 We will introduce the third model today that is theory of production and cost and we will start the first topic of our third model is on introducing the input-output production. Generally, what are the productions theory and also how the production function differs in the case of a short run and case of a long run. So, today's session outline will be mostly on defining input-output production. Then how we reach to the production function, then we will talk about the short run production function and in that context we will talk about the law of diminishing return and we will get few examples of law of diminishing returns, how it actually works in case of the real life. So, before getting into the details of production, let us understand what is production and if you define that production is basically an activity of transformation which connects factor input and output. It means when the production is basically the activity which converts the inputs into the output. So, we can call it a process, we can call it a technique, we can call it a activity and which transform the different kind of inputs into the output. So, production is the activity of transformation which connects the factor input into the output. Now, this process whether it is transforming input into the output or the may be the intermediate product into the final product, this process of transformation is the basically two kinds. One is when there is a change in the form and second one when there is a change in the place. Let us see what happens in case of change in the form, raw material transport to finished goods. So, in this case if you look at there is a change in the form all together the inputs get transformed into the finished goods. But the second category of change that is change in the place. So, here we talk about the supply chain, how the output move from factory to the retailer. Because output generally get produced in the plants, output generally get produced in the factory, but that is till the time it is not reaching to the retailer, it is not reaching to the market at least for the individual consumption unit. So, in this case the second form of transformation comes and which also part of the production activity is the change in place. So, the process of transformation involve two kind of changes. One change in the form which leads to the raw material into the final goods and second one is the change in the place which includes the part of production activity, because it moves the goods and services to the retailer to the factory to the retailer. So, they makes the products consumables till the time it is with factory no access to market the goods cannot be called as finished goods or the goods cannot be called as the final output, because it is not in a consumable form. So, once it reaches to the retailer it leads to a consumable forms and that is the reason in this case the change in the place is also one kind of production activity and this is considered as the activity of transformation. So, production is a activity of transformation which has two type of changes which involve two types of changes. One change in the form from moving from input to output that is raw material transform to finished goods and second is the change in the place that is the supply chain typically involves supply chain that is the movement of the goods from the factory to the retailer and this also add to the production activity, because till the time it is not reaching to the retailer it is not the consumable goods. So, with this the kinds of transformation whether transport whether it is may be the change in whether it is the change in the place whether it is change in the form the usability of the goods and materials increases. So, if you look at like we are giving one example till the time it is not reaching to the retailer the consumer is not getting access to the consumption of the goods and that is the reason if you look at there is no usability of the goods till the time it is there with the factory no access to market. So, this kind of transformation usability of the goods and materials increases and summarizing this we can say production is an activity that increases the consumers usability of goods and services. So, whether it is in the change till the time it is in the raw material form consumer cannot consume it till the time it is lying in the factory with the plant consumer cannot consume it. So, with the change in the transformation with the activity what is called production through this through the transformation activity that increases the consumer usability of the goods and services and that is the reason production is also one kind of activity that increases the consumer usability of goods and services. Now, we will introduce some basic concept of production theory and we will start with the classification of inputs. Now, what is inputs? Inputs generally what are the raw materials or the different kind of inputs getting used in the production process and which helps in the converting the input into the output. So, generally if you look at the age old definitions say that there are four kind of factor of production or four kind of inputs like land, labor, capital and entrepreneurship. But if you look at time is also one of the important factor which is considered as the part of input. So, one is labor, two is capital, three is land, four is raw material and so there is one more addition of inputs over here that is time. All these variables are measured per unit of time and hence refer as the flow variable. Since there is a time dimension to land, since there is a time dimension to labor, since there is a time dimension to capital, since there is a time dimension to the raw materials, since there is a time dimension to the time factor age well all these are flow variable none of the variables are known as the stock variable. Stock variable is one where in the entire timeline the inputs are remain fixed, but since it is changing with the time in this case all these inputs are considered as the flow variable. So, inputs are one which helps the production process to get into the output or maybe this is the inputs in the production process and apart from this five inputs, entrepreneurship is considered as the one of the foremost inputs in the production process and that is not in the physical unit rather that is in the human unit and it is a part of production and it can be measured by the managerial expertise and the ability to make things happen. So, if you have labor, if you have capital, if you have land, you have raw material time. So, the role of entrepreneurship comes here when they manage the all these inputs and when they measure the targets and when they reach the targets using their managerial expertise or maybe all this kind of