 As I told you that even if there is a increase in the labor still at a certain point in the 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 is 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 is 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 photocopy machine is the capital or the photocopy 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 one person it is over burden 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 a 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 photocopy 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 usage. 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 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 units 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 or 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 3 point or the 3 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 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 3 curves starts from origin that is total product marginal product and the average product product. Total product is initially convex through 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. According 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. So stage 3 is decreasing 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 labor input, the marginal product is more because the additional unit of labor 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 labor, 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. It means it is the overuse of the both the inputs like whether it is machine, whether it is a worker, whether it is labor with the capital. The there is a overuse of labor, there is overuse of capital and that is the reason the total product is decreasing and marginal product is negative. So, stage one if the producer is operating, there is a underutilizing 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 three they are over utilizing it that is the reason. It is not possible to operate in stage three 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 labor, they are not contributing to the total product. Let us see what happens or what is the logic for stage two. In stage two, 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 labor 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 laborer 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 two 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 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 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 at the level of six worker if you remember the previous table the information of 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 use seeds planted water consume and all other inputs remain same. But if more than one inputs 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 and 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 in the next class we 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.