 Hello everyone. It is a great pleasure to present my paper with Doshin in this seminar series. So as the title indicates in this paper, so we aim to identify potential biases in technology adoption in platform markets. So to motivate our study, so one challenge to competition policy in the digital platform markets is the many services are provided free to consumers. So when the service is free, the exercise of market power and the consumer harm come in the form of a low quality of service, less innovations, or less privacy of protection. And this concern is particularly important because this industry is very dynamic and the innovations play a major role. So the same message has been conveyed by many recent policy reports on platform markets. For instance, CMA report and the Foreman report in the UK and the Kramer report in the EU and also the Chicago School Stigler report and actually more recently House anti-trust report on big tax in the US make a similar point. So to quote some of the reports, for instance, the CMA report says that first competition problems may inhibit innovation and the development of new valuable services for consumers. So this impact on innovation is likely to be the largest source of consumer harm. And the same sentiment is also echoed in the Stigler report. So in this paper, we address one particular aspect of innovation, which is to identify potential biases in technology adoption incentives in two-sided markets. So there are two distinct groups of users in the market. One issue that can arise is how the platform will allocate its limited resources between the two. In other words, whether to favor the consumer side or the advertiser side if there is some conflict between them and whether this decision is socially optimal. So we analyzed this issue first in the context of a monopoly. So then we considered a Diopoli situation to see how competition influences this tradeoff between the consumer side and the advertiser side. So in this exercise, we consider two cases. One is the case where the service is provided at a positive price and the demand can respond to the price change. And the other is for the case where services are provided free. And in the paper, we continuously derive the conditions under which free services are optimal for the platform. And one main result is that the biases in technology adoption can be very different depending on whether the non-negative price constraint is binding or not. And our result also suggests that the optimal regulatory policy response may also differ across the two cases, whether depending services are provided at a positive price or free. And even though we culture our analysis in the context of technology adoption, so our framework and the results can be applied to other contexts. So in particular, we can reinterpret the results as biases in platforms, certain business policy choices. So you can see the two such examples. One is a privacy policy and the other one is ad-load policy. So when we say ad-load, this is the decision of the platform, how much advertising to show and how to show it. And these policies inherently involve trade-offs between the consumer side and the advertiser side in that more advertising can inflict a nuisance cost on consumers but may generate a more advertising revenue. And the same can be said for privacy policy because my screen is not moving. Okay, so for the interest of time, I will not go over the literature review. So let me just mention that many people in the audience have been major contributors to the related literature. Okay, so plan of talk is the following. So I will spend most time to talk about the monopoly model. And in this case, we are going to consider two cases, whether the non-negative price constraint is binding or not. In other words, whether services are provided at a positive price or for free. And then in case I may run out of time, so I will discuss some policy implications before the monopoly model. Then I will present the monopoly model and then if some time remaining, then we can do some further discussions. Okay, so let me start with the monopoly platform. So we consider a monopolistic platform with consumers and advertisers. So on the consumer side, we denote the gross surplus per consumer by U and the P is the price paid by the consumers to the platform. And then the difference between U and P is net surplus provided by the platform to consumers. And this is denoted by S. And then demand will increase in the net surplus provided to consumers. So in particular, so we are going to assume that D prime S is positive. In other words, the more surplus is provided, there will be more demand. And more importantly, we assume that when the platform attracts consumers, each additional consumer allows the platform to generate additional revenue from the advertiser side. So more specifically, we assume that the platform can generate a total surplus of beta from the advertiser side. And the platform can extract a tau proportion of the surplus where tau is any number between zero and one. So that means each additional consumer generating advertiser revenue. So this can be written as a tau multiplied by beta. So beta is the total surplus and out of the total surplus beta, tau proportion will be captured by the platform. And we provide some micro-foundation of the model in the appendix. And admittedly, we adopt a very simple reduced form to describe the advertising side. So