Week 2: Utility PDF

Week II – Compulsory Reading Utility What is Utility? ‘Utility’ means the satisfaction obtained from consuming a commodity or it could also be considered as the ‘Want Satisfying’ power of a commodity. As consumers, we are constantly consuming somethi...

Week II – Compulsory Reading Utility What is Utility? ‘Utility’ means the satisfaction obtained from consuming a commodity or it could also be considered as the ‘Want Satisfying’ power of a commodity. As consumers, we are constantly consuming something or the other, have you ever thought why we consume them? Why do you crave chocolates, cakes, and specific cuisine? What happens when we can get the item of your craving? You are delighted and content. This is nothing but the utility or the satisfaction, you derive from consuming the commodity. Classification of Utility It is important to note that there are two major classifications of Utility – One being Cardinal Utility and the Other being Ordinal Utility. Cardinal Utility Cardinal Utility was Propagated by Alfred Marshall, and the cardinal utility theory says that utility or the satisfaction that we derive from consuming any goods/ services is measurable, meaning whenever we consume something, we can say what is the level of satisfaction we derived from that particular commodity by giving our satisfaction level a numerical value. Further, by placing a number on the alternatives, the utility can be added, meaning that if we consume more than one unit of the commodity or if we consume multiple commodities we can say how our satisfaction level has increased again by giving it a number. So, for example if we eat a chocolate, we can say our satisfaction is 20 units, if we eat another chocolate we can say our satisfaction has increased to 40 units, after this if we eat a pastry we can further add our satisfaction level and say that it has gone up to 80 units. The unit used to measure utility is called “utils” and a very important and famous law, the Law of Diminishing Marginal Utility (LDMU) is based on Cardinal Utility approach. However, do note that it is extremely difficult to measure the level of satisfaction in Utils or in numerical terms. Further, at different points in time the number would be different because our satisfaction level would be different (because it is dependent on multiple factors). Because of these limitations of the Cardinal Utility Approach, there is another approach to understanding Utility called the Ordinal Utility Approach. Ordinal Utility The Ordinal Utility approach was propagated by Hicks & Allen, and the ordinal utility theory says that utility is not measurable but it can only be compared. The Ordinal approach uses the ranking of alternatives as first, second, third and so on, meaning that when a consumer is faced with options they can only say what they prefer more and what they prefer less, but cannot give it any numerical value. The Indifference Curve analysis is based on Ordinal Utility approach. Total Utility and Average Utility Total Utility (TU) – The total satisfaction that a person gets from the consumption of goods and service. o So, if consume something the level of satisfaction is the total utility, if you consume an additional unit, your total satisfaction goes up and hence your total utility goes up. Average Utility (AU) – The average satisfaction that a person gets from the consumption of a unit goods and service. AU = TU/n (n = number of units) o If you divide the total utility from the number of units consumed, you get your average utility. Marginal Utility (MU) Marginal Utility (MU) is the addition to the total utility as a result of consuming one additional unit of the same good or service. 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 ∆𝑇𝑈 MU = = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 ∆𝑄 MU = 𝑇𝑈𝑛 − 𝑇𝑈𝑛−1 In microeconomics, we are more concerned with what we get with the additional unit that we consumed, and it is this that helps us make our decisions.  Law of Diminishing Marginal Utility (LDMU) Law of Diminishing Marginal Utility (LDMU) The Law of Diminishing Marginal Utility is an interesting and important law in microeconomics, it says that the additional benefit that a consumer derives from an increase in stock of a thing diminishes, other things being equal, with every increase in the stock that he already has. In other words, the Law of Diminishing Marginal Utility states that as consumption increases more and more, marginal utility diminishes. In simple words, it implies that as you go on consuming more quantity of any good, the satisfaction that you get with every additional unit goes on decreasing. As we progress through this lecture, this idea will become clearer. The assumptions of the law are: Cardinal Utility – which means you can give numerical value to your level of satisfaction Rational Consumer – which implies that you will make decisions that would increase your level of satisfaction or utility Continuous Consumption – meaning that you go on consuming one unit after another without any break, this law would not work if you have the good in the morning and then in the afternoon and finally in the evening. Even if it does, it will take a much longer time to be realized. Standard Units – The unit of the commodity has to be standard, for example a cup of tea/ coffee or a slice of cake. This is important because if the unit size is too big you may not even consume one unit, while if it is too small then you may see the effect after a number of units. MU of Money remains constant – meaning that there would be no change in the money of the consumer, if there is a change in the money income you may be motivated or demotivated to consume the