input. So, entrepreneurship is the guiding factor for all the inputs to lead them into the desire form of the output. So, in this case we have listed six different kind of inputs land, labor, capital, then we have raw materials, then we have time and finally, entrepreneurship is considered as the one of the input at least in the modern form which generally with their expertise they lead to the desire form of the output. So, as defined input is a good services that goes into the production process and economics refers to input is simply anything which a firm buys for the huge units production process. So, electricity unit is one kind of input, maybe the building is one kind of input, the manpower requires to produce the output one kind of input, raw materials, the suppliers they are all considered as the input in the production process. So, an input is simply anything which a firm buys for huge units production process can be considered as the input and what is output? Output is on the other hand is any goods and services that comes out of the production process. So, input is always input in the production process and the outcome is generally known as the output. Generally the outcome is known as the output and output is any goods and services that comes out of production process that is generally known as output and input is any goods and services that goes into the production process. So, in a typical economic jargon we always say that anything which gets used in the production process is a part of input. The inputs are considered as fixed or it is variable. So, how they are considered as the fixed or the variable? It depending on how readily their usage can be changed. If it is can change immediately this is generally known as the variable input, but when there is a time factor associated with the change in the input generally this is known as the fixed input. So, input can be categorized into the fixed input or the variable input and whether there are variable or whether there are fixed it depends on how readily the usage can be changed. So, fixed input and input for which the level of usage cannot readily be changed. So, as we mentioned that there is always a time required to change the level of input and the level of usage when it is cannot readily be changed this is called as the fixed input. And in typical economic jargon a fixed input is one which supplies inelastic in the short run. So, inelastic is what? Inelastic where it is less sensitivity if there is no even if there are external factors still the variable does not change accordingly they are generally rigid they are rigid fixed in their changes and that is the reason in case of fixed input the supply of the fixed input is inelastic it does not changes much in the short run. So, in technical sense a fixed input is one that remain fixed or constant for a certain level of output. So, suppose you take the example up to producing 100 units of output if the input requirement for suppose input require for the first category is 10 units if that is not changing for 100 units that this is the part of the fixed input or maybe we can take the example maybe more generic sense that to produce 100 units of output if 10 units of electricity is required then electricity will be considered as the fixed input because it is not getting change when there is a 100 units of output. But if the electricity units getting change to produce 100 units of output at different level that is considered as the variable input. So, in economic sense fixed input is one which supply is inelastic in the short run whereas in the technical sense a fixed input is one that remain fixed or remain constant for certain level of output. So, with the defined level of output the input level is not getting change that is in the technical sense. In contrast to this we have variable input variable input is one which supply in the short run is elastic like it get changes the level of input get changes on the basis of the change in the external factor. So, typically we take the example of labour we take the example of raw materials and the like and user of such input can employ a larger quantity in the short run right. So, if the input gets changes accordingly the output changes if the variable input is one where it changes like suppose to produce a typical output you require only 10 units of labour right. But if there is a time factor associated with it and if you want to produce the output in half day you can very well change the unit of labour associated with the production of the output and how it gets changes because you can just may be develop whatever the labour unit is getting used and that is the reason these inputs are consider as the variable input because it can readily change or the usability of the usability of this inputs readily change ready there is a variation over here. So, variable input is one whose supply is short run in which supply in the short run is elastic typical example we take labour raw materials and typically inputs in that category and user of such inputs can employ a large quantity in the short run. Now, technically what is a variable input a variable input is one that changes with the change in the output in the long run typically all the inputs are variable. So, technically what is a variable input if you are consider the same level of a same example what we took for the fixed input to produce 100 units of output only there is a requirement of 10 unit of electricity, but once there is a increase in the output once the production unit whatever is getting produce if that is getting change immediately there is a change in the electricity unit also and that is the reason in this case we can consider electricity as the variable input because once the output is getting change accordingly the input is also getting change and that is the reason this is consider as the variable input. In the long run all the inputs are variable because long run is a sufficiently long time period where it is difficult to increase the output by changing only few inputs not all the inputs. So, we will discuss about the short run and long run may be in the next slide, but for this for the time being let us have the understanding that in the short run few inputs are fixed and few inputs are variable, but in the long run all the inputs are variable because long run is a sufficiently long time period where output cannot be increased by changing only few of the inputs rather they have to change all the inputs. So, as we discussed now we will see one of the important concept here in case of production theory is the short run production and the long run production. Now, what is short run what is long run in case of short run the time period is little bit may be less than the time period what is associated with the long