one main reason for our modeling strategy is that the boundary of the advertising market is much broader compared to the product market on the consumer side. And potentially many more players are involved. So for instance, if you consider the display advertising market, there is a variety of publishers and the content providers that compete along with social media on the supply side. And they rely on the various advertising intermediaries to sell their advertising inventories to a large number of advertisers. So hence, if a publisher is monopolized, even if a publisher is monopolized in the product market, it may have less market power on the advertising side. So in this regard, one important factor determining tau is what is called the ad tax, which represents the share taken by ad intermediaries from the advertising expenditure paid by advertisers. So for instance, small platforms that rely on ad intermediaries will have a smaller tau, while a big tech platforms that have built their own digital ecosystem so they don't have to rely on ad intermediaries, then they will not be subject to ad tax and they will have a larger tau. So this is the way we model the advertising side. Now with this setup, the monopolist property can be written in this way. So can you see my mouse moving? Yes. Okay. So there are two sources of revenue for the firm. So one is from the consumer side. So that is captured by P. And there is another source of revenue, which is coming from the advertiser side. So as usual, we can get the optimal price by deriving the first of the condition. And the one thing to notice is that as the tau beta increases, the optimal price will go down. Okay. So this can be easily derived. So the intuition is that as advertising revenue become more important, so it is more beneficial to expand the consumer side of the market. So in fact, if tau beta becomes too large, then it may be optimal to charge a negative price. Okay. So in other words, if you denote the P tilde as the argument maximizing the property function, this number can be potentially a negative number. So in that case, we impose what you call the non-negative price constraint. So what that means is, okay, the reason we impose non-negative price constraints is that there may be various moral hazards and adverse selection reasons why negative price may not be feasible. So in that case, we are going to impose the non-negative price constraint. That means that optimal price will be maximum of P tilde and zero. In other words, P tilde turns out to be negative. Then the preference price will be constrained to be zero. So then when we substitute back the optimal price in the property function, then we have the maximized property as a function of U and beta. So to study the monopolist's incentives in technology adoption, which can affect both U and beta, we analyzed how change in U and beta affects the firm's profit. In other words, we totally differentiate the profit function with respect to U and beta. So then as a standard in the consumer theory, we can derive the firm's indifference curve called the isoprofit curve, which is nothing but the locals of U and beta that would provide the same monopoly profit. Then the slope of the isoprofit curve represents the platform's marginal willingness to substitute U for beta and can be derived as the ratio of what you call the private marginal value of U and the private marginal value of beta. So private marginal value of U is how much additional profit the monopolist can get when U increases by one unit and similarly for beta. So we perform a similar analysis for social welfare. So we first define social welfare as the sum of the monopoly profit and the consumer surplus and the advertised surplus. Then we can derive isoprofit curve as we did for the isoprofit curve, so which is the locals of U and beta that would yield the same welfare. Sorry, JP, Jack, can I ask a question please? Yeah, sure. The P star which are in the social welfare curve will not be the same as the P star in the Okay, so here actually we are looking at the second best outcome. In the end of the P star and P is chosen by the platform. We are not going to consider the case where the social planner chooses the P. Okay, so you're assuming that the social welfare can only control U and beta? Yeah, that is correct. Yes. So I should have mentioned that. Okay, thank you for pointing that out. Okay, so the slope of isoprofit curve can be also similarly derived as the ratio of the social marginal value of U and also social marginal value of beta, so which will be different from the private marginal values due to the existence of what they call external effect on the consumer surplus and the advertised surplus. So in other words, when U and beta changes, they can affect the consumer surplus and the advertised surplus, but those effects will be ignored by the platform, so which leads to biases in the platform's technology adoption. So to analyze private and social incentives for technology adoption and identify potential biases in the market outcome, so we compare the slopes of the isoprofit and the iso-welfare curves measured at the current level of U and beta. So to elaborate on this point, if the platform values an increase in U because this is relative to beta, more than a social planner does, then we say that the platform's technology adoption is consumer side bias. And similarly, if the platform values an increase in beta, this