Chapter 2 Consumer s Equilibrium Who is Consumer A consumer is one who buys goods and services for satisfaction of wants. What is Equilibrium An equilibrium is a point of state or point of rest which every economic agent want to attain for maximization of his motive of economic activity by the optimum use of scare resources. But after attaining this level he has no tendency to change this point. What is Consumer s Equilibrium It is a situation in which a consumer utilize his income in such a manner that he maximize his total satisfaction at the given income at constant prices. The consumer have urge to reach at this point but do not want to go beyond this point of state. Approaches of Consumer s Equilibrium 1. Cardinal Approach Cardinal approach is propounded by Prof. Alfred Marshal in 1890. This approach also known Marginal Utility Analysis. According to cardinal approach utility of the goods and services are measurable in cardinal numbers (1, 2, 3,.) and express in terms of util. 2. Ordinal Approach Ordinal approach is given by R.G.D. Allen and J.R. Hicks in 193. This approach is well known as Indifference Curve Analysis. According to Marshall, ordinal approach satisfaction derives from goods and services cannot be measure but preference can be given to consumption like 1 st, 2 nd, 3 rd,.etc. Cardinal Utility Approach The cardinal utility theory was developed by classical economist like- H.H. Gossen (185) of Germany, William Stanley Jevons (1871) of England Leon walrus (187) of France, Karl Menger (180 1921) of Austria Neo-classical economists particularly Alfred Marshal (1890) redefine the cardinal utility theory. This lead the cardinal utility theory to be known as Marshalian Utility Theory. Before we proceed to describe the cardinal utility theory, we will first understand the basic concepts used in this theory. Utility Utility is the want satisfactory power of goods and services. Util Util is the measuring unit for utility. One util is equal to the money units those a consumer is willing to sacrifices for a commodity. How to Measure Utility? According to classical economists, utility can be measured, in the same way, as weight or height is measured. For this, economist assumed that utility can be measured in cardinal (numerical) terms. But, 1 Contact No. 77930-11198
there was no standard unit for measuring utility. So, the economists derived an imaginary measure, known as Util. Utils are imaginary and psychological units which are used to measure satisfaction (utility) obtained from consumption of a certain quantity of a commodity. Do not confused with the dictionary meaning of utility The dictionary meaning of utility is given as usefulness. However, to an economist, higher utility does not mean greater usefulness. For example, liquor is considered to be harmful for health, yet it may have a high degree of utility for an alcoholic. Satisfaction v/s Pleasure The word Satisfaction must not be confused with pleasure. For example, treatment of a patient for his broken arm is a source of great satisfaction for the patient. However, it does not provides him any pleasure as it is merely a relief from pain. Measurement of Utility 1. Marginal Utility (MU) Marginal utility is the additional utility derived from the consumption of one additional unit of a commodity. OR Marginal utility is the addition to the total utility. MU = ΔTU or MU = TUn Tun-1 ΔQ 2 Total Utility (TU) Total utility refers to the total satisfaction obtained from the consumption of all possible units of a commodity. OR Total utility is the sum total of marginal utility. TU = MU TU = MU1 + MU2 + MU3 + MU. MUn Units MU TU 1 6 6 2 3 2 12 0 12(Max) 5 2 Positive Marginal Utility: If total utility increases from consumption of additional units of a commodity, then marginal utilities of these units will be positive. Zero Marginal Utility: If the consumption of an additional unit of a commodity causes no change in the total utility, then marginal utility of the additional unit is zero. This point is also known as the Point of Satiety or the Point of Maximum Satisfaction. Negative Marginal Utility: If the consumption of an additional unit of a commodity causes a fall in the total utility, it means that the marginal utility of that unit is negative. Negative utility is also known as disutility. 2 Contact No. 77930-11198
