EthCC 2: Julien Prat

okay okay sorry for that so you already know my name so I'm a professor at the University Polytechnique so this is joint work with Vance on the nose and estefania Mikasa so we started working on this project year ago and what a difference a year makes so last year when tokens we are selling like hotcakes most people we are not really bothered about token omics the idea was anyway it sells and we will figure it out after now one year later let's say that the market is going a rough time he's going through a rough time and people are learning that actions have consequences so on the one end it's becoming very difficult to raise money because too many investor have been born on the other end you have very good project son technological project which are stuck with badly design flawed tokens okay so one can be optimistic and think well this is just a correction things will get better but the truth is that wishful thinking will not be enough it's clear that if we want investor to come back we will need to define a set of rules and practice that will protect them okay so I'm not going to touch upon the many aspect of investor protection and token investments because this will be really beyond the scope of any talk I believe I'm just going to look at one specific but important question how to price a token and let me be clear by that I don't mean and will not give you a model that will help you to forecast the market price because markets do all kind of stuff there is animal spirits there is speculation there are Furies for that but it's kind of yeah it's kind of complicated anyway what I'm looking at is and this is what economists think when they think about pricing is fundamental pricing so can I realize the value of a token to really its intrinsic values Florrie will generate so I know that some people in this community are dubious about that because I talk to them alone for five been talking to many people well that last Charles and they were saying you know Marquette you know it's just floating it's like you know whatever is people believe it's 100 it's 100 okay very well but that's not our financial market operates okay financial markets in equity and debt they have benchmarking techniques for any kind of financial products then the market may deviate but at least you have a focal point on which most people can agree right now the issue if the token market is that since we don't have a reference point anything goes and until we have at least a focal point which will help us to have a common language I think we will see this wave of incredible speculation and devaluation and so on so that's really the question we are tackling now you may say since people have been doing that in finance for 200 years we can just look in finance book and do what they do yeah that's probably a good start the problem is that tokens are nothing we have never seen anything like tokens tokens are not equity and tokens are not depth so they are not equity because you don't have control over the film you issue tokens and you don't dilute your capital and that's exactly why people wants to issue token because they want to stay in charge I don't want to delegate to the equity holders but yeah so then are tokens like depth no they are not like that because you cannot go bankrupt so they are they don't look like anything so you can try to pick up a book in finance and say okay I'm gonna use that to price my token but you will not find formula there is no off the shelf techniques for pricing tokens we need to come up with a pricing formula okay a good one and then this has to become the benchmark so that's what we're trying to do and this is what is written their pricing model will be required if I see you as ever to match into a standard investment vehicle so now people have realized that and the thing that came up was the quantity theory of money now the quantity theory of money is nothing new it's one of the oldest equation in economics it goes back to Copernicus so but it's written them so what is the problem MV equal py or P Q I think maybe you've seen that before so M is the monetary mass V is the velocity of circulation of the token P is the price of your token and Y is your market size so py is basically what's happening in the real world like in fiat that's what people buy the price times your output and MV is your monetary economy is a number of token and the speed at which the ciock rates now the problem is that equipment is that you have two endogenous variable V and P and you have one a question so this is not rocket science this is not gonna work this is not a model this is that might be part of a model but it's not a model more than that it's actually a tautology because it's always true it's just an accounting identity so it doesn't tell you anything so what people have been doing is like they fix the velocity of money okay and then they get surprised by some of your means but you cannot do that the velocity will be endogenous to your token economy and it's even more complicated than that as you will see in the talk because the price itself is going to change because this is not the price you paint scat you paint token so you want to discount so the price also is endogenous I want to say one thing so I realized people say but you know what I can control the velocity if I'm centralized and I will force people to stack the stuff so then the velocities I can fix it you know so that it's okay I've controlled one endogenous variable and I can solve that equation but the problem is that the way you're gonna control velocity is going to fit back into the price it has to be because if I all the token what you're going to do is a token as a central platform with matter for my price okay and actually it's much more difficult to price a token with when you start to play with the monetary mass and the velocity so this is not even getting you out of trouble so the question so what I'm going to show you now that we have a model we have a pricing formula and these endogenous okay we're not like making any assumption on V it's going to come up I mean you will