 So, today's class we will try to take up some simple models and use it to further understanding of complex issues. So, the first example or first scenario that we are going to consider in using small models to understand complex issues is this notion of societal aging. So, societal aging is one of the biggest challenges in many developed countries as well as in developing countries, in developed countries such as say Finland or Japan. The population pyramid is such a way that the number of people above the age of 50 is much higher than the number of people below the age of 15. So, people are worried what is going to happen in future. A rather simplistic SD model description is given, suppose in year 2010 there are initially say 9 million adults, 3 million retirees and 4 million children. Suppose retirees die after an average retiree period of 20 years, adults retire after an average adult period of 40 years and children mature and hence become adults after an average childhood period of 22 years. So, here the total average lifespan you can just add all the three numbers is 40 plus 20 plus 22 which is about 82 years is considered as average lifespan here. Furthermore, the average birth rate per adult amounts to 20 children per 1000 adults per year, just taken as average birth rate. Second factor, the burden per active adult is defined as inactive population divided by the number of adults on the labour market. The inactive population equals the sum of children, retirees and adults not on the labour market. The number of adults not on the labour market and the number of adults on the labour market depend on the average adult participation ratio. Suppose that this ratio amounts to 50 percent, the grey pressure could be defined as fraction of retirees and adult and green pressure could be defined as fraction of children or adults. It is a very, very compact and brief description and download that model, go through this description and correct the model. While doing the model and reading the description, why do not you also think about what is this grey pressure burden on active adult, green pressure mean and once you simulate and also discuss some policy to improve the evolution. So, go ahead download the model and correct it based on the description given. Just to pay attention for a minute, so we have the stock, it is inflow of X outflow, so that is very obvious in this, but we also want to specify the initial value. So, suppose you go to the equation of stock, you will find that it is in minus out, but initial value does not appear here in this area. So, I have to enter some constants, I cannot do that. So, to avoid that or to include that initial value, you first connect that initial value to stock, so you will get this arrow. Then you click equation, go to stock, stock is in minus out, you will see the initial value as a variable here, you click it and put it under initial value and click ok. The arrow becomes grey or it can disappear altogether in your model depending on your setting, indicating that it is the initial value. If it was grey, you would have been happy, but in the model it is colour is removed. So, in case you want to add it, this is how you do it, ok. To define initial value, first you connect the initial value to the stock, put or go some in connected to stock, then go to the stock and under the initial value, you select the initial value, whatever the variable name initial value, click ok. Then that arrow from blue becomes grey here, but in your screen it may just disappear altogether also. The arrow may not be visible, but still it will take the value, so do not worry about it, that is all. In your model, all the stocks has an initial value somewhere variable name, but you will find that that variable is not connected to the stock. I am trying to explain why it is not connected, that is all. Ok, so these are all the things I think I can remember, but I have to figure out what are all the bugs I introduced. Retiring is not connected to retirees, you need to connect that flow and then update your balance equations. Grey pressure is defined incorrectly, green pressure is not defined, there will be units error at least minimum two locations, it will not move. Birds are affected by adults not children, take that so that these are logical errors. None of these errors will actually cause runtime error, meaning they are just logical errors, so little more difficult to spot. And along with it, hopefully you got ideas of how to, you know represent large numbers, millions you can see how pencil represents it, how to give initial values outside the stock, so that there is no constants inside the equations and we have all the variables explicitly defined, what else? Yeah, so this is what we have, let me open the, may win some hang, I do not know, got it. Ok, so this should be the model you have, do not worry about the right part yet, we will come to that. So, once you simulate, let us do children, adults and retirees as a graph and let us do grey pressure, green pressure and burden on active adult as a graph. So, we will have two graphs, one for the population, strata, for each strata and other for the burdens. So, the population graph if you see, the adult population starts at 9 million and goes down to less than 7 million, the children population on the other hand starts at 4 million and drops down to 2 and a half in the next 2010 to 21 and another next 90 years and retirees increases until 2040 or 2050 and then slowly starts to decline until 2100. Did you guys figure out how to write these years earlier in all the graphs, it just started at 0, right? To start with the year, all you have to do is go to model settings and give the start year as 2010 and then it will just start to decline. Now, if you observe the burden, the burden starts at around little, say around 2.5 and saturates at around 2.8, green pressure starts at 2.2 and then saturates at 2.6 and grey pressure starts at less than 0.4 and saturates around little close to 0.58 or something. Though your population dynamics is reducing, still these variables stabilized because the ratio did not change, right? These are things that you can see. Now, the purpose of this model is not just to get this graph. I do expect you to, this is the first introduction to discuss on this. So, you looked at the model structure, right? Let us go back to the model structure. Now, what do you think this burden per active adult actually means in reality? What is this burden per active adult? Go ahead, venture, I guess. Tax payers, fiddles, number of people from whom he has to, he earns, yeah, yeah. So, that is what it is trying to capture. If