run, but in case of short run at least there is one input is fixed all changes in output achieved by changing usage of the variable inputs. And in case of long run all inputs are variable output change by varying usage of all inputs. So, in case of short run there is one precondition that at least one input has to be fixed at least one input is fixed all changes in output achieved by changing usage of the variable inputs long run all inputs are variable output change by varying usage of all the inputs. Now, we will see what is the production function. So, till now we know that production is an activity production is a technique which connect the factor inputs into the factor output or which transform the input into the output. Now, we will see what is a production function it is a tool of analysis used in explaining the input output relationship or maybe it describes a technical relationship between the inputs and output in physical terms. In its general form it holds production of a given commodity depends upon the certain specific input. So, this is basically a technical relationship between input and output in physical term. And in its general form it holds a production of a given commodity depends on certain specific input it is it gives a combination of the inputs which produce the certain level of output and how the inputs and outputs they are related. So, in its specific form it presents a quantitative relationship between the inputs and output and it is may take a form of a schedule it take a form of a graph line or a curve or an algebraic equation or a mathematical model. So, the relationship between the production the relationship between the input and output that is represented in the form of a production function may take a form of a schedule it can take a form of a graph line it can take a form of a curve it can take a form of a algebraic equation or it can take a form of a mathematical model. The production function represents the generally the technology of the firm because we are explaining this as the technique which connects the factor input into the output. So, in that sense the production function represents the technology of a firm. So, as mentioned production function is its gives us the input combination to produce a certain level of output production function is the maximum amount of output that can be produced from any specified set of inputs given the existing technology. So, it is the maximum amount of output that can be produced with a given set of technology and the specified set of input what is the maximum output that can be produced generally production function explain this if it is typically connecting the factor input into the output. We get two type of efficiency when we talk about the maximum amount of output one technical efficiency second is the economic efficiency. Technical efficiency is achieved when maximum amount of output is produced with a given combination of inputs and economic efficiency achieved when firm is producing a given output at the lowest possible total cost. So, first one in case of technical efficiency it is achieved when the maximum amount of output is produced with a given combination of inputs and second it is firm is producing a given output at the lowest possible total cost. So, if you look at the two level of efficiency in the first case combination of input is given and in the second case the level of output is fixed. The first case the challenge is to maximize the output in case of technical efficiency with a given set of input and in the second case to the challenge is to minimize the input to produce a given level of output. So, first is the optimization problem which relates to the maximization of the output and second optimization problem relates to the minimization of the input. So, if you look at the entire production also entire production theory it focuses on two optimization problem one is maximization of output and second one is the minimization of input and in both the cases the producer is getting the benefit one in term of increase output and second in term of the decrease input. So, in case of technical efficiency the optimization problem is to maximization of output with a given combination of input and in case of economic efficiency the challenge is to minimization of inputs or the minimization of the total cost to produce a given level of output. Now, if you take a example we have the information about three kind of process, process one, process two and process three. Suppose the first row talks about the input combination one that is suppose capital and second row talks about the input combination two that is labor. So, in case of process one to produce the output the firm is using 10 unit of capital and 15 unit of labor, process two is 15 unit of capital 15 unit of labor, process three is 5 unit of capital and 20 unit of labor. A process of production is technically efficient if it uses less of one factor and no more from other factor compared to any other process of production. Now, among these three processes process one, process two, process three which are using different input combination we need to find out which one is technically efficient. What is technically efficient? Maximization of output with a given combination of input and how to find out the technically efficient here if it uses less of one factor and no more from other factor compared to any other process of production. So, now let us look at process one and process three. Even if process three is using less of capital it is using more of labor. So, process three is rolled out in case of technically efficient. If it is between process one and process two even if it is using more of even if it is the same amount of labor it is using less of capital. So, between process one and process two always process one is more technically efficient as compared to process two. However, if you look at process one, process two, process three, among these three processes nothing is clearly emerging out as a technical efficient because even if they are using less of one they are always using more of the other input and in that way closely or clearly will not find any technically efficient process. However, if you compare between process two and process three, process three is rolled out, process two is rolled out, but if you compare between process one and process two at least process one is emerging as the more technically efficient process as compared to process two. Then we will see how this production function is leading to a empirical production function or how we convert this production, the theoretical production function into a empirical production function. Generally it is complex because it includes wide range of inputs starting from land to the technology like land, labor, capital, raw