 We will introduce the third topic under this model theory of demand that is theory of consumer behavior today. And the session outline for this consumer behavior will be, we will first look at generally what are the precondition or assumption for consumer preferences, what is utility analysis both cardinal and ordinary utility analysis. Then we will discuss about the indifference curve, budget line and the consumer equilibrium. So, if you remember in the very first class, we talked about the optimization problem of all the market agents or all the economic agent. So, like for producer always the optimization problem is to optimize or maximize the output. Similarly, for the consumer always is optimization problem is to maximizing the total utility or the maximizing the total satisfaction when he or she consumes the various goods and services. So, the today's focus in on consumer optimization problem because we are talking about specifically the theory of consumer behavior. And what is consumer optimization problem? Consumer optimization problem is to maximize the satisfaction from its limited money income or the limited budget available to him, how he can maximize the total satisfaction from the various goods and services what he consume. Now, what is the constraint over here? The optimization problem is to maximize the satisfaction, but the constraint over here is to the income constraint or the budget constraint because whatever the consumer wish to buy it is not possible always because there is always a value associated with the each of the goods and services and there is a money income required to consume the different goods and services. So, the optimization problem is to maximize the satisfaction or the maximization of the utility by consuming various goods and services and here the constraint is the spending on the goods should be exactly equal to the consumers money income. Now, what are the assumption to be practice here? We assume that the when the consumer are making decision regarding consumption of goods and services, we assume that the buyers are completely informed about the ranges of products available. What are the products available in the market? Then what is the market prices of all the products? Like what is the value of the products? Now, what is the capacity of product to satisfy? This is a subjective term, but if we can always bring it to a monetary form suppose if we are spending 10 rupees or 100 rupees on a goods, whether the satisfaction or whether the usefulness of the product is worth of the value of the product or not. Like if I am spending 100 rupees on consuming a product, I always look for whether the product has the usefulness or not. Is it worth to produce 100 rupees or not? So, the first the consumer or the buyers has to be information about all the products available in the market. What are the market prices available for the all the products or at what price all the products are available? The capacity of the products to satisfy and what is the consumers money income? This requires that all the consumer can rank all consumption bundles based on the level of satisfaction they would receive from the different unit of consumption. Like if the products are 10 or the products are 20, the consumer can rank all the consumption bundles based on their level of satisfaction. Suppose there are 10 products available to me and on the basis of my income I can spend only on two or three products. Now, what is a role of the rational consumer here? The role of a rational consumer here is to first rank on the priority basis that what is the requirement and second is that what is the usefulness I am getting from each of this product and after ranking the various product then only I will see how much I can buy from this different kind of products. So, that requires the consumers can rank all the consumption bundle based on the level of satisfaction they would receive from the different unit of consumption and all this information will help them to rank all the consumption bundle like range of product available, price of all the products, the capacity of the product to satisfy and what is the consumers money income. There are few assumptions when it comes to the consumer theory or the theory of consumer behavior. First one is the completeness for every pair of consumption bundle A and B. Suppose there are two consumption bundle A and B and may be consumption bundle A consider different category of goods, consumption bundle B consider different bundle of goods or the different combination goods. The consumer can say one of the following either A is preferred to B, B is preferred to A and the consumer is indifferent between A and may. What does this imply? This implies that whether it is A or whether it is B the consumer is getting the same level of satisfaction or the same level of usefulness after consuming the products. That is the reason the first one is the since the consumer has the information about what are the goods available under bundle A, what are the goods available under bundle B and on that basis the first assumption goes that if A is preferred to B and B is preferred to A the consumer is also indifferent between A and B. Then we have this transitivity the under transitivity if A is preferred to B and B is preferred to C then A must be preferred to C. So, here A is one consumption bundle B is another consumption bundle and C is another consumption bundle. So, transitivity assumptions say that if a consumer prefer B to A or B to C or C to B then A must be preferred to C because A is preferred to B, P is preferred to C and A must be preferred to C. The third assumption or the most important assumption in case of consumer theory if you look at the non-satiation it means the consumer never gets satisfied with the consumption of goods and services and more of good is always preferred to less. The consumer never says that I have an up of this I am not going to demand for more I am not going to consume more. So, always they prefer a combination of more goods and services which the consumption bundle consists of rather than less goods and services what the consumption