 We will study consumer preferences and properties of the feasible set under the chapter of consumer behavior. When we say the feasible set and the properties of the feasible set, we should keep in our focus that the main problem that is faced by a consumer is the optimization. It means the optimization of the resources to attain all the wishful list or we can say the multiple ends. So, the optimization problems, they have several constraints. They cannot be utilized by as such. So, whenever there are the several constraints, we are having various linear inequalities and these linear inequalities, they are solved via certain available set. That solution set that is available with the consumer that is called the feasible set for the consumer. This consumer's feasible set has a number of the properties that are various relevant issues for the analysis of the optimal consumption decision. These properties, they are actually the essence of the feasible set that makes possible the solution of the consumption decision or even the same it can be utilized by a producer during the decision of the production. Now, coming to the properties we are having in our hand, the main four properties are of a feasible set. One, the non-emptiness, second, closeness, third, boundedness and fourth, convexity. Now, we will discuss these properties one by one. When we say non-emptiness as it is very much clear by the name, it means that set of the feasible properties it should not be empty. It means there should be certain thing in our set. And in other words, we say that as we read earlier that there is an empty set and a set in which there is a unit available. So, the basic property of the feasible set is that it should not be empty. Either any one solution or any one element that should be available, then we will say otherwise there can be more than one solution that can be more than one opportunities but being available of only one it will make it a non-empty. Coming to the second that is the boundedness. As the topic tells us the boundedness means that this feasible set will have certain boundaries or it will have certain two points or the edges. So, we can say that this feasible set will have two boundaries. On the one hand, we will say that there will be a lower boundary of this feasible set and on the other hand, there will be a upper boundary. The limit of the lower boundary if we say it, then it should be non-negative. It means, first we said that non-negative means it should not be empty. And when we say non-negative, then if we always say above non-negative, then we say it is zero. But when we see it, then the price in the market is not zero. So, it means it will start with any positive integer and that integer can be a very small number, no issue. And likewise this the upper limit will be there, but there will not be the infinity. So, it will be a finite case starting from a very small number to any large number. But that will be the bounded property of the feasible set. When we come to the third property that is closeness, this is called a set will be closed. If all the points on the boundaries and the other points available in the set, they all are included as the elements of the set. So, if any point that lies on the boundary of the feasible set that will not be excluded, rather it will be included in the feasible set, then we will say the feasible set is totally closed. Because the available points on the boundaries, they are very much important for our decision making because they make possible the process of optimization and it may make possible when the constraints they are very tight and when the constraints are very limited particularly. And even if we consider even in future we will study the corner solution, then we consider this that even sometimes the consumption decision or the optimization even it is possible a very corner type of the point. Now, coming to the convexity, so when we say convexity, it means any set of the point it will be convex. When the pair of the points available on that plane or that curve or that line that can be joined from one line to the other and it joins in that manner that all the other points available in that set they comes within that set. So, means when any point it will not be excludable, so it means that set will be convex. And when all the points they will be covered within those points that we have joined on that plane, that set will be called convex and that is the main property of a feasible set. So, considering the various effects of the changes in M means money income and the prices on the feasible set because the feasible set is available related to opportunities and any consumer when it has various opportunities in hand it is related to the money that is within the pocket of a consumer and the other limiting factor that is the prices of the commodity. So, when the price will change, consumer will respond through the change in the quantity or due to the change in the consumption bundle. So, various combinations that a consumer will make in response to change in income or in response to change in prices these are combinations of the goods or the bundle they will be the available opportunities to the consumer. So, if income will increase or decrease or if price will increase or decrease consumer feasible set may change either it will expand or either it will reduce. In the slide we can view there are the three cases pertaining to the feasible set. In the case A we can see that there are the two prices and there is the income M and we can say that the price P1 remains the same of the commodity at x axis price P2 remains same in the both lines at the y axis but the only change that is evident that is M naught that is the original income and that has shift to M1 and when the income increases from M naught to M1 so that is the case of increase in income. We see that the feasible set it moves to the right and it is the case of expansion in the feasible set likewise there is an other feasible set option when income remains the same but now the price has changed and in this case the price of the commodity at x axis and that is x1 that changes and that changes in the form that it shifts our cut point or the axis from here to inside it means when our numerator that is M naught it remains the same but our denominator has changed from P1 to P1 prime it means the commodity price has increased so this increase in the price of x1 shifts the feasible set from here to inside but the price of commodity at y axis means x2 price remains same now there is another case when the price of the commodity x1 and the price of the commodity x2 both changes and they change in the manner that now the total feasible set it shifts from this point to inside when we compare this case T with the case B we can see that it is the case of gift of budget constraint or our constraint set or the feasible set and this is not the case of shifting rather it is the case in which only one point has moved so it will not be the case of total shifting likewise this there can be an other case when the price of the both commodities it decreases so if it will be the case we can draw here that if the price it will decrease in the both case and it can move towards right side so it will be the case of expansion of the feasible set and there can be another case when the increase in the prices of the commodity that is in one direction means either it is decreasing but not decreasing with the same context or the same magnitude so then we can say have this feasible set and now the price of the two has decreased but with different percentage so we can have like this or at the same time we can have like this when y will be shifting more and x will be shifting less so these can be a various set of the opportunities that we can draw keeping in view the information provided to us Thanks