 And we are going to study the indifference curve of the consumer when the goods are perfect substitutes. As the nature of the commodities can be different, mean goods can be complement to each other, goods can be perfect substitute to each other or goods can be limited substitute to each other. Keeping in view this nature, we can derive various types of the indifference curve when the consumer is having a decision of consumption. So if there is a case when consumer has to decide the consumption and among that bundles, he is having one combination of the goods X1 and X2 but when X1 and X2 both are perfect substitutes to each other. Now here comes the question that what will be the property of these commodities or in other words if we say, what will be the features because of which we say that these two commodities are perfect substitutes to each other. If we say that if a consumer leaves one commodity and wants to take another commodity but at the same rate, so he means these two will be perfect substitutes to each other and if the consumer wants to decide between one to one and if in the other form we say that when both commodities have mostly features so common that they both are indistinguishable so we say that they both are perfect substitutes to each other and in fact many times this can also happen that some of their features are not helping to identify them but utility is the same. So if we say in the example form that if a consumer has a blue pen and a yellow pen and wants to make a difference then actually all the utility that is taking it, writing, its feature, its design means the only difference is the color so they are both perfect substitutes to each other. If there are two pens then they will also be substitutes so likewise a lot of things can be done that are totally identical but near to each other so we keep these features as perfect substitutes and some of them will be exactly the same. Now if we look at this situation then it means that the commodities whose purpose of usage will be the same then they will be perfect substitutes and since their purpose of usage will be the same then almost their prices in the market can be 100% but almost they should be the same and the maximum important feature if we say is that between these two units the substitution is infinity because it is not limited meaning with every type of mean if it has 100 units then the other commodity also with 100 units and the infinity level of substitution can be substituted. And between these two if the trade-off is because of the price difference then if there is a change in the price then if there is an increase in the price then the consumer can shift to another immediately. So any price decrease or any price increase among the perfect substitutes is the rate of substitution between these two is very big and very valid. Similarly if we see that when we have to draw the indifference curve then the example we had said that if there is a combination in two combinations in which red and blue pencils come and if we say that it is taking 10 units of blue and it is taking 10 units of red pencils and this is its one bundle and because the total after that is 20 pencils in this combination. Now similarly if we say that it has to be made into a third bundle in which it has 5 pencils of red and 15 of blue or 15 of red and 5 of blue then the consumer will have no difference because it should have a total number of pencils of 20. So in this condition the indifference curve of consumers in any form then it is switching from 5 to 5 and it is switching from 10 to 10 so in this condition we say that its rate of change is constant and we explain it from minus 1. And therefore in this form we say that the indifference curve of the consumer will always come in the form of a straight line. Now if we see in this diagram then we have shown that indifference curve is here and commodity X2 is here and now these are various type of the indifference curve of the consumer in which they are moving from this indifference curve sorry to draw if it is not straight and if this is its next indifference curve when it can be in the form of a single level price change or in the form of income it can be in the form of a straight line but straight line does not mean that its slope will remain the same way we can draw one another in which we can say that the indifference curve of a steeper level can be in this form also and in the same way in the form of indifference curve if we check its slope straight line then if it is ratio it is giving 2 by 1 then it means it can be 2 and in the same way we can also have a flatter form and we can also see the rate of change so if we see in this then it can be 2 by 1 divided by 2 which means 0.5 so it can be 0.5, it can be 2, it can be 1 whatever the factor it is but when we have its rate we can say it is the perfect substitute to each other so like this, if we say this bundle of pencils in the same way then we said that its preference went to the right side and in the same way if we reduce any of its bundles then we can explain its preference in the same way but whatever the perfect substitute they will always be straight line for the consumer having constant rate of substitution throughout the indifference curve thank you