you look at it, burden and per active adult is defined as total inactive population divided by the adults on the market, correct? So, for each adult person, how many person has he to support? He has to support children, he has to support elderly people. He has to also support non-working adults, right? It is not that every adult has to work, there are non-working adults, right? So, the person is not only working for them, he has to work for a bigger group of people. So, here are results show that an average people has to work for nearly, each person has to work for three people apart from oneself, so that is what it means. What is this grey pressure and green pressure and how do you think it can, what is the implication of that? Let us take the green pressure, green pressure is defined as ratio of children to adults, right? So, that means that is the kind of proportion of children who are being supported by the adults to nurture them, you have to provide education, that is one of the primary thing, healthcare, education, other facilities has to be provided to them. And grey pressure, now grey pressure is not a non-earning, it is people above, as per this say above the age of 40 plus, on an average above 62 years of age, as represents grey population and it is assumed that they are not earning. So, what, when it is a grey pressure, what is the kind of pressure it is going to exert? In green pressure, we saw that the pressure will be for say to give a better education or complete education, yeah, let us keep that, healthcare, right? So, as retirees more than that, as grey pressure increases, you need to provide better healthcare facilities, old age home or other support facilities as to be provided on a primary being the healthcare, so that is the pressure that is being captured by this variable called as grey pressure, right? So, now when we start looking at these kind of demographic changes, this model can help link, this model is not complete, we have to improve on the model in various dimensions, simple things can be, maybe we have to include death rate for every stock, fine, it is a minor thing, we can definitely include it or that is one, other is we can actually expand the model by incorporating, suppose you know, if we expect an average adult participation ratio and the adults on labour market is going to affect or be affected by the actual jobs available in the market, so if the less number of jobs are available, so that means only that much portion of the active adults can actually participate, even if everybody wants to, there is not enough jobs. So, this average adult participation ratio need not be external, you can actually expand the model to make it okay, we have some jobs, suppose this is a total jobs available, then what happens to the adults on labour market? So, even if there is one person is working, right, we cannot say give jobs to everyone, so we have taken a average of say 50 percent get jobs, but even if you take 50 percent of the working adults get job, you find that, that means 1 in 2 is getting job, but still they are supporting 3 more people, because while doing this we fail to account for children and retirees, whenever jobs are considered it is only looked at people unemployed or that is adults not on labour market, unemployed adults and then say okay I have to fill that gap, but even if you do that still there will be a burden, even if average adult participation ratio is 1, you still get burden on active adult, because children and retirees also contribute to that, correct. So, that has to be also factored in when actually jobs are provided and that affects the level of jobs that is being provided, jobs, huge spectrum, minimum wage, if at all it exists in India to whatever CEO top position where you are earning millions per month. So, the entire spectrum is there, so wealth distribution need not be unique, so including that aspect we will also make this much more interesting. The number of retirees in the grey pressure can actually impact how much effort the government needs to spend on health care, geriatrics health care. So, this grey pressure is supposed to be the pressure felt by the government to provide geriatrics health care, provide support for people above the age of 60, 65 or 62 in this case. Green pressure is the pressure that you have to provide immediate education and other facilities for children for their whatever what can I say best development of them things like that. So, this the green pressure may show what is the in future how much people are going to come into work force. Today's children are tomorrow's work force 10 years later. So, though initially now we are fine we have lot of adults working to look at the graph. Now, adults are 9 million you will say there is lot of people are there we do not need to worry about it, but your birth rate your children is also falling. So, less children here means less adults in future, but initially this two graphs of adults actually result in increase in population of the retirees that is interesting only a 50 years retirees are going to fall down. So, where we want to invest? So, this kind of models can help increase the dialogue which is thing you have to start looking at it and start understanding what it is where it can link to what is external variable. Good catch, thank you. Yep, good catch, burden change only this one changed. Yeah, it is not as high as told one more thing to do good. Thanks, you got it. Yeah, green pressure reduced over time we have population reduced and this increased. So, even later when population of retirees fall down since adults population also falling down the ratios saturated. I corrected the equation for green pressure I had wrongly written as adult by children and it should be children by adults. Good catch. Thank you. Now, we have it. So, let us take various things can happen. Let us take of different scenarios to see what happens we can stop progress or technological advancements. So, one of the most common technological advancement where people work towards is increasing life expectancy with increase in better healthcare facilities comes increase in life expectancy or average lifespan. So, let us suppose that in future medical advancements for next many decades will further increase the life of retirees average retiree period from 20 years to 25 years. So, overall the life expectancy just increased by 5 years. How do you expect dynamics to change? First then it shows how to model it but intuitively what do you feel? What should happen to the dynamics? If average life expectancy of retirees increases, gray pressure should increase within the system. Green