see there's an assumption but it's not fixed like from nowhere so what we need is to go beyond the quantitative theory of money and propose model that dajin eyes velocity of money and then when they are microphone did so that's how a column is like to talk you know you have micro foundation then you have a proper pricing model which will allow to benchmark I SEOs so okay so I apologize this is economics too so yes there is a reference Legos and Wright is a famous framework in economics so so I've been thinking about that question for two years and then eventually I realize that natural thing to do and it's obvious I should have thought about it much faster actually is to go to the fear of money just to take the fear of money and you adapt it it's not it's not surprising because tokens out form of money so what is a cutting-edge theory of money in economics is the Lagos and right framework which is a search theoretical framework but I will give you a very simple summary of it there is a comedy commodity market where people can buy and sell token so that's now sorry this is where you buy the output of the platform so this is why you use your let's say your easier to buy like some computing power and then there is a trading market which is an exchange platform where you can sell your tokens okay now the platform has monopoly power on the community on the community market so if you want to use a tea room you have to you have ito you cannot come with another token so I think this is a popular description of our tokens work okay so I know I'm gonna make a very simple assumption one unit of token gives you one unit of service it can be relaxed it's no big it just makes the exposition exposition sorry easier okay so now you have this following time line you have the utility of that so users know okay so let's say it's going to consume C so that's let's say some units of computing power he has a UT T which is going to become care but it can be linear and then there is a shifter of D I so di means that in each period maybe you need the service maybe you don't need it and you will need it with probability lambda so sometimes you don't need to use a smart contract and some time you do okay but the point is that you don't know that beforehand before you enter the period it's stochastic and then you wake up and you're like okay with a probability lambda you say okay I really need to use it now I need to execute that smart contract so this is the preference Shakthi is reveal at the beginning of the period now the key thing is that you cannot go to the exchange market after knowing that so what I'm saying is that you cannot say oh I need to execute a smart contract I don't have any fur I'm gonna buy some now and then I'm going to do my smart contract if you can do that then the value of ETA zero because nobody we all them they will only hold them for one second the times they need it for the smart contract so that what this model tells you already is that it's key that in your system speed is at the center that people need to execute fast so they need to have the token in their pocket if they can wait you know and go and find the target then they won't talk and there won't be any demand you can have a stacking model stacking is a solution to that I'm not looking at stacking okay if you force people to stack you go around that but if you don't force people to stack they will have to stack on themself and so it means that it cannot respond to the shock so this is an assumption and by the way is the same assumption that economists need to explain why people have beers in their pocket okay because otherwise you will only have bond and when you want to buy bread you will go to the market exchange your bonds and get some money so this is an old conundrum in economics so now M is your token holding lambda is the probability at which you need the service o is your interest rate or this contrite use your utility what is your value P is the price of the token the value of the price the value the value of the users given the price at time T and the time that price at time T plus 1 you have to maximize this so what is this with a poverty lambda I'm gonna use my token and I'm gonna get the utility U of C maybe I'm not going to use all my token some will be left so n minus C time the price next period because I can sell them next period with a probability 1 minus lambda I'm not using the token because I don't need them so then I have a monetary mass M next period I have M times the price of tomorrow and then and this is key if you stop tokens you lose something it's the opportunity cost instead of having tokens you could have put them on the financial market and earn the interest rate do you agree with that so that's what you did use on the right you did use the last interest so now if you solve that it's very easy you get this expression so here you have the price of the token times the interest rate is equal to two things convenient ZL and capital gain so convenient CL is what you gain when you own something so typically in the future market you can have future with about wits but you don't all wait or you can all the wheat itself so it gives you an additional benefit to have the product itself so that's the convenience yield so what is the convenient CL with a priority lambda you're gonna get the marginal utility of the last token - its price because when you consume your token you lose its value no you agree you cannot sell it in X period so that's what you gain and on top you have capital gain now look at this expression imagine that there is no convenience held imagine that the marginal utility is equal to the price then you have up equal PT plus 1 minus PT what is that that's a bubble when the price change at the rate of interest it's a bubble that's a definition of a bubble but here it's not above all because you get some utility from it it has some value because sometimes you need the service okay so then if you solve it you get this expression P at that the equilibrium price is equal to lambda divided by R + lambda time u prime of M where now M is a monetary mass