bundle consists of. So, more is always better that is according to the non-satiation assumption of the consumer theory. Then we will come to the core of this consumer theory because all the if you look at the basis we are always using the word the consumer should get satisfaction the consumer should get usefulness the consumer should make a decision on the basis of the satisfaction what we receive from the goods and services after consuming this. So, the core for this is that how to identify how to measure the satisfaction what the consumer gets from the product the basis for this is the utility. So, we will come to the utility analysis now we will define what is utility we will see what is a utility function and how this utility get used when the consumer takes a decision regarding the product regarding buying a typical product or not. So, utility is this the benefit what the consumer gets from goods and services they consume. So, when they consume a goods and services whatever the benefit or whatever the usefulness of the product that becomes as the utility. So, basically it is a numerical score representing that the representing the satisfaction that a consumer gets from given consumption basket. So, it is like if I have a consumption basket which consists of 10 goods after consuming the consumption basket if I am able to give a numerical score if I am able to identify what is the benefit associated with the consumption basket then the consumption basket has the utility. So, basically this is the benefit what the consumer gets from goods and services after consuming and generally you can convert it to a numerical score which represent the satisfaction that a consumer gets from a given consumption basket. So, if you take an example if buying three copies of books give more happiness than buying a shirt it can be said that books give you more utility than shirt right. There are two food item and if you are food item A and B if you get more satisfaction in A as compared to B you can always say that A has more utility than in compared to B, but this utility is always a relative concept it is not that all the consumer they are going to get the same level of utility by consuming A may be some consumer they get more utility when they consume B and for them B is always having a major more utility as compared to the A. So, utility is the benefit what the consumer gets after consuming a product or consuming a consumption basket and it can be converted into a numerical score which represents the consumer satisfaction and on that basis they can take a decision whether to buy this product whether to consume this product or not. So, what is a utility function if you are making it to a mathematical relationship this utility and the consumption of goods and services. So, utility function is an equation that shows an individual perception of the level of utility that would be attained from consuming each considerable bundle of goods. So, whatever we are explaining learning the numerical score of the total satisfaction same way when you are bringing down it is to a mathematical equation utility is the function of the different goods or the function of the level of utility of the different goods. So, u here is the utility x and y is the two goods what the consumer is consuming. So, the total utility what the consumer is getting is the utility of the x and utility of the y or we can always say that this is the satisfaction what the consumer gets after consumption of both the goods that is x and y. There are two way to measure this utility one is cardinalist approach and second one is the ordinalist approach. So, when utility can be measure in subjective unit according to the cardinalist approach and according to ordinalist approach utility cannot be measure, but can rank only in order of preferences. So, in case of cardinalist approach the core is again utility can be measure utility can be quantified whereas, in case of ordinalist approach utility cannot be measure rather it can be rank in the order of the preferences. The unit by which we can measure the utility under cardinalist approach is utils that is called utils the unit of measurement under cardinalist approach is util whereas, in case of ordinalist approach we cannot quantify it or we cannot measure it rather we can rank them in the order of the preferences. Like if you are taking the example of may be having food in different restaurant. Now, how it works for post the cardinalist approach and the ordinalist approach in case of cardinalist approach I can say if I have taken food in three different restaurant I can say after having food in restaurant one I get 10 units of utils after having food in restaurant two I get 12 unit of utils and after having food in restaurant three we can get I get 8 units of utils this is cardinalist approach, but how this example can be taken in the ordinalist approach after having food in all these three restaurant if I am asking to give my preference I will give always third is the first preference second is the second preference and first is the first last preference because I have got more satisfaction in having food in third restaurant. So, one is assigning some unit in term of utils that is cardinalist approach and second one is that on the basis of the preference I can rank the different goods or I can rank the different products, but if you look at the basis is again same in first case again it is a total satisfaction represented in utils term and second is again the basis is total satisfaction which is represented on the basis of a rank key. So, if you take an example now suppose there are five goods x 1, x 2, x 3, x 4 and x 5 and the second column gives us the utility what we get that is in case of x 1 we get 14 utility in case of x 2 3 utils of utility in case of x 3 10 units of utility in case of x 4 8 units of utility and in case of x 5 17 units of utility. So, if this is the utility what I am getting the first column always give us gives us the cardinalist approach because it is assigning a number to the satisfaction what the consumer is getting from the different unit of goods. But the second one