 Then, we will take a numerical example that how this total utility, marginal utility they are related. So, in the first column we have Q, in the second column we have total utility Q is the total product that is getting consumed, second column this is total utility, third column we have the marginal utility. Total utility in general increases with Q. So, if you look at from unit 1 to unit 4, the total utility is increasing. At some point total utility can start falling with the Q. So, if you look at from Q from 6, total utility is decreasing between fourth unit and fifth unit total utility is constant. Marginal utility is if you look at its goes on decreasing from the beginning. If total utility is increasing, marginal utility is always greater than 0 that is evident in the fifth unit because total utility is increasing and marginal utility is greater than 0. When total utility is maximum beyond this the marginal utility is 0 and the negative. So, from Q is equal to 1 onwards, marginal utility is declined which follow the principle of diminishing marginal utility as more and more of a good or consume the process of consumption will at least at the same point yield the smaller and smaller addition to utility. So, if you look at between after consuming the first unit thus in the second unit the additional utility is just 7 units that is marginal utility. When it comes to third unit again the marginal utility is 5, when it comes to fourth unit marginal utility is 3, when it comes to fifth unit marginal utility has become 0 and in case of sixth and seventh unit there is negative marginal utility. It means when you are consuming more and more you are getting a negative utility which leads to negative marginal utility. And this is the evidence of law of diminishing marginal utility initially when total utility increases marginal utility decreases, when total utility is maximum marginal utility is 0 and when total utility is decreasing marginal utility goes to the negative segment and the consumer get a negative marginal utility from it. Then we will come to the ordinal utility analysis and this ordinal utility analysis is through the indifference curve and the basis of ordinal utility analysis is that the consumer is not assigning any utils rather they are ranking on the basis of their preferences. So, indifference curve analysis is part of the ordinal utility analysis and what is indifference curve analysis? Indifference curve is one it is the locus of points of different combination of goods which gives the equal level of satisfaction to the consumer. So, whatever the combination between two goods it gives the equal level of satisfaction to the consumer. So, it is a technique how choices between two alternatives are made because it gives a exposure to the different combination what the consumer can consume. So, it is a locus of point representing different bundle of goods each of which yield the same level of the total utility. So, it defines the combination between two or more good that gives the consumer the same level of satisfaction and it is negatively slope and convex. Let us take an example of indifference curve or how we can draw the indifference curve. So, we are saying these are two goods suppose consider X and Y, X is food and Y is clothing. So, there are different consumption basket which gives different combination of food and the clothing. So, suppose we consider this as the market basket or consumption basket. We take the good one is food second one is clothing then A, B, D, E, G and H what are these A, B, D, E and G, H these are the different consumption basket which consist of different combination of food and clothing. So, O has 20 A has 20 unit of food and 30 unit of clothing B is 10 unit of food and 50 unit of clothing, D is 40 unit of food and 20 unit of clothing and E is 30 unit of food 40 unit of clothing, G is 10 unit of food and 20 unit of clothing food and 20 unit of clothing and H each 10 unit of food and 40 unit of clothing. Now, let us see how when we put it in a graph how it looks like or how we can draw in difference curve. So, basically this is a market basket which consists of both the goods and what are the two goods here food and clothing. So, if you are picking up A it gives one combination of food and clothing, if you are picking up B it gives another combination of food and clothing, if it is E or G it gives an again another combination of food and clothing. The consumer can take a decision whether they have to consume the basket A, whether they have to consume the basket C or whether they have to consume the basket H, it depends on their preference that what how much quantity of food they require and how much quantity of clothing they require and it always different for the different consumption because different consumer because their consumption needs are different. So, let us graphically see how this how we can plot this in difference curve with the help of different combination of two goods and the of the help of the different consumption basket. So, suppose we can take food here in X axis clothing here in the Y axis we will take 10, 20, 30 and 40 here also we can take 10, 20, 30, 40 and 50. So, combination say A is 20 unit of food and 30 unit of clothing, combination A, combination B say 10 unit of food and 50 unit of clothing, combination D say 40 unit of food and 20 unit of clothing, combination E says 30 unit of food and 40 unit of clothing, combination G say 10 unit of food and 20 unit of clothing and