 to test ourselves and our knowledge, let us try this simple one, not a simple, very compact one. Suppose, this is the description, currently known convention oil reserves will be depleted within 40 years. So, the demand for oil keeps on increasing by 2 percent per year, can we build a stock flow diagram of this? The thing about description is, it is very less, for first thing, very less description ok. You can read it again, not much to read just one sentence right, there is some oil reserves which will be depleted within 40 years, if demand for oil keeps on increasing by 2 percent per year. So, there is some oil reserves and there is some demand which also keeps changing and we know the total time that it is to be depleted that is the 40 years right. So, if you are ask ok, if you want to build a kind of a model for this, we need to ensure that the model actually, the oil will deplete in that particular time. So, let us model it and see that we just give a small type of question case, year, the only thing I know is the description set years. So, let us just take it years, we have the description right here. Oil reserves will be depleted within 40 years, if demand for oil keeps on increasing by 2 percent. How does this stock, any suggestion for a stock? Oil reserves is a physical quantity that can be a stock, so let us just put oil reserves. So, then this has to drain right, meaning we have to keep removing from this reserves. So, then there has to be a rate ok, let us call it extraction. So, I just modeled it as a just oil reserve and rate of extraction. Now, usually we would have put the rate of extraction would be affecting the demand, but now we got a information that demand is also increasing at 2 percent per year right. So, how do we model the quantity which keeps increasing? Suppose, when you say population increases 2 percent per year, what does it mean? We have a population stock on the net flow, in such a way that population is going at 2 percent per year right, it is not a linear, it is going an exponential, so perhaps we can consider that for demand. So, let us define a demand and then change, just change in demand, demand is changing 2 percent per year. So, this is fraction, fraction per year. So, demand has to increase by 2 percent per year, the way we need to model or we know how to model it is, we can give the fraction per year as 2 percent, 0.02, change in demand is 2 percent of the demand, I just multiplied these two. Now, you got change in demand, it is going to increase right. Then you can make a simple assumption that this demand is going to affect the rate of extraction and I can only extract until oil reserves fall down, it just says that oil will be depleted within 40 years. So, once it is depleted, I cannot extract any more. So, then the rate of extraction can be minimum of oil reserves and demand. Let us just model it, perhaps I should introduce units, let us make it fraction as 1 by year, change in demand will be, what do you call, what is the units for oil reserves? Million, million barrel, billion barrel per year, demand is 2 per year. Initial value I do not know, let us come to that. So, the rate of extraction becomes, so I need a, we will assume a simple time constant of 1 year every year, because we will take an annual demand. So, let us keep a time constant of 1 year, just to ensure my units match here, even if you do not do time constant it is ok. What you did here is, change in demand is demand times fraction per year, rate of extraction is minimum of oil reserve and demand, that is it. That is all, this others are only for unit distance. So, what do you assume for oil reserve and demand? Tell me some initial values, we started some arbitrary initial values and start now, we do not have anything else. So, let us just start, what do you want? Oil reserves, how much? We take up numbers which are easy for our maths, right. So, let us just say take 100, let us just take 100 whatever 100 million barrels of oil is there and let us suppose demand is say 1. So, I take complicated numbers when, let us just do 1, right. So, without simulation itself we can actually do some things with it. Imagine if demand is always 1 constant, demand is 1 constant, oil reserve is 100. So, then it will take 100 years to deplete, that is not the case we want, right. But now, 1 is also increasing at 2 percent per year, right, 2 percent per year then from 1 unit to what will be is doubling time 0.69 divided by 0.02, 0.7 into 50, 35 years, ok. So, what we did was the doubling time for demand, so demand from 1 unit to 2 units, it is going to take 0.7 divided by the fraction, fraction is 0.02, so 0.7, 0.02 is nothing but 1 by 50. So, we are multiplying by 50, 50 times 0.7 is 35, right. So, above 35 years it will take for 1 to become 2, because suppose it is always 2 then the entire thing oil reserve can finish in 50 years, right. So, on an average now we have 1 to 2 it went in 35 years, right. So, on an average for the 35 years it was 1.5 million barrels per year. So, 1.5 times into 35 will come to 35 into 1 and 0.5 that is 55, right. So, it is slightly around 50, 50, 54 million barrels should have been finished. So, we will have another 50 million barrels to complete, right. So, that will also take some time. So, again what you are trying to figure out is when the oil is going to deplete that is what you are trying to figure out. If it is always constant 1 it is going to take 100 years, if it is going to constant 2 it is going to take 50 years, if it is constant 2 million barrels a year that is the rate it goes then 50 years it will 100 barrels will finish. If it constant was 3 then it is going to take 33 years which is less than or 40 years what you want is 40 now. Now, we do not have it constant hours is increasing, ok. So, instead of figuring out how it is increasing we are just figuring out, ok. 1 to 2 it goes on an average of 35 years. So, the average during the time is 1.5 liters. So, for first 50 will finish in 35 years. The next 35 years the average is between 2 to 4, right. The next 50 years average is 3. Next doubling time, next 35 years is average is 3. So, in that case it is going to take much longer to it will take 35 into 3. So, it should take about another 35 plus another 17 years to finish. So, 35 plus 17 comes to more 54 years to exhaust our resources, what is this oil, ok. Let me just very go further let me just simulate. I have just simulated the model let us look at oil reserve and demand, demand increasing oil reserve falls down at around 54 years like we kind of estimated now 55 years maybe. What we wanted is it has to finish in 40 years. So, let us just go back to do that let me just change the initial value of the demand. Let us assume that the initial suppose initial value starting at 2 let us say then oil reserve ends in less than 40 years your oil reserve depletes, ok. So, that means my initial value should be between 1 and 2. So, let us try 1.5 comes to slightly more than 40 years do not give it exactly at around 40 perhaps I should try say 1.75 somewhere close to 40 it is able to kind of deplete itself if you assume 1.75 starting point. So, earlier thought process I was trying to look at when doubling time etcetera I was trying to figure out this 1.75 as a thought process because we can we already know doubling time we know total reserve which is 100. So, you can always do our mental math to figure out approximately what should be the starting values where you want to start from. So, this we must be able to try since given very simple descriptions not much we are still able to build a stock flow model saying that oil reserve depletion 40 years we can actually build a demand stock flow and oil depletion and then all we then we played with the starting values until we actually did deplete it. Any questions on that model? It is a small interesting fund model to play with.