the second column that is rank order in this case if you look at this the example of a ordinalist approach because here the number is not given for each goods rather it is preferred according to the satisfaction or according to the preferences. So, in this case if you look at x 5 is given as the first preference x 4 is given as the fourth preference x 3 is given as the third preference x 2 is given as the fifth preference and x 1 is given on the second preference. It means according to the priority according to the preferences or may be according to the satisfaction received from each of the goods the goods are ranked and in case of first one in case of cardinalist approach it is like whatever the total satisfaction the consumer is receiving after consuming each goods and services. So, if you take an example that the measuring utility in utils that is again example of a cardinalist approach like if you are taking the example that jack derives 10 utils from having one slice of pizza, but only 5 utils from having a burger this is the example of a cardinalist approach. And in case of ordinalist approach we can always take the example like Jill prefers a burger to slice of pizza then slice of pizza to a hot dog. So, in the first case in case of cardinal if jack is the consumer we can always quantify in this case that what is the utils he is getting when he is consuming one slice of pizza and what is the utility he is getting when he is consuming one burger, but when it comes to ordinalist approach we cannot quantify what is the utility rather we can always prefer like if you look at Jill here is the consumer Jill prefers a burger to a slice of pizza it means he assign more utility more satisfaction after having a burger than a pizza and a slice of pizza to a hot dog. So, if it is a between a comparison between a hot dog and slice to slice of pizza again he give more importance to slice of pizza because he gets more satisfaction from slice of pizza than to the hot dog. So, in the second case Jill is preferring one product over another product on the basis of the satisfaction he receives or on the basis of the satisfaction on the basis of the utility what he gets from the different quantity of or different types of goods and services. Now, so when it comes to again the measurement of utility there are two approach one is cardinalist approach second one is the ordinalist approach. If you look at often consumers they are more are able to more precise in expressing their preferences like in the previous example if you look at Jill is willing to trade a burger for four hot dogs, but she will give up only two hot dog for a slice of pizza. So, look at the trade now they are very all the rational consumers there are very precise in expressing their preferences which products they want and which products they can give up. So, if you are taking a case of Jill he is willing to she is willing to trade a burger for four hot dogs, but she will give up only two hot dogs for a slice of pizza. She is ready to for go four hot dog for one burger, but two hot dog only for the slice of pizza. It means he prefers burger more than pizza and we can infer to that to Jill a burger has twice as much as utility as slice of pizza and a slice of pizza has twice as much as utility of the hot dog because he is exchanging four hot dogs for one burger and two hot dogs for one slice of pizza. So, when it comes to measurement of utility for him the highest utility is always the burger, the second highest utility is the pizza and third utility is the hot dog because he is ready to sacrifice four hot dogs for one burger two hot dogs for one slice of pizza. So, burger has twice as utility as the slice of pizza and slice of pizza has twice as utility as the hot dog and he can when it comes to ranking the preference he can always say the Jill can always prefer the burger then pizza and then the hot dog. Then we will see what is the total utility we will introduce two new concept here one is total utility and second one is the marginal utility. Now, what is total utility? Total utility is the total utility of a consumer derives from the consumption of all the units of goods and services or a combination of goods over a given consumption period, satri paribas all other things constant total utility is nothing but the total utility of the consumer what he or she gets after consuming the all the units of goods and services. And what is marginal utility? Marginal utility is the additional utility that a consumer derives from the after consuming goods and services any additional unit of the goods and services. So, marginal utility is the utility a consumer derives from the last unit of consumer good see or he consume during a given consumption period satri paribas all other things remaining constant. So, if you plot it the total the total utility curve is or the from the total utility curve we can get the marginal utility curve and this is nothing but the change in the total utility when there is change in the quantity of the consumption. So, if there are 10 units to consume the marginal utility between the 9th and 10th is always what is the last additional unit of utility the consumer has added to the total utility after consuming the last unit of the product. So, total utility is the sum total of the utility what the consumer gets after consuming all unit of goods and services and marginal utility is always the additional utility to the total utility when the consumer consuming one more additional unit of the goods. So, if you graphically represent then total utility is generally take a inverted u shape initially it increases reaches the maximum then it decreases and marginal utility is generally the slope of the total utility. So, that is the reason if you look at marginal utility start at a higher level and then slowly slowly decreases and then it reaches 0. We will see why the shape of the total utility is like this why it increases at the beginning and why it decreases at the may be after reaching the threshold level and to a simply may be a simple version of this marginal utility is the slope of the total utility. So, initially the