combination H say 10 unit of food and 40 unit of clothing. So, if you look at then here we have 5 different combination A to H. So, if you consider this as the two kind of box in this segment A will be more prefer if someone is at the point of G because A gives us more of goods and more of both the goods food and clothing. But, if someone in the segment E they will always prefer E rather than A because E gives us a better quantity of both the goods and services. So, if you join now point B, point A and point D this is one indifference curve. Now, what is the basis of this indifference curve? Any combination G and H they will prefer G and H than A any consumer if they are between G and H. Any combination between E and above if you are any other combination they will prefer not A rather than the other combination because that gives more quantity of both the goods. So, between this three point now B and A and D the consumer will remain indifferent because even if at this point B the consumer is consuming more of clothes and less of food. In case of D the consumer is again consuming more of food and less of clothing and between and this combination A the consumer is consuming moderate amount of both food and clothing. So, this is 20 30 this is 10 50 and this is 40 and 20. So, between this three combination the consumer will remain indifferent whether it is point B, point A and point D whatever the combination between food and clothing whether it is 10 50, 20 30 or 40 20 the consumer gets the same level of satisfaction. So, E 1 is known as the indifference curve which gives the same level of satisfaction irrespective of the whatever the quantity of food and the clothing. So, that goes with our basic philosophy of the indifference curve the locus of different points which gives the equal level of satisfaction and what are the locus of different points and what are the different points implies the different points imply different combination of goods and services. So, in this case there are two goods food and clothing and if you look at in the indifference curve we got three points which gives three different quantity combination of food and clothing, but it is at the end it gives the same level of satisfaction the consumer. The consumer can remain indifferent between point B point A and point D and that is the known that is the reason it is known as the indifference curve because indifference curve is generally in the consumer generally the consumer is remain indifferent between all this point in the indifference curve because irrespective of the combination they are getting the same level of satisfaction. Now, we will say what are the different properties of the indifference curve? The first property of the indifference curve is that it will be downward sloping. Now, why it should be downward sloping? If they slope upward they would violate the assumption that more is referred to less. Now, if you are saying that this is the indifference curve suppose here it is x here it is y each point of the indifference curve gives a different combination of two goods x 1 suppose this is y 2 this is y 3. So, this is point A this is point B this is point C by the indifference curve is negatively slope the slope has to negative because at any point of time if the consumer is moving from point A to point B he is consuming more of x and less of y. So, this more of x is by sacrificing some amount of y here. Similarly, for if the consumer is moving from point B to C he is consuming more of x and this more of x by sacrificing some amount of y. If the consumer has to be at the same indifference curve when they are consuming more of one commodity they have to reduce the consumption of the other commodity then only they can be indifference between different combination and that is the reason when they are consuming more they have to sacrifice some unit from the other goods. The indifference curve is negative slope and that is first property of the indifference curve that the indifference curve is downward sloping and if they are sloping upward if it is a positive slope then from one point to another point it is two different quantity and it gives a higher level of satisfaction and the consumer has not in between the indifferent between all this combination. Now, the second property is that indifference curve must be convex to the origin as more of one good is consumed the consumer would prefer to give a fewer unit of the second good to get additional unit of the first one as food become less scarce here she would give up less clothing for the additional food. So, if you are taking again take the example of the same graph initially in order to get this much amount of x the consumer was ready to sacrifice this much unit of y then to get more unit of x the consumer is satisfying the consumer is sacrificing some unit of y which is again less than the first one. It means when you are consuming more and more of x in exchange of y initially this del y is on a higher side, but when are going on consuming the same unit by sacrificing the other one then it slowly slowly this del y decreases and that is the reason the slope decreases and if you are taking the typical example of food and clothing again when the consumer has enough of food and still he is getting more food in exchange of clothing the trade the trade up between the trade up between the clothing and food and the whatever the amount of clothing he is going to sacrifice that will become less and less when he is going to consume