going to look 01:01:55.230 --> 01:01:57.000 align:middle line:84% like high-profit industries, they're 01:01:57.000 --> 01:01:59.760 align:middle line:84% concentrated because they're the firms that just have 01:01:59.760 --> 01:02:01.740 align:middle line:84% a few firms that have theta draws 01:02:01.740 --> 01:02:04.090 align:middle line:84% much lower than everybody else's theta draw. 01:02:04.090 --> 01:02:07.650 align:middle line:84% And so you get this correlation between profits 01:02:07.650 --> 01:02:11.820 align:middle line:84% and concentration that comes from the distribution 01:02:11.820 --> 01:02:14.740 align:middle line:90% of realized costs. 01:02:14.740 --> 01:02:17.970 align:middle line:84% So we get a profit concentration cross-section, 01:02:17.970 --> 01:02:22.140 align:middle line:84% but it's caused by a correlation with the omitted variable 01:02:22.140 --> 01:02:24.690 align:middle line:84% of distribution of firm costs rather than 01:02:24.690 --> 01:02:26.495 align:middle line:84% caused by competition and causal effect. 01:02:26.495 --> 01:02:30.880 align:middle line:90% 01:02:30.880 --> 01:02:33.730 align:middle line:84% Industry concentration is also correlated 01:02:33.730 --> 01:02:36.290 align:middle line:84% with cross-sectional variance in profits. 01:02:36.290 --> 01:02:39.460 align:middle line:84% So again, if you have an industry that has-- 01:02:39.460 --> 01:02:42.580 align:middle line:84% if I do histograms of costs, if I have an industry that 01:02:42.580 --> 01:02:47.020 align:middle line:84% has a mass of firms that have very low costs and then 01:02:47.020 --> 01:02:49.930 align:middle line:84% some firms that have higher costs, 01:02:49.930 --> 01:02:52.180 align:middle line:84% this industry is going to end up very concentrated 01:02:52.180 --> 01:02:54.530 align:middle line:84% because the low-cost firms are going to produce a ton. 01:02:54.530 --> 01:02:56.720 align:middle line:84% All these firms are going to produce small amounts. 01:02:56.720 --> 01:02:59.590 align:middle line:84% And so we're going to see highly profitable firms and very 01:02:59.590 --> 01:03:01.920 align:middle line:90% nonprofitable firms. 01:03:01.920 --> 01:03:05.010 align:middle line:84% If you're going to have an industry that's 01:03:05.010 --> 01:03:06.810 align:middle line:90% not concentrated-- 01:03:06.810 --> 01:03:08.550 align:middle line:84% an industry that's not concentrated 01:03:08.550 --> 01:03:13.560 align:middle line:84% is one that has much less cost heterogeneity. 01:03:13.560 --> 01:03:16.050 align:middle line:84% And so if it's got much less cost heterogeneity, 01:03:16.050 --> 01:03:18.340 align:middle line:84% no one produces a large quantity. 01:03:18.340 --> 01:03:20.040 align:middle line:84% And that also means that everyone's 01:03:20.040 --> 01:03:22.020 align:middle line:84% getting similar profits to everybody else 01:03:22.020 --> 01:03:26.700 align:middle line:84% because their costs are all similar to everybody else. 01:03:26.700 --> 01:03:29.770 align:middle line:84% Note that these guys are all making essentially zero profits. 01:03:29.770 --> 01:03:31.770 align:middle line:84% And so it's like small numbers and 0, 01:03:31.770 --> 01:03:35.490 align:middle line:84% but small numbers and 0 are not so different in this model. 01:03:35.490 --> 01:03:37.910 align:middle line:90% So anyway, you get this. 01:03:37.910 --> 01:03:41.390 align:middle line:84% Concentration is both correlated with levels of profits 01:03:41.390 --> 01:03:44.810 align:middle line:84% and with cross-sectional variance in profits. 01:03:44.810 --> 01:03:52.050 align:middle line:84% Anyway, so there's a large, large literature 01:03:52.050 --> 01:03:54.660 align:middle line:84% on the empirics of entry that bears out 01:03:54.660 --> 01:03:56.770 align:middle line:84% that many of these things seem to be true. 01:03:56.770 --> 01:03:59.640 align:middle line:84% And I guess this is the way we often 01:03:59.640 --> 01:04:01.440 align:middle line:84% think about-- we make sense of that data, 01:04:01.440 --> 01:04:04.370 align:middle line:84% is that it's not that all firms have the same technology. 01:04:04.370 --> 01:04:08.100 align:middle line:84% Some firms are just more efficient than others 01:04:08.100 --> 01:04:10.520 align:middle line:84% for no observable reason-- for no observable reason. 01:04:10.520 --> 01:04:17.970 align:middle line:90% 01:04:17.970 --> 01:04:20.260 align:middle line:90% Any questions on this framework? 01:04:20.260 --> 01:04:22.510 align:middle line:84% I think that's all I had to say on it. 01:04:22.510 --> 01:04:23.050 align:middle line:90% Yep. 01:04:23.050 --> 01:04:25.930 align:middle line:84% So what I want to do in this lecture-- and I covered this-- 01:04:25.930 --> 01:04:28.540 align:middle line:90% I don't always teach Jovanovic. 