 module 58, production function. Production function basically refers to the physical relationship between output and input. It basically depicts how a different level of output can be produced by using different quantities of input. Now to understand this, if we assume that Firm is producing output that we are denoting with y. And for the production of that particular output, Firm is using n different inputs. And in the form of a functional association, I am depicting that y is a function of x1, x2, x3 up to xn. And when this functional association is denoting y in the output, x1 denotes quantity of input factor 1, x2 denotes quantity of input factor 2, or the same way up to xn denotes quantity of input factor n. We measure the output and input here in physical units. How will I measure the output? If I talk about weight, it might be possible we are measuring the quantity of output of weight in the form of months. If I talk about milk here, then it might be possible we are talking about the quantity of output of milk in the form of liters. If I talk about inputs in the same pattern, then how will we denote those inputs by using their physical units? If I talk about fertilizer, then how will I measure fertilizer? It might be possible we are measuring the quantity of fertilizer in the form of pounds. How many pounds of fertilizer is used to produce output? When you talk about milk, it might be possible we are using here an input in the form of fodder. And which form of fodder will I measure? It might be possible I am also measuring the quantity of chara in the form of months. If we use chara, then how much output will be produced in a particular form? If there is, what we do is to study the association between output and input. We do that there is only one variable factor of input while we keep the quantity of other inputs constant. Sometimes instead of varying all the inputs, we talk about there is only variation in one input. Then what will we say? Suppose I am writing in this function, output is a function of labour for given amount of capital, land and management. Here there is only one factor that is variable factor production, that is labour. When we assume capital, land and management, we are using the given quantities of those inputs. And I move a little bit specifically that the output of a wheat is a function of fertilizer against the given quantities of seed, land, labour, capital, number of plowing and watering and many other inputs. Now what I am denoting here is that this bar basically separates the inputs, first input with other input. What we have separated from the first input is that first input is a variable input while all other inputs are given. We can represent this production function in the form of a schedule. And what does that schedule indicate? Again this schedule basically depicts an association between output and one variable input factor while we keep the quantities of other inputs as given quantity. My assumption here is that output of wheat is a function of fertilizer against the given quantities of all other inputs. And this hypothetical schedule indicates that if a farmer is using 0 pounds per hectare of fertilizer, then there is 0 months of wheat per hectare. If farmer chooses 50 pounds of fertilizer, then he is in a position to produce 10 months of wheat per hectare. What we are observing here is that there is some association between output that is wheat per unit of land. We are measuring the quantity of wheat in months and we are basically reporting here production of wheat per hectare. And one thing that you can observe here is that there is some association between these two variables. The quantity of input is increasing, the output is increasing. But at one stage, when we are using too much quantity of one input, keeping the quantity of other inputs constant, it might be possible that there is a decrease in output. Now you might have understood what is the production function. Production function is a physical association between output and inputs. But to simplify things, we have explained this association here in a table form, by wearing one quantity of one input only while keeping the quantity of other inputs constant.