materials, time, technology and sometime this is also the entrepreneurship. These variables form the independent variable in the firm's actual production function. All the inputs they are the independent variable and what is the dependent variable over here? The dependent variable here is the output. So, if firm's long run production function is of the firm that is Q is equal to function of L D L K M T and small t where L T is the land and building that is being used in the production process, L is the labor, K is the capital, M is the materials that is raw materials, T is the technology and small t is the time. So, Q output that is a function of the different input that is land and buildings, labor, capital, materials, technology and t is the time. For the sake of convenience, economics have reduced the number of variable used in a production function to only two that is capital and labor. Therefore, the analysis of input output relation the production function is expressed as the Q which is a function of capital and labor. For understanding for may be making it is simpler to understand the other concept related to the production theory, generally economics they use the production function which is a combination of two input that is capital and labor and considering this the production function the empirical production function is Q which is a function of just only capital and labor and this is strictly used only for making the other concept simple there is no other reasoning that why capital and labor only consider as the production process. Now, given production function Q which is a function of capital and labor here Q is the dependent variable K and L is the independent variable. So, at any point of time in order to increase the production Q there is a requirement of changing the K and L either the firm can increase both capital and labor or only labor depends on the time period it is taken into account for increasing the production. So, if we know in case of short run at least one input has to be fixed given that scenario if it is a short run generally the increase in the Q will be only with the help of labor because capital is considered as fixed because that is inelastic in the short run. Whereas, in case of long run whenever there is a need to increase the Q both the capital and labor gets changed and that is the reason in case of long run the both the capital and labor will be increase in order to increase the Q, but in case of short run in order to increase the Q the labor will also labor only the labor has to change because capital remain fixed in the short run. So, Q consider as to be a dependent variable whenever the change is required it has to be changed with the help of capital and the labor. H there is a popular belief or the economics believe that the supply of capital K is inelastic in the short run and elastic in the long run. So, that is the reason in the short run firm can increase production only by the changing the labor or increasing the labor since the supply of capital is fixed in the short run, but in case of long run the firm can imply more of both the capital and labor as the supply of capital will become elastic over time. Then we will move to the short run where capital is consider as the fixed only changes in the variable labor input can change the level of output and how the short run production function empirically now? Q is a function of labor and capital and capital remain fixed if you again simplify is Q is just a function of labor because initially whatever the capital is being fixed that is being fixed whenever there is a need to change in the Q that has to be changed with the help of labor. So, in the short run capital is fixed only changes in the variable labor input can change the level of output and in case of short run empirical production function Q is a function of the labor. There are three concept associated with the production analysis whether it is short run whether it is a long run. One is total product, second one is the marginal product and third one is the average product. Now, what is total product? It gives maximum of output that can be produced at different level of one input assuming that the other input is fixed at a particular level. So, suppose capital is fixed at a level whenever you change the labor input the total product increases in the short run and also in the long run when you change the capital and labor, but in a specific case of short run this is the maximum of output that can be produced at different level of one input assuming that the other input is fixed at a particular level. What is marginal product? Change in the output resulting from a very small change in the one factor input keeping the other factor input constant. Average product that is the total production per unit of output. Now, how to find out this average and the marginal product? Average product of labor A P is total Q that is Q is the total product total output divided by the labor. Marginal product of labor is the change in the Q with respect to change in the L whenever there is a change in the labor unit how much unit of output gets changes because of that. Similarly, average product of capital is the total output divided by the K that is Q is the total product divided by the number of capital unit that will give us the average product. Marginal product of capital is the change in Q with respect to change in the K that is change in the output whenever there is a change in the capital unit. So, this is just a hypothetical example of the total average and marginal product of labor when K is equal to 2. So, in the first column if you look at this the number of workers considering this the short run case only labor is variable capital is fixed at 2. Total product changes whenever there is a change in the labor unit and if you look at it is going on increasing at up to ninth unit and after that even if there is a change in the labor still there is no change in the total product. We will explain the logic behind it that why even if there is a change in the input why it is not leading to change in the output. Average product is nothing, but the total product divided by the unit of the labor and marginal product is again it is the change in the Q with respect to change in the labor. So, this is del Q with respect to del L. So, if you look at the difference between the first unit and second unit by changing by just increasing one unit of labor the product increases by may be 52 in the first case and again 16 in the second case. So, this is the additional change in the product when there is a use of one more labor unit that gives us the marginal product. This is typically in the case of a short run when capital is fixed and the output is getting changed only with the help of the labor.