product. No change in price – The price of the good is to be constant, since if there is a change in the price of the commodity, then it will impact your decision to consume more or no. If the price goes up you would consume lesser and if the price goes down you would consume more. Quality is Constant – The quality of the good should not change, otherwise it will impact your decision to consume more or no. The most important assumptions of the law are continuous consumption and standard units; all the other assumptions are simply trying to ensure that there are no external factors that impact your decision. Example: Let’s say that you have a sweet tooth and after a long time you were able to find your favorite chocolate. Since, this is your favorite chocolate you of course want to consume it, when you consume the first unit your satisfaction is 20 units, with the second it is 35 units, with third 45, with fourth 50, with fifth 50 and with the sixth unit it comes down to 45 as can be seen in the table. Units TU MU (TUn – TUn-1) 1 20 0/ -/ 20 2 35 35 – 20 = 15 3 45 45 – 35 = 10 4 50 50 – 45 = 5 5 50 50 – 50 = 0 6 45 45 – 50 = -5 The Total Utility increases from consumption of 1st unit the 5th unit. After the 5th unit, TU decreases. The Marginal Utility decreases from the beginning and become zero at the fifth unit and further consumption of the chocolate will not satisfy the consumer as the MU shows negative signs. So, what’s happening here, as you go on increasing your number of units of consumption, the total utility goes on increasing from 25 units to 50 units, since you are getting more and more satisfied. If you are a rational consumer you would stop consumption at the fifth unit, where your total utility is the highest and the marginal utility is zero (meaning the additional unit is not giving you any additional satisfaction). If you consume any further then you would start feeling sick and that is exactly what happens at the sixth unit of consumption, when the total utility reduces. Relationship between the Total Utility and the Marginal Utility: As depicted in the graph, ✓ When TU is increasing, MU will be positive – which implies that the consumer can continue to consume ✓ When TU is at its maximum, MU will be zero - which implies that the consumer is completely satisfied ✓ When TU is decreasing, MU will be negative - which implies that the consumer is now feeling sick as a result of excess consumption and hence the level of satisfaction has decreased (like getting a stomach ache due to excess consumption/ or a feeling of uneasiness) The importance of this law, is that it was able to show that although all the wants/ desires of a consumer cannot be fulfilled any one desire can be satiated at a given point in time. Exception to the law of Diminishing Marginal Utility: Money – The amount of money required for one to be satiated with money, is extremely high and majority of us do not reach that level, hence it could be regarded as an exception. Since the more money we have, the more money we want.  Addictive Commodities – In this case it is not that LDMU does not set in, it is just that the consumer is unable to realize the LDMU setting in, rather feels that their satisfaction or utility is increasing, hence it is regarded as an exception. It is clearly evident for the others that LDMU has set in. Rare Collection/ Articles – In this case, since there is just very limited quantity of these goods, the more one has the more satisfied they are, because of the feeling of exclusivity, and hence this is regarded as an exception. Indifference Curve An indifference curve represents all the possible combinations of two goods which will give the same level of satisfaction or it is a locus of points showing different combination of two goods which gives the same level of utility or the same level of satisfaction to the consumer Which implies that where ever you are on the curve, the level of satisfaction would remain the same. Hence you would be indifferent towards choosing any point on the curve. The assumptions of the Indifference curve are : Rationality - which implies that the consume is rational and will make decisions that would increase their level of satisfaction or utility Order/ Rank Preferences – The consumer is in a position to rank or order their preference, meaning that given a choice between two goods A & B; the consumer should be able to say whether they prefer A to B; B to A or they are indifferent between the two good. Non-Satiety – This implies that the consumer is not yet satisfied with the goods they have and hence as they consume more, their level of satisfaction goes on increasing. Consistency and Transitivity of Choice – Lets understand this with the following example: Consistency – consider two goods A & B, the logic of consistency implies they if at a point the consumer prefers A to B, then they must always prefer A to B, when they are given a choice between the two. Hence, the consumer has to be consistent in their preference. Transitivity – In the case of transitivity let us take the case three goods A, B & C; transitivity of choice implies that if the consumer prefers A to B (when they have a choice between the two) and they also prefer B to C (when they have a choice between the two), then by the logic of transitivity they would also prefer A to C. Diminishing Marginal Rate of Substitution (MRS) This is again an important concept to understand, MRS is the rate at which the consumer is willing to trade one good for another. As consumers, the good that we have lesser of is valued  more and vice-versa; lets us understand this we the two goods A & B; as we move along the Indifference Curve from one extreme to another, we initially