 We will continue our discussion on consumer theory or theory of consumer behavior in this session also. So, if you remember in the previous session, we talked about the assumption what is generally taken in the theory of consumer behavior or when we do the consumer behavior analysis. Then we introduced the concept of total utility, marginal utility, how both of them they are related to each other and this is all the total utility and marginal utility this is only based on the perception of the consumer on the satisfaction what they get after consuming the product. Then we introduced the concept of law of diminishing marginal utility which tells us that when a consumer go on consuming a product after a certain point of time generally the marginal utility diminishes and sometimes it even reaches to 0 and sometimes you get it the negative marginal utility. Then we introduced the concept of indifference curve analysis which is a part of ordinary utility analysis and here we discussed about the different properties of indifference curve. Then what is the rate at which the goods get substituted with each other like the marginality of substitution and also we discussed about the different kind of indifference curve like when the nature of goods are different like complementary goods or may be the substitute goods. So, in today's class we will carry out discussion on the budget line how the consumer incomes get limited by the consumer preferences then we talk about the consumer equilibrium keeping budget line the constant as the budget line or the budget constant. Then we will introduce the concept of law of equimarginal utility then we will discuss about the price income substitution effect and finally our discussion point will be on consumer surplus. So, what is a budget line? So, till the time we know that indifference curve gives us the consumer preferences and at the same point it also gives us the different combination of goods and services which gets the same level of satisfaction. Now, more is always better for the consumer, but when it comes to affordability of the consumer always the income pose as a constant. So, the consumer income is here we consumer income we represent in term of the consumer budget line and budget line describes the limits to consumption choice and depends on consumer budgets at the prices of the goods and services. So, it show all the possible commodity bundle that can be purchased at a given price with fixed money income. So, income is fixed budget line shows us the different kind of goods and services what the consumer can consume with this typical fixed income. So, in this case if you consider M is the money income and if the total consumption basket of the consumer is just consist of two goods X and Y then the total budget line will be represented in term of M which is equal to PXX plus PYY. Now, why this is only PXX and PXY we are assuming that the entire money income of the consumer is getting spent only on consumption of goods X and Y. So, PX is the price of X, PY is the price of Y. So, the X is the quantity of X and Y is the quantity of Y. So, entire money income is getting spent on X and Y and since it is equal to income the price of X and price of Y is also multiplied along with the quantity of X and Y. So, this is the graphical representation of the budget line and if you look at here we represent in the graph A and B as the budget line. Then at the point A if you get the value is equal to M is equal to PY and how you get the value of A at the point YXX is equal to M by PY because the entire money income is getting spent on only in the consumption of one of the goods. Similarly, M by PX if you look at the other extreme here also the entire consumption is getting spent only on the consumption of the goods and services. Let us see how we can draw this budget line. So, if you remember this the budget line equation is PXX and PYY. So, if we assume that the entire money income is getting spent only on consuming Y then this term becomes 0 and if you solve for Y then you get the value which is M is equal to PY which we get here that is M is equal to PY. Then similarly if you spend the entire money income or if the consumer is spending entire money income only on consumption X then the second item becomes 0. So, this M is equal to PX by X and the value of X is M by PX. So, here we get the value which is equal to M by PX. So, if you join this two point what is the significance of this two point suppose this is A suppose this is B at this point A the entire consumption is entire money income is getting spent only on consumption of Y and at this point the entire money income of the consumer is getting spent on the consumption of X and in between all this point it gives us the different quantity of X and Y. So, any point in this range will give a mix of combination of goods X and Y whereas, this two extreme point gives us that when the entire money income is getting spent only on the consumption of the specific good in case of horizontal axis this is on the consumption of good X and in case of vertical axis in the consumption of good Y. So, indifference curve gives us the consumer preferences on goods and services and whatever the satisfaction they get out of it and budget line gives us what is the possible combination of X and Y can be consumed with a fixed money income of the consumer. We have simplified this analysis of indifference curve and the budget line to two goods just for the simplicity of it when you just take two goods otherwise also there is an option when you have more goods and services you can cluster them into specific groups and you can represent them in the indifference curve. So, we have introduced the concept of the indifference curve in the previous session and this session we have introduced the case of the budget line. With the help of this we will see how the consumer is reaching the equilibrium, but before analyzing the condition of consumer equilibrium we will see that in which case the budget line get changes. First when there is a change in the income so whenever there is a change in the income it increases of the in the income leads to a parallel outward shift in the budget line. Like if you look at the third line that is the increase in the income from the original budget line and decrease always in the downward direction. So, increase