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 and 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 altogether 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, the 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 maybe 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 when 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. variable is 1, where in the entire time line 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 1, which helps the production process to get into the output or may be this is the inputs in the production process. And apart from this 5 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 may be all these 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 6 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, may be the building is one kind of input, the manpower equals 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 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 they are variable or whether they 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 may be we can take the example may be 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 defile 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 is 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 double up whatever the labour unit is getting used and that is the reason these inputs are considered as the variable inputs because it can readily change or the usability of the usability of these inputs readily change ready there is a variation over here. So, variable input is one whose 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 consider the same level of same example what we took for our 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 produced if that is getting changed 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 changed accordingly the input is also getting changed and that is the reason this is considered 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 a 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 changed 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 changed 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 may be 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 give combination of the inputs which produce the certain level of output and how the inputs and outputs there related. So, in its specific form it presents a quantitative relationship between the inputs and output and it 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 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 farm 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, a 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 D 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 a understanding for a 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 a reason in case of long run the both the capital 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 considers to be a dependent variable whenever the change is required it has to be changed with the help of capital and the labor. As 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 become elastic over time. Then we will move to the short run where capital is considered 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 remain fixed if you will 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 concepts 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 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?  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 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 change only with the help of the labor. As I told you that even if there is a increase in the labor still at a certain point if you remember the previous table certain level there is no change in the output or there is a small change or there is a small decrease in the output. Now, what is the logic behind it? The logic the relationship between the total product, the marginal product and the average product that is explained with the help of a law of diminishing return and that explains the logic also that why there is no change in the output or why the output decreases when you increase more and more of the input particular input keeping the other input as the fixed. So, the law of diminishing return or the law of the variable proportion the logic or the theory that is generally known as the that is generally at the background of the shape of the total product curve. So, now, what is this law of diminishing return? It state that with a given state of technology if the quantity of one factor input is increased by equal increment quantity of other factor input remaining fixed the resulting increment of total product will first increase, but decrease after a particular point. So, in a typical in case of a short run if capital being fixed only there is a change in the labor initially the total product will increase, but after a particular point even if there is a increase in the labor still it will decrease. It state that as we go on employing more of one factor of production other factor remaining same the marginal productivity will diminish after a some point. So, keeping capital as fixed the if you are going on increase the labor after a particular point generally the marginal productivity will diminish and that is the reason the shape of marginal product curve is inverted you see. I will just give you a small example of a photocopy machine right. If there is a copy or if there is a photocopy machine now what is the working hour can be the working hour can be 8 hours 10 hours. Here what is capital or what is k? The photocopier machine is the capital or the photocopier machine is the may be the capital or it is may be the k. Now to run that to 8 to 10 hours may be 2 persons are good enough for 1 person it is over, but then for 2 person it is good enough, but if the shop owner is going to employ more than 2 workers it is not going to increase the total product rather it is going to decrease. So, the same concept or the same logic over here if the capital is fixed there is the ideal match of labor should be used. Even if once you cross that ideal match of both capital and labor if you are still going on adding labor to it the total product is not going to increase initially may be it will increase because the photocopier machine can be run for 12 hours 15 hours, but there is also a capacity of the capital you cannot overuse it and that is the reason it will increase initially up to a level and after that it will decrease. So, the shape of the marginal product and once it decreases if the total product decreases it means the