of the economy so there is several things to realize so lambda if you remember is a probability at which you need the service so when lambda goes to infinity this is going to 1 lambda divided by R + lambda so here you have P equal u prime of M so what means P equal u prime of n so Mary Alice economics but the price equals the marginal utility I don't know if any of you have done economics but Trice equal marginal utility is equal 1 1 that will be the price if you pay and shut if you could pass since shot you will have P equal u prime of M but now you have P smaller than u prime of M so what does it mean it means that if you do an IC o---- you will forever sell your product at a cheaper price you have embedded in your system and at the annual discount and I think it's important to realize because when you talk to people I mean I don't know but I took several people told me the problem with when I see you is that you issue tokens it's like you promise that you're going to repay all the token it's not true because you can put them back on the market immediately what you are doing in fact is that you are committing to selling at a lower price and the discount is going to be proportional to the rate at which people need your service so why is that so what is the economic intuition the intuition is the following okay I'm gonna old some tokens and the consumer but if I didn't have the token that could have them on the market and another interest rate so the only reason why I all this token is when I'm gonna buy the service I need some profit in utility I need some rent so you have to give me a discount for me to all the token otherwise why will I do it I will just go on I put my money on the stock market on the on the bond the only reason why you will convince me to all this token is that when I trade against something and this is from the point of view of the firm of the platform it's a discount okay so what I'm saying that if you don't do an IC o---- you say you can buy in fiat you can sell at a higher price it says to me yes what do you mean by that I'm not yes fantastic so if I'm looking at the long-run equilibrium steady state so that's not what I'm doing now okay so you're right so most people don't buy token because they want to use it right now because that's really most of the project don't run so that's really not work they buy it because they think it's the next big thing now so this is the long run so now what you need to do is to find the trajectory and early on yes I'm gonna buy it because I think it's going to appreciate right but so mathematically if you want to solve this trajectory of price you have to shoot so I Nick you should for the long run equilibria and you find the path that gets you there and it turns out there is only one that gets you there all the other paths are going to go to unstable equilibria so now what I'm doing and thank you great transition is I'm doing the dynamic model which is going to shoot toward this equilibrium but I needed that you know and a lot of intuition is already there so then you need some dynamics okay so yes I have ten minutes yes okay it's going to be rough sorry I'm gonna be sorry tell me it's for what let's try so okay so first you need stuff to change over time now so at the beginning so here you have the utilities so now there is a parameter Z which is capturing your technological progress so what I mean early on let's say Z is very small so people I mean you're selfish is really basically it's crap now nobody uses it but other time it's going to get better and better and better and this side take a sec drowsiness it's like your business plan when you come to you want to get money you come to with a business plan you do a projection on Z now my model takes your projection and give you the price it's not my question how you get your business plan to what is so now you have people we are different they have different technological abilities so the people in this room you have the best in technological ability you are the first a doctor but there are many people and and you realize that if it's only you it's not gonna be a big industry your objective now is to make it usable for everyone so over time people were less than less technologically savvy we start to enter the market because the utility is going to go up ok so now what happened is that the value of choosing the token has to be higher so Chi is 1 over your technological ability the value of having the token has to be superior to your technological ability ok so at the beginning it's only a bit and so then you have the number of users if you assume that the technological ability is distributed with distribution G now what you get you get to differential equation and I okay I don't have obviously the time to get into the detail but I hope I can give you the intuition for these equations and this is interestin so there is basically two regimens there is one regime where as the marginal investor where the marginal token older is a speculator this guy he also token only because he hopes that is going to appreciate I'm not saying all everybody's in a speculator think the marginal one so basically the user of the they still some speculators and at some point you will have a market where everybody holds a token because they want to use the service now you're gonna tell me why are we gonna go there you have to go there because if you always have speculator in your market that's the law of motion of price it's a bubble P dot equal RP like before I showed you before P particular P means the price increase that the interest rate but you understand that this cannot happen forever because if this happens forever the price has to go to infinity so this not a rational equilibria rational equilibria is one where one day your services will be used and the people that all the token will be users and then you have this other equation and here you have this convenience here you know this term it's the same term than before it's more complicated but it's basically your marginal utility minus the price when you trade and so Y of P dot is lower than our and you