 It is the continuation of our previous relationship to the price indexes. So, consumer preference for price indexes way we have measured with the help of partial index and now the second is the less pure index. So, less pure index is again it was developed by a German economist and its name was given on the name of that German economist and in this index mostly we are going to utilize the quantity of the commodity from the base period. And when it is developed from the quantity index that the previously developed now what we are going to take that in the quantity index these quantities were explained and these all quantities are now substituted with the particular commodities quantity at the base period. So, in less pure index when we take this all the commodities quantities they will be expressed with the notation of B means base period and as we have explained in the form of partial index that consumer is not only utilizing two commodities rather he is utilizing a series of commodity. So, when there is a basket of goods might be consumer is having 10 commodities or the 15 and he want to compare over various time periods. So, then he will be able to compare when we take that in numerator we will take the sum of all the commodities that are at base period and we will multiply with all these quantities with their respective prices of current time. So, in summation I can say that it is the summation of all the commodities prices of time period t with their commodities quantity at time period B. So, divided by all the sum of the prices at time period B multiplied by their respective commodities quantity at the time period B. So, the numerator will be the expenditure on all the items at the current time period t as compared to their respective base period. So, when less pure index is greater than one or it is less than one what does it mean to the consumer we will explain in the next slide. Here we are going to say that this index is also having certain merits and demerits when we say the advantages we say that this is very easy to calculate and it is cheap because in this all the factors that we are going to construct the quantities of base period are here and that quantities data have already been collected over the years and quantities for the future they are not needed to be calculated here. So, here its calculation it gives us a very meaningful comparison of the index that is attributable only with the change in the prices. But the certain disadvantages that it have that over the time from the base period to the current there is a possibility that due to the utilization of technology various features have been added in the same commodity or there may be the change in the quality of that parameter or at the same time there can be possibility that the consumer from the base period to the current period has changed its preferences or he is able to substitute certain commodities of with relatively cheaper features but now that commodity that he has substituted is having more features. We can take this example as such that when a mobile phone came in the market 20 years ago, it had very few added features but its value if we look at it today then it was somewhere more over the time of 5 years and again 10 years like this we can say now that one mobile is having many added features so the same mobile which is 20 years ago at that time was 3000, if we compare it to today then that cannot be compared because today's mobile has a lot of added features and we get the same added features cheaper today. When we want to utilize this index in real life it is not possible to explain because in numerator or denominator the prices that are being used are being used at different levels. So that difference of prices is not possible for us to make it easy for us to include expenditure index in one of these and in expenditure index in numerator all the commodities of which the price and quantity will be of all the current time and the denominator in which the price and quantity is all the time will be of base period. So we will utilize this in our calculations so if less than one we will say less than index is less than our expenditure index and keeping in view this equation we will now cross multiply our this equation and when we cross multiply our this part of denominator it moves here and this part of denominator it moves here and this upper left side numerator it is going to be cancelled out with the other side and we see that now on the left side we are having all the expenditure of the commodities at the base period and on the right side we are having the all the commodities quantity of the current but in the prices of the base period and we can say that the consumer he is better off in time period t than in the year b. Now if we do these two examples then in front of us we can see that in partial and in last period there is some deficiency in some one and some plus over the time we have now come to know that the partial index and the last period index they are having certain advantages and at the same time certain it is the advantage to overcome this scenario economists have developed a new price index that is called Fisher price index and this Fisher price index incorporates the effect of both indexes in the form that it is the weighted average of the partial price index and the last period price or we can say that the consumer is having the 50% effect from this and this so economists utilize both price indexes and then take the weighted average of these two indexes and explain them in the weighted average form in the shape of Fisher pricing. Thank you.