Disutility is the opposite of utility. It refers to loss of satisfaction due to consumption of too much of a thing. TU and MU 1. TU increases till MU diminishes but positive (unit 1 to ) 2. TU is at maximum as MU reached at zero (unit number 5) 3. TU start declining as MU goes negative (unit number 6 and on ward) The Law of Diminishing Marginal Utility (LDMU) Law of Diminishing Marginal Utility (DMU) states that as we consume more and more units of a commodity, the utility derived from each successive unit goes on decreasing. The law of diminishing marginal utility state that as a consumer consumes standard unit (consumable unit) of a commodity in continuous manner, satisfaction derived from every additional unit will diminish continuously. Such a decrease in satisfaction with consumption of successive units occurs due to Law of diminishing marginal utility. Example:- Suppose you are very hungry and you are offered sandwiches to eat. The satisfaction which you derive from the first piece of sandwich would be maximum because intensity of your hunger was the highest. When you eat the second piece you derive a lower satisfaction because maximum hungriness was satisfied by first piece of sandwich. As you go on eating more and more pieces of sandwich the intensity of your hunger goes down. It is known as law of diminishing marginal utility. Assumptions of the Law of DMU:- Unit of the commodity should be standard unit in term of size or volume. There should be no time gap in the consumption period. Purpose of the consumption should be satisfaction, not for demonstration or show off. Mental status during the consumption time should be the same. Price of the good, income of the buyer, taste, preference and fashion should not change. Commodity should be Identical. Relationship between TU and MU:- Units MU TU 1 2 3 5 6 20 16 0 6 20 36 6 50 50 Point of Saturation :- It is a point where a consumer is fully satisfied after the consumption of certain units of a commodity. This point has no concern with the price of the commodity. At this point MU = zero, TU = Maximum. (at unit number 5) 3 Contact No. 77930-11198
Consumer s Equilibrium Consumer s Equilibrium refers to the situation when a consumer is having maximum satisfaction with limited income and has no tendency to change his way of existing expenditure. Consumer equilibrium refers to a situation under which the consumers spend his given income on the purchase of a commodity or combination of goods in such a way that gives him maximum satisfaction (or total utility). If consumers choose less to consume than the equilibrium unit will have less satisfaction and if he consume more than equilibrium unit than the total satisfaction will reduce. Hence a consumer do not have tendency to change the equilibrium. It is assumed that the consumer knows the different goods on which his income can be spent. It means, that the consumer has perfect knowledge of the various choices available to him. Two case of consumer s equilibrium under marginal utility analysis. (a) One Commodity Approach (B) Two (Multi) Commodity Approach (A) One Commodity Case A consumer purchasing a single commodity will be at equilibrium, when he is buying such a quantity of that commodity, which gives him maximum satisfaction. Being a rational consumer, he will be at equilibrium when marginal utility is equal to price paid for the commodity. While purchasing a commodity, a consumer compares its price with the expected utility obtain from it. He will buy the commodity so long as marginal utility is greater than price. How many units he will buy depends upon following condition of equilibrium. MUX = or MU of commodity MU of money = Price or The condition implies that MU of a commodity must be equal to price. MU X MU M = Price Example Units of icecream MU (Utils) MU in money MU X MU M 1 120 30 > 20 MUX > 2 0 25 > 20 5 Price Net gain (surplus) Remarks 3 80 20 = 20 0 MUX = 60 15 < 20-5 MUX < 5 0 < 20 - Suppose MU of money = Utils Price of ice-cream = Rs. 20 MU should decrease as consumption increases. Assumptions 1. Marginal utility of the good is measurable in terms of cardinal numbers. 2. Price of a commodity is constant. 3. Marginal utility of the money is also constant.. Consumer is a rational person. Contact No. 77930-11198
