 Now, let us take one simple example and try to solve and we have already seen in both the, in the last module as well as in this module how to do the calculations. Now, let us do this for the, for this example. So, there are two sectors given here, the agriculture and the manufacturing sector, agriculture and manufacturing and so agriculture, manufacturing and let us say that we are talking of this in terms of money terms in million rupees and what has its partial table has been given to you of transactions. So, the questions the unit is million Indian rupees, we are considering a two sector economy with an input output table as shown for 2017, we are asked to fill in the blanks in the input output table, compute the A matrix and the L matrix. Then we are supposed to consider two cases, one is where the agricultural final demand increases by 200 million rupees in 2018, while the final demand for manufacturing remains constant. So, if agriculture increases and manufacture remains constant, the second one is where agricultural final demand remains constant, while manufacturing demand increases by 200 million rupees. We want to compare the two cases in terms of the input output tables, is the total output of the economy the same in both the cases. And then we also want to ask in concept, how can we use the input output table to compute the impact of employment of two different options. So, let us do this example, please try this, it is fairly simple it is related to whatever we have done so far. So, we had this is 300, 500, 800, 200, 400, 1500 and then you have the payments sector and then the total, it is given to you, this is the value is given, payments sector outside. So, this is fairly straightforward, we have already seen this, we can sum this up 300 plus 500, 800 plus 800, 1600, this will be the total output, here 200 plus 400, 600 plus 1500, 2100 million tons, alright. Now we know that the column when we are looking at agriculture, agriculture is being used for agriculture and these are the transactions here. So, the total payments in terms of wages, profits, everything which is there must be such that this total output is the same. So, this total output here will be 1600, total output here will be 2100, as we subtract we can take 1600 minus 500 and that will give us 1100. Similarly, when we look at this, it is going to be 2100 minus 900, it is 1200. Then when we add this up, this is 8000, 2300 plus 1300, let us add this up 2300 plus 1300 Now this 2 has to add up and that is clear, so 2100, 1600, 3700 plus 3300 is 7000, 7000 million tons is the total output of the economy, right. And now let us see the question which has been asked is to see what happens if we change, if this increases, if the, let us see the question says that agriculture final demand increases by 200 million, final demand for manufacturing remains constant. Before that we are asked to fill in the blanks which we have done, compute the A matrix and the L matrix. So, A matrix is straightforward, let us look at the A matrix, A matrix is going to be 300 by 1600, this is 500 by 2100, this is 200 by 1600, 400 by 2100. So, this comes out to be 0.1875 and this is 2381, let us just rounded it off, this is 0.125, this is the A matrix, remember the F matrix is 800 and 1500, right. So, when we look at this A matrix we can now calculate I minus A, I minus A becomes 1 minus 0.1875 is 0.8125, 1 minus 0., so this is minus 0.2381, this is minus 0.125, 1 minus 0.1905, this is 0.8095, this is I minus A. Now, we can take the inverse of this and excuse me, you can do this, I am not going to show you all steps, you just with the rounded off values you will find that this is turns out to be 0.29, 1.29, 0.38, 0.2 is in the rounding off, this is almost similar. So, this is your I minus A inverse and very interestingly these are the diagonal elements and when you now multiply this by now the value of F we will change, F new is going to be 800 will become 1000 and this remains as 1500, right. We can multiply this and what you will find is X new, you can calculate this, multiply this with this and add this and then you get, you will get 1858 and 2340, remember the total output last time which we had, this was earlier it was 1600 and 2100. So, obviously both of them have increased and they have increased by different amounts. So, this is increased by 258 and this has increased by 220, right. And of course, the increase in the agriculture, the percentage increase in agriculture is higher. Using this we can then make the final table that we had and you will see that now agriculture, manufacturing, agriculture, manufacturing. So, we have the final values which we calculated 1858, 2340, the direct coefficients will remain the same, we can just multiply by the direct coefficients to get these values and you can cross check that and round it off you will get 348 and here you get 509 and that is basically 0.1875 into the value that we had and then this is 232408, final demand that we had was 1000 from 800 to 1000 and this is 1500. When you add this up, you should get 1509 plus 348, you get the same value that we had 1858 and here also 1912315401500 and this comes to, sorry this should have been the value of x new here when you multiply it is 2140, 2340, it is 2140. So, we have a slight increase in the value of the industrial manufacturing output from 2100 to 2140, but significant increase in this. So, this is 2140. Now when we look at the payments sector, we get this as the subtraction, we take this as 1858, 2140, this one will remain constant, the remaining part 1000. So, then this is 2000 and 1500, 3500 and these values we will get as 1277 and this is 1223, when we add this up, this comes out to be 3600 and when we add this total up, we will get a total of 7584898, 7598. Now, just compare this with what we had earlier, this was 7300, 2100, 1600, this has now become 7598. If you look at the overall output growth, this is 7598 by 7000. It is less than 10 percent, you can calculate the amount, 598 by 7000, that is the percentage growth. So, let us look at the section B where we now keep agricultural final demand remaining constant, while manufacturing demand increases by 200 million rupees. So, the question is whether increase of 200 million rupees in the agricultural final demand, that is what we saw last time and instead of that, we keep that constant and manufacturing increases by 200. So, now, the final demand that we are looking at is going to be 800 million rupees for agriculture and industry increases from 1500 to 1700. So, we can take this pre-multiply by the inverse that we had and that is going to be 0.20, 1.29 multiplied by 800, 1700. This will give us the value of x new and you can multiply 1.29 into 800 plus 0.38 into 1700 and you will see this comes out to be 1676 is the total final output of the agricultural sector and for the industrial sector, this will be 0.2 into 800 plus 1.29 into 1700, this will come out to be 2358. This is now x new. Now, we can take this and multiply it by the coefficients that we had calculated last time, which are the a coefficients. If you remember, these were the values 0.1875, 0.2381, 0.125, 0.1905. Assuming that these