 And we are going to study what will be the shape of indifference curve if the consumer is having a bundle of the goods which are complement to each other. Before going to decide the shape of indifference curve, we should know that what are the attributes or the features that make certain commodities complement to each other. Two commodities will be complement to each other if the both commodities they are quite distinguishable to each other. It means one commodity has different utility as compared to the other but the consumer is going to utilize always them in a particular proportion and in a particular combination. So consumer will utilize them number one in the form of a combination and number two the proportion by which the two commodities will be utilized that will remain constant throughout its utilization. And number third, these two commodities they will be having the utility always when it is in the form of combination means their single utility and the other whatever it will be but for consumer their maximum utility is in the form of the combination. So if these properties are followed by the commodities they will be complement to each other. So the fixed proportion between two and number two the complement to each other whenever they are utilized they will make the completion to each other. So the process of utility they will meet in the form that if pen we have to utilize would require the pen ink. So it cannot be utilized separately so they will complement to each other and the elasticity of substitution between two is never possible. So keeping in view because they both are not having the same utility they both are not having the same features they both are not having the homogeneous features so we cannot say that they both are indistinguishable rather they both are very different it is like this that we are going to utilize that one vehicle cannot be utilized without the fuel. So the features of vehicle is different and the features of the fuel is different but whenever we have to utilize in collective because consumer is going to derive the utility from their both combination to travel. So travel is not possible until and unless the vehicle is having fuel or if I say consumption it is just like this that you are going to ask your mother at the breakfast that to give you two slices of bread with one egg so this will make one complete breakfast. So any type of the combination that we are going to utilize that will be complement but when we say the perfect complement it means they both will be might be identical in nature and they both are identical in nature means now they both are not indistinguishable but they are identical but they will be complement to each other so and here the example will be the best example will be a pair of shoe in which the right shoe is the complement of the left shoe with the only difference that their shape will be somewhat different and we can distinguish them with the right and left features. And any price difference either it is going to affect the price of X1 either it is going to affect the price of X2 but this will not affect the total bundle because the total bundle will only be purchased up to a similar that level where it can be utilized in combination so its combination will be affected only and only when the prices of the both goods will be utilized if the price of one good will be increased we have to decrease the total bundle not only the one so the choice between any two we will make from this example we can say so if anybody if has to increase just the right shoes so to complete the total pair he or the she has to purchase also the right part of the shoe so complement will go always in the same proportion so keeping in view this shape we can say the utility derived from the combination of these two goods is possible only at the vertex where the both they are combined and either utility is decreased either utility is going to increase so the in difference curve they will move only along the vertex so if I am going to make various combination here we can say that there are the various combination of this thing that this is on Y axis one commodity that was the left shoe and on X axis the other commodity that is the right shoe and if any consumer has to utilize one pair it will make at this point so if on right side we say that the right shoes they are going to increase like at this point this change will be of no use to the consumer until and unless he is provided with the same number of the left shoes and when these will be provided they both will be making the consumer to shift from this point to this point so this is the combination that makes the consumer at the higher level so this in difference point will be less and this B will be of higher level so like this the C will be of higher level but only utilization or the possibility of working is at the vertex likewise if I make an other example so here we can say there is any other combination of the goods so now there are the three combinations one combination when we are going to say mean four and four if X1 is utilized in the form of four and X2 is also utilized in the form of four so this is one combination and if this is the combination so consumer will move whatever like this to this so means all the combination will move to the right of and now if the combination is like this that 8 units of X and 4 units of X2 it means either this combination so we can say consumer is at this point so if it is like this so consumer is making this combination so if this is the combination consumer whenever has to be going on the higher level he again will maintain the combination like this now this will be his shape and this will be the straight line and if there is the third combination in which consumer is having X1 in the form of four and X2 in the form of eight we can say now the consumer is having this much level and if consumer is having to increase its consumption he will increase again in the form of the straight line and now he will again move on like this so if we will join these points this again can be in the form of the straight line it means for the complements consumer will always have in difference curves in the form of the L shape and either consumption is going to decrease or increase consumer has to move in the form of the straight line that is going to join the vertex of the indifference curve and this behaviour of the consumer will remain same whatever the commodities he is going to utilize but if these commodities they are complement and the perfect complement to each other thank you