in the income lead to a right shift in the budget line and decrease in the income leads to a left shift in the budget line. So, one is upward in case of increase and downward in case of decrease. Now, what is the change in the budget line when there is a change in the price? A decrease in the price of good x rotates the budget line counter clockwise if you when you can see in the graph. So, the initial budget line is the black line and when there is a change in the price of the goods now with the same amount of money income the consumer can consume more of good x and because of this the budget line shift to the right. So, if you look at this case if you are considering here as the x here you are considering as the y this is the original budget line. Now, price of x decreases. So, with the same money income now the consumer can still have more quantity of x as the price of price of x has decreased. So, in this case the budget line will shift to the right this is the new budget line. So, this is a b this is a b 1. Now, suppose the price of y decreases now the same money income now the consumer can have more quantity of y. So, at this point b remain constant now the curvature will change in case of y and suppose this is a 1 b. So, the new budget line is a 1 b if the price of y is decreasing. Now, it will move in the opposite direction if the price of x is price of x is increasing or price of x is price of y is increasing. This is the case in the previous case we analyze the decrease in the case decrease in the price of x and price of y and the scenario will change when the price of x will increase and or price of y will increase. Now, we will see how to reach the consumer equilibrium. Consumer equilibrium is the point this is the optimal consumption for the consumer. And what is the optimization problem for the consumer the optimization problem for the consumer is to maximize the satisfaction. So, consumer behave rationally and would always aim to maximize the utility given the money income prices of the goods in the consumption basket. So, irrespective of the price of goods and services the income keeping this as a constant the consumer always behave rationally and they always see that how they can maximize the utility. It is it is at a point where the budget line is tangent to the highest attainable indifference curve by the consumer subject to the budget constraint. So, graphically how you get the point of consumer equilibrium? It is at a point where the budget line is tangent to the highest attainable indifference curve by the consumer subject to the budget constraint. So, what is the consumer objective or what is the consumer optimization problem to maximize his or utility subject to the income constant. We have kept two goods in this case, one is X and other is Y. So, the consumer consumption basket is consist of two goods X and Y. Price of both the X and Y are fixed like PX and PY are fixed, consumer income is given. So, price X and Y is fixed, income is fixed, two goods are there X and Y and the consumer objective is to maximize his or her utility subject to the income constant. Now, what is optimal consumption? Optimal consumption is the point at which the consumer maximize the utility or where the utility maximizing takes place or that is the point of the consumer equilibrium. Now, what is the precondition for this optimality or what is the precondition for this utility maximization? It requires the slope of the budget line should be equal to the slope of the indifference curve. So, in the previous case if you remember the budget line is AB like right. So, at the point A this is we get a value that is M is equal to PY and at the point B we get a value which is equal to M by PX. So, corresponding to this what will be the slope of the budget line? The slope of the budget line will be PX by PY and as we know previously that the slope of the indifference curve is marginal rate of technical substitution that is sorry marginal rate of substitution that is MRSXY which is also equal to the ratio of marginal utility of X and marginal utility of Y. So, optimality requires the equality between the ratio of marginal utility and price of X which is equal to the marginal utility and price of Y. So, we have two goods in this case price of X, price of Y is fixed, income is fixed, the optimal consumption or the point at which the consumer will reaches the equilibrium at this point the ratio of marginal utility and price of X should be equal to the ratio of marginal utility and price of Y. So, now if you look at in the graph at this point you look at the arrow mark this is the point of the consumer equilibrium. Why this is the point of the consumer equilibrium? Because this is the equilibrium consumption bundle is the affordable bundle that will the highest level of satisfaction. The consumer can pick up the combination in the indifference curve 1, the consumer can pick up a combination in indifference curve 2, the consumer can also pick up a combination of goods X and Y in the indifference curve 3. But the consumer since the optimality or since the optimization problem for the consumer is to maximize the satisfaction, maximize the utility that is the reason the consumer will reach the equilibrium at this at the point in the indifference curve 3 because that gives a highest level of satisfaction and also the combination in indifference curve 3 can be achieved with the constant in the form of the budget line or constant in the form of the income. So, the straight line is the budget line, there are three indifference curve and the consumer will always pick up a point in the highest indifference curve because that will give a higher level of satisfaction or the higher level of utility and that goes with the basic optimization problem with the consumer. Now, we will check what is the condition this consumer equilibrium in detail. So, del Y by del X or ratio of marginal utility of X or Y is the slope of the indifference curve. P X by P Y is the slope of the budget line and what is the what is the preconditions or what are the condition for the optimal consumption that is ratio of marginal utility of X and Y is equal to the ratio of price of X and Y. So, if you look at there are three points, point A, point B and point C, all these three points the consumer is reaching the equilibrium because U 1 is one