is relative to beta more than a social planner does, then we say that the platform favors advertising side, so we call that technology adoption is a bias. And this idea can be captured by the definition given below here, so more specifically, if the slope of the isoprofit curve is steeper than the iso-welfare curve, this means that the platform is willing to sacrifice more beta to have one unit of increase in U. In that sense, we say that a platform's technology adoption is a CS bias. So let me explain this concept by using a graph. So this graph illustrates a situation of a CS bias. So if you look at this quadrant, so this area represents technologies that provide a higher U and less beta compared to the current level of U and beta. So the origin represents, let's say U null and beta null. So this is the current level of U and beta. So then if one unit, to increase one unit of U, so here actually, so I should say that here the blue curve is iso-welfare curve and the red curve is isoprofit curve. So to have one more unit of U, social planner is willing to sacrifice beta only this much, but platform is willing to sacrifice more. So that is the source of discrepancy. And the shaded area in this here, we represent the areas where social planner incentives and the platform incentives diverge. So this area is the case where the technology adoption is profitable for the platform, but it would be very clear reducing. And the other side is the area where technologies are giving more beta and less U. And in that case, we are going to have the opposite case. So those technologies will be actually, will be socially beneficial, but will not be adopted by the platform. So similarly, AS5 technology adoption can be explained in a similar way. So this would be the case where isoprofit curve is actually better than the isoware curve. Okay, so to gain some intuition, so let me start with a very simple case of inelastic demand. So there is no change in demand. So we are going to assume that consumer size is fixed at D. And let's assume homogeneous consumers having the same reservation value over U. So then when new increases by let's say one euro, then the monopolist can charge one euro more for each consumer because here the demand is assumed to be to be inelastic and fixed. So the benefit for the platform will be simply D. And if beta increases by one euro, then the monopolist will receive additional revenue of tau beta. So the private marginal value of beta of one unit increase will be given by tau D. So if you look at the slope of the isoprofit curve, that is given by one over tau. So this is bigger than one. So this is bigger than one. So that means that one unit of increase in U is more valuable than one unit increase in beta. There will be equal only when tau is equal to one and the platform can extract the whole surplus from the advertised side. Now if you look at the social marginal value of an increase in U and D, there are simply D and D. So here when you look at the social marginal value of beta, so the social plan will also look at the surplus given to the advertisers. So it will be just D. So then a social planner will value an increase in U and beta exactly in the same way. So the slope will be one. So if you just compare these two, so it is immediate that a monopoly platform the technology adoption is just CS bias. So another way to look at is we can also compare private marginal value of U and the social marginal value of U. So then there's no difference. They are equal to each other because the platform will extract all consumer surplus. But if you compare these two, so there is a difference of one minus tau D. So that's another way to see the bias. So now let me move. So in fact, the reason I started with the elastic demand is that the result here carries over to the case of elastic demand. So the result will be the same even though we allow elastic demand. And I will try to explain why that is true by just by using some intuition. So recall that for elastic demand, as I showed in the previous slide, so there's no difference between social marginal value and the private marginal value in terms of U, but there will be some difference in beta. And now we do the same exercise for the elastic demand case. So then when we look at the difference between social marginal value and private marginal value, so then this is zero is the same as here. And then we have one additional term here. And also if you look at the beta component, so the first term is the same as the one we see from the elastic demand case. And then there is also additional term. So the main reason why the result for elastic demand curve carries over to the elastic demand is that actually these two additional terms turn out to cancel out in a sense. So to interpret, so let me look at this component. So what this means is that when the value of the value U increases by one unit, so this expression shows okay, how much of that benefit will be passed on to consumers. Usually when U increases by one unit, the platform will not increase the price by one unit. So some of them will be some of the benefit will be passed on to consumers. That is captured by this term. And as a result, the demand will increase and there will be some demand price mediated effect. So that is the additional term we have here. And the system can be also interpreted in a similar way. So when beta increases, it will also affect price. Okay, so if you remember