 Under the chapter of consumer behavior, we are going to study the idea of revealed preft, a very unique idea that was presented by Paul Samuelson. And actually, when we study the consumer divine, there are the two very evident ideas that we mostly study. So, most of the students, you must have heard of. Means, one related to the utility, that is the cardinal approach, the other, the ordinal approach, in which we read the Indifference Curves, Bedahasha, in all the books. This is the third idea, that is the revealed preference. And, if we look at it, the utilization of the techniques is mostly the same, which is in our other two, but the behavior of the consumer is somewhere different that is studied. So, the idea of revealed preference, if we understand it in simple words, is that when we apply any consumer's behavior with its purchase, with the consumer, not with its prices, not with its income, we are not collecting any information, rather whatever we are going to study, that is from the observations that we gather from the different consumption bundles that a consumer is going to buy. Now, if we look at it, the income and the other prices, they are kept constant. And during this analysis, whatever income is of its consumer and whatever prices are of various commodities, we do not take any change in it in the analysis. So, observing the consumer's behavior of the consumer from the unobservable preferences, means, those preferences or those decisions can be made, they are not done as a showery effort, they are not done as a showery effort. So, when we capture them, we analyze them, that will be the revealed price. Now, when we come to its assumptions, that if we are studying it, then in its assumptions, we have the first assumption that there should be unique bundles that the consumer is dealing with and purchasing it. Now, if we look at it, when the consumer is purchasing about one commodity, then maybe we should not apply this rule to it. This is always possible when the consumer is facing various commodity bundles. Now, in various commodity bundles, it is also possible that in one bundle, there are the same types of bundles, in another bundle, there are the same types of bundles. If I say that one bundle is like this, in which we say that there are several bundles, in the same way, there is another bundle, there are also several bundles. But in one bundle, there are four bundles and there are five bundles and four bundles. So, the number to be said is also complete in that bundle and it is also equal in the other bundle. But the preference of the consumer can be more for one commodity. So, the number of bundles in that bundle will give the treatment that it is a complete bundle. And it can be more in one bundle, and the number of bundles is also equal in the other bundle. But if there are five bundles in one bundle and four bundles in the other bundle, the number to be increased will also be seen as a separate bundle. So, if we look at it now, the concept here is that the consumer can afford to buy this basket A, basket B, basket C, whatever it is, but the bundle which he will buy for this basket then we will say that this basket and this bundle is preferred to the others because it had three bundles, two bundles but the one that he actually bought, we will say that he does not want or he does not want in any form, he has expressed his preference, he has his desire, he has expressed his desire. And that bundle, that combination which he has purchased, we will say that this is his optimal bundle or his preferred bundle based on his preference. And for this, the main assumptions that we have already discussed in economics, if we look here then it is that the line of income or the bundle of income should always be with us. If we are buying the first bundle then its price and quantity and the second share then it becomes one bundle of both. So this bundle is in the visible or the affordable limit of the consumer means its total expenditure either it is less or equal to the income. And likewise, if we buy a second combination, X1 and X2 bundle which becomes total expenditure then it should be equal to the income and it should not be more than. So from here, if we look then both bundles, they are in the pocket or the price range or the income range of the consumer. But if he is purchasing this bundle which he has affordably buying the Y one then we will say this bundle is directly revealed preferred than the other. If we look here then the sign of quality and the sign that it can be equal or less then if we assess from here then it is possible that the bundle which he has purchased of X combinations is a little bit expensive but despite of this fact which the consumer is purchasing this bundle based on his preference. Now if we look at this form in the form of a diagram then we say that the combination of the bundle of X1 and X2 which the consumer is buying then that is called revealed preferred of the other bundle Y1 and Y2 although he could also buy it. If we look here then this bundle is just on the exact budget line and although the bundle of Y1 and Y2 is within the budget line then he could also purchase it. And if we look here then during the gap a portion of the income to be left to the consumer it was an additional bundle but despite of this he has purchased the bundle which he had preferred. That is why all the bundles which are coming in this shaded area it is not necessary there are many other bundles that can be used. We will say that they are worse as compared to this bundle that was just he purchased. So this is what we will call all the bundles which he has rejected and this is his preferred or selected bundle. For this he has made his choice through his purchase through his selection. So here we call it express without any price or income or any other data through the purchase combinations of the consumer the behavior of the consumer. Thank you.