01:04:28.540 --> 01:04:35.890 align:middle line:84% But I like to have some recent theoretical papers in the class. 01:04:35.890 --> 01:04:38.860 align:middle line:84% So anyway, this is a paper by Nikhil Vellodi, 01:04:38.860 --> 01:04:41.770 align:middle line:84% who's an assistant professor in Paris. 01:04:41.770 --> 01:04:46.000 align:middle line:84% Anyway, so basically what Vellodi has done in this paper 01:04:46.000 --> 01:04:52.780 align:middle line:84% is gone back to Jovanovic 1982 and used Jovanovic 1982 01:04:52.780 --> 01:04:56.680 align:middle line:84% to think about the effects of rating intermediaries 01:04:56.680 --> 01:05:00.580 align:middle line:84% and what types of policies we'd want rating intermediaries 01:05:00.580 --> 01:05:02.810 align:middle line:84% to have or what effects rating intermediaries have. 01:05:02.810 --> 01:05:06.772 align:middle line:84% So by rating intermediaries, he has-- 01:05:06.772 --> 01:05:09.790 align:middle line:84% thinking about firms like Amazon and Yelp, 01:05:09.790 --> 01:05:13.510 align:middle line:84% where on Amazon, you can leave feedback-- like Amazon, 01:05:13.510 --> 01:05:15.160 align:middle line:84% majority of the merchandise on Amazon 01:05:15.160 --> 01:05:17.840 align:middle line:84% is not actually sold by-- it's not by Amazon itself. 01:05:17.840 --> 01:05:21.370 align:middle line:84% It's sold by third parties selling on Amazon. 01:05:21.370 --> 01:05:24.500 align:middle line:84% There are lots of-- you want to buy an umbrella on Amazon, 01:05:24.500 --> 01:05:27.093 align:middle line:84% you go there and you look at the reviews of that umbrella 01:05:27.093 --> 01:05:29.260 align:middle line:84% and whether people say that umbrella is good or bad, 01:05:29.260 --> 01:05:31.360 align:middle line:90% and then you buy it or not. 01:05:31.360 --> 01:05:34.180 align:middle line:84% You get Yelp or Tripadvisor or whomever 01:05:34.180 --> 01:05:37.097 align:middle line:84% that has lots of reviews of restaurants and tells you, 01:05:37.097 --> 01:05:38.180 align:middle line:90% Is this a good restaurant? 01:05:38.180 --> 01:05:39.690 align:middle line:90% Is this a bad restaurant? 01:05:39.690 --> 01:05:41.865 align:middle line:84% Consumers use that to learn about product quality. 01:05:41.865 --> 01:05:44.900 align:middle line:90% 01:05:44.900 --> 01:05:49.160 align:middle line:84% And so there's this sort of challenge in coming up 01:05:49.160 --> 01:05:51.110 align:middle line:84% with these in this business model 01:05:51.110 --> 01:05:59.080 align:middle line:84% is that there are big firms that everybody buys from. 01:05:59.080 --> 01:06:00.830 align:middle line:84% On the big firms everybody buys from, 01:06:00.830 --> 01:06:02.440 align:middle line:84% there are going to be a zillion reviews and people are 01:06:02.440 --> 01:06:04.910 align:middle line:84% going to be able to find out the quality of those firms. 01:06:04.910 --> 01:06:07.630 align:middle line:84% But you have many, many small entrants 01:06:07.630 --> 01:06:10.687 align:middle line:84% and many, many new entrants all the time into these models. 01:06:10.687 --> 01:06:12.520 align:middle line:84% And it's the new entrants that people really 01:06:12.520 --> 01:06:14.978 align:middle line:84% want to know about and learn about whether their quality is 01:06:14.978 --> 01:06:15.940 align:middle line:90% good or bad. 01:06:15.940 --> 01:06:18.310 align:middle line:84% But there's this effect of if you have new firms, 01:06:18.310 --> 01:06:21.010 align:middle line:84% people are hesitant to buy from them because they're new. 01:06:21.010 --> 01:06:22.930 align:middle line:84% And because people are hesitant to buy from them because they're 01:06:22.930 --> 01:06:24.370 align:middle line:90% new, there are very few reviews. 01:06:24.370 --> 01:06:26.078 align:middle line:84% And therefore there are very few reviews, 01:06:26.078 --> 01:06:27.800 align:middle line:84% therefore people can't learn about them. 01:06:27.800 --> 01:06:29.320 align:middle line:84% And so he wants to think about is, 01:06:29.320 --> 01:06:34.300 align:middle line:84% what would be the optimal design for a rating intermediary 01:06:34.300 --> 01:06:39.290 align:middle line:84% that wanted to promote an efficient level of competition? 01:06:39.290 --> 01:06:42.190 align:middle line:84% In some sense, we think there could be-- 01:06:42.190 --> 01:06:44.182 align:middle line:84% why could there be too little entry in models? 