when power beta increases, advertised revenue becomes more important. So price will go down. So when beta increases, the platform will have incentive to reduce consumer side of price. That will be also beneficial. And if you look at the term, this term and this term is the same. So and then we compare the how much is passed on to consumers through U and beta. It turns out that there is a very special relationship between these two. So that is coming in the next slide. So in particular, if tau is equal to one, so then the pass through rate turns out to be exactly the same. If tau is less than one, so then it will be given by this relationship. So then this special relationship turns out to make these two terms just cancel out and we are going to have a very similar result as the inelastic demand. Okay, so that's kind of like an intuition we have. So, okay, so basically, okay, so we are going to have a lemma, so we are going to compare the slopes of the isopropyl curve and the isopropyl curve. And the system is the one we actually derived earlier for the inelastic demand. And then we have some additional term to reflect demand responses, but this term is always a positive. So it will not change the sign of this term, okay. So as a conclusion, so if the non-negative price constraint is not binding, so in other words, price, the service is provided for at a positive price. Okay, so then we are always going to have CSO bias, the technology adoption by the platform. So the only exception is the rent tau is equal to one. Okay, so in that case, there will be no distortion. J-Bill, can I interrupt for one second? So Jacques has an interesting question. Jacques, would you like to ask it directly? Sure. Jacques, you are muted. Yeah, yeah, I'm unmuted now. Yes, here you are basically assuming that you can conclude social welfare by adding the welfare of the consumers and the welfare of the advertisers. But the welfare of the advertisers is not really directly social welfare. It depends, you know, where it's coming from, whether it distorts the consumption choices and so on. So I'm a little bit worried about you. How do you use the results for guide to policymaking? Okay, so that is an excellent point. Okay, so I mean, as I mentioned earlier, we actually adopt a very reduced from a modeling strategy. And when we do the social welfare calculation, so our assumption is that advertising side surplus, okay, so that is not a pure waste. Okay, so essentially, we have in mind where advertising is maybe, I mean, if you look at the crash case, whether advertising is informative or wasteful. So essentially, we are looking at the case where advertising is more informative case. Okay, so we provide some micro foundation in the paper. But yeah, I mean, but obviously, there will be some cases where advertising may be purely socially wasteful. Okay, but couldn't you, at the minimum, you could add a parameter, which would be the percentage of advertisers profits, which is wasted. Okay, that could be. So I think that we could introduce another parameter, how much is wasted. So then I think we can, in our framework, we can do the analysis. Yeah, I think so. So can I go on? Finally, we, thank you very much. Okay, so now, so we look at the case where the NPC is not binding. Okay, in other words, the services are provided for free and the prices can adjust. Okay, so then we look at the case where the NPC is binding. So price is constrained to be zero. So if you look at the first of the condition, so this is the condition. But if this condition is not satisfied for any positive price, and this term is even negative at, when it is evaluated at the price equal to zero, then the NPC constraint is binding. In other words, under this condition, the optimal price we derive will be a negative number. And then if we impose the non-negative price constraint, then now price will be equal to zero. So in that case, the monopoly profit revenue source is only coming from the advertiser side. So now we have a profit function given in this way. So in other words, the P term is P term disappeared. So then we can derive isopropyl curve and isoephyl curve, and we do the usual analysis. Then what we derive is that always the isoephyl curve will be steeper than isopropyl curve. So what that means is that the monopolistic platform, the technology adoption will exhibit the advertiser side bias. So intuitively, right, so if you are now going to receive any revenue from the consumer side, so then the incentive to provide the more valuable service will be limited for the platform. That's one or two to think about. Okay, so the summary is the following. So when we consider a monopoly, monopoly two-sided platform, okay, so we consider two cases, whether the NPC bind or does not bind. And as you can see, we have a completely different results. So if the NPC is not binding, then it will be consumer-side bias. But if NPC binds on the consumer side and services are provided for free, then it will be advertiser-sized bias. So this implies that it is important when we formulate a public policy. So it is important to distinguish the two cases. So before we go to the monopoly model, okay, so let me do some, let me discuss some policy implications. So as I mentioned in the introduction, so our analysis can be reinterpreted as a platform that incentives to adopt certain policies that may have a differential effect on the consumer and the advertiser side. So we