 chapter production analysis and we are going to study marginal physical product. What we mean by the marginal physical product? Basically when we utilize various inputs there is no notation that we are going to utilize without any decision or without any conscious effort. So when any entrepreneur it will decide certain production process, it will decide that how many or how much number of the inputs I have to utilize. So might be he is going to utilize 4, he is going to utilize 5 and likewise add up more and more. For one ith unit or we can say for one additional unit of input, what will be the relative change in the total output? That total output that is associated with only one that additional input that will be called marginal physical product. And now if we see a production process it is not going to utilize only one input, it may have more than 1, 2, 3, 4 on many. But the simplest model that we are going to utilize here that if one production function is going to be utilized two inputs, so if those two inputs are like one capital and the other is labour, so we can say the change in the total product quantity due to change in capital that will be called marginal physical productivity of capital. And what will be the change in the total output when we change one unit of the labour that will be called marginal physical productivity of labour. So, when we can see here and we are utilizing these terms, the most important thing that I am going to explain here is that when we say this marginal physical productivity of capital with respect to capital the second term or we say that marginal physical productivity of labour it includes change in total quantity due to change in labour. And here q mean it is the total function due to capital and labour, so this marginal productivity it depends not only on that ith unit rather it also includes or it entails the response of the other inputs also. And likewise we can say that this marginal productivity it can be made with respect to the change in other associated inputs also likewise as we are going to check here that it is the change in the marginal physical productivity of the capital due to further change in capital and marginal productivity of labour due to further change in labour and likewise we can say marginal physical productivity of capital due to change in labour or we can say marginal physical productivity of labour with respect to change in capital. So, in second stage even we can measure that that how the change in one unit of labour is going to change the marginal productivity of labour or we can say with the change in one unit of capital is going to have the change in marginal productivity of labour. So, even this reciprocally we can change or we can check here. One another property that reflects that all other inputs utilization it has to be held at constant when we have to check in the change in the total output with respect to this either labour or either with capital. So, it depends upon that how much amount of only that particular input is used. So, whenever this marginal productivity or the marginal physical product has to be ascertained we have to only and only consider that input capital keeping all other inputs constant. And in this table if we see this column of the marginal productivity it shows that this is the total amount of the labour but now from 4 to 10 if we see that we are going to measure only this change due to change in one unit of input. So, we say that there is a change in the output and if we see here this is the change in Y divided by change in the input. So, this was the labour it will give us the marginal physical productivity of labour. So, because here it this change was 6 units divided by 1. So, for this cross-ponding it was 6 but if from 4 to 5 for this one unit change input we have to check we can see that here the change in total output is from 23 to 25 mean this change is total number 5 and this 5 is divided by 1 and it gave us the marginal productivity as 1. So, for if we have to move two step or the three step but we have to decide only for one unit of the input or we can have the one ith unit or one additional unit. So, after the table if now we are coming to this graphical form now the total product is explained in the table but if we have to plot the marginal physical product we can see that this marginal physical product is also sometimes going like this and like this. This will be the marginal product and we can see that this total product is maximum when we will see this marginal physical product it does the base and it is having the zero value. So, when marginal physical product will be equal to zero it will show the total physical product as maximum or we can say because when marginal physical product is equal to the change in output due to change in labour here. So, when this change will be zero and this change is zero when there is no change from this point. So, marginal physical product it also shows the rate of change in the total physical product.