more and more of the food. So, initially the consumer is ready to sacrifice more amount of the other good in order to get one additional unit of one of the good, but slowly slowly when he is going on consuming more of one good that takes less amount of sacrifice less amount from the other goods that is the reason the slope goes on on a the rate of change in the slope is decreasing and indifference curve is convex to origin. Then are two different two other properties of indifference curve the first one each two indifference curve cannot intersect each other. Now, if you take the example of two indifference curve why they cannot intersect each other suppose this is y this is this is y this is x this is our indifference curve one that is I c 1 and this is our indifference curve two I c 2. Now, why they cannot intersect each other point a corresponding to also I c 1 and corresponding to I c 2. So, suppose if you are taking a different point suppose b and c this is not following our the basic transitivity assumption that at any time of any point of time if a is preferred to b and a is preferred to c b also preferred to c. That is not going to happen because if a and b if you are considering under one indifference curve may be a is preferred to b, but in case similarly if a and c in the second indifference curve I c 2 a is preferred to c, but b cannot be preferred to c because c is lying on a lower indifference curve which gives less unit of combination of goods and services. That is the reason two indifference curve cannot intersect each other because the level of satisfaction between two points are different even if they are lying on the same indifference curve. So, that takes our third property of indifference curve that two indifference curve cannot intersect each other because it is pilot the basic assumption of the consumer theory. Then the fourth assumption is higher difference indifference curve gives a higher level of satisfaction. So, this we can explain through a indifference map which generally consists of different indifference curve of different quantity of goods x and y. So, to describe the preference of all combination of goods and services we have set a different indifference curve and indifference map and when there is a increase in the quantity of goods and goods and both the goods quantity x and y the indifference curve shift to the right. Let us see how through this indifference map we can prove our fourth property of indifference curve that is higher indifference curve gives a higher level of satisfaction. So, suppose let us find out first the indifference map we have I c 1, we have I c 2 and we have I c 3. Now, suppose we take a point here, point here and point here this is this gives us one combination, this gives us the second combination and this gives us the third combination. So, if you look at when you are moving from one indifference curve to another indifference curve it gives. So, suppose from point a to point b, point b consists of more of both x and y again between point b to c again it consists of more of x and more of y. So, if the consumer is taking a point in c taking the point c since it is consume more of both x and y it always gives us a high level of satisfaction as compared to point b and point a because when the consumer moves to a higher indifference curve it helps them to consume more of both the goods and services and that is the reason they are moving from when they are moving from one indifference curve to another indifference curve they are getting a higher level of satisfaction and that goes with your fourth property of indifference curve that higher indifference curve gives a higher level of satisfaction and lower indifference curve gives a lower level of satisfaction. Higher indifference curve consists of more of both the goods and lower indifference curve consists of less of both the goods. Then we will see what is the rate at which both the goods get substituted for one another. If you look at in the typical indifference curve we have said that when they they are consuming one more of one good they have to sacrifice some amount of the other. How this is possible or what is the rate at which the marginal rate of at which the both goods get substituted to each other and the rate at which one good can be substituted for another is the marginal rate of substitution and here the precondition is that we have to keep the utility level constant. So, the combination gets changed, but they have to in the same indifference curve because we have to keep the utility remain constant. Now, what is marginal rate of substitution? This is the rate at which one good get substituted for another goods while keeping the utility level remain constant. It is the negative of the slope of the indifference curve it diminishes along the indifference curve as x increases and y decreases and this is the ratio of marginal utility of goods and services. So, marginal rate of substitution is the change in the y with respect to change in the x and this can be also considered as the marginal utility of x and y. The marginal rate of substitution diminishes along the indifference curve as one consumes more of good x, they will be less willing to give up more of move of good y and the relative price of good y increases and that is the reason the indifference curve is generally convex to origin because the marginal rate of substitution of the generally the slope that diminishes along the indifference curve. So, this is the numerical example