marginal utility if you look at marginal utility decreases and then it reaches 0 and then it goes to negative. That means, there is a decreasing slope of total utility even if total utility is increasing it is increasing at a decreasing rate then when it decreasing then marginal utility goes on a negative direction. Now, what are the assumption of this total utility curve as the quantity consumed per year increases total utility increasing at a decreasing rate. So, when there is more and more quantity if the consumer is consuming more and more of the goods generally the total utility increases at the decreasing rate. So, utility some utility the benefit the consumer is getting, but whatever he was getting earlier that becomes less now. When total utility reaches maximum it attains the satiation quantity. So, if you look at the top point may be when it has stopped increasing the that point the total utility reaches maximum and that is the satiation quantity or that is the threshold level up to which the consumer gets the satisfaction. Total utility declines if more quantity consume after the satiation quantity. So, if you look at how this total utility and marginal utility they are related. Here suppose if you are considering total utility this is the quantity of the good getting produce. So, initially it increases then it reaches the maximum and then it decreases. So, corresponding to this or marginal utility initially decreases. So, corresponding this when this is maximum we get a 0 marginal utility and after that this is negative. So, how these two are related initially total utility increases, increases at the decreasing rate reaches the maximum and after this total utility decreases. Corresponding to this the marginal utility is decreasing up to the point total utility is increasing at the decreasing rate. Marginal utility is nothing, but the slope of the total utility. So, if the slope is decreasing similarly the marginal utility has to decrease and that is the reason marginal utility is reaching at this point 0. Then when it is maximum marginal utility is 0 and when it is decreasing marginal utility is become negative. So, from there the concept of actually the diminishing marginal utility comes and what is diminishing marginal utility or why we get a negative slope of the total utility. Over a given consumption period the more of a good the consumer has or has consumed the less marginal utility and additional unit contributes to his or her overall satisfaction. Alternatively we could say over a given consumption period as more and more of a good is consumed by a consumer beyond a certain point the marginal utility of additional unit is begin to fall. So, if you look at why the total utility is decreasing like take a small example of the consumption of coffee or tea. Maybe when you take the first cup of tea or first cup of coffee you get a maximum usefulness or the maximum satisfaction from this product. Then when you have the second cup of coffee again you get some amount of some amount of the benefit or some amount of the satisfaction. But if you compare between the first cup of the tea of the day and the second cup of the tea of a day then again there is a difference because whatever the satisfaction you have got in the first cup you will not get in the second cup. Then maybe again it happen again you are going to have the third cup of tea or third cup of coffee within a specified time period. So, if the time period is fixed and the same amount of product you are having then whatever the satisfaction you are getting at the initial consumption you are not getting that in the following consumption where following consumption when you are having more and more of that. Similarly, if you can take a example of watching a movie or reading a book. When you first time read a book you get a maximum utility because this is a newer one and you get to know all the thing in a new version. When you watch a movie for the first time again you like it most. Maybe you have like something that is the reason you are watching the movie for the second time, third time or so on. But whatever the satisfaction you have got or whatever the utility you have got in the first unit of consumption that is always higher and when you are going on watching the same movie watching the same book or maybe consuming the same product the marginal utility goes on decreases and finally it reaches a 0. So, at a point of time you can say that I am not going to have any more tea today because I have had enough. At any point of time you can say that I am not going to watch this movie for next three months next one or next two year because I have watched it for 10 times or 12 times. I can say that you can say that I am not going to read this book for next few weeks because I have had enough in last few weeks. So, if it is a specific time specific product the utility decreases when we are consuming more and more of it. Now, what are the precondition in which case the law of diminishing marginal utility is valid? The unit of consumption must be standard one means if you are taking the example of a book, if you are taking the example of a movie, if you are taking the example of a coffee or tea. In this case if the first time we are having just half cup of coffee, second time we are having a quarter cup of coffee, third time again you are having less of it. The possibility is that you may get still the same amount of satisfaction what you would have got in the first cup of coffee. So, the unit of consumption should be standard one otherwise this law of diminishing marginal utility is not going to be valid. Or like if you take the example of a movie or if you are taking the example of a book, you can always say that you have to read the book full, you have to watch the movie full, not only part of it, if you are watching part of it again you are if you can get the same utility level, if you are watching a different part may be next few errors or next few it is. So, unit of consumption has to be standard one then only the diminishing marginal utility has to be valid. Consumption must be continuous, you cannot give a gap. Suppose you