01:06:44.182 --> 01:06:46.390 align:middle line:84% There could be too little entry here-- another reason 01:06:46.390 --> 01:06:48.280 align:middle line:84% I didn't put my theory in my first part was 01:06:48.280 --> 01:06:50.350 align:middle line:84% there'd be too little entry because people don't know 01:06:50.350 --> 01:06:52.183 align:middle line:84% the quality of new firms, and therefore they 01:06:52.183 --> 01:06:54.220 align:middle line:84% won't buy from new firms, and therefore no one 01:06:54.220 --> 01:06:58.510 align:middle line:84% will enter and have people learn about their quality. 01:06:58.510 --> 01:07:00.343 align:middle line:84% Jovanovic was very convenient that the firms 01:07:00.343 --> 01:07:02.427 align:middle line:84% could enter and then produce these tiny quantities 01:07:02.427 --> 01:07:04.720 align:middle line:84% and get highly informative signals about their quality 01:07:04.720 --> 01:07:07.450 align:middle line:84% and know whether to start producing more. 01:07:07.450 --> 01:07:11.230 align:middle line:84% In practice, that's not something restaurants 01:07:11.230 --> 01:07:13.450 align:middle line:84% can do, is come in and produce a tiny quantity 01:07:13.450 --> 01:07:17.610 align:middle line:84% and get a lot of reviews on Yelp. 01:07:17.610 --> 01:07:20.070 align:middle line:84% So anyway, models got a continuum 01:07:20.070 --> 01:07:21.460 align:middle line:90% of small potential entrants. 01:07:21.460 --> 01:07:23.280 align:middle line:84% So think of these as new restaurants 01:07:23.280 --> 01:07:26.130 align:middle line:84% or new guys just trying to sell black folding umbrellas 01:07:26.130 --> 01:07:27.840 align:middle line:90% on Amazon. 01:07:27.840 --> 01:07:31.920 align:middle line:84% They have a fixed cost K of entering. 01:07:31.920 --> 01:07:34.587 align:middle line:84% They're going to have some flow cost of operation. 01:07:34.587 --> 01:07:35.920 align:middle line:90% I didn't put a letter down here. 01:07:35.920 --> 01:07:36.630 align:middle line:90% Maybe this is c. 01:07:36.630 --> 01:07:38.850 align:middle line:84% But every period that I'm continuing to operate, 01:07:38.850 --> 01:07:42.420 align:middle line:90% I have to pay some flow cost. 01:07:42.420 --> 01:07:45.070 align:middle line:84% Just to make the model have a steady state equilibrium, 01:07:45.070 --> 01:07:47.040 align:middle line:84% he has some exogenous death rate delta. 01:07:47.040 --> 01:07:48.870 align:middle line:84% So every firm with some probability 01:07:48.870 --> 01:07:52.140 align:middle line:90% just disappears in each period. 01:07:52.140 --> 01:07:58.110 align:middle line:84% And then firms have some discount rate rho. 01:07:58.110 --> 01:08:02.920 align:middle line:84% In his model, he's simplifying the theory 01:08:02.920 --> 01:08:05.320 align:middle line:84% by assuming that it's a discrete type model. 01:08:05.320 --> 01:08:09.860 align:middle line:84% All restaurants have either quality 0 or quality 1. 01:08:09.860 --> 01:08:13.190 align:middle line:84% So it's just a pure bimodal distribution. 01:08:13.190 --> 01:08:17.080 align:middle line:84% Again, like in Jovanovic, it's a symmetric information model. 01:08:17.080 --> 01:08:22.250 align:middle line:84% There's prior mean p0 that the firm has quality 1. 01:08:22.250 --> 01:08:24.680 align:middle line:84% And that information is symmetric among everyone 01:08:24.680 --> 01:08:25.290 align:middle line:90% in the market. 01:08:25.290 --> 01:08:27.248 align:middle line:84% No one knows or everyone knows new restaurants, 01:08:27.248 --> 01:08:29.520 align:middle line:84% there's probability p0 that their food is good, 01:08:29.520 --> 01:08:33.500 align:middle line:84% probability 1 minus p0 that their food is bad. 01:08:33.500 --> 01:08:38.260 align:middle line:84% Every firm has exactly one table. 01:08:38.260 --> 01:08:44.590 align:middle line:84% And the firms can do is set prices qit for their table 01:08:44.590 --> 01:08:45.314 align:middle line:90% at time t. 01:08:45.314 --> 01:08:49.700 align:middle line:90% 01:08:49.700 --> 01:08:53.990 align:middle line:84% What he assumes is that you have this prior p0, 01:08:53.990 --> 01:09:00.140 align:middle line:84% and then you have a posterior-- every period, if somebody-- 01:09:00.140 --> 01:09:04.130 align:middle line:84% if you're operating, then reviews 01:09:04.130 --> 01:09:06.740 align:middle line:84% arrive according to a Poisson process. 01:09:06.740 --> 01:09:10.250 align:middle line:84% And those reviews are going to make the quality, 01:09:10.250 --> 01:09:12.109 align:middle line:84% the posterior quality go up or down, 01:09:12.109 --> 01:09:14.540 align:middle line:84% whether it's a good review or a bad review. 