MUx = Px OR MUx = MUm MUm Px Satisfaction derived Sacrifice for an Actual satisfaction an Estimated satisfaction from unit of a good additional unit additional from an from an additional of a good addition unit unit Marginal Utility of Money MUm refers to worth of a rupee to consumer. The consumer is expected to define it himself. Equilibrium Condition Consumer in consumption of single commodity (say, x) will be at equilibrium when: Marginal Utility (MUx) is equal to Price (Px) paid for the commodity; i.e. MU = Price If MUx>Px then consumer is not at equilibrium and he goes on buying because benefit is greater than cost. As he buys more, MU falls because of operation of the law of diminishing marginal utility. When MU becomes equal to price, consumer gets the maximum benefits and is in equilibrium. When MUx <Px, then also consumer is not at equilibrium as he will have to reduce consumption of commodity x to raise his total satisfaction till MU becomes equal to price. Explanation of consumers equilibrium Suppose Px = MUm = 1 Util So MUx = Px MUm = Px (Mum = 1) Units of X 1 2 Price (Px) (Rs) Consumer s Equilibrium in case of Single Commodity Marginal Marginal utility Difference Utility In Rs (MUx) MUx and Px (units) 1 util = Rs1 20 16 20 1 = 20 16 1 = 16 20 = 16 = 6 3 1 = =0 5 6 0-6 1= 0 1=0-6 1 = 6 = -6 0 = 6 = 16 Remarks MUx > Px So Consumer will increase the consumption Consumer s Equilibrium (MUx = Px) MUx < Px, So Consumer will decreased the consumption 5 Contact No. 77930-11198
Consumer Surplus Consumer is in surplus situation at unit 1 and 2 because he is gaining more satisfaction than what he is expecting or scarifying (price) for the good. So consumer will choose these units for consumption. Consumer Equilibrium Consumer is in equilibrium situation at unit 3. Because he is obtain equal satisfaction to what he is expecting or sacrificing for the good. This equilibrium point is also known as point of rest, point of state. Because consumer have urge to react this point but do not have tendency to cross the point. Consumer Loss A consumer would not like to consume any unit after the equilibrium point. Because marginal satisfaction fall less than marginal sacrifices (price) for the unit (unit onwards). (B) Two (Multi) Commodity Case (Law of Equi- Marginal Utility) In real life, a consumer normally consumes more than one commodity. In such a situation, Law of Equi-Marginal Utility Helps in optimum allocation of his income. Law of Equi-marginal utility is also known as: (I) Law of Substitution; (II) Law of Maximum Satisfaction; (III) Gossen s Second Law. Under single commodity, we assumed that the entire income was spent on a single commodity. Now, consumer wants to allocated his money income between the two goods to attain the equilibrium position. When consumers choose two (or more than two) commodity for consumption then the maximum satisfaction will be at a point where ratio of marginal utility of both (or more) the commodities become equal to price ratio of both (or more) the commodities. This is according to law of equi marginal utility. There are two necessary conditions to attain Consumer s Equilibrium in case of Two Commodities: 1. A consumer attain equilibrium when he spends his given income in such a way that utility obtained from the last rupee spent on each good is equal. 2. Marginal utility should fall as consumption increases (Law of LDMU). Example Suppose 1. Consumer money income = Rs. 50. 2. Price of good X = Rs. per unit. 3. Price of good Y = Rs. 5 per unit. MU of money = Rs. 7 utils (constant) Units MUX MUY MUX/PX MUY/PY 1 90 60 9 12 2 80 50 8 3 70 5 7 9 60 35 6 7 5 50 25 5 5 When the consumer buys 3 units of X good and units of Y good, he will be in equilibrium. MU X = MU Y = MU M ; 70 5 7 = 7 = 7 6 Contact No. 77930-11198
