 The principle of revealed preference under the chapter of consumer behavior, as we have already studied in the previous module, the revealed preference of the consumer, but this revealed preference should have certain postulates or the assumption to study. So, any economic theory which is understanding the behavior of the consumer and its choices and its likes and dislikes should be discussed just by observing, i.e. by looking at the pattern of its purchase and consumption. So, we will say that whatever decision is being made in the market, while looking at it, that will be the revealed preference. Here, if we say that this theory is very much relevant and important with the perspective of the producers or the marketing companies, whose purchases and consumption actually observe decisions and decide their production, packaging, pricing and different units. So, this theory is very much important for them. Now, if we look at the principles and assumptions of this theory, then the basic thing we will have to see is that actually it is related to a person, either he, she, any younger, any older, whatever, who is going to the market and buying the shares, then they decide between two bundles. Although, he may have one, two, three, ten bundles, but in that particular time frame, in that one moment, what is its decision, it is after two bundles. And if we say about these two combinations, the bundle which he is purchasing, it may be a little expensive compared to the other bundles, but if he is purchasing it, then for this, what is his choice, we will say that will be revealed preference or the choice which he has expressed. Now, if we go into his assumptions, then it is simple, there should be two bundles. And during this time frame, when we look at those two, for a long time, or some time, or one day, or an hour, it should be expensive, it should not be a change. In one bundle, the shares and in the other bundles, both are expensive. The analysis in front of him, in front of him, his value is not changing, nor is his income changing. So, the two factors which we will say the most are the prices of goods, of all the goods that are available in the both combinations. And the income of the consumer. The third thing which we see is that his preference should also be constant. The choice of the consumer means that his previous purchase, which he bought yesterday, which he bought two days ago, or four days ago, his preferences should be the same. The third thing, with his preference being consistent, his taste should also be the same. And for an analysis of consumption, whenever the consumer is making a decision, we assume that he makes a rational decision. And the rest of the analysis of the shares, the bundles that he is purchasing in the market, he makes an estimate of his value, he studies the different attributes of his. And all of these assumptions are of a large size. If we look at the basis of these assumptions, the theory of wheeled preference, which is his strength, the strongest point is that this economics, the environment, which gives an important thing, that we can decide about any consumption, or about the bundles of production, or about the preferences of individuals, without knowing the details of them, without asking them further, or without surveying them, he only purchases them. But the biggest weakness that comes to us in this, is that we assume that we have done all the information information, which is not possible many times. And the second thing for us is that consumers, the tastes and preferences, are being changed very quickly in the digital world today. So it is possible that the preference, which was two days before the consumer, when it came today, might be due to certain marketing strategies, or might be due to certain other information, which he has achieved in these two days, his preferences have changed. Or it is possible that his own related means, which he did not know before, or of any disease, which he wanted to share, these are the related events, which can affect his taste and preferences. Now, if we look at this graph, what we are showing now, it is slightly different from the previous one, and the title is telling us that, previously it was revealed preference, but now we are saying that it is the indirect revealed preference. Here if we look at it, it means that, there is a translation, which was shown by the consumer, between two bundles. But in this diagram, if we look at it, we are talking about three bundles, means that is one combination, that is second combination, and in the same way, there is a third combination, which is also present in it. Now, if we are looking at it, we will see that, available budget line and combination is present, which we are looking at on this line, that while this budget line was present, he gave preference for this bundle, whenever the bundle Y was also its approach, its affordability and its range. So, this bundle X1, X2, we are saying that is directly revealed to the bundle Y1 and Y2. Now, if we look at it here, while looking at the budget line or another situation, we see that the bundle Y1 and Y2, is its preference on Z1, Z2 bundle and this preference the consumer may have expressed at some other time. Now, if he has shown his this preference then we can say here that at this time the combination of the consumer is not of X and Z, it is of X and Y, but keeping in view the previous information or the consumption pattern or the preference, we can say that now, the situation of the consumer in which he has shown his preference and when we said that his bundle Y1 and Y2 is his already preferred bundle Z1 and Z2. Now, from here indirectly we can assume that bundle X1, X2 is directly revealed but indirectly revealed, it is preferred revealed on that bundle which he has not bought and may be available to him. Now, if we look at this theory then it is basically consumption and preference of some properties of the theory. Now, if we look at this then we have decided that the consumption expenditure on bundle X is equal to income and expenditure on Y is also equal to income or less or at least equal to that. So, if we look like this then it fulfills the theorem of our budget constraint. Now, this means that X is preferred on Y and if we look at that form then our bundle here is preferred on Y and if we look at it then the theory of transitivity says that if A is preferred to B or B is preferred to C then A will be indirectly or directly preferred to C condition so keeping in view this theory of transitivity or the principle of transitivity we say that bundle X1 is indirectly revealed to the bundle C. Now, if we look at these three conditions then this is not directly but indirectly revealed or it will be preferred to Zahid. Thank you.