01:09:14.540 --> 01:09:19.760 align:middle line:84% He goes with this continuous time, 01:09:19.760 --> 01:09:25.160 align:middle line:84% Brownian motion learning process where my posterior "pit" 01:09:25.160 --> 01:09:30.810 align:middle line:84% evolves according to dp "it" equals square root of lambda 01:09:30.810 --> 01:09:35.870 align:middle line:84% "it" "pit" 1 minus "pit" times dZit, 01:09:35.870 --> 01:09:38.390 align:middle line:90% where Zit is a Brownian motion. 01:09:38.390 --> 01:09:42.200 align:middle line:84% But you can roughly think of this as lambda "it" 01:09:42.200 --> 01:09:44.510 align:middle line:90% is the review arrival rate. 01:09:44.510 --> 01:09:47.779 align:middle line:84% And each of these is like a normal signal. 01:09:47.779 --> 01:09:49.680 align:middle line:84% And so if it's a normal signal, I'm 01:09:49.680 --> 01:09:52.229 align:middle line:84% going to get information that either pushes me to the right 01:09:52.229 --> 01:09:52.979 align:middle line:90% or left. 01:09:52.979 --> 01:09:57.420 align:middle line:90% And the variance of-- 01:09:57.420 --> 01:09:58.980 align:middle line:84% since I have a Bernoulli quality, 01:09:58.980 --> 01:10:03.240 align:middle line:84% the variance of my distribution is just "pit" 1 minus "pit" 01:10:03.240 --> 01:10:05.490 align:middle line:90% if it's Bernoulli probability p. 01:10:05.490 --> 01:10:09.330 align:middle line:84% So anyway, the new information is arriving, 01:10:09.330 --> 01:10:11.947 align:middle line:84% and I'm getting square root of lambda "it" 01:10:11.947 --> 01:10:14.280 align:middle line:84% is how much the standard deviation changes when you have 01:10:14.280 --> 01:10:15.630 align:middle line:90% lambda "it" reviews. 01:10:15.630 --> 01:10:17.940 align:middle line:84% And then dZit is a Brownian motion that's 01:10:17.940 --> 01:10:19.272 align:middle line:90% just positive or negative. 01:10:19.272 --> 01:10:20.730 align:middle line:84% So you can think of it as the limit 01:10:20.730 --> 01:10:24.270 align:middle line:84% as you get a number of normally distributed 01:10:24.270 --> 01:10:25.890 align:middle line:84% signals saying this one was good, 01:10:25.890 --> 01:10:29.460 align:middle line:84% this one was bad, this good, this bad, this good, this bad. 01:10:29.460 --> 01:10:32.935 align:middle line:84% That pushes you back and forth in like a Brownian motion 01:10:32.935 --> 01:10:33.435 align:middle line:90% process. 01:10:33.435 --> 01:10:37.520 align:middle line:90% 01:10:37.520 --> 01:10:40.277 align:middle line:84% And why is he doing this in continuous time? 01:10:40.277 --> 01:10:42.860 align:middle line:84% He's doing this in continuous time instead of in discrete time 01:10:42.860 --> 01:10:45.170 align:middle line:84% because it's a state of the art thing, 01:10:45.170 --> 01:10:48.450 align:middle line:84% but it's also that sometimes continuous models are easier 01:10:48.450 --> 01:10:49.700 align:middle line:90% to solve than discrete models. 01:10:49.700 --> 01:10:52.148 align:middle line:84% You have to keep track of what your posterior could be. 01:10:52.148 --> 01:10:54.440 align:middle line:84% If you've had three and for and five and seven signals, 01:10:54.440 --> 01:10:57.320 align:middle line:84% the continuous model is easier to solve. 01:10:57.320 --> 01:11:01.530 align:middle line:84% So every consumer in each period decides which-- 01:11:01.530 --> 01:11:04.050 align:middle line:84% so every consumer goes to exactly one restaurant. 01:11:04.050 --> 01:11:07.250 align:middle line:90% They decide which firm to visit. 01:11:07.250 --> 01:11:11.420 align:middle line:84% If excess consumers visited any type of firm, any firm, 01:11:11.420 --> 01:11:12.750 align:middle line:90% then service is rationed. 01:11:12.750 --> 01:11:17.600 align:middle line:84% There's a line outside, and only some of the people go in. 01:11:17.600 --> 01:11:23.870 align:middle line:84% Consumers get utility theta i plus epsilon ij if they're 01:11:23.870 --> 01:11:25.295 align:middle line:90% served by restaurant i. 01:11:25.295 --> 01:11:29.000 align:middle line:90% 01:11:29.000 --> 01:11:34.490 align:middle line:84% So given that all the firm's priors are common knowledge, 01:11:34.490 --> 01:11:39.290 align:middle line:84% in equilibrium, everyone's going to get served with probability 1 01:11:39.290 --> 01:11:42.570 align:middle line:84% at firms that have a rating of at least p tilde. 01:11:42.570 --> 01:11:47.280 align:middle line:84% And if your prior is-- like, you have one table, 01:11:47.280 --> 01:11:48.410 align:middle line:90% so it's going to be like-- 01:11:48.410 --> 01:11:49.785 align:middle line:84% you're going to clear the market. 01:11:49.785 --> 01:11:52.610 align:middle line:84% If your quality is high enough, you're going to price at some-- 01:11:52.610 --> 01:11:54.110 align:middle line:84% if your quality is at least p tilde, 01:11:54.110 --> 01:11:55.818 align:middle line:84% you're going to price at some equilibrium 01:11:55.818 --> 01:11:58.190 align:middle line:84% price that gets people to come to your restaurant. 