coefficients remain constant, that we get the value of z new and this z new value is done out to be 314, 562, 209, 449. You can check this for yourself to see if these numbers are what we get. So, unless you made some error in the multiplication, this is the value that we will get. So, now, we can go back and replace the matrix, final matrix that we get in this scenario that is agriculture, manufacturing, final demand and the total and here you have the payment sector, then you have the total. So, this we can write this as 314 million rupees, this is 562 million rupees and then we said f is 800. When we add this up, this will come to the total value that we are looking at which is 1676 and here we have 209, 449 and this was increased from 1500 million tons to 1700, this turns out to be 2358. Now, remember this totals will be the same. So, this is 1676, this is 2358 and this value will remain unchanged as 1000. Once we do this, you can now take this minus 314 minus 209 and we will get 1152 and this is 1348 and this turns out to be 3500. Now, when we look at this now, you will find that when you add this up, you get 1152 plus 1348 plus 1000 and this turns out to be 3500. Now, when we add this up, this will be 1676 plus 233945, you get, we get total of 7535. Remember if we now compare this with the original value that we had, this was 7000. As compared to 7000, we have got 7535. So, if you see the growth, this is 7535 by 7000 and that comes out to be the growth rate is 7.1 percent. That is where the industry grows by 200 million rupees. Now, let us compare that with the agriculture not growing, industry growing by 200 million rupees and let us compare that with what we got for the agricultural case. Now, in the agricultural case, if you see there is an error that we have made here, this is should be when you add it up 1277 plus 1223, this will give, this will give you 2500 plus 1000, this is 3500. So, this will be 7498. So, when we do 7498 by 7000, we get the growth rate, this is 107.1. So, the growth rate is 7 percent, 7.1 percent. So, the interesting thing that we find, sorry, this one is the earlier case 7535, this is 7.6 percent, this is under 107.6. You can just see this. So, as compared, so this is the B part, this is A. In the case of A, when we increase the agricultural output by 200, but the industry remains the same, we find that the overall growth rate increases to 7.6 percent, that is B. But when we increase agriculture by 200 and the industry remains constant, then it is only 7.1 percent. So, given a choice, you would prefer that this growth happens in terms of the overall growth, the impact of the industrial growth on the total growth is more than the incremental change in the agricultural growth. And then this of course depends on the way in which the transactions are done. So, you can do this in, you know, you can do these matrix inversions either on Excel or in Matlab and you can create this. We have shown this for a 2 into 2 matrix, but we could as well show it for 7 by 7, 10 by 10 and sometimes we have these 78 by 78 input output tables which you can get from the central statistical organization. These are given at some different years and then we can take that and make this calculation. The next part is the total output of the economy the same, the answer is no, the total output is different. So, it depends the differential growth rate reflects in differences in the overall growth. And we saw that in industry manufacturing growth increase results in a slightly higher overall output as compared to the agricultural growth. And then the question which is asked is explain how you can use the input output table to compute the impact of employment of 2 different options. So, in this case if we had in the case of payment scenario, we knew how much are the wages which are being paid for each of these sectors and we took a factor in terms of the wages or the people employed with the wage rate. So, you can get a factor in terms of per million rupees how many people are employed and we can take that to make the comparison when we have different outputs and we can see whether the employment increases in which case will the employment increase and that will depend on the employment factors. Typically industry for a certain amount of investment or output from the industrial sector typically the employment is higher and then there is an indirect effect because it has ancillary units and other things. And so, that is why in many of the countries the emphasis on industrial growth is there in terms of the employment. Now, let us discuss before we move on to the next topic let us discuss what are the what have we learnt in terms of the input output method. So, when we talk in terms of an economy we have multiple sectors and then there are transactions between the sectors. Energy the energy sectors are important sectors in this there are other outputs in terms of manufacturing and agriculture. When we compute what happens in terms of transactions we can look at transactions from energy sector to the other sectors and growth of these sectors. And with this result we can actually see what is the impact of differential growths of the energy sector, what is the impact for instance if we have a high renewable growth scenario and we want to cut down on the coal sector or the oil sector. And so, we can look at the overall economy wise impacts and the social impacts of this including the effects of employment and jobs. When we we have also talked about this in terms of seeing as a result of this what happens in terms of equality and the Gini coefficient. And we I just pointed out that there is a paper where we have shown you how this can be done and you can look at that paper. What are the limitations of the input output model? The main limitation of the input output model is that the coefficients are static they are fixed coefficients and the linearity is assumed. If there are fixed coefficients if the structure of the economy changes quite a bit the coefficients will change. There have been modifications to this input output method where people have got some methods by which they modify or have dynamic coefficients or they look at the changes in the coefficients. So, you say 10 percent decrease in the energy intensity per unit of industry and so, the AIJ corresponding AIJ decreases by a certain percent. So, there have been ways in which people have thought of this, but this remains the most this is one of the limitations of this method. This is suitable to understand short term impacts. It can also help you understand the kind of interlinkages which are there between the different sectors of the economy. The biggest advantage of the input output method is that it is linear, it is transparent you can understand clearly what are the linkages and so, it is in a sense it represents some of the flows in a way in which it is easy to understand. For those who are interested in different kinds of models you may also want to look at partial equilibrium models or computable general equilibrium models. With this we will complete this module. In the next module, we will start looking at primary energy analysis and net energy analysis.