 In this module, we are going to study the assumption of consumer preference ordering under the title of the feasible set. Feasible set is basically that the conditions or the restrictions, or in other words, these are the viable options or the opportunities that are available with the consumer to achieve its objective function. So if we say this on one side, there are restrictions as well. On the other side, we have available options that our consumer decides that his objective function might be utility maximization, it might be cost minimization, the viable option that he will utilize to achieve it is his feasible set or the available it. So if we look at the combination of possible solutions, the combination of all the available possible solutions is basically the feasible set. And this is the feasible set that he wants or desires to meet. And if we look at this, this is the limit of his values that a consumer cannot further move beyond. So feasible set, it can be explained by any linear inequality. And this linear equality, in which form, if we explain it, any linear inequality of this form. Now if we look at this, this form plus this form, it should be greater than B. Or we say that this plus this is greater or equal to B. And in this way, if we say that a naught x plus a1y is less than B. And in this form, if we say that less than or equal to B, then this will be our constraint. Now if we look at this, I haven't used any generalized notation yet. Likewise, it can be a naught is expressing the price of commodity x1. And in this form, if we put it, then it will be our condition that price of x into x plus a1, if we say that this is price of y. So this will be our thing, price of y into y and must be equal to B. And here now the B is that parameter of the restrictions. And in the same way, if we do, then this is Px into x plus Py into y, either greater or equal to B. So B is that budget. So expenditure either it should be like this or here or it should be less or like this. So if we talk about the price or budget in this form, then it cannot be greater. So in the mathematical form, our equations can be constrained, this can be and this can be. Because it is possible that on the place of its budget, we have to take it in the form of minimization or utility. That is why if we say, then we did not solve it from this notation here. Because if we take the form of the budget or the quantities of its commodity, which are satisfying, then we will basically take our objective function for those commodities. So we will make a constraint for that. So mathematically, these functions and any other form that comes in this form is called our constraint. So if we see this here, then basically A naught is constant. Similarly, our A1 is constant and B is constant here. Now if we take an example of this in this form, we have two commodities. And if we look at those two commodities, then we have the price of those two goods available. Now if we plot it, then when price of X into commodity quantity plus price of Y into its commodity, then our total, either it should be less or equal to the total money or the income of the consumer is in this form. And if we say suppose it is equal, then this P S of X into X and P Y into Y is equal to M. And at any point when we say that we are consuming all the budget on the consumption of X and Y is given 0, so price of X X is equal to M and X is equal to M by price of X. So this is the point that has been calculated on which we purchase all the income or the budget on the X commodity and similarly if we total utilize M in this form for either Y or X2, then we have this commodity. So when we joined these two extreme points, then this line that gave us the complete area, if we look at this in one form, then this is the constraint that we have. The constraint in the form that we cannot go beyond this. This right side of this is for us. In one way, it is for M. We are not possible there because it is beyond our income or budget. And the internal these all the options available, we have all available viable options. In which the consumer's budget, if it is at the optimal point, then it is possible. And even in it, because we look at the available options of all the different curves, then it can attain all of them. So it takes all the viable options and optimally it can also attain that curve. With which the feasible set is tangent. So if we look at it in its first condition, then the budget should be either expenditure less or equal. And if we look at it in the same form, then if we are coming here while solving that point, then if we had already assumed that we would take two goods cases, or instead of two goods, if we take one good which we have to keep in front or which we have to look at from the NEL, then we have taken it, suppose this form has taken x2. So the second good, we will call it all other goods. So all other goods, if we look at it in the rule, then we have purchased either x2. And except for x2, now the rest of the budget is m, money, minus. If we look at it, if I solve this, then we have it in this form, a price of 1x1 plus p2x2 like this m. And from here, now this form, when it goes here and we do minus from both sides, m minus p1x1. Now it has been cut from here. So here we have p2x2 like this m minus p1x1. And now from here, when we have to move p and take it there, then we have divided it. So x2 has been left and m minus p1x1 divided by p2. So commodity x2 expenditure and the remaining that part that is consumed on purchasing of all other goods other than x2. So it has come to us in this form. And similarly, if we have more than one bundle of goods, then if we assume that we have this from 1 to n. So for analysis, because we can count only one change at a time. And in the form of Marshallian approach, if we say that keeping all other things constant, we will apply the rule of Satras Paribas. So while looking at one change, at that time we keep all the other amounts constant. So if we take x2, then that will be greater than. And now since it is equality, then we have converted to it. And we said that if we take it for x1, then we took it for x2. Now if we take it for x1, then we put it for x1. So we took all other things on this side. Now in this form, if we look at the slope of the budget line, which we previously calculated, then on this slope, if we look at the change on the x-axis of y, then the change on the y-axis, now if we look at it, it is 0 to m by p2. So if I show this change, then we will say that will be m divided by p2. And on the x-axis, this is 0 to m by p1. So this is divided by m by p1. So m by p2 multiplied by... We converted it to m. So this slope of the budget line, now we have p1 by p2. Now in other words, if we say that we have slope of the budget line, it will always be the inverse of price ratio. And if we look at this, then we have minus p1 and p2. And again, this minus sign expresses its negative slope. Thank you.