indifference curve, U 2 is the second indifference curve and U 3 is the third indifference curve. Similarly, we have three budget line B 1, B 2 and B 3. Now, suppose the consumer has the income which is equal to B 1. Now, having the equilibrium B 1, the consumer can only pick a point in case of or only pick a combination in the indifference curve 1 that is U 1 and the suppose the income increases for the consumer from B 1 to B 2. Now, the consumer can prefer a quantity or prefer a combination of X and Y in the higher indifference curve that is U 2. So, that is another consumer equilibrium point at the point B. Similarly, when the price of B 3 increases or the sorry income of the consumer increases from B 2 to B 3, the consumer again can achieve a higher level of satisfaction by choosing a combination as indifference curve 3 that is U 3. So, if you join this three point A, B and C, we reach to a path which is consumption path and why this is known as the consumption path because when the income increases this is the consumption pattern of the consumer and if you look at at each equilibrium point, the consumer maximize the satisfaction. So, after joining point A, B and C, all these are consumer equilibrium point we get as the consumption path. So, consumer equilibrium is the point this is also known as the optimal consumption or this is also known as the may be the best consumption for the consumer because they get a higher level of satisfaction or the highest level of satisfaction with the limited income with the fixed income and when the prices are also fixed. And how this can be achieved? There are two points to achieve this one at this point where the ratio of the marginal utility and price of X is equal to the ratio of marginal utility and price of Y and geometrically this is at the point where the budget line is tangent to the indifference curve. So, consumer there is a equality between the ratio of the marginal utility and price of X and marginal utility and price of Y. So, consumer allocates income so that the marginal utility per rupees spend on each good is same for all commodity purchase. So, like since there is a ratio is equal to ratio of one goods is equal to the another goods it can be said that the marginal utility per rupees spend on each good is same for all the commodities purchase. Till the time the equality is maintained then this is fine, but when there is a disturbance in the equality or at any point of time the ratio of marginal utility and price of one good is greater than or smaller than the ratio of marginal utility and the price of the other goods. In this case we can say that like in this case the ratio of the marginal utility of X is greater than price of X price of X is greater than the marginal utility of Y and price of Y. The consumer will spend more on good X and less on Y because he is getting more marginal utility by spending on X as compared to Y. The situation will again change if the marginal utility and price of Y is greater than the ratio of marginal utility and price of X. In this case the consumer will prefer to spend more on good Y as compared to X because the consumer is getting a higher level of satisfaction or higher level of utility by spending on good Y because the marginal utility what he is getting by spending one additional rupees on it is giving a higher utility as compared to the additional utility that is getting from good X. So, if it is equality then the consumer is spending money in such a way because the marginal utility is getting that is equal, but sometime there is a mismatch the consumer always spend more money income on that good where they get a higher level of marginal utility. Now, we will take an example that how generally these choices are made when it comes to the decision making in term of the marginal utility. We will take a case of Jill that how much ice cream does Jill buy in a month. There are some facts this is limited income and there is also a opportunity cost involved of making a choice buying ice cream leaves Jill less money to buy other things each dollar spend on ice cream could be spend on the hamburger. So, how much ice cream Jill should buy it there are few facts on this he cannot buy unlimited because there is limited income and also there is a opportunity cost associated with it whenever he is buying the ice cream because the same dollar or the same money income could have been spent on buying other goods like the case of the hamburgers. So, whether it is Jill or any other consumer they always make a comparison when before deciding on where they have to spend the money income. So, in this case if it is ice cream or it is the case of hamburger Jill has to decide on the basis of the marginal utility how much marginal utility he is generating when he spending money on the ice cream or spending money on the hamburger for example. So, some more facts the price of hamburger and ice creams are market given the consumer cannot change the price of the goods Jill like any other rational consumer which has to maximize her utility. So, prices are given marketing given consumer cannot change it and Jill maximize her utility because this is the general optimization problem for any rational consumer. The opportunity cost of one dollar spent on ice cream is the foregone utility for one dollar that could be spend on the hamburger because what is the opportunity cost here if he spending one dollar on ice cream then the opportunity cost of this one dollar is to foregone the utility of one dollar that could be on hamburger. So, if he is not spending on the ice cream he could have got it on the he could have bought a hamburger. If the utility of one additional dollar of ice cream is greater than the utility of the last dollar spent on hamburger Jill can increase her total utility by spending one dollar less on hamburger and one dollar more on ice cream. So, it is like when he is getting more utility by spending additional dollar on ice cream rather than on hamburger in his next consumption what he will do he will reduce his consumption from hamburger and he will spend more on ice cream because he is getting a higher level of utility if he is spending on ice cream. So, here the decision rule is when he spending or when any consumer is spending one more unit of money whether it is in the form of dollar in the form of the rupees whatever