are having one cup of tea in the morning and one cup of tea in the afternoon again you will get the same level of satisfaction. So, in this case law of diminishing marginal utility is not valid because the consumption is not continuous. If you are giving a gap the possibility is that you are getting the same level of satisfaction again. The taste and preference of the consumer should remain unchanged during the course of consumption. So, if you are if you are generally having coffee or if you are generally having tea, the taste should not change during the course of consumption. If you like the product then only you are consuming it. So, that should be there till the end of this consumption period. The good should be normal not addictive in nature. Like if I am addicted to coffee, if I am addicted to tea, if I am addicted to smoking or if I am addicted to liquor I will go on consume I will not get the less satisfaction because I am addicted to it. Someone is addicted for smoking. So, the more they consume more satisfaction they get. Someone is addicted to tea more they consume more they get satisfaction. Someone is addicted to liquor more they consume more they get the satisfaction. In this case the law of diminishing marginality is not going to valid because these goods are not normal they are addictive in nature. So, one of the precondition for the application of law of diminishing marginal utility is the good should be normal not addictive in nature. So, like if you are taking a specific example you are taking two products. One is the may be the paper vending machine another is the candy vending machine. So, if it is a simple question how many people take more than one paper from the vending machine? May be the answer is none of them because if you take the newspaper it is a durable goods you go on reading for the throughout the day you do not require a second set of newspaper. But when it comes to candy may be again people they go on dispensing candy because may be they are having one now they are having may be one later. So, in both these cases if you look at that there is a case of the diminishing marginal utility. But in case of diminishing marginal utility that comes at the very first unit in case of the newspaper, but for candy it comes it a little later because they go on consuming candy till the time the marginal utility is not reaching 0. But if you have already taken a newspaper from the vending machine the second one is again not generate any level of utility because you are always having the similar one for the first time. You are not going to consume again and again the same newspaper even if you are getting a chance to get it from the vending machine. So, these are the typical examples that how the law of diminishing marginal utility is valid as the consumer consume more and more of a specific product the utility generally goes on decreasing. 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 decreasing 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 utilities 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 1 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 2 goods it gives the equal level of satisfaction to the consumer. So, it is a technique how choices between 2 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 2 or more goods that gives the consumer the same level of satisfaction and it is negatively slope and convex. Let us take an example of indifference curve how we can draw the indifference curve. So, we are saying these are 2 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 this 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 and H is 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 on 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 is 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 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 help of the different consumption basket. So, suppose we can take food here in x axis clothing here in the y axis will take 10, 20, 30 and 40 here also we can take 10, 20, 30, 40 and 50. So, come up with the combination say A is 20 unit of food and 30 unit of clothing, combination A, combination B is a 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. 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 here any other combination they will prefer not here other than the other combination, because that gives more quantity of both the goods. So, between these 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 these 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 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 chosen 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 taken 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 clothing 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 and 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 less unit of a 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 violate the basic assumption of the consumer theory. Then the fourth assumption is higher indifference curve gives a higher level of satisfaction. So, this is 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 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 consist of more of both x and y again between point B to C again it consist 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 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 consist of more of both the goods and lower indifference curve consist 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 which is 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. So, this is 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 we 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 1 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 and other 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 T and coffee. So, one cup of T is just equal to one cup of coffee. If someone is having one cup of T, 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 be 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 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 is 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 consumer 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.