pressure may not because there is no change in that part of the model it should remain roughly the same. So, gray pressure could increase but how much will it increase? Not sure. What about burden on active adult? It should also increase. Population will reduce or what kind of graph we make it? It will keep increasing or gradual increase or it will graph will increase first and then decrease. It may not be very clear which is fine. So, go ahead and implement this in the next 5 minutes. Done. So, as per this build the table function connected. Again these models are I wanted to just start with simple models to initiate dialogue and see what it is and how we can build it, improve modeling still. To make a very realistic model then if your research areas in population dynamics we will start discussing. So, because each one will take a lot of time to build and implement and have the real thing. Implement this. I am just showing the same thing in once in here. It is a graph look up inside the average retiree period variable here. On the right side, the one in orange color you have to create time connected to that and write and draw the graph as given. Values are given, graph shape is given you just have to use that. As I had mentioned on the start of the class one of the main purpose of the SD models is to help build our intuition. Many times we may not have intuition on many of these complex issues. So, we can use this to conduct what if analysis to build our intuition. Like one of the assumption we have made is average children's age is 22 when they become adults and then 40 years service and then they become retirees. So, that has to 62 years. With average retirement age becomes 65 then we get from 48 becomes 43. There is a 3 years additional service what impact will it make or what if the retirement age is 70 additional 10 years or additional 8 years how it will affect. Here you have taken for children the age is 22 years average that is assuming you finish your this thing and get a 4 year degree and then start working right it is a 21 22 when you start working. But if that age is lesser then how is it going to impact. Again this is average so there will be some proportion of proportion of children who start working early. Some people who start working very late like me who start doing masters and Ph.D. etc. So, we start late. So, you can actually change the numbers and see whether there is population increase at any point or it is only constantly decreasing. That is as a separate exercise you can think about it. I am going to just change the test. ID, simulate, look at the pressure graphs. First pressure graph if you look at burden per adult is exactly the burden per adult has increased the red line is the new one burden per adult went from less than 3 to slightly above 3. So, look at green pressure there is no change in green pressure it is the same. Gray pressure also increased from less than 0.6 to greater than 0.6 slight increase and stabilizer higher value because of that extension of whatever its longevity increases. Let us look at the actual population the adult population no change, children population no change, the retirees population after increasing at 20 to year 2050 and then decreasing. This now keeps increasing until year 2070 and then slowly and decrease is much more at a slower pace. So, this is going to constantly increase getting that. If you observe the total population the total population has shown an initial increase for next 10 years and then it starts to decrease in the original case because of better health facilities the peak occurs now 5 years later and then population slowly starts to decrease overall. So, this is significant even if you can see better health care facilities is going to instead of 14 million in year 2080 it is 14.8 million 2080 that is about how much percent increase 5 percent approximately 5 percent increase in the population more than what we want right. So, those are the interesting things to note what is going even that seems like a small percentage, but that many jobs has to come or the other way so many people are retired age, but then who is going to do all the jobs. So, as soon as you put a job one and available jobs may be more than the number of active adults who are able to do the jobs. What will that result in if there is more jobs and less people to do the job in a region it will attract people from other regions to move in it is going to you are going to cause migration and people proceed look at job opportunities are available and locally they are unable to fulfill it either they themselves will invite people from elsewhere to fulfill their job opportunities right because the jobs have to be done even if it is health care somebody has to you know take care of the health and provide the basic services. So, that becomes interesting even in case of India in another more another 25 years it is expected the proportion of grey population in south of India will be much larger. So, resulting in huge migration from north to south to support that facilities and provide the services. What kind of population dynamics it is going to create and conflicts and strives we do not know that is separate discussion. Why did you try this one? Three what-of scenarios you have to just simply say change the initial condition and for each you observe the total population there is total population increase or decrease your pyramidal population that is currently population has lot of children less adults and less retirees versus a column population we have proportion of I mean 6 million children 6 million adults and say 4 million retirees almost comparable or we have inverted pyramid where we have less children 5 million adults and 9 million retirees. So, then what kind of dynamics are we foreseeing when this population collapse faster or slower or is there a population growth at all you can simulate it and see it and what is happening to the burden as we go along in each of these scenarios. Without running also you can think about it a minute how it works like when there are more children in the first case they are going to become models. So, in future we can expect that the burden will go down but what happens over 100 years remains to be seen inverted pyramid structure the pressure is at least a grey population is very high. So, over time but eventually it will be lesser because initial children population is less and adults are less than retirees but look at it A and C the adults are exactly the same and B also is quite similar. Let us see what happens when only children adult proportion changes simulated check it and think about it I will stop here.