 So, let us figure out how non-owners owners are going to be influenced through this word of mouth in our model. So, let us try to achieve that. See, for the word of mouth to spread initially, there has to be some body who has actually owned it. So, let us assume there is no advertisement, only the red circles are available. So, we will make an assumption that owners whatever initial value is strictly greater than 0. That means there is at least some owner, right and only the people who own it can actually give a positive or some feedback on that, okay. Until then, if there is nobody owns it, there is nobody to give a feedback on because nobody knows that product even exists. So, we will assume that there is some owners already available. Now, if you assume the population to be homogeneous, you can imagine this entire classroom and people are going to be interacting with each other. So, let us assume that some amount of population you are going to be interacting with. So, let us introduce a term called as population interaction. Imagine yourself as a non-owner, okay, so you are going to be interacting with many people. So, among the many people you interact, there has to be some chance that you are going to be interacting with the people who are going to own the product, right. If you are only going to talk to friends who do not have the product, then you do not get the information. So, when you interact, imagine you are again as a non-owner and you are interacting with say 10 people per day, let us assume. So, and population homogeneous, so it can be any 10 people. So, this population interaction, you may get convert, you may be tempted to buy or may become aware of the product. If you buy chance, meet a person who owns the product. So, then we will have a thing called as probability of contact with owner, what is the probability you are going to actually meet a person who has the product and even if you meet a person with the product, you are not going to immediately go and buy it. You may think of other factors like price or quality or current cash in hand and your own inclination to buy the product, etcetera. So, let us just capture all of that by simple parameter called as probability of buying. So, with this view, let me try to define the buying rate. So, now, if you are going to look at a systems view for individual person, I know I am going to interact with some amount of people and what is the probability that I am going to meet a person who is actually going to own the product and even if I meet them, what is my probability of buying it. So, when you think logically, so that gets affected by the population interaction multiplied by the probability of contact multiplied by the probability of buying. So, that is for one person. So, now, if I have lot of non-owners, then I have to do it for everyone, right. So, I have to multiply by total number of non-owners, which is pretty much what you are going to do. So, I am going to define buying rate as non-owners multiplied by population interaction multiplied by probability of contact multiplied by probability of buying. Let us write out the units here. So, assume you already know the product, ok. So, the buying rate is number of people who are buying the product per time unit. So, buying rate can be people per month say number of non-owners are people, I am just using PPL for people. The population interaction is number of number per month, probabilities are dimensionless values right here. So, how do you get the probability of contact? Again, remember total population is conserved, right. So, if I know how many owners are there, the probability I am going to meet owner is number of owners divided by total population, correct. So, the probability of contact will be nothing but owners divided by non-owners plus owners, right. That should be the probability I am going to meet a owner, right, the proportion of owners that are there in the group. And probability of buying will assume we know some value there. So, this I need to represent in my as a model. So, let us just do that. So, you will define population interaction, you will define probability of buying and probability of contact. So, non-owners affects buying rate directly. So, let us link it here. Population interaction affects it directly, let us link it. Probability of contact, probability of buying, as each of them increases I am going to have larger buying rate, but the probability of contact is ratio of owners by non-owners plus owners. So, I can I need to connect it like this, right, here. This is the model we have and complete the model by including population interaction, probability of contact and probability of buying and connect with arrows. So, the model you would have downloaded, it will have just non-owners, buying rate and owners, this is the stock and flow will be represented, create the new variables and complete this model. Then we will simulate and see what kind of behavior we get for different input parameters. So, this is the model, this is how it should look. So, values should be entered are also given there, urge you to go ahead and build this model and we can start with the first scenario. As you can see in all the scenarios, the total population is 100, total population is 100, new product diffusion class that is the name of the file, download it and open it once. You should see only the stock and flows, you can open it to see what is there, nothing would be written except the initial values. You can set the initial value of non-owners as 95 and owners as 5, you can create these three variables, connect them with arrows and population interaction you have to write the value 10 probability of buying 0.15 and probability of contact with owners, the equation I showed, probability of contact with owners is nothing but owners divided by non-owners plus owners that is only equation you have to write for this. You can quickly