marginal product is negative and that is the reason the shape of the marginal product is therefore, inverted u shape. So, when there is a increase in the total product marginal product increases because the addition to the total product is positive and that is the reason marginal product is increasing and after reaching a threshold level where after that point whatever may be the increase in the labor still the total product is not going to increase then in this case the total product decreases the and the marginal product becomes negative. That will explain through a graph that how the behavior of the total product average product and the marginal product changes when there is a use of more of one of the input keeping the other input as the fixed level. There are few assumptions being taken the state of technology is given one factor of production must always be kept constant at a given level k has to be constant only there has to be change in the labor the law is not applicable when two inputs are used in the fixed in proportion. Anyway the third one will not come into picture if you are maintaining the second one that one factor of production must always be kept constant at a given level. So, the second input should not be used at the same level and because the law will not be applicable when the two inputs are used in the fixed proportion. Like the typical photocopier machine if you are buying one more photocopier machine and still you are using two inputs of labor your total product bound to increase, but that you cannot do in the short run because one input has to be fixed in the short run otherwise the law will be not valid or the law will be not applicable. This is the typical explanation of the total average and marginal product curve. If you look at the total product initially increasing reaching to the maximum and then it is decreasing average product is increasing and then it is decreasing and similarly marginal product is also increasing and decreasing. Now, we will see the logic of this shape of the total product curve. Here we will take the labor unit here we will take the total product here we will take the average product where we will take the marginal product. Initially total product increases at the increasing rate up to this point then it increases at the decreasing rate at the up to this point and from this point onwards it decreases. So, this is the total product of the labor. We will see corresponding to this our marginal product is maximum then corresponding to this when the total product is maximum our marginal product is 0 and after this the marginal product of is become negative. This is our point A, this is our point C. Now, what is the behavior of the average product? Average product changes in the same way as the total product changes. So, average product will initially increase and then it will decrease when there is a decrease in the total product. So, we get three point or the three turning point of this graphs. This is our total product that is initially it increases at the increasing rate then it increases up to the decreasing rate up to the point C and then it decreases. Then average product initially increases then it starts decreases, marginal products increases and then it decreases. Now, what is the logic behind this? Why it is increasing or why it is decreasing? Now, at the point 0 if you look at the origin point at this point 0 the labor unit is equal to 0 and the value of total product will be equal to 0. Obviously, the value of marginal product average product has to be also 0. So, all the three curves starts from origin that is total product marginal product and the average product product. Total product is initially convex for the origin till the point A and then it becomes concave. As long as total product curve is convex marginal product is increasing. When the total product curve is concave marginal product is decreasing and it is also sometimes in the negative segment. The point A on the total product curve is called as the point of inflection because at this point the curve is changing its curvature and corresponding to this the marginal product will be maximum. Average product is maximum at this point B and at this point also the average product is equal to the marginal product. Corresponding to the maximum point of the total product curve that is the point C marginal product has to be the 0 to the left of point C total product is increasing to the right of point C total product is decreasing and the marginal product is negative. Now, since the marginal product is decreasing when the average product is maximum then the marginal product curve which is the maximum before the average product curve. Now, what is the relationship between this marginal and the average product? When average product is increasing marginal product is greater than average product. So, if you remember in the first phase when the marginal product is increasing till the time the total product is convex if the marginal product is increasing then the average product is also increasing and it is less than the marginal product. When average product is decreasing marginal product is less than average product when when average product is reaches its maximum then average product is equal to the marginal product. In this case we have identified the three stages of production. Now, what are the three stages of production? On the basis of this relationship between the average product total product and marginal product there are three stages of production. Now, we will see what are these three stages of production? This is the total product of labor this is the marginal product of labor and this is the average product of labor. So, point 1 is A, point 2 is B and point 3 is C. At this point A marginal product is maximum at this point B there is a equality between the average product and marginal product and average product is maximum corresponding to point C total product is maximum and marginal product is 0. In the x axis we take labor, y axis we take average product, marginal product and total product. Corresponding to this we have identified the three stages of production. From origin to point B we have stage 1, between point B to C we have stage 2 and beyond point C we have stage 3. Stage 1 is known as increasing return because in this case average product is increasing marginal product is increasing partly and when it is decreasing also it has not reached 0 and total product is increasing that is the reason stage 1 is known as the stage