 Income consumption curve and the angel curve. Any curve that expresses the locus of the points that joins the various optimal choice bundle of the consumer that will be called the income consumption curve. And in other manner we can say that when the consumer income it increases consumer it expands its consumption. So, when we take one optimal choice on one income and then again the other optimal bundle on the next budget line and then the third optimal choice point on the third budget line with the increase in the income and we join this then we will draw a curve that will call the income consumption curve. And this income consumption curve as it express the expansion of the commodities consumption with respect to income. So, it is also called the income offer curve or the income expansion path. If we draw the diagram we see that there are the various level of the indifference curve and when one budget line optimal choice bundle is having one this point A with the increase in income there can be this optimal point B. And if I draw one and other income line here so with the shift with increase in income to the right side there can be one and other optimal bundle C here and if we join these optimal choice bundle with a line or the graph this will be called the income offer curve. But in the previous as we see that we have shown two commodities one on x-axis and the other on the y-axis one on x-axis and the other on y-axis but when we see the behavior of one commodity with respect to income so the income will be on vertical axis and now the commodity will be on the x-axis or we can say the other commodity if we have to study the behavior of x2 that will also be plotted on the x2. So the relationship of single commodity with the change in the income when we study we will come to a graph that will call the angel curve. Actually this was the behavior that was studied by the economist named angel when he was studying the various consumption behavior of the people and he saw that the people they are actually allocating a very limited amount of their income on the food consumption despite of the fact that their income is going to increase and increase but they are not going to increase their consumption for the food. So he plotted this consumption and then he came up with the curve that was called the angel curve means how a particle commodity will respond to the change in the income. So with this concept of the angel curve now we can explain various commodities that which commodity will respond to the change in income in which manner. When we take a example of the bundle then one we say that these commodities they are perfect substitutes. So the perfect substitute it means we can substitute x1 with the x2 in any shape but if there is a situation when commodity x1 is cheaper then the x2 definitely the consumer will spend more on the x1. If now the consumer income will increase it will increase but the consumer is having already a preference. So consumer will allocate more and more only on the previously preferred bundle of the x1 and when we explain this on the diagram we see that the consumer is having a corner solution and in this way these are the various different bundles of the income that was available to him and the consumer's optimal choice we see that consumer was having already one optimal choice on x axis the second will always again on the x axis and the third like this and when we join these points of the optimal choice bundle we come up with a straight line and when we draw now the behavior of the commodity x1 with the income we will have one increasing curve but with the straight line now we take the example of the complements if consumer is having a bundle of the commodities which are complement to each other that means consumer will utilize the both commodities only in the fixed proportion so the commodity that he is having on x axis if its income of the consumer has increased now we can say that the consumer is having with the increased change in the income various bundles like this that one optimal choice bundle is here and the other optimal choice bundle is here and this optimal choice bundle is here so if we join these bundles we can have income consumption curve in the straight line and if we plot now the curve of that commodities again we will have a straight line if now we take the example of the inferior good there will be something different because the inferior goods now the consumer it will shift the demand for the commodity for which he is treating that commodity as the inferior so with the increase in income from here to right side from budget line 1 to budget line 2 now the consumer rather than increasing his consumption he is going to reduce and if we join these two points like this we are having income consumption curve that is upward but backward bending and in this way we can draw that if commodity X2 is treated as inferior the consumer will have the backward bending curve towards X2 but if X1 will be treated as inferior then the consumer will have the income consumption curve like this so backward bending angel curve will be there if a good can be normal over some range and at the same time there is a possibility that commodity it may have different type of the behavior at different time so any commodity that may have the behavior up to a range as a normal and after that point it may be treated as inferior when we take the example of this we see that there are the various income bundles and we are having various optimal point like this this is point A, this is point B and this is point T and with the increase in income we are having more of these commodities but we see that in this manner that consumer has first increased up to this and then decreased the utilization of the commodity X2 that is very much explained here so consumer has behaved in the manner that he treated commodity X2 as normal good up to this range and from the U2 level to U3 or in difference curve level 2 to in difference curve 3 he treated the commodity as the inferior so this income demand analysis provides us various type of the solutions to deal with the nature of the commodities and to decide that which commodity will be treated by the consumer as inferior or for which the consumer will allocate more with the increase in income or with the decrease in income