make note of the parameter values, so that I can open Vensim and show the model there, population interaction keep it 10, probability of buying 0.15 15 percent chance to buy. So, interesting thing happens is this probability of contact initially is going to vary along with the number of, as the number of owners increases that is also expected to increase, correct because the denominator is constant, the only thing affects is the owners, as the number of owners increases it will keep increasing, but overall this buying rate itself is nothing but a product of all these, buying rate is, equation is product of non-owners multiplied by population interaction multiplied by probability of contact multiplied by probability of buying. But the total number of non-owners keep falling down, which acts as the limiting factor constraining and leading the model into a shape behavior. We noted some of the parameters, the equation for buying rate is just a product of all the arrows that is going in, equation for probability of contact is owners divided by non-owners plus owners. Let me open my Vensim, this is what you will have, so this will be the equation for probability of contact with owners, owners divided by some of non-owners plus owners, use parenthesis to ensure the division happens properly. Buying rate is nothing but a probability, the product of all the parameters, all the variables that is linking into the rate, use multiply everything, non-owners multiplied by population interaction, multiplied by probability of contact, multiplied by probability of buying. You can check the initial values, non-owners is 95, owners is 5, if not change it, non-owners is 95, owners 5, population interaction is 10, probability of buying is 0.15, so run the model, click buying rate, click cause a strip after you run the model, once you do that you should get a graph like this, 1 over month is the units for population interaction, value is 10, probability of contact with owners is here, you can see it, unit is dimensionless, here is the equation, owners divided by non-owners plus owners, if you got this you can play with other values, make owners as 0, non-owners as 100, since non-owners as 0 and we are multiplying it, there should not be any behavior that is unstable equilibrium, we need at least one owner cause entire system to start, since instead of buying it you can assume things like it is say spread of some infectious disease, one guy gets it and then everybody gets it, if everybody is healthy then nobody gets it, it will be similar model, you can try it with larger values, ensure the sum of owners and non-owners initial values 100, suppose you have non-owners as 95 or rather non-owners as just 5, owners as 95, that means only 5 people have not bought it, you can see what will happen, you just reverse it, the expected behavior in that case is you should just asymptotically converge, you may not get a growth it will just increment, it will asymptotically converge to the value, you can try that, how many got it, same number of hands, I hope there will be more hands every time I ask, you can play with it, let us take the non-owners as say 60, owners as 40, again we can run the model, so you can see the owners, here S shape is not that pronounced within this model for obvious reasons, again note that the S shape is to be seen on the owners, the S shape that we are looking at should be whatever is pronounced at the owners only, the others need not exhibit S shape, the S shape that we are talking about is we are solving for the owners, buying rate usually increases and then decreases, the S shape we can find are the owners and non-owners we expect are inverted S and not rather mirror image of it, in this case you will get S in owners, one small thing, you can make very simple modifications that is, let us suppose the product fails or reaches end of life after some time, pens, mobiles, consumer goods whatever it is, then products reach end of life, the owners become non-owners, then they again buy the product. So, let us modify the model that you have built by including this reverse flow, again as you can see here, there are two rates that is affecting non-owners and owners, we are not having a, we are not doing any extra calculation for it, all we are saying is owners will abandon the product after some time and then become non-owners and again once they again can contact with other owners, then again they end up buying the product. So, we can include this in the model. So, the equation for abandoned rate is owners divided by product life, again it is very intuitive but you need to pay attention sense, owners is connected to abandoned rate and here the arrows you see, owners is going into abandoned rate, product life is going into abandoned rate, product life units is 2 months, after couple of months they are going to abandon it. So, then the only equation for abandoned rate has to be, rate means it has to be people divided by time, I already have the time. So, that means this equation has to be owners divided by product life. So, you can try a similar scenarios in this one also, let us, so the abandoned rate here is owners divided by product life, owners initial value is 5, non-owners initial value is 95 and I simulate this model, once you finish it you can do it, you click owners, you will find that the owners saturated at a much lower value of maybe 67 or something. But in the previous case, the owners would have saturated at 100, when there is no returns rate, the owners would have saturated at 100, you can check that. That means all non-owners will eventually become owners, non-owners will drop to 0, owners will drop, will peak at 100, but you have any external flow that means you cannot reach the stated capacity, some people always come back, that value is tops at 67. So, let me just stop here and to any questions you can ask or please try out this model and complete it.