01:11:58.190 --> 01:12:01.230 align:middle line:84% And you're going to price it exactly one customer comes. 01:12:01.230 --> 01:12:03.380 align:middle line:84% If your price is attracting multiple customers, 01:12:03.380 --> 01:12:05.880 align:middle line:84% you should be raising your price and getting fewer customers 01:12:05.880 --> 01:12:08.360 align:middle line:90% until you fill your capacity. 01:12:08.360 --> 01:12:13.640 align:middle line:84% At all higher prices, everyone is going to be-- 01:12:13.640 --> 01:12:17.550 align:middle line:84% yeah, so you can tell Nikhil is a theorist not an IO economist. 01:12:17.550 --> 01:12:20.270 align:middle line:84% He's using q for prices and p for qualities, 01:12:20.270 --> 01:12:23.280 align:middle line:84% rather than p for prices and s for qualities. 01:12:23.280 --> 01:12:26.900 align:middle line:84% So anyway, the firms are setting these prices q. 01:12:26.900 --> 01:12:30.980 align:middle line:84% In equilibrium, the prices are just p minus a constant. 01:12:30.980 --> 01:12:33.440 align:middle line:84% And that makes consumers indifferent to going 01:12:33.440 --> 01:12:36.470 align:middle line:84% to all high-quality restaurants and has 01:12:36.470 --> 01:12:40.760 align:middle line:84% all high-quality restaurants attracting exactly one customer. 01:12:40.760 --> 01:12:44.180 align:middle line:84% Why you price it p minus w, it's because there 01:12:44.180 --> 01:12:46.933 align:middle line:84% are low-quality restaurants that people 01:12:46.933 --> 01:12:48.350 align:middle line:84% aren't going to want to go to that 01:12:48.350 --> 01:12:49.645 align:middle line:90% are willing to sell at a loss. 01:12:49.645 --> 01:12:51.020 align:middle line:84% Because they sell at a loss, they 01:12:51.020 --> 01:12:54.180 align:middle line:84% get people to come and review them. 01:12:54.180 --> 01:12:58.470 align:middle line:84% So in his model, basically the lambda "it", 01:12:58.470 --> 01:13:02.570 align:middle line:84% the review arrival rate, is going to be a sum of two terms. 01:13:02.570 --> 01:13:03.705 align:middle line:90% It's going to be a sum. 01:13:03.705 --> 01:13:05.580 align:middle line:84% Lambda is going to be the number of customers 01:13:05.580 --> 01:13:09.630 align:middle line:84% who visit your restaurant because it's optimal to do so, 01:13:09.630 --> 01:13:10.660 align:middle line:90% plus epsilon. 01:13:10.660 --> 01:13:13.410 align:middle line:84% So there's this epsilon background rate of arrivals. 01:13:13.410 --> 01:13:15.510 align:middle line:84% We'll call them tourists from out of town 01:13:15.510 --> 01:13:17.880 align:middle line:84% who have no idea what the qualities are and just show up 01:13:17.880 --> 01:13:19.390 align:middle line:90% randomly at your restaurant. 01:13:19.390 --> 01:13:22.890 align:middle line:84% So most reviews come from the one person 01:13:22.890 --> 01:13:25.270 align:middle line:84% who knows your quality and buys there. 01:13:25.270 --> 01:13:29.410 align:middle line:84% But there is this epsilon arrival rate. 01:13:29.410 --> 01:13:33.250 align:middle line:84% The firms that are hanging around that have low quality, 01:13:33.250 --> 01:13:35.620 align:middle line:84% they would like people to come to their restaurant 01:13:35.620 --> 01:13:37.960 align:middle line:84% and review it so they can learn if their quality is high 01:13:37.960 --> 01:13:40.418 align:middle line:84% and they can start charging more money for their restaurant 01:13:40.418 --> 01:13:43.690 align:middle line:84% if it's high or exit if their quality is low. 01:13:43.690 --> 01:13:46.810 align:middle line:84% But there's only so much they're willing to pay. 01:13:46.810 --> 01:13:49.313 align:middle line:84% So they're willing to price below cost to get people 01:13:49.313 --> 01:13:50.480 align:middle line:90% to come to their restaurant. 01:13:50.480 --> 01:13:52.355 align:middle line:84% But there's only so much you're willing to do 01:13:52.355 --> 01:13:55.000 align:middle line:84% that because, at some point, you're just better off exiting. 01:13:55.000 --> 01:13:59.350 align:middle line:84% But anyway, so that's why you have this positive w. 01:13:59.350 --> 01:14:02.890 align:middle line:84% That is, everybody is giving consumers 01:14:02.890 --> 01:14:05.932 align:middle line:84% some surplus because the guys who are on the outside looking 01:14:05.932 --> 01:14:08.140 align:middle line:84% in are going to give the consumer some surplus to try 01:14:08.140 --> 01:14:10.690 align:middle line:90% to get the customers to come. 01:14:10.690 --> 01:14:13.630 align:middle line:84% OK, so I'm going to write V of p for the value function 01:14:13.630 --> 01:14:16.660 align:middle line:90% of a firm that has posterior p. 01:14:16.660 --> 01:14:19.480 align:middle line:84% Free entry implies that V of p0 equals 01:14:19.480 --> 01:14:21.760 align:middle line:84% K. When the firms are entering, it 01:14:21.760 --> 01:14:23.590 align:middle line:84% must be that their lifetime expected 01:14:23.590 --> 01:14:26.200 align:middle line:84% discounted value of profits is exactly equal to the fixed 01:14:26.200 --> 01:14:28.240 align:middle line:90% costs. 