Since MU are equated here to obtain max satisfaction. This is called principal of equilibrium utility. MU X > MU Y implies that per rupee MUX is higher than per rupee MUY. This induces the consumer to purchase more and max units of good X. Prices of the two goods remaining unchanged. Buying more of good X would reduce per rupee MUX and buying less of good Y would raise per rupee. MUX per rupee < MUY per rupee This will continue till MU X = MU Y. If MUX > PX, consumer will increase his purchase. If MUX < PX, consumer will decrease his purchase. If MUX = PX, consumer will attain equilibrium. According to diagram consumer will attain equilibrium when he purchase 8 units of good X and 12 units of good Y. What happen when MU X This meant that is more than MU Y? MU from last rupee spent on X is greater than MU from last rupee spent on Y. (MUM on X good > MUM on Y good) So the consumer will transfer expenditure from Y good to X good. The consumption of X rises, while that of Y falls (Law of LDMU). As a consequence MUx falls and MUY rises. The act of transfer of expenditure continues till MU X = MU Y. What happens whom MU X This mean that is less than MU Y? MU from last rupee spent on X is smaller than MU from last rupee spent of Y. So the consumer will transfer expenditure from X to Y. The consumption of Y rise, while that of X falls (Law of LDMU). The act of transfer of expenditure continues till MU X = MU Y. Note :- For fulfillment of first condition MU X = MU Y. Second condition (Law of LDMU) is also necessary. Finally, it can be concluded that a consumer in consumption of two commodities will be at equilibrium when he spends his limited income in such a way that the ratios of marginal utilities of two commodities and their respective prices are equal and MU falls as consumption increases. 7 Contact No. 77930-11198
Explanation Suppose Px = Py = Rupee 1 Income = Rupees 7 Units MUx MUy 1 2 3 5 6 1 12 8 6 12 8 6 3 Limitation of Utility Analysis Utility is a feeling of mind and there cannot be a standard measure of what a person feels. So, utility cannot be expressed in figures(numerically). Because satisfaction is a mental phenomenon. Ordinal Utility Approach (Indifference Curve Analysis) This approach given by R.G.D Allen and J.R. Hicks in 193. Ordinal approach is strongly opposing the marshal s concept that the marginal utility of goods and services are measurable. Hicks and Allen said that a rational consumer can only give preferential order to his consumption but no cardinal number use by him to show satisfaction level. Ordinal approach use Indifference Curve and Budget Line to show consumer s equilibrium condition. Modern economists disregarded the concept of Cardinal Measure of Utility. They were of the opinion that utility is a psychological phenomenon and it is next to impossible to measure the utility in absolute terms. According to them, a consumers can rank various combinations of goods and services in order of his preference. For example, if a consumer consumes two goods, Apples and Bananas, then he can indicate: 1. Whether he prefers apple over banana; or 2. Whether he prefers banana over apple; or 3. Whether he is indifference between apples and bananas, i.e. both are equally preferable and both of them give him same level of satisfaction. This approach does not use cardinal values like 1, 2, 3,, etc. Rather, it makes use of ordinal numbers like 1 st, 2 nd, 3 rd, th, etc. which can be used only for making. Meaning of Indifference Curve Indifference curve refers to the graphical representation of various alternative combinations of bundles of two goods among which the consumer is indifferent. or Indifference curve is a curve which shows different combination of two goods those gives equal level of satisfaction and the consumer become indifferent between two combinations of two goods when it comes to make choice between them. Indifference Set (Schedule) 8 Contact No. 77930-11198
It is a set of those combinations of two goods which offer the consumer same level of satisfaction. Combination Apple Orange Satisfaction A B C D 1 2 3 7 5 2500 calories 2500 calories 2500 calories 2500 calories In the diagram, X-axis measures good 1 while Y-axis means good 2. A curve is drawn by joining different bundles A, B, C and D of good 1 and good 2 and it form the IC curve. The different bundles give equal satisfaction to the consumer. An indifference curve represents all the combinations, which provide same level of satisfaction. Monotonic Preferences Monotonic preference means that a rational consumer always prefers more of a commodity as it offers him a higher level of satisfaction. In simple words, monotonic preferences implies that as consumption increases total utility also increases. Indifference Map Indifference Map refers to the family of indifference