have more of good A and lesser of good B so we value good B more and are willing to give up multiple units of goof A for an additional unit of good B. As we reach the centre of the IC the rate of tradeoff is almost 1:1, and finally when as we approach the other extreme, now we have more of good B and lesser of good A, hence now good A is valued more, and we would be willing to give up an additional unit of good A only in exchange for multiple units of good B. As a result, the MRS goes on diminishing. Combinations Good Y Good X A 12 2 B 6 4 C 4 6 D 3 8 E 2 12 Figure: Graph of the Indifference Curve Tabulation As shown in the Figure which is the graph of the Indifference Curve, based on the tabulation, you can see the different point on the graph from A to E, as you move from A to E you will see that the MRS is declining. An indifference map shows a set of indifference curve on the same graph, so the graph on the screen is that of an indifference curve. The higher the indifference curve from the origin will always give you a higher level of utility. Thus, IC3 gives higher level of satisfaction as compared to IC2 and IC1. Hence, a rational consumer would always prefer to be on IC3 which is the highest possible IC on the IC Map. Figure: Indifference Map The characteristics of an indifference curve are: Downward Sloping Convex to Origin Higher IC gives higher level of satisfaction No two ICs can intersect each other Downward Sloping The first is that the IC is downward sloping, to ensure that the satisfaction level remains the same throughout the curve. Instead of downward sloping, if it were any other slope the satisfaction level would not be the same. Think about what Happens if the Indifference Curve is: Upward Sloping – as you move along the IC you get more of both the goods so the satisfaction level goes on increasing. Horizontal (parallel to X-Axis) – as you move along the IC you get more of the good on the x-axis and the same amount of good y, so the satisfaction level goes on increasing. Vertical (parallel to Y-Axis) – as you move along the IC you get more of the good on the y-axis and the same amount of good x, so the satisfaction level goes on increasing. Hence, in all the 3 cases satisfaction increases, therefore an IC necessarily has to be downward sloping. Convex to Origin The second is that the IC is Convex to the origin, because of Diminishing MRS as we had seen earlier the IC has to have diminishing MRS to ensure that the level of satisfaction/ utility remains the same. Think about what Happens if the Indifference Curve is: Concave to origin – In this case the MRS would be increasing instead of decreasing Straight line downward sloping – In this case the MRS would be constant, as is only possible in the case of perfect substitutes. Hence, if the assumption of diminishing MRS is to be true the IC will have to be convex to the origin. Figure: Indifference Map Higher IC gives higher level of satisfaction Third is the case, that Higher Indifference Curve gives higher level of satisfaction, this is because we have assume non-satiety (that the consumer is not yet satisfied with the goods they have and hence as they consume more, their level of satisfaction goes on increasing); hence more is preferred to less and as we move from a lower Indifference Curve to a higher Indifference Curve, the consumer get either more of both the goods (if at the centre of the IC) or at least more of one of the goods and the same amount of the other good. Thus, a higher IC gives a higher level of utility or satisfaction, since the consumer is able to get more of the goods. No two ICs can intersect each other The fourth and the final one is that No two ICs can intersect each other, Because of law of Transitivity. Graph If two Indifference Curves intersect. The graph shows that there are two Ics that intersect each other and in this case: If we consider points a & b; a is preferred to b, since it is on a higher IC If we consider points c & d; d is preferred to c, since it is on a higher IC Also, a = e = c (same IC) Further, b = e = d (same IC) Hence: a = b = c = d = e But we know that a is preferred to b and d is preferred to c; based on the fact that a higher IC gives a higher level of satisfaction, hence the law of transitivity is violated and no two ICs can intersect each other. Perfect Substitutes – The IC for perfect substitute is a straight-line downward sloping, this is because in the case of perfect substitutes we are not bothered about good a or good b, but only in the total number of the goods. For example: Black pen and blue pen; if you are not very fussy about the colour, you would only be bother about the total number of pens you get and not whether you get black pens or blue pens. As a result, the MRS is 1, and the IC is a straight-line downward sloping. Perfect Complements – The IC for perfect complement is a L-shaped curve, this is because in the case of the perfect complements, you would consume the goods in rigid proportions, like 1 cup of tea and 2 spoons of sugar, of a left foot shoe and a right foot shoe. In this case, if you have just one cup of tea and 20 spoons of sugar, you would still be able to enjoy just 1 cup of tea, if the utility has to go up you would need addition cup of tea in addition to the sugar. Hence, you would require both the goods in multiples of the same proportion if your satisfaction has to go up and as a result the IC is a L-shaped curve.  