 In this module, we are going to study under the topic of consumer behavior, assumptions of consumer preference ordering and the one assumption that we will study that is the strict convexity. Convexity property of a set or of a function that describes the curvature or curvature is shape. So, if we have to look at the shape of any curve, then the property through which we will check it, that will be the other shape function, so we will call it convexity. So, the actual shape of the curve of consumer preference is the strict convexity assumption that is very important. So, similarly if we say that if any curve which is inverted or left-banded, then that curve will always be called our convexity. And if we look in the other form, if we can join any two points together and after joining, all the points present in the curve will be present on the left of the line, so that form or curve will be called convexity. Now, if we talk about the strictness in front of its examples, that if we draw a curve in this form, then it is basically our inverted or left-banded curve. And if we draw these two points on it, if I draw two points from a line somewhere, then if we see that all the points of the curve will be available on the left of the line, then this curve will be called convexity. And in order to be convex, if we look at it, then what are its assumptions? Any curve cannot be convex till it is not able to slope in this way. Because if it is not slope, then we have a straight line. So, slope is actually rate of change. So, the slope being present for us, again the rule of calculus is very important. Because otherwise, if we look at it, then we will look at a point over the contouring. So, it will be our minimum and maximum point. But when we solve the condition of the second derivative case, that is typically that curvature. And similarly, if we say that its slope will not be convex and it is a straight line, then if we talk about this straight line, then if we draw any of our indifference curves on this straight line, then it means that the substitution between them will be a perfect substitution. And if it is a perfect substitution, then it can be one case. It is not possible in life that any of the two commodities can be so identically perfect substitutes for each other. And similarly, we can say that if we want to look at the rule of convexity, then there will be an underlying assumption for it that the consumer should explain his preference through very well balanced or well behaved curves. And if we look at the well behaved curve, then its property is this. So, it expresses the very small changes in smooth form through very well balanced. And in that, the point of optimal choice is unique and it is single. It does not have two or three points. And since the budget line, mostly if we look at it, then our budget line is always coming in front of us in the future. And the reason for that is that the market prices, the consumer cannot change them. They take the price for that. So, since the prices are straight lines of the market and based on that, we draw the two points of the budget. So, we join the two extreme points with straight lines. So, the property of the market is helpful in solving the tendency. Otherwise, if we look at it, then if we have a budget line that is also in the form of a straight line and our consumption line is also in the form of a straight line, then these two lines will mostly coincide with each other. So, it is impossible for us to optimize on a single point. Now, if we go into the form of its example, then in this drawing, we have explained one commodity on X axis, which is our commodity X1. And in the same way, we have shown another commodity X2 on Y. Or, if I say in another word, like we have taken previous examples, we say that we have taken apple on this side and we have taken banana on this side. Or, if we want to keep someone else, we say that we have a book on this side and we have taken food along with the book on this side. So, we keep two commodities of any form. And the various combinations of these products that are available to us, now we will explain them. From this point, we can see that we have various combinations on this point. But we have shown only this point and this point for the time being. Otherwise, we can see a lot of points between these two. Now, if we have joined these two points, then this straight line and again the bundles of our consumption are shown on the left side of the straight line. So, it means our convex curve is showing that property. And this shows us that its rate of change from this to this. This can be explained from its slope. And that is why, if we look at it, this is expressed in the form of this convexity. And the better set, now if we say better set, or the property that we had in the first assumption that the one that is in the wishful thinking or the property of non-satiation will come in front of us. For the future or the wished property, the bundle is present on the right which it has to approach now. And this will be on the left which is being attained below the convex line. Now, the budget line that we have here, because we have drawn the hypothetical that if I say this point as my equilibrium point on this point, the budget line is crossing from here. So, actually because this straight line budget is tangent at this point, then the tendency is possible due to the convex nature of this curve. Otherwise, if we look at this budget line, it can also cross from here. And this below curve can also cross from here. But at this point, the slope of the budget line will equate with the slope of the consumption function and equate with the point of the tendency. And the point of the tendency is clear because of this convex curve's property. Similarly, if we have a curve that is present which is not in a strict convex form, rather it is in a weaker convex form, then if we look at that curve, then we have it in this shape. Overall, its shape is a little bit convex, but at this point or the other side, if we look at this point, then it should have come in this way while showing the actual convexity. And if we look at this point in the same way, then it should have gone in this form. But between those two points, it is showing a straight line from here. And this straight line means that at this point, if there is an amount of x2 and its amount is at this point, and if we draw x1 perpendicularly, then it will give us the shape of a perfect substitution. And from this point to this point. So this shape is not a strict convex form, rather it will show a weaker convex form. So those segments, during this part, there is a substitution, but at this point, it will be showing a perfect substitution. And during this part, when it is showing, it will be showing a perfect substitution. And otherwise, the curve of a strict convex form, if we make it, then it will, when it is in this form, then if we look at it, then it will be showing a perfect substitution. It will show a limited substitution, in which the possibilities on very small points are all showing.