 Chapter production analysis and we are going to study the average physical product. When we say average physical product, this term means the average productivity and this average physical product means total product divided by the total number of the inputs. But here when we say the total number of inputs, it will be the respective input means if it has to be calculated with respect to labor, then we will divide the total output with total number of the labor. If we have to check average physical productivity with respect to capital, then we will divide the total output with respect to total number of the capital used. So average physical productivity like the marginal physical productivity can be average physical productivity of labor or an average physical productivity of capital. And it is the best measure of the efficiency of any firm or the productivity because if the average productivity of a firm or average physical productivity of a field, it increases over the time, we say that this firm or that is on the higher growing stage of the productivity. And if we say in other words that when the productivity of labor of a country, it is already increasing, then it is not possible that all of them are increasing. But how do we count the total output of that country divided by the total number of the workers? So we say that compared to the previous years, this is giving us more output. So we will say that average productivity of labor of that country is on rise. Now here we are also looking at the equation, so these are all the aspects that we are looking at. But the main aspect here, if you look at the average productivity of labor we are measuring, then our numerator above is the capital and labor is using the total product because of both. Similarly, if we look at the average productivity of capital, then that too, our numerator which is being utilized will be capital and labor, because of both, the total product produced will be explaining it. Now if I give an example in front of you, which I mostly give to my students in my classroom, and which you may understand easily, you see the match of the people. So in the match of Kirkat, when you see that if one or two players come and say that our Shah Dhafirdi Sahib used to go on and on, then at the end you say that our run rate is increasing, so the run rate that is increasing is our actual total, if we say that, then average productivity is being enhanced. So when two or three or four people have done this work, then our competitor is giving the required run rate more. So in the same way, if we look at this example, then many times we are getting the average, so this can be less than one or more, but when we count all the players, then our average run rate will be more. Now if we come to this table, which we have used many times before, then our average physical product table, if we look at it, then this total product and divide by the total number of inputs we are showing. And if we look at it, then when our total output here is four and this divide by one, then this four will come. And likewise for each product, it shows us the level of different productivity. Now if we look at it this way, then in all these aspects, the average physical productivity, we should keep in mind that it can never be zero. Why can't it be zero? Because the average physical productivity, whenever it has to be, if we can say that this is y by l, we can say it is y by k. And in other forms, if we use in other terms, then we say that this is total physical productivity divided by labour and total physical productivity divided by capital. If we use q somewhere, then because our numerator, until it is in any form, it can never be zero. Whereas previously we have seen that marginal productivity is zero. Because it is expressing for one unit change. So when we show graphically, then I have shown you earlier that this can be like this, the marginal productivity with respect to labour because we are using workers here. And in this form, if we look at our marginal productivity in comparison to average productivity, if I go to the previous table, then you will see that the marginal productivity in the beginning was 4, 6, 7 higher than our average productivity. And one point came that our average productivity, if you look here, it increased here. Here also the average productivity increased. But when it came to one point and decreased here, how much? The marginal productivity also decreased. So the least point of average productivity is 2.5. And while the marginal productivity is at least equating between this point, the 6 and 7 is equating it. So when we come here, then if we look at the 5 and 6 points, then here they intersect each other. And if now I will hypothetically draw because I haven't made it, so the average productivity will be like this. Now if we look at these points, then this will be one point where the average product or physical product, the marginal product will be equal. And from that, on previous points, the marginal product is greater than the average product. And after this particular point, if we look here, then the average physical product, this is higher than the marginal physical product. And at this point, these two are equating, this is a point of inflection, this is a point of change. Similarly, if we look here, then this average product throughout the range tells us that how our total productivity of that firm is average.