01:14:28.240 --> 01:14:31.810 align:middle line:84% And then exit occurs when your posterior gets down 01:14:31.810 --> 01:14:35.410 align:middle line:84% to p lower bar, where V of p lower bar is 0. 01:14:35.410 --> 01:14:38.620 align:middle line:84% And V of p lower bar is 0 in this model without the scrappage 01:14:38.620 --> 01:14:41.256 align:middle line:84% because there's this flow cost of operation. 01:14:41.256 --> 01:14:45.633 align:middle line:90% 01:14:45.633 --> 01:14:48.050 align:middle line:84% A complicated model, but I thought what I would do is here 01:14:48.050 --> 01:14:49.675 align:middle line:84% is just show you a couple of the graphs 01:14:49.675 --> 01:14:52.580 align:middle line:84% and talk through what ends up happening. 01:14:52.580 --> 01:14:56.470 align:middle line:84% So first observation-- so it's not-- yeah, 01:14:56.470 --> 01:15:01.780 align:middle line:84% so if you're a new firm and people-- 01:15:01.780 --> 01:15:10.290 align:middle line:84% in some sense, in equilibrium, if the number of customers is x, 01:15:10.290 --> 01:15:14.010 align:middle line:84% the x best restaurants are going to all get one customer each. 01:15:14.010 --> 01:15:15.690 align:middle line:84% And every restaurant below x is going 01:15:15.690 --> 01:15:20.760 align:middle line:84% to get no customers, other than the randomly arriving tourists. 01:15:20.760 --> 01:15:24.330 align:middle line:84% But firms-- if you're just on the outside looking 01:15:24.330 --> 01:15:29.700 align:middle line:84% in-- so if we have this sort of posterior on my quality, 01:15:29.700 --> 01:15:31.690 align:middle line:84% I think it was p tilde I called it-- 01:15:31.690 --> 01:15:33.730 align:middle line:84% so everybody up here fills their restaurant. 01:15:33.730 --> 01:15:37.530 align:middle line:84% Everybody else here only gets the epsilon flow of tourists. 01:15:37.530 --> 01:15:40.830 align:middle line:84% If your quality is right here, you're 01:15:40.830 --> 01:15:43.195 align:middle line:84% willing to lose some money in order 01:15:43.195 --> 01:15:45.570 align:middle line:84% to get the customers to visit your restaurant to find out 01:15:45.570 --> 01:15:47.820 align:middle line:84% whether your restaurant is good so you can 01:15:47.820 --> 01:15:49.830 align:middle line:90% get in or out of the market. 01:15:49.830 --> 01:15:53.070 align:middle line:84% So anyway, firms price somewhat below cost to attract customers. 01:15:53.070 --> 01:15:57.030 align:middle line:84% Because this guy is selling at-- this guy is willing to sell 01:15:57.030 --> 01:15:58.950 align:middle line:90% at a loss, everybody else has-- 01:15:58.950 --> 01:16:02.700 align:middle line:84% everybody else can only charge their marginal value 01:16:02.700 --> 01:16:04.230 align:middle line:90% above this guy-- 01:16:04.230 --> 01:16:07.390 align:middle line:84% their marginal quality above that guy. 01:16:07.390 --> 01:16:11.030 align:middle line:84% So consumers get-- consumers get some profit. 01:16:11.030 --> 01:16:12.920 align:middle line:90% What is the consumer surplus? 01:16:12.920 --> 01:16:15.820 align:middle line:84% The consumer surplus here is the amount of money 01:16:15.820 --> 01:16:17.560 align:middle line:90% this guy is willing to lose. 01:16:17.560 --> 01:16:21.490 align:middle line:84% Because the amount of money that this guy is willing to lose is-- 01:16:21.490 --> 01:16:23.530 align:middle line:84% the w is then whatever what you get 01:16:23.530 --> 01:16:27.040 align:middle line:84% at all higher-quality restaurants. 01:16:27.040 --> 01:16:32.260 align:middle line:84% With full information, learning about new entrants is very slow. 01:16:32.260 --> 01:16:35.120 align:middle line:84% And firms exit after they just get some bad news. 01:16:35.120 --> 01:16:35.940 align:middle line:90% So here is his-- 01:16:35.940 --> 01:16:38.620 align:middle line:90% 01:16:38.620 --> 01:16:43.060 align:middle line:84% this is an example where p0, the prior, 01:16:43.060 --> 01:16:48.030 align:middle line:84% is in the range where you're not in the money on customers. 