can think of two search policies. So the first is platform privacy policy. So collection of consumer sensitive information may allow the platform to engage in more precise targeted advertising and hence increase added revenue, but impose a private cost on the consumer. So the platform, the decision on how much information to collect can be thought of, can be thought of how much you to give up to increase the beta in our frame. So and whether the trader of calculation by the platform is a bias compared to the socially optimal one, so they can be analyzed in the same frame. So the infamous Cambridge Analytica scandal is due to Facebook's lax privacy policy and our results suggest that the lax privacy policy can be a consequence of the Facebook's market power and each free service. And the platform's add load decision, so that is how much advertising to show to consumers can also be analyzed in a similar way. So in the case of Google search, showing a great greater share of ads relative to organic search results can induce users to click on ads more, but some ad content will be less relevant to the user's search query. So it may compromise the quality experienced by the user. So this is the same as beta increases, but at the expense of you. So the same trade-offs exist for display advertising done by platforms like Facebook. So a higher ad load can lead to higher advertising revenue, but inflict more nuisance costs on consumers. So there are some evidence for that in the CMA report. Okay, so now I have how many more minutes? Maybe 10 minutes? Okay, so let me briefly mention, let me briefly go over the Diopoli model. So we are going to consider Diopoli model with horizontal differentiation. So we are going to consider a symmetric Diopoli and a representative platform I demand on the consumer side can be written in this way. So how much net surplus is provided by platform I and how much net surplus is provided by rival platform. And we are going to do exactly the same method. Okay, so we are going to define platform the profit function and the derived iso welfare curve, I mean iso-profit curve and compared to the iso welfare curve. So here one, so when we have a Diopoli model, so there's one additional thing to consider. So that is what we call a strategic effect. So when we look at how the platform's profit changes, okay, when you and the beta change, okay, so there'll be some strategic effects. Okay, so when platform one's U1 increases, okay, so that will affect the other platform's price. Also when beta one changes, it will also affect the other platform's price on the consumer side. But it turns out, okay, even in the Diopoli case, our results, as long as the non-negative price constraint is not binding, you know, as long as the price is positive, surprisingly, we get exactly the same result. And also the reason behind that robustness is also coming from, so let me call the Diopoli path through rates, okay, result. We, this is a very similar result we had earlier. So in particular when tau is equal to one, so this is the condition, okay, we derived for the monopoly case. And now when we look at, okay, when we look at the effect of a U1 increase and the beta one increase on P2, so that we call path through rates via a strategic effect, that also turned out to be the same, okay, across U and beta. So this pass through rate equalization results, okay, actually yield the same result. So I'm not going to go, I mean, due to the lack of time, I'm not going to go into the detail. So the punchline, okay, punchline is, once again, when you compare isopropyl and isoverectal curve, so that can be expressed in the following way. So this expression is the same as the inlass demand when we look at the, when you look at the, so in the simple case of inlass demand. And there'll be additional term here, okay, but this term is once again, non-negative, so the sign will not change. Okay, so let me summarize. So when we consider a competitive bottleneck model, as long as the MPC does not find and the price is positive, then technology adoption incentive will be once again CS biased. So then what if the non-negative price constraint is a binding? So then we can derive that, we can derive the following result. So when you compare the isoverectal curve slope and isopropyl curve slope, so if you remember, so this is the term we had for the case of the monopoly. Now with competition, we have one more term, okay, so what we call a business stealing effect. So in the monopoly case, because the second term does not exist, so isoverectal curve is already steeper than isopropyl curve, which, which says that the platform choices are advertising-side biased, but now the result can be reversed. Okay, if this business stealing effect is sufficiently large, and this is bigger than one. So that leads to the following proposition. So when we consider a monopoly model, if MPC bonds on the consumer side, then it can be AS biased as in the monopoly model. If competition is not strong, okay, so in the in the in the extreme case, I mean, if there's no competition, it will be boiled down to essentially the same as the monopoly model. So then we are going to replicate the same result. But if the business stealing effect is sufficiently large, well, another way of saying is that competition is very intense. Okay, so then we cannot rule out the case where in the MPC binding case, the platform bias can be, can be, can be towards CS. Okay, and