can have a stable solution so let me give you very quickly I have five minutes maybe yes so let me give you a quick quick illustration so first you start with a demand curve so that's your business model so this is taken as an input from my model I don't explain that so you come so you say okay I think that this is the service the quality of my service of your time or how many people we want to use it over time it's one projection now your question is given this business plan what is the price of your token today now there is a couple so now what's gonna happen is gonna be an investor region and user regime so in the investor regime as I explained it's a bubble regime and then in the user regime all the token are you'll all elbahr user and you can converge to the steady-state so if your productivity is very high and the price is low of course people will want to use it but if your productivity is low and the price is I this is only gonna be for speculators because people don't want to use it but maybe speculate or believe it's going to go up now you can solve this or for the text so for people who like math it's a shooting algorithm it's a boundary problem super standard one one order or the inner finger nothing fancy you should so you should for the equilibria and this is what you get so this is an example with number I picked out of thin air but make kind of sense but this all this parameter you can adjust so now you can do some comparative statics so you have your token price in the year it's a long run it's what I started with it's yours equilibria when everything is stable your token increase and here is the time when you switch from user to speculation so what I put there is a number of token order it about all did so this is the number of speculator so at the beginning 100 percent of people are just speculating but other time it's decreasing it's decreasing and at some point it's only people who wants to use the stuff and what you can see not very well here is that the derivative as an inflection point because you will go from a bubble at the interest rate to a smaller because you have to did use the convenience here and you converge to the long-run so that's giving you a quantitative and so I started by saying the velocity of money so here you have the velocity of money so I want to say one thing it's not ah city for people who speculate on the financial market because tokens circulate also because people are just speculating on the appreciation among them and yeah all my speculators I mean if it's the velocity of users so it's the rate at which people exchange a token but because they use it right so at the beginning as I said it's not I didn't make any assumption it's coming out of the model okay at the beginning velocity is zero because nobody uses it and then over time it goes up it goes up until it goes to the parameter lambda which is the rate at which users need the service so the velocity of circulation will increase over time as more and more people use your service I repeat velocity of circulation for uses now maybe we have a lot of velocity because people are exchanging this stuff just to make money in the short run so okay so I have one minute yeah so okay so let me wrap it up this is the general pricing models that endogenous the velocity of money so there is some insight so it can be used to price tokens so now we're working on more complicated stuff like double-talker and the decoupled token so then after you can do all variety of tokens so this is the simplest one so tokens are valuable so but it has some general insight so why are tokens valuable because you need to old them in advanced token you know you understand you cannot respond to when you need the token you need to have them exactly when you when the service is needed so you can call it token in advance and if you look in economic books it's called cash in advance and that's how economists explain why people have cash in their pocket it's exactly the same reason it's not surprising in the end now four people would do an IC o---- you have to realize that you're gonna sell your stuff cheaper you have anchored in a discount in your service okay and now you have to design your token economy well so as to minimize that discount otherwise it's going to cost you a lot and the discount is proportional to the agents in patience to the speed at which n is the service and so on so to conclude as I said we do many stuff now so there is many things you can do so yeah I didn't have a network effect but you can add it the model was deterministic you can make it stochastic now I didn't have optimal token policy you can add on top that the platform optimize its token velocity or whatever okay so this is going to be animal Tanja and you can do it optimal policy and then you can look at more complex design more micro foundation and so if I want to say one last thing is that I think there are two problem is the token economy one is that nobody wants to all 1,000 tokens people start to realize that that's problematic and the user will never have like all these tokens and so if you look at the model and nobody wants to paint tokens so people prefer to paint yet but if you look at the model what the model tells you is that if people were paying in fee at your service they will be ready to pay a higher price and if you paint token why because you have to add all the token and this is costly so this means that I can very see and that's my bad for the future the industry there will be an intermediate sector because the model J's of space there is a gap between what people are ready to paint yet and what people are ready to paint in tokens so you could have users pain fiat and then they will not see they will go to a website they painted and then you will have intermediaries that all tokens for them and convert them for the platform and what the model tells is that there will be economic space for such an economy so I think the way out of the for the industry of people having 1,000 token is intermediation and it looks like a song business okay so yeah that's what I want you to say [Applause]