that why the how the marginal revenue generally decreases when you are moving from one to another. So, the combination A gives us 1 unit of x and 6 unit of y, when the move from combination A to combination B, combination x is combination B consist of 3 unit of x and 3 unit of y. So, for additional 2 unit of x the consumer is sacrificing 3 unit of y, when they are moving from point B to point C for additional 1 unit of x the consumer is getting sacrificing 1 unit of y and for moving from combination C to combination D for additional 3 unit of x the consumer is sacrificing 1 unit of y. So, if you look at what is the rate of substitution, the rate of substitution is change in the y with respect to change in the x. So, in the first case this is 1.5, in the second case this is 1 and the third case this is 0.3. So, the marginal rate of substitution decreases when the same good is get substituted for the another good for typical time period. So, graphically this marginal rate of substitution is if this is the indifference curve graphically this is nothing, but the slope of the indifference curve. So, moving from point this to point this is the slope. So, this is del y this is del x. So, marginal rate of substitution the rate at which one good get substituted between another. So, x there is a increase in the x due to decrease in the we have to decrease the y and that is the reason the marginal rate of substitution is the del y by del x. And this is nothing, but the slope of the indifference curve and when we move further you look at the slope the change in the y and x is again smaller than the initial change in the y and x and that is the reason the marginal rate of substitution goes on diminishing and we get a convex indifference curve because of this. So, next we will see how this marginal rate of substitution is also equal to the ratio of marginal utility of x and y. So, marginal rate of substitution is the change in the y with respect to change in the x and this is also the slope of the indifference curve and when there is a increase in the x that leads to decrease in the y. Now, what is the change in the utility when there is a decrease in the y that is marginal utility of y multiplied by change in the y and what is the change in the utility when there is a increase in the x that is marginal utility of x multiplied by the change in the x. So, marginal utility of x multiplied by del x, marginal utility of y multiplied by del y and if you simplify this we get del y by del x is equal to mu x by mu y which is the slope of the indifference curve and this is again also the marginal rate of substitution. Then we will see what are the different type of the indifference curve. In the first case if you remember there are two types of good one is substitute goods another is the complementary goods. So, indifference curve with a different shape imply a different willingness to substitute for both the goods. So, perfect substitute is one when the marginal rate of substitution of one good is for the other is constant because they are perfectly substitute to each other it is like tea and coffee. So, one cup of tea is just equal to one cup of coffee if someone is having one cup of tea he has to reduce the consumption of the one cup of coffee. Like a person might consider the apple juice and orange juice is perfectly substitute they would always trade one glass of orange juice for one glass of apple juice and in case of complementary goods when the indifference curve for the goods are saved as the right angle. So, like if you have one left shoe and one right shoe you are indifferent between having more left shoe or may having more right shoe must have one right for one left and that is why you always get a pair of shoes not one by one. Now, we will see what shape it takes when it comes to the when it comes to the perfectly complementary and perfectly substitute. So, in case of perfectly substitute goods we get the indifference curve which is straight line and both of them they are perfectly substitute to each other. So, one unit is the slope has to be constant. So, this is the slope this is the slope and so on this is the slope. So, in case of perfectly substitute the indifference curve which straight line and in case of complementary the indifference curve is right angle because if you are considering x as the left shoe and y as the right shoe if you have only one of left shoe irrespective of how many right shoe you have there is only one pair valid. Similarly, if you are having only one pair of right shoe irrespective of whatever the pair of the left shoe still it is only one point is valid. Similarly, if you are getting another indifference curve when you have two units of both left hand and left shoe and the right shoe in this case again you get a indifference curve which is at a higher level higher satisfaction, but it still gives the only one valid point where there is a matching between two products. So, because it will not have any effect even if you have 10 left running shoe and you have only one right shoe and you have 10 right running shoe you have only one left running shoe. So, we will continue our discussion for the budget line how the consumer reaches the consumer equilibrium then the income substitution effect and finally, the consumers surplus which comes under the theory of consumer behavior in the next class and these are the session references for this specific session where we discuss about the utility analysis and indifference curve analysis.