actually we verify this one in the hoteling model. So actually we look at the hoteling model and the logic demand model, okay, to illustrate our results. So when we look at hoteling model, so hoteling model is, we can consider competition is very strong because the market size is fixed. So the only way you can increase your demand is at the expense of the other firm. So in that sense, competition is intense. And we show that in the hoteling model, indeed bias is actually CS biased, rather than AS biased as in the monopoly case. So I'm not going to go over hoteling model and the logic model in detail. So in summary, this table, just summarizes everything I presented today. Okay, so regardless of the market structure, if the MPC is not binding, then we are going to have a consumer side bias technology adoption. But when MPC is a binding, in the monopoly case, we are already going to have AS biased. So this one shows that actually whether MPC binding or not binding, okay, can make a huge difference. But if you compare the market structure, in the duplicate, we also have AS biased technology adoption. If competition is weak, but if competition is very strong, then the monopoly result can be reversed. Okay, so I mean, so that's about it. Okay, so then maybe some potential extension we can consider maybe. So our analysis in the sense is a local analysis. But if there's a big change in UN beta, so then the regime itself may change. Okay, so we separately analyze the non-negative price constraints of binding one out. Okay, but with big change in UN beta, then there can be some regime change. And also when we look at the technology adoption in the monopoly case, we only look at the unilateral incentives to adapt. But if the arrival can also adapt similar technology, okay, so then that's something some additional consideration we have to look at. And also in the monopoly case, we look at only the symmetric case, but maybe asymmetric initial condition can be also explored. Okay, so as a concluding remarks, okay, we emphasize the role of non-negative price constraint, meaning that whether services are provided for free or not, okay, then we make a huge difference. And our result may provide a rational for a tough competition policy to curb concentration in platform markets, as long as competition authorities are concerned about consumer surplus. Okay, so that's about it. Thank you, JPL. Martin, sharing movement to the discussion. If there's nothing better we can do, I can start. That is the best thing we can do. Yeah, okay, let's see. So first, thank you very much for allowing me to read this paper. I guess it has great bones, and you may still work a little bit on the flash. So JPL was, I think, explaining very clearly the bones. And then in terms of the interpretations, I'm not completely convinced yet, and it may just require spelling out things more carefully for me. For example, the privacy policy part, my understanding would be that consumers typically would be affected differentially, so it's not just a you. There's something else going on, and then I don't see how the analysis directly can be used to address such a privacy issue. Regarding the ad load, I thought, well, this is actually a model we have seen a lot in the literature, but the way it's a different take, because what you're doing is really doing a second best, which means that you're looking at a regulator, which, for example, can fix the ad volume, but then cannot control the price charged to the consumers in the two-sided pricing setting. And perhaps it has been done somewhere, but I haven't seen it. So in that sense, even though this literature is pretty big, it still kind of takes a new angle, at least, as far as I understand. And I think the paper may benefit from working a bit more on these kind of applications, because at the beginning, you say, well, you don't know any formal investigation on the relationship between platform market power and innovation incentives. And then you exactly explain that, actually, there are other ways of interpreting it, and those things we have seen before. And so when you say that there are limited resources to provide U and B, so that's, I guess, resource interpretation, which then links you to B. So you fix one, and then the other one follows. A different way to think about it, and there are a number of papers on this, is to think about seller competition on the platform. So in some sense, the platform chooses the number of sellers, which then affects your beta, and it affects the U. And so I think that's another way of thinking about your model, allowing for this choice of the number of sellers as a separate decision by the platform. And so there are a number of papers doing this, and I think the one which is closest, but I mean, he's in the audience, so he might tell us more, is Tatau Tei with a paper from last, he wrote last year, where he exactly looks at the kind of platform design regarding the number of sellers allowed on the platform. And I think this fits within your setting. So overall, I think it's really great. One thing I was a bit surprised, I understand it's nice to think about whether zero price constraint is binding or not. But there may be other reasons why there are zero prices on the buyer side. So it's not because of a binding zero price constraint, but say because of technology. If you look back, commercial television, so it was just not feasible in the early days