 Module 130 in production analysis we are going to study the production function and what is the classification of production function. When we say production function it means we are going to utilize our relationship and relationship between two things inputs and output. So those inputs they will be utilized for the production of a certain output they all will come under the domain of the factors of production or the input. These inputs can be a single that can be two, then be three or the multiple combination. So these inputs can be in various forms. These can be in the form of the capital, labor, energy, resources and anything like this. And these are mostly are a long list but generally we have four types of the factors of production that are called land, labor, capital and now the one the fourth that is the most important that is called the management skill or the entrepreneurship. So a mathematical or the technical relationship by which we are going to utilize the various inputs to convert these inputs in the form of the output that relationship will be called the production function. So here now will be one thing that if there are two or the three inputs there are also various possible ways to combine these inputs. There is no one formula we can say that they will be utilized only and only in one combination. It means there is also a possibility that this is there can be the a basket of the inputs that we have to utilize but these inputs they are in one way or the other they are mutually we can say or within inside they are mutually substitutionable. But at the same time there can be certain inputs that they cannot be substituted to each other. So keeping in view the substitution of these inputs we are having various types of the production function. So production function is a technological summary or a technical aspect that tells us how we have to produce a particular level or particular amount or a particular nature of the output and what are the inputs to be used to utilize that output. Because if we see the inputs of agriculture which we have talked about are different but similarly the inputs of wheat and cotton and the production of rice from cotton can be somewhat similar but it can be that they are varying in some way. Similarly if we see the chemical industry, textile industry, pharmaceutical industry which factors mean the managerial scale, the entrepreneur, the energy that will be same but at the same time the nature of the chemicals, the amount of the expertise of the labor, what are the sophistication level of the technology that may vary. So the purpose of the production function is not only to tell about the nature of the output is also to tell about that how much output we have to produce but with various combinations of the inputs and various amounts of the inputs. Now these various combinations of the inputs if we explain in one example in the form of a table then we can say which we have taken in many of the previous examples, we have taken a gene stitching example. So if we look at the same level of output, if we look at it means it is coming to an end but when we scale it sometimes we increase one input and sometimes to another so we go to various combinations. Now according to this table if we look at it, when we have just kept one capital constant and on the right side we are enhancing the labor so in the start production is going to increase but up to a certain point if we look at the increase also when it is happening then at increasing rate means from 15 to 34 if we look at a big jump then here this 19 points jump along one unit is coming but from next 34 to 44 the jump is of 10. So marginal productivity of labor if we look at it then it is explaining the diminishing points and after a certain point if we look at it then it is equal to 0 means change in output due to one unit change in labor if we look at it then it is 0 and after that it is declined. So along this row marginal productivity of labor is further is in the start increasing at increasing rate then stagnate and then decreasing. So diminishing rate of return or diminishing marginal productivities are explained and likewise if we go to two pages in which we say that we have kept capital amount 2 then same behavior we can explain in the same way. And if we look at its various combinations then there are combinations when we look at this when we see that one unit of labor and one unit of capital say we are looking at the optimal level of 15 genes but on the diagonal if we look at two units of labor and two units of capital we have utilized then we went to 46. Now if we look at the figure of 46 then we have a figure of 50 units below this 50 units are produced by two units of labor and three units of capital. But in the same way if we look at it then 50 units we have genes of one unit of labor one unit of capital or five units of labor we are getting. So if we look at it then this 50 units of output or this 50 units of output then our output is same but with this our respective input is one for capital and if we look at it then five of labor and here we look at three of capital and two of labor. So it means that production function tells us various combinations which we can attain the same level of output and at the same time it also tells us that by looking at it we can attain the highest level of output. So in this table if we look at it then our lowest level of output is 15 and the highest level of output is 103 but this is not clear still up to us that in both combinations or the other we have various combinations of output from these our optimal level of output or we tell it that what is our within range or efficient. Now for that we have to further work on it but a production function we have various combinations of inputs and along with that various combinations of inputs with their substitutability we provide all information about them. Thank you.