01:16:48.030 --> 01:16:54.260 align:middle line:84% So at a p0 restaurant, you're not getting very many-- 01:16:54.260 --> 01:16:57.480 align:middle line:84% you're out of the money, and customers are not coming to you. 01:16:57.480 --> 01:16:59.900 align:middle line:84% And so what we get is, there's a lot 01:16:59.900 --> 01:17:04.930 align:middle line:84% of firms who just entered about who the prior quality is p0, 01:17:04.930 --> 01:17:07.450 align:middle line:84% and only epsilon people go to them. 01:17:07.450 --> 01:17:09.670 align:middle line:84% And so we get a lot of mass there 01:17:09.670 --> 01:17:11.650 align:middle line:84% because when there are only epsilon customers, 01:17:11.650 --> 01:17:14.200 align:middle line:84% people don't learn much, and your posterior 01:17:14.200 --> 01:17:16.910 align:middle line:84% about their quality doesn't move very fast. 01:17:16.910 --> 01:17:23.480 align:middle line:84% If you get one or two bad reviews, then you just exit. 01:17:23.480 --> 01:17:27.020 align:middle line:84% So you start here, you get a bad review or two, 01:17:27.020 --> 01:17:28.350 align:middle line:90% you just exit the market. 01:17:28.350 --> 01:17:30.230 align:middle line:84% And then also, there aren't many firms 01:17:30.230 --> 01:17:33.560 align:middle line:84% down here with these qualities because two bad reviews, 01:17:33.560 --> 01:17:34.080 align:middle line:90% you leave. 01:17:34.080 --> 01:17:35.663 align:middle line:84% And then even if you would have gotten 01:17:35.663 --> 01:17:38.160 align:middle line:84% a third review coming back up, you're not there anymore. 01:17:38.160 --> 01:17:41.130 align:middle line:90% 01:17:41.130 --> 01:17:44.400 align:middle line:84% Then there are fewer firms with qualities 01:17:44.400 --> 01:17:47.130 align:middle line:84% here because once your quality, your posterior 01:17:47.130 --> 01:17:50.680 align:middle line:84% gets above p upper bar, people learn about you very quickly. 01:17:50.680 --> 01:17:52.200 align:middle line:84% People learn about you very quickly, 01:17:52.200 --> 01:17:53.520 align:middle line:84% your distribution moves, and it either 01:17:53.520 --> 01:17:55.437 align:middle line:84% moves back to this range where no one's coming 01:17:55.437 --> 01:17:59.080 align:middle line:84% to your restaurant, or it moves up, and people learn it's good. 01:17:59.080 --> 01:18:01.090 align:middle line:84% And in this model, everyone is either 0 or 1. 01:18:01.090 --> 01:18:03.510 align:middle line:84% So very quickly, people learn that you're a quality 1 01:18:03.510 --> 01:18:06.010 align:middle line:90% restaurant. 01:18:06.010 --> 01:18:08.200 align:middle line:84% So we get this distribution of firm qualities 01:18:08.200 --> 01:18:10.450 align:middle line:84% where there are a lot of firms that are having trouble 01:18:10.450 --> 01:18:12.190 align:middle line:90% attracting anyone's reviews. 01:18:12.190 --> 01:18:15.130 align:middle line:84% They stay, hang out here, and their posteriors 01:18:15.130 --> 01:18:16.280 align:middle line:90% don't move much. 01:18:16.280 --> 01:18:18.130 align:middle line:84% And then once you get up to some threshold, 01:18:18.130 --> 01:18:19.480 align:middle line:84% you move very quickly, either back 01:18:19.480 --> 01:18:21.188 align:middle line:84% into the range where you don't learn much 01:18:21.188 --> 01:18:23.890 align:middle line:84% or into your quality is 1, and then 01:18:23.890 --> 01:18:25.245 align:middle line:90% people all start going to you. 01:18:25.245 --> 01:18:32.070 align:middle line:90% 01:18:32.070 --> 01:18:34.230 align:middle line:84% Consumer welfare under any policy 01:18:34.230 --> 01:18:36.850 align:middle line:84% is the W that arises given the policy. 01:18:36.850 --> 01:18:41.160 align:middle line:84% So consumer optimality, like what's best for consumers 01:18:41.160 --> 01:18:42.660 align:middle line:84% if you're trying to-- if you're Yelp 01:18:42.660 --> 01:18:44.910 align:middle line:84% and you're trying to design my platform 01:18:44.910 --> 01:18:47.670 align:middle line:84% to be consumer optimal so that people will continue to use 01:18:47.670 --> 01:18:51.820 align:middle line:84% Yelp, what's optimal for the firm to do 01:18:51.820 --> 01:18:55.150 align:middle line:84% is to give firms the incentive to be 01:18:55.150 --> 01:18:59.220 align:middle line:84% willing to price below cost to have firms learn about them. 01:18:59.220 --> 01:19:01.620 align:middle line:84% And so then what do you get about-- 01:19:01.620 --> 01:19:04.080 align:middle line:84% what would be the optimal policy if you're 01:19:04.080 --> 01:19:06.270 align:middle line:84% trying to get these guys to be willing to pay a lot 01:19:06.270 --> 01:19:09.270 align:middle line:90% to get more reviews? 