to charge viewers. And then later on with the cable programs, it became possible. So it's sometimes it's just also the question whether pricing is technological feasible, or even if it is feasible, there are opportunity costs of making consumers pay. And so there are number of reasons of why in some environments, we have a zero price and others we don't. Also, you may even think of that in some environments, it is actually possible to avoid kind of free writing behavior and have negative prices. So therefore, I would start more broadly and then only talk about whether or not the zero price constraint is binding as one way of structuring your result. But I think there are many other market environments where it's not about whether the optimal price is negative or positive on the consumer side, but whether say technology allows you to charge it or whether the opportunity costs of making consumers pay are high or not. And I think I used my time, but at least I used a few minutes. Thank you. Thank you, Martin. So we can now open it up to a general Q&A. So to respond to first of all, thank you to Martin for a great comment. So yes, I mean, in our paper, actually, it does not matter where the source of the non-negative price constraint is coming. It could be technologically, I mean, region. So whatever the reason, okay, we can just straight forward, we can apply our analysis. And the reason we actually indulge in it is that if we just assume the price is equal to zero, then people will ask, why, why, I mean, the platform charges zero price, okay? So we just try to justify by indulging the driving. But in our paper, if the platform can charge a negative price, so the reason, the usual reason that the platform cannot charge a negative price is various moral hazard and adversarial problem, and there's some monetary problem. If that issue can be addressed and the platform can actually charge a negative price, then we can just apply the case where the first case, which is a non-negative price, is a non-finial. We can, I mean, it doesn't matter whether the price is negative or not, we can just straight forward, we can apply the large. And also one difference, so actually we have also non-negative price concern in my paper once again with Toshin on the leverage theory of time. So in this paper, actually non-negative price constraint is actually essential, essential in the sense that that is necessary to derive the leverage mechanism. But in our paper, the non-negative price constraint is not essential, okay? If it's not binding, then we just apply the first model. And then if it happened to be binding, then we just apply the second model, okay? So in our paper, we just consider the two cases, but non-negative price constraint is not essential for our story. I have a question. Do you assume that the price is positive or negative, or can you denogenize the condition under which the price is positive or negative, when it's negative, your assume is equal to zero? No, I mean, I just explained that we denogenously derive the condition under which the constraint is binding. So that is the slide. Okay, so where is it? So that is, okay, so this is the, okay, so this is the condition, okay, when the non-negative price constraint is binding. As you can see, tau beta is a very big. In other words, advertiser side is very important. So then the price will be, the up-end price will be negative. So I had a question about the menus of contracts on the consumer side. This is Oslan speaking. So I was wondering how the results would change if you allow the menus, like premium models, you know, free option. So the price zero, if you allow me to see, if I allow you to show me more ads versus price version without our fewer ads? Okay, so I mean, so that's a good question because in the real world, okay, we actually see that kind of a menu, like a Spotify, okay, there's a premium account and then you just pay and you do not get any advertising and the free service and you get free service but in return for advertising, okay. So that's an excellent question. But to address that question, I think we need a more, I mean, a more elaborate model on the consumer side, okay. So we have to introduce some kind of vertical dimension, okay. So that means, so high types, we will get premium service and the low types, we'll get free service, okay. I think we need a more elaborate consumer side model. Because at the end of this past, sorry, actually, one constraint is that we are assuming that demand is depending only u minus p. So when new increases, right? So all consumers value will increase by one unit. So maybe we need to have some kind of like a set you kind of like we need some heterogeneity in terms of how quality will be, will be, will be, yeah, valued by different consumers, okay. So we need another parameter to address that issue. Actually, we have a companion paper on actually we are looking at now R&D incentive in two sides of the markets. So here we look at just a very simple technology adoption choice. But in that companion paper, which is in progress, I mean, it's been sitting for many years, but we have not able to complete the paper. But in that actually paper, we look at the platform incentive is how much to invest on the consumer side and on the advertising side. So in that case, actually, we introduce this kind of parameter and we do this along the line that you mentioned. Okay, but here in the current paper, you also