the additional utility they are getting and their decision always go for the product where they are getting a higher level of utility and the same is happening in the case of Jill even if she is spending both an ice cream and hamburger, but if she is getting more utility in ice cream she will prefer to spend more on ice cream rather than the hamburger. So, utility maximizing rule as it is say that there is a ratio of marginal utility of X and Y. Similarly, if you take two goods here I and H the two good rule is the ratio of marginal utility and price of I it should be equal to the ratio of marginal utility of H and price of H. The rational consumer would buy an additional unit of good H the perceived dollar value of utility of one additional unit of that goods say marginal dollar it is greater than its market price like till the time the ratio is equal the consumer is spending on both the goods, but when it comes to there is a inequality as we discussed in a brief before few minutes if there is a inequality the consumer always spend more on the goods where they are getting a higher level of utility. Now, we will see how the utility maximizations takes place under an income constant. Consumer spending on consumer goods is constant by their income like here the if you can look at the budget line equation is p x q x plus p y q y or p w q w or p z q z and the income the income constant or the budget constant consist of the price of the goods and the quantity of the goods. So, that what can be purchased with a fixed money income. So, in this case even if the consumer tries to always the equal the ratio of the marginal utility and the price of all the goods. So, that they can spend equal amount of money on all the goods, but to maximize her total utility if it is a case of jill her total spending cannot exceed her income. For example, with an income of 86 dollar jill is trying to decide how much ice cream and how much hamburger she should buy. So, if jill income is 86 then he can she can consume both the goods may be ice cream and the hamburger. So, if it is 5 multiplied by 10 plus 6 multiplied by 6 then it comes to 86 rupees. Now, we will see how we get this number 5, 10, 6 and 6 which one is the unit and which one is the price and what is the requirement for here. We should know what is the price of ice cream, we should know what is the price of hamburger, we should know what is the money income what jill is having. So, we know that the jill is having the income which is equal to 86 dollar. Now, we will see with the help of 86 dollar how much unit of ice cream or how much unit of hamburger jill can buy with the income and whether after this she is reaching the optimization or she is reaching the optimal consumption or not. So, this is the example of the quantity, the price of both the ice cream and hamburger. So, the first column gives us the quantity, the second column gives us the marginal utility of ice cream, the third column gives us the price of ice cream, the fourth column gives us the ratio of marginal utility and price of ice cream, the fifth column gives us the marginal utility of hamburger, the sixth column gives us the price of hamburger and the last column gives us the ratio of the marginal utility of hamburger and price of hamburger. Now, if the price is 10 for ice cream and 6 for hamburger, then how many units of ice cream jill should buy and how much unit of hamburger jill should buy. What is the ratio? The ratio is again, if you remember the equality condition, optimal consumption is one where the marginal utility and price of both the goods has to be equal. So, in this case, in which case we are getting the marginal utility and price of good is equal either at the unit 5, when the 5 unit of where the price is, price is 10 rupees and price of ice cream is may be 10 dollar and price of hamburger is 6 dollar. Now, looking at this, if you plot it in a budget line, when the entire 86 rupees is getting spent on ice cream, then the value of Y is 8.6 because price of ice cream is 10 dollar and with the help of 86 dollar, the consumer can only buy 8.6 unit of ice cream and if the consumer is buying hamburger, only hamburger, then in this case, the consumer can buy 14.33 unit of hamburger because price of hamburger is being fixed at 6 rupees. So, 2 extreme, 1 extreme 8.6, the other extreme 14.33 and what is the optimal consumption? The optimal consumption, when the consumer is buying 5 unit of ice cream and 6 unit of hamburger. So, price of ice cream is 10 rupees, 10 dollar. So, it comes to 5 units. So, it comes to 50 dollar and price of hamburger is 6 dollar, when the consumer is spending 6 unit on hamburger that gives us the 36 dollar. So, 50 plus 36 that gives us the 86 dollar and what is the slope here? Slope here is 6 by 10 because 6 is the price of hamburger and 10 is the price of the ice cream and that comes to 0.6 as the slope. So, if you look at, now what is the optimal consumption? The optimal consumption is 5 unit of ice cream and 6 unit of hamburger, which gives the level of satisfaction to gel and also this fits within the income that is 86 dollar. So, if you recall the utility maximizer rule, this is always the ratio of the one goods as compared to the ratio of the other goods and if price of x increases, this equality would be disturbed. It is not only the utility will disturb this equality, also when there is a change in the price that will also disturb the equality. So, mu x p x will be less than mu y p y if there is a increase in the price of x and the similar thing will happen also if there is a change in the price of y. So, to return to equality, the consumer must adjust his or her consumption. Have in mind that the consumer cannot change the price or he has an income constant. And what are the consumer options? If there is a mismatch to reach to the optimal consumption, the consumer has to adjust his or her consumption. Here we need to remember here is that the consumer cannot change the price, the consumer cannot change the income available to him. Now, what are the consumer options? In order to make the two sides of the above inequality equal again, given that p x p y could not be changed, we could have to increase mu x and decrease mu y. Recalling the law of diminishing marginal utility, we can increase mu x by reducing x and we can decrease mu y by increasing y.