01:19:09.270 --> 01:19:11.700 align:middle line:84% And it turns out that the answer is 01:19:11.700 --> 01:19:15.870 align:middle line:84% that you want to have a partially revealing customer 01:19:15.870 --> 01:19:20.370 align:middle line:84% policy where you don't publish all the reviews 01:19:20.370 --> 01:19:22.190 align:middle line:90% about high-quality firms. 01:19:22.190 --> 01:19:24.030 align:middle line:84% What you want to do is, in some sense, 01:19:24.030 --> 01:19:29.400 align:middle line:84% as soon as a firm's posterior passes p tilde, 01:19:29.400 --> 01:19:33.180 align:middle line:84% you want to stop publishing any reviews about them whatsoever. 01:19:33.180 --> 01:19:36.560 align:middle line:84% And you do that because that way, 01:19:36.560 --> 01:19:40.490 align:middle line:84% by having a flat benefit from being quality p tilde 01:19:40.490 --> 01:19:44.720 align:middle line:84% or all the way up to here, when you have a flatter 01:19:44.720 --> 01:19:48.080 align:middle line:84% benefit from high quality, there's 01:19:48.080 --> 01:19:52.118 align:middle line:84% greater incentive to make the jump from here up to here. 01:19:52.118 --> 01:19:54.410 align:middle line:84% And therefore, these firms are willing to price further 01:19:54.410 --> 01:19:57.110 align:middle line:84% below cost in order to make that jump. 01:19:57.110 --> 01:19:59.520 align:middle line:84% And then you are disadvantaging some firms. 01:19:59.520 --> 01:20:02.390 align:middle line:84% You're hurting firms up here, helping firms down here 01:20:02.390 --> 01:20:05.030 align:middle line:84% by not promoting-- providing quality information on them that 01:20:05.030 --> 01:20:07.940 align:middle line:84% lets them show that they're really good. 01:20:07.940 --> 01:20:11.000 align:middle line:84% But since new firms are much more 01:20:11.000 --> 01:20:14.120 align:middle line:84% likely to be here than they are to be here, when you're here, 01:20:14.120 --> 01:20:15.780 align:middle line:84% you're willing to pay more to get up. 01:20:15.780 --> 01:20:18.560 align:middle line:84% If you take some of the surplus away from the really successful 01:20:18.560 --> 01:20:21.650 align:middle line:84% firms and give it to the moderately successful firms, 01:20:21.650 --> 01:20:24.750 align:middle line:84% that raises the incentive to price in that way. 01:20:24.750 --> 01:20:29.140 align:middle line:84% So what he argues is that what a platform would like 01:20:29.140 --> 01:20:30.940 align:middle line:84% to do in this model is to actually 01:20:30.940 --> 01:20:33.790 align:middle line:84% give incomplete information about restaurants 01:20:33.790 --> 01:20:35.890 align:middle line:84% and to selectively give information, 01:20:35.890 --> 01:20:40.180 align:middle line:84% where we restrict information about the good products so 01:20:40.180 --> 01:20:42.930 align:middle line:90% that we have more-- 01:20:42.930 --> 01:20:44.400 align:middle line:84% so that there's more of a benefit 01:20:44.400 --> 01:20:46.440 align:middle line:84% to having a pretty good reputation so 01:20:46.440 --> 01:20:48.120 align:middle line:84% that new firms will then invest more 01:20:48.120 --> 01:20:50.215 align:middle line:84% in trying to get the pretty good reputation. 01:20:50.215 --> 01:20:51.840 align:middle line:84% And then obviously, all the other firms 01:20:51.840 --> 01:20:55.955 align:middle line:84% are pricing off half the price to outcompete those guys. 01:20:55.955 --> 01:20:59.570 align:middle line:90% 01:20:59.570 --> 01:21:00.843 align:middle line:90% OK, that is it. 01:21:00.843 --> 01:21:02.010 align:middle line:90% That's what I had for today. 01:21:02.010 --> 01:21:07.430 align:middle line:84% So Wednesday, I'm going to talk about empirical work on entry. 01:21:07.430 --> 01:21:10.970 align:middle line:84% I would say Bresnahan, Reiss is really 01:21:10.970 --> 01:21:13.280 align:middle line:90% the classic paper on entry. 01:21:13.280 --> 01:21:16.370 align:middle line:84% Again, Bresnahan, Reiss is a little old by now, 01:21:16.370 --> 01:21:19.130 align:middle line:84% so I would say that if you want to read things-- 01:21:19.130 --> 01:21:21.020 align:middle line:84% I will tell you what's in Bresnahan and Reiss 01:21:21.020 --> 01:21:23.600 align:middle line:84% with slightly more modern econometrics 01:21:23.600 --> 01:21:24.560 align:middle line:90% or what would be in it. 01:21:24.560 --> 01:21:27.710 align:middle line:84% And then maybe read Berry, Waldfogel, or look 01:21:27.710 --> 01:21:30.785 align:middle line:84% at one of the Bronnenberg, maybe Bronnenberg, Dhar, 01:21:30.785 --> 01:21:32.240 align:middle line:90% and Dubé or whatever. 01:21:32.240 --> 01:21:34.960 align:middle line:84% But I'll talk about those four papers. 01:21:34.960 --> 01:21:48.000 align:middle line:90%