of increasing return. Let us see what happens in case of stage 2. Stage 2 total product is increasing average product has started decreasing marginal product is decreasing, but marginal product is reaching 0 till now it has not reached the negative segment. So, stage 2 is known as the decreasing return because both average product and marginal product is decreasing and also the total product is increasing at the decreasing rate. Let us see what happens in case of stage 3. Stage 3 is known as the stage of negative return because total product is decreasing, marginal product is negative and average product is also decreasing. So, stage 1 is increasing return, stage 2 is decreasing return and stage 3 is negative return. From origin to point B is stage 1, between point B to point C decreasing and beyond point C this is the stage of negative return. We have three stages of production process. In case of stage 1 it is known as increasing because total product average product is increasing, marginal product is partly increasing up to point A and then it is decreasing. Stage 2 is known as decreasing return because average product marginal product is decreasing and total product is increasing at the decreasing rate. Stage 3 is known as the negative return because marginal product is negative, total product and average product is decreasing. Now, the question comes if it is a case of a rational producer where the optimization problem is to maximize the output the minimum of cost in which stage would the rational producer would like to operate whether in stage 1, whether in stage 2 or whether in stage 3. Now, let us see what happens in three stages of production. In stage 1, marginal product and average product both are increasing, but marginal product is more than average product and what is the implication of this? A given increase in the variable factor lead to more than proportionate increase in the output. So, whenever there is a change in the labour input the marginal product is more because the additional unit of labour is contributing more to the production. So, the producer is not making the best possible use of fixed factor, a particular portion of fixed factor remain unutilized. Like if you are taking the case of a photocopier machine and if you are using only for one machine only one labour, the maximum capacity the worker can work or worker can run the machine is for 8 hours not more than that. So, in this case there is a under utilization of the machine and the same logic is here that in the case of first stage the producer is not making the best possible use of the fixed factor a particular portion of the fixed factor remain unutilized. In the second stage the marginal product of variable factor is negative and total product is also decreasing.  There is a overuse of labour there is overuse of capital and that is the reason the total product is decreasing and marginal product is negative. So, stage 1 if the producer is operating there is a under utilization under utilizing one of the resources which is not in the line of their optimization problem where they have to maximize the output using all possible options of using the inputs. Stage 3 they are over utilizing it that is the reason it is not possible to operate in stage 3 because the total product what they are getting that is negative, but the that is decreasing and the marginal product is negative. So, when they are using more unit of labour they are not contributing to the total product. Let us see what happens or what is the logic for stage 2. In stage 2 marginal product average product both are decreasing and marginal product is positive and less than the average product. What are the implication of this? There is a less than proportionate change in the output due to change in the labour force. Hence, at this stage the producer will employ the variable factor in such a manner that the utilization of fixed factor is more efficient. So, in this case the additional contribution what the labourer is giving that is less than the average product. So, at this stage the producer will employ the variable factor in such a manner that the utilization of the fixed factor is most efficient. So, it is not under utilization of the fixed factor not the over utilization of both the fixed factor and the variable factor. So, stage 2 is basically consider as the ideal stage for all rational producer to operate because at this stage the producer will employ the variable factor in such a manner that the utilization of the fixed factor is more efficient or the simply we can put the logic is like this that there is a efficient utilization of both the inputs or both the factor of production that is variable factors and the fixed factor and that is the reason the rational producer should operate in the case of the second stage in order to optimize their maximization of output with all possible options. Now, what are the examples when you take into the real life whether there is a really evidence of this law of diminishing return and we have taken a case of the chemical fertilizer when it is getting used as the one of the input in the to increase the output. So, here the good example of diminishing return includes the use of chemical fertilizer and a small quantity it leads to big increase in the output, but there is always a limit increasing its use further may lead to decline the marginal product as the efficiency of the chemical decline. You know that for one acre of land or for may be 10 units of output what is the chemical required fertilizer required chemical fertilizer required till the time it is given in that amount it always contribute to increase the output, but the overuse of that is not going to increase the output. So, you cannot just going on increase the input the chemical fertilizer in order to increase the output and if you are continuing to doing so may be there will be decrease in the output because there is a overuse of one of the inputs. Similarly, we can take the example of the number of workers or unit of product produce. So, the first column in this case gives us the number of workers that is from 1 to 6 and unit of product produce is from 10 to 16 and here we can see how the marginal product behaves actually or how the marginal product takes place. In the first case the number of worker is 1 unit of product produce is 10 marginal product is 10 because this is the total contribution. Number of worker is 2 unit of product produce is 25 and the marginal product is 15. Three workers hired they