Budget Line The budget line is a line representing the maximum of 2 goods that can be bought with a given level of Income 𝑀 = 𝑝𝑥 𝑞𝑥 + 𝑝𝑦 𝑞𝑦 Where: – M = Money Income – 𝑝𝑥 = price of good x – 𝑞𝑥 = quantity of good x – 𝑝𝑦 = price of good y – 𝑞𝑦 = quantity of good y This shows what is the maximum the consumer can consume given their level of income. Figure: Graph of Budget Line Now, if you look at the graph, what we have is the budget line. This line showcases that all the points under the line (towards the origin) are attainable and the consumer can choose any point. Any point above the budget line is unattainable. So, a rational consumer would choose to be somewhere on the budget line, where they are using their income to get the maximum goods they can. X Intercept = Money Income/ Price of Good x; so, if the money income is Rs. 100 and the price of good y is Rs. 20 per unit, then the X Intercept would be 100/ 20 = 5 units, it basically tells us what is the maximum units of the good x that the consumer can consume, if they spend all their income on good x only. The Y Intercept = Money Income/ price of good y; so, if the money income is Rs. 100 and the price of good y is Rs. 10 per unit, then the Y Intercept would be 100/ 10 = 10 units, it basically tells us what is the maximum units of the good y that the consumer can consume, if they spend all their income on good y only. When we join both the x intercept and the y intercept, what we get is the Budget Line. Change in Price of goods: – As a result of the change in the price of the good, the budget line will change its slope and pivot around the x or the y axis, depending on the good whose price had changed Change in money income of consumer: – As a result of the change in the money income of the consumer, the budget line will shift parallelly outward or inward, depending on whether the money income has increased or decreased. Let us now see in more detail what happens to the Budget Line as a result of the change in the Money income of the consumer: Figure: Budget Line Graph As you can see on the graph: If the money income increases the budget line shifts outward parallelly; why does this happen, lets see an example – if the money income is Rs. 100 and the price of good x is Rs. 20 and the price of good y is Rs. 10; then with the money income a consumer could by a maximum of 5 units of good x & 0 of good y or 0 units of good x & 10 units of good y or any other combination between these two extremes. Now if the money income were to increase to Rs. 200, keeping the prices constant, then with this increase in the money income a consumer could by a maximum of 10 units of good x & 0 of good y or 0 units of good x & 20 units of good y or any other combination between these two extremes. Hence as a result of doubling of Money income the x & y intercepts have also doubled and there would be a parallel shift in the budget line outward. If the money income decreases the budget line shifts inward parallelly, why does this happen, continuing with the earlier example, if the money income were to decrease to Rs.  50 from Rs.100, keeping the prices constant, then with this decrease in the money income a consumer could by a maximum of 2.5 units of good x & 0 of good y or 0 units of good x & 5 units of good y or any other combination between these two extremes. Hence as a result of halving of Money income the x & y intercepts have also halved and there would be a parallel shift in the budget line inward. Let us now see in more detail what happens to the Budget Line as a result of the change in the Price of Good X: Graph: Changes in Budget Line due to Price Change of Good X As you can see on the graph: If the price of good x increases the Budget line will pivot inwards (less of good x); why does this happen, continuing with the earlier example where the money income is Rs. 100 and the price of good x is Rs. 20 and the price of good y is Rs. 10. Now if the price of good x goes up to Rs. 25, as a result the consumer can now purchase a maximum of just 4 units of good x (lesser than the earlier case) so the x intercept comes down and the budget line pivots inwards. The Y intercept remains the same since there is no change in the price of good y. If the price of good x decreases the Budget line will pivot outwards (more of good x); In the other case if the price of good x decreases to Rs. 10 from Rs. 20, as a result the consumer can now purchase a maximum of just 10 units of good x (much more than the earlier case) so the x intercept goes up and the budget line pivots outwards. Again, the Y intercept remains the same since there is no change in the price of good y. Let us now see in more detail what happens to the Budget Line as a result of the change in the Price of Good Y: Graph: Changes in Budget Line due to Price Change of Good Y As you can see on the graph: If the price of good y increases the Budget line will pivot inwards (less of good y); why does this happen, continuing with the earlier example where the money income is Rs. 100 and the price of good x is Rs. 20 and the price of good y is Rs. 10. Now if the price of good y goes up to Rs. 15, as a result the consumer can now purchase a maximum of just 6.67 units of good y (lesser than the earlier case) so the y intercept comes down and the budget line pivots inwards. The X intercept remains the same since there is no change in the price of good x. If the price of good y decreases the Budget line will pivot outwards (more of good y); In the other case if the price of good y decreases to Rs. 5 from Rs. 10, as a result the consumer can now purchase a maximum of just 20 units of good y (much more than the earlier case) so the y intercept goes up and the budget line pivots outwards. Again, the X intercept remains the same since there is no change in the price of good y. Having understood the individual effects of changes in the budget line as a result of changes in the money income or the changes in price of the commodity, let us now see what