have this parameter or the measure, which is how much platform pass through the changes in the u. So it's a very, it's a reduced form thing, but this should depend on specification of the demand. So you have results depending on this pass through basically. Yeah, yeah, I agree with that. Yeah. So obviously some research, yeah, yeah, yeah, we depend on the specific details of our model. Yes. Okay. Thank you. Okay, Bill, it's Andre. One thing I was wondering, I think this is the the the issue of like looking at the conflict between advertisers and users. I think it's a super interesting problem. I think it's actually more general than that. So you can ask more generally, it doesn't have to be two sided platforms between advertisers and users. It could be generally, you have two sides. And let's assume you have like design issues or sorry, the decision problems that can affect the welfare on two sides. It strikes me that you can sort of generalize the model. And of course, the more complex what becomes more complicated, then you have two sided pricing. But as a first cut approach, maybe one thing you could do is to basically take the, let's say the pricing structure is exogenously given. And then basically look at the, you know, do the exercise and figure out like the, you know, the would you have the iso profit curve, just looking at the utility parameters for the two sides. And then you maybe you can endogenize pricing. It becomes more complicated. Obviously, like in the advertising model, well, you only have one, one price here. That's endogenous. But I think it's a very interesting exercise to do more broadly. So when you say it can be applied more generally, do you have some specific example in mind? Sure. I mean, you can ask this for any, I mean, I can, we can run through like all kinds of two sided platforms. There's always going to be choices that are going to pit interest of one side with the other side and take Uber, like I can take, I can take Uber, like there's drivers and riders. Well, there's certain things that Uber does that are going to please drivers, but they're going to hate, right? Okay. Okay. So it's, it, it will lead to the same kind of, I mean, draw the graphs, you can do the iso profits. I think it's, I think it is very valuable to have that. Okay. Okay. Okay. Thank you. Well, can I just add, so just as a announcement, the paper also has a nice logic analysis in there for the competition case. I think Jay, you didn't really have time to, to talk about that. So I thought that was pretty nice. Okay. Thank you. Yeah. So I mean, if I knew that we have some time left that I could have covered today, I didn't know that how much time we are going to spend on discussion. But you can, I mean, anyone can read our paper. It's available. Actually, so if we can go back up a little bit, what would you say are the main lessons? I mean, so you gave two examples, but what are the main lessons for competition policy you would draw from your analysis? I mean, what type of cases should, does it provide lessons about what type of cases to pick up by, by a competition authorities? Does it you know, provide the lessons about type of remedies and so on? I mean, one, so one example might be, so let's say, so let's go back to the, okay, so, so look at this table. So then we may say that, so we can consider your dynamic situation, right? So then there are competing platforms. So imagine a situation. So it also depends on whether the competition authorities only care about consumer welfare or they also concerned with advertising side of welfare, right? So points is if we look at the case where initially there is a strong competition among platforms, okay. So then we may have some condition like this one. So consumer side will get more benefit. But as one firm becomes a dominant, as it happened in the big tech merger case nowadays, okay. So some, some like Facebook, Google, they become a dominant firm and become like a monopoly. Then now as you can see the bias will change to AS bias, right. So I'm just making, I'm just kind of like a very, I mean, she's kind of a comment, but yeah. So then if you are really care about actually consumer side of welfare, then maybe you, there is some justification to try to maintain competition in the platform. And that's kind of one implication we may have. And maybe the portion can add, yeah. Sorry, just to follow up on this. So what would happen if you have a symmetric situation, say there is a kind of a monopolistic situation vis-a-vis consumers, but there is competition vis-a-vis advertisers, like search markets, for instance. Okay. So that, yeah, we have not yet analyzed. I mean, so that's basically the last comment I had, right. So we look at symmetric geopolitics, but obviously one firm is more timely than the other, okay. So what will happen? Yeah, that's something we have not yet analyzed. That will be interesting, I think. Yeah, yeah, I fully agree. Thank you. And I think you did some comparative statics in the competition case and the degree of differentiation between platforms. And I think the, perhaps the one also in line with your introduction, the interesting part would be the comparative statics in the, in the tau. Okay. Yeah, because in a way you can see that Big Tech is becoming more powerful and is extracting more of the surplus. And so I think that would be useful to see and whether then the bias in some sense becomes worse for the consumers.