are producing 45 units the marginal product is for the third unit the additional contribution to the total product is 20. For the fourth unit is 15, fifth unit is 10 and sixth unit is go in a negative direction because after fifth unit even if they are hiring a additional unit of laborer he is not contributing rather he is decreasing the total output. So, number of workers increasing so it is the total product is increasing up to a level and then there is a decrease in the additional contribution. How we can interpret this? It is with three workers that the firm production is most efficient because marginal product is at its highest. Beyond this if the worker is getting used if there are more number of workers is being higher then the marginal product is declining and total product is increasing at a decreasing rate. Beyond this point beyond the hiring of three workers the firm begins to experience a diminishing return and the at the level of six worker if you remember the previous table the information the previous table the firm actually begins to see the decreasing return as production level decline because when there are a hiring of five units of laborer that leads to 70 units of output and when there are a six unit of laborers being higher the production level decline from 70 units to 60 units and that also leads to cost continue to increase. So, that is the evidence of the decreasing return and but you can again twist to this example that it is not only changing the input in this example only the number of workers changes while the land used seeds planted water consumed and all other inputs remain same. But if more than one puts were to change the production level will not decrease rather it will increase, but that is beyond the scope of a short run production function in case of short run we can only increase one input keeping the all other input constant. But if it is not a case of short run if more than one input were to change the production result would vary at the law of diminishing return may not apply if all input could be increased and that is the reason if you look at one of the assumption we took in before discussing the law of diminishing return that there is only one factor input has to variable other factor input has to be constant and that is the reason you can get the evidence of law of diminishing return if you are keeping strictly within the framework that you can only increase one factor input all other inputs remain constant. So, with this we will complete this short run production function these are the session references the books that is being followed to preparation for this session and then the next class will continue the long run production function the long run analysis and then we will see the different kind of production function like cup Douglas and C.S. production function.


Hi, I'm Ross Gardler, a Program Manager on the Azure Compute Team. You know, the portability, small size and rapid start-up and tear-down times of containers is bringing an agility and flexibility to all phases of the development and operations lifecycle. That's what I want to talk about today. After a short introduction, I'll dive straight into a demo. I'll show you how a developer might use containers locally to provide an approximation of their production environment right there on their dev machine. I'll make some edits to the application, test them in the simulated environment, and then push those changes to the development repository so that our co-developers can work with the latest code. We'll then look at how the Azure Container Service provides an easy way to build and manage a staging or production environment for our containerized application. This environment will provide a scalability and availability far beyond that of our single machine developer environment. By the time we finish discussing this service, we'll see how our developers' changes have gone live into an Azure Container Service cluster. Let's take a look at the process we're going to see here. Like all application development teams, we will start off with one or more developer workstations. Here, our developers will build and test their code. Once happy with it, they will push the code to version control. At this point, co-developers on the same team can retrieve their changes to ensure that their own work is aligned. Whenever a new code is committed to the master branch of the repository, a continuous integration service pulls those changes and rebuilds the affected containers. Integration chests are run against this new configuration of the application, and when tests pass, the new containers are shared via a Docker registry with other teams. This means that our development teams are always working with the latest development versions of containers produced by other teams, whilst also working with the latest development code from within their own team. As a result, any bugs introduced are identified as early as possible and therefore resolved more quickly. When new versions of containers are made available in the Docker registry, a continuous delivery system will manage the rollout to staging and production environments. This may be a fully automated process, or it could involve control steps in which operations teams verify the deployment pound at key stages of the operation process. Now that we understand what the workflow looks like, let's take a look at it in practice. Here's our demo application. It's a really simple Hello World application. It consists of three containers. The first container is a PHP container, and it returns this part of the page. Notice it says Hello Connect World from the PHP web application. It tells you the host that it's running on and a title here. And then this little bit at the bottom, the PHP app calls a Java REST API, which responds with the text that you see here. So it's a really simple application. The third container is a load balancer in front of the web application, and we'll see that in action in a moment. I want to draw your attention to the URL here. We're running on an instance of the Azure Container Service. This particular instance has three virtual machines on it, and we'll look at more detail at that very shortly. So first of all, let's go to our development machine and see what that looks like. So I'm a Linux guy. So here I am on my Linux development machine. On the bottom half of the screen down here, you can see the three containers that are running. We have the load balancer I mentioned earlier on. We have the