happen when they all change together as mentioned below: 1. Money income increases by 50% 2. Price of Good x decreases by 25% 3. Price of Good y increases by 25% Let us take it step by step: Graph: Changes in Budgetline as a result of changes in money income & Price of goods As you can see on the graph, the green budget line is the original budget line. As a result of the Money income increasing by 50%; (budget line would shift outward parallelly) the budget line shifts outward and the new budget line is the brown budget line. As a result of the Price of Good x decreases by 25%; (the budget line would pivot around the y axis and move outward, as a result of price decrease); as a result of this price change, the new budget line is black budget line As a result of the Price of Good y increases by 25%; (the budget line would pivot around the x axis and move inward, as a result of price increase); as a result of this price change, the new budget line is yellow budget line Thus, as a result of all the three changes, the green original budget line, gets modified to the yellow budget line. Consumer Equilibrium The conditions required for the Consumer Equilibrium are: IC should be downward Sloping IC should be tangent to the budget line; i.e. slope of IC (MRS) = Slope of Budget Line (Price Ratio) 𝑃𝑥 Thus, the Consumer equilibrium is determined at a point where: 𝑀𝑅𝑆𝑥𝑦 = 𝑃𝑦  Graph: Consumer Equilibrium We saw the conditions required for the Consumer Equilibrium, now if you see the graph, you will be able to observe that: Point b is not attainable – since it is above the budget line, although we would like to be on point b, but our budget constraint does not let us reach that point. Points a, c, d & e are attainable – since they are on or below the budget line, and we can choose to be on any of those points. Point a is below the budget line indicating that a rational consumer would definitely not choose point a. Points c, d & e are also attainable – since they are on the budget line, and we can choose to be on any of those points. Among the points c, d & e, we have to determine the equilibrium point and graphically we can see that since point e is on a higher IC a rational consumer would definitely choose to be on point e. But then how are all the three points, c, d & e on the same budget line, let us discuss that as we progress. The difference between the slope of the Indifference Curve and the Slope of the Budget Line. Just to bring some more clarity and to give you a slightly different perspective, make a note of the following which is in extremely simple terms: Slope of IC – Is the Marginal Rate of Substitution (𝑀𝑅𝑆𝑥𝑦 ), dependent on the individual consumer and his/ her preference; meaning each consumer may decide their own MRS for the two goods depending on their preferences. Slope of BL  𝑃 – Is the price ratio (𝑃𝑥 ), which is the market exchange rate for the two goods, based 𝑦 on their prices in the open market; meaning that the price ratio is going to be the same for all the consumers irrespective of their preferences. Point A – This point is below the budget line, and hence a rational consumer would never choose to be on this point. Point B – This point is above the budget line, and hence a rational consumer would definitely want to be on this point, however, the budget constraint would never let them reach this point. Points C & D – These points are on the budget line and hence although the budget constraint allows the consumers to be on this point, since it is on a lower indifference curve they would be better of if they could reach a higher IC Point E – This point is on the budget line and hence the budget constraint allows the consumers to be on this point, yet it is on a higher indifference curve as compared to points C & D and hence any rational consumer would definitely choose point E, since that is the maximum they can get in their budget. At point C & D: At point C – the consumer has more of good Y and less of good x, so he values good x more than good y as a result they are willing to give more units of good y for an additional unit of good x and the reverse is true at point d. As we have seen earlier the slope of the IC or the MRS tells us the trade of between the two goods as determined by the consumer. This will continue to change depending on which good the consumer ha more and which they have lesser. At point C good x is valued more while at point D good y is valued more. So, at point C the consumer is willing to trade off multiple units of good y for an additional unit of good x. While if they are at point D, then they are willing to trade off multiple units of good x for an additional unit of good y. So, instead of giving more of either good in exchange for the one that they have lesser of, they can exchange the goods for one another at a better rate from the market, since the market exchange rate for the two goods determined by the price ratio remains constant and can move along the Budget line to reach a higher IC at point e and be better off. As they move along the budget line from point C or D to point E, they become better off, since they get more of both the goods from the same level of income. At point E; As the consumer moves from point C or D towards E, they become better off, since they get more of both the goods and in the process reach a higher indifference curve. 𝑃𝑥 At point e, 𝑀𝑅𝑆𝑥𝑦 = ; i.e. the way the consumer values the two goods are exactly the 𝑃𝑦 same as the market values them, and cannot do anything to any better. This is the point of tangency between the IC and the budget line. Also, both the conditions of the Consumer Equilibrium are fulfilled at point E Hence, point E is the point of consumer equilibrium.