 Under the chapter of consumer behavior we are going to study weak axioms of revealed preference. So it is in the connectivity of our previous modules where we have studied revealed preference and non-revealed preference or indirectly revealed preference. So when we say the weak axioms of the revealed preference, so we can say that these are those principles that at least should be met when we are dealing or we are studying the revealed preference. So consumer is always facing certain competition and consumer is always in a fix. If I say that since the wish list is always big and resources are limited, then allocation is always decided between some combinations to optimize and optimize resources. So whenever consumer is facing these types of situations, then the behavior we study will be the consumer behavior. And now there are two bundles in which we are saying that there will be one bundle A in which there is a combination of x1 and x2 and there is a second bundle B in which there are some commodities which are y1 and y2. So it means these two bundles are so that the commodities included in these bundles, they are different to each other. They are not the same. So the concept of reflexivity will not be here. These two are the different bundles. And the minimum condition in this is that if the consumer has given a bundle A to B at any time, at any decision, then we have to see that he has expressed his own interpretation. He has revealed preference. So our principle is that whenever he has to decide between these two bundles, the bundle he has given today, he will always keep the same interpretation on bundle A, bundle B or combination of x1 and x2 on y1 and y2. Now if we see in this, then our assumptions are that we have to see that these two bundles are present on his budget line because any bundle may be outside of his budget line or in other words, we can say that he is outside of his precious purchase. So about the two bundles, the decision or competition is taking place. The first assumption is that the both bundles, they are within the price range. And we can see here that if we see that both bundles which are available, because the commodities are different, the commodities are different, their prices are also in the market. They can be the same or different. But because they are different commodities, we will note them in a different way. So our bundle is one in which we said that the bundle is x1 and x2. The second bundle is our y1 and y2. And the weak axiom says that they both are available on the same budget line and within the same budget range. Despite being inside or above the same budget line, if we say that he is purchasing one of them and both bundles are not the same, they are different. And this means that because they are not the same and he is purchasing x1, then x1 is directly revealed over y1, y2. And if he is purchasing y1, then y1 is directly revealed to x1. Now if we look at this, there are three assumptions at the back end. The one that is available for our consumer preference, no satiation or non-satiation means that the consumer always wants to purchase more and more commodities. He never completes the demand for them. Yes, there is some time, some time, it can be for one commodity that it can be because it is the concept of diminishing modernizability. Transitivity will be present here. Third, monotonicity. Monotonicity in simple words is that most of the things are preferred on the minimum or most of the amount of any commodity will always be in its translation. So if all the elements in any bundle that we have seen are in the bundle in which x1 and x2 are present, if the things in it are increased in any other combination, if the things are increased in size, then that bundle was already preferred, now it will be preferred. And A must be preferred to B. And looking at this condition, our conclusion is that whenever a bundle A is preferred to bundle B, in one condition, so whenever there will be any type of the situation, when A and B have to be decided, then they always prefer bundle A. And this is in its weak axioms. If we look at it as its diagrammatic, then if we look at this line which shows its budget line, if we look here, the budget line does not mean that its income changes in any other length. Because we always say that the budget means that will be equal to price plus like this. Or it can be equal to price 1 of y1 plus p1 y1 and the third level, it can be p1 z1 plus p3 z3. So these prices can be different. So when these prices they are different, so when we divide M by price, so this one, if x is the point, then this will be more because this is price of x. When we decide the price of y with respect to the income, then this point will be more. And similarly, when we divide the income for p1 which is z, then this will be more. So because of this, our budget line is that prices of x, y and z that can be different. So if x is selected when y was available, not in the market, rather within the budget line. So if we look at this budget line, within this budget line, what was available to it was just this preference of x whereas y was also available. And similarly, when y was selected and when x was also available, then we say that y was preferred over x. Now, looking at all these situations, we say that x and y are in budget line but z is not in the range of the budget. So if the z combination was not bought, then it was out of the range. So the two decisions that he made, if he was not buying one, then we will say that he did not prefer and whoever he purchased that is x. So in every future combination, he would prefer the combination of y. Now if we look at when is its violation? The principle we have explained is that he will always do it or there could be a difference. It is possible when we said that if x is preferred to y, that is one direction. But similarly, if he had to decide between these two combinations and he changed the last decision i.e. the decision that he would prefer on y, rather he would prefer the combination of y on x. So we will say that the violation that he did was the consistency of the preference theory. Because the consistency says that whatever he did today, he will always do it. So the consumer has bought the combination of x1 and he could buy the y1 one. And when he bought the y1 one, when he could do the x1 one, these two things show the opposite direction. So in the first bundle we say that x1, x2 was preferred on y1, y2. And in another combination y1 and y2 is preferred on x1, x2. So this is the theory against and if we see this then if we say the weak axioms of the revealed then it comes to the violation and rather the theory of consistency of the consumer preference is also against it. So that's why we decided that all these principles would be the same when our assumptions would be valid in which our consistency transitivity, reflexivity we follow all of them. Thank you.