web front end. That's the PHP part of the application. And we have the Java REST backend. That's the Java part, obviously. On the top half here, we have the PHP page that we're returning. And we're just going to make a simple edit. We're going to remove that word connect. So we're just saying hello world, make the application more generic. So we'll save that. We'll drop out to the console here, and we'll take a look at what it looks like. So I'm going to use a text-based browser. It's just very convenient when you're working in a text environment to use a text browser. And I'm going to look at the version of this application that's running locally. And you'll see that we have that changed. The word connect has disappeared from the title up here. So that looks good. Normally we'd run some tests at this point. I'm not going to do that in this in the interest of time, but we do have tests available in this test application, which is available on GitHub, if anybody wants to have a look at it. So one other thing that we want to do here is we want to make sure that none of our changes have actually broken the application in terms of performance. So we're going to scale up the application. So using this command Docker compose, and we use the configuration file that's a YAML file there called Docker compose dev. We're going to scale the web container up to three. And so what happens here is we're going to start two more containers. We already had one, we'll start two more. This takes just a few moments. And when complete, we'll have three containers running. You can see that there are two new containers appeared at the bottom here to show that they're running. And now we'll use the links browser to go back again. Looks just the same seems to be working. Let's check that we're going through the load balancer. If I refresh, keep your eye on where the host is here. You'll see that it changes to the different hosts, which they have three of them going in a round robin through this load balancer. So that all works great. Let's commit that change now. Let's make that change available to our development team. So this is backed by commit git. So I'm going to do a git commit. And I'm going to say trigger builds for demo. And then push that into the repository. And so there we go. We've now pushed our changes to the rest of our development team who can now start working against the latest code. So Docker in a development environment is great. It allows us to build a closer to production application on our laptop or dev work machines. However, in reality, there's only so far we can go on a single machine. What we really need is a staging environment that's even closer to production. Such an environment will span multiple hosts, possibly multiple geographic regions. We'll need redundancy and high availability. And we'll need the ability to scale both the application components and the underlying hardware on which those components are running. All this needs to be managed. This is where the Azure Container Service comes in. This is a forthcoming service that allows you to quickly create a cluster of Docker hosts with a preconfigured set of masters for managing the application running on those hosts. Azure Container Service includes tools such as Docker Swarm and Apache Mesos to orchestrate your applications while your underlying hardware is managed through the Azure Resource Manager tooling. Let's take a look at the Azure Container Service that we're using for our application. So what we're looking at here is the Apache Mesos UI. This is running on a Linux virtual machine again. This time I have a GUI display, and so I'm able to use a proper browser. This is inside of the Azure Container Service, and the Mesos interface here is showing us what's happening on that container service. So the first thing we should notice is that we have three agents available. These are each virtual machines that are available to us to deploy applications to within this cluster. If I scroll down a little, you can see that that is giving us some resources. We have three CPUs and 2.5 gigs. So these are just small virtual machines. We're using 1.2 CPUs and 1.5 gig of memory. And what we're using them for, you can see over here, these active tasks, and you'll recognize these. It's the load balancer, the web front end, and the REST API that we were talking about earlier on. But in this instance, they're running on the container service. Those are being managed by a project called Marathon. And here you can see, again, the three applications being managed, the amount of resources that each one runs, and the number of instances that we have running. So if we wanted to scale up like we did on the development machine, we can click through to the web application, click on scale, tell it that we want, for example, three, and then click OK. In the interesting time, I won't do that now, but it just takes a few moments to create the new instances just like it did on the dev machine. You can also do this through a REST API. All of this information is available for you, and the changes you would want to make are available through a REST API. But what I promised we would do is we would see that our application would automatically deploy to this cluster for us. So let's look at how we've done that. Here we have a project called Jenkins. And Jenkins is a continuous integration service. Again, it's an open source project like everything else that we use in here. And you can see that we have three tasks running here. We have the integration tests, and this test is triggered when it sees a change in the code in the Git repository. That runs, if those tests pass, then the load test is run to make sure that we've not broken performance. And if that passes, then deploy to staging is run, which actually pushes the new containers into our development cluster. So if I go to this tab, we can see the application. And this is the same version that we had running earlier on. You'll note that the URL is the same here, and that we have the Hello Connect world. But if I now refresh, we see that the word Connect has gone. And so we see that the developer changes have gone through version control, through the Docker Hub, where they've made available to the rest of the development environment, and then on to the staging server, which in this case is being run by the Azure Container service. So there we have it, an end-to-end deployment using Docker and the Azure Container service. Thanks very much, and enjoy the rest of the content.