curves that represent consumer preferences over all the bundles of the two goods. It must be noted that Higher Indifference curves represent higher levels of satisfaction as higher indifference curve represents larger bundle of goods, which means more utility because of monotonic preference. Marginal Rate of MRS Substitution:- It is the rate at which the consumer is willing to sacrifice one good to obtain one more unit. MRS = Y axis (Loss) X axis (Gain) Y = Change in good Y X = Change in good X. For example, in the example of apples (A) and bananas (B), MRS of A for B, will be number of units of B, that the consumer is willing to sacrifice for an additional unit of A, So as to maintain the same level of satisfaction. Units of Bananas (B) willing to Sacrifice MRSAB = Units of Apples (A) willing to Gain MRSAB is the rate at which a consumer is willing to give up Bananas for one more unit of Apple. It means, MRS measures the slope of indifference curve. 9 Contact No. 77930-11198
Combination P Q R S T Apples (A) 1 2 3 5 Banana (B) 15 6 3 1 MRSAB - 5 5B:1A B:1A 3 3B:1A 2 2B: 1A Why MRS Diminishes? MRS Falls because of the law of diminishing marginal utility. The negative slope of IC implies that two commodities are not perfect substitutes for each other. If a consumer having more and more of Apple, his intensity of desire to have it reduces and its willingness to sacrifice less and less Banana for every additional unit of Apple. Properties/Features/Characteristics of an IC 1. ICs have negative slope It implies two facts, (a) That the two commodities can be substitute with each other. (b) If quantity of one commodity increases quantity of the other commodity must decrease to Stay on equal level of satisfaction. 2. ICs are convex to the origin An indifference curve is convex to the origin because of diminishing MRS. MRS declines continuously because of the law of diminishing marginal utility. It must be noted that MRS indicates the slope of indifference curve. 3. Higher IC means higher the level of satisfaction Higher IC have more quantity of two goods in a bundle as compare to lower IC and we know more quantity consume more satisfaction.. Two ICs never intersect each other The two ICs never intersects each other. If they intersects, at some point, both the ICs Shows same satisfaction and at same point lower IC gives more satisfaction that the higher one which is not possible. Because it discard the third properties. 5. An IC never touches X and Y axis An IC is draw for two commodities not for one hence it never touch any axis. If an IC touches any axis means it is for only one good. Assumptions of Indifference Curve 1. Two commodities: It is assumed that the consumer has a fixed amount of money, whole of which is to be spent on the two goods, given constant prices of both the goods. Contact No. 77930-11198
2. Non Satiety: It is assumed that the consumer has not reached the point of saturation. Consumer always prefer more of both commodities, i.e. he always tries to move to a higher indifference curve to get higher and higher satisfaction. 3. Ordinal Utility: Consumer can rank his preferences on the basis of the satisfaction from each bundle of goods.. Diminishing Marginal Rate of Substituting 5. Rational Consumer: The consumer is assumed to behave in a rational manner, i.e. he aims to maximize his total satisfaction. Budget Line or Price Line Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer. When all these bundles are represented graphically, we get a downward sloping straight line, known as Budget Line. It is also known as Price Line. Budget Set Budget set is the set of all possible combinations of the two goods which a consumer can afford, given his income and prices in the market. Diagrammatic Explanation of Budget Line Suppose, a consumer has a budget of Rs 20 to be spent on two commodities: Apples (A) and Bananas (B). If apple is priced at Rs each and banana at Rs 2 each, then the consumer can determine the various combinations (bundles), which from the budget line. The possible options of spending income of Rs 20 are given in Table. Combination of Apples and Bananas E F G H I J Apples (A) (Rs each) 5 3 2 1 0 Schedule of Budget Line Bananas (B) (Rs 2 each) 0 2 6 8 Money Spent = Income (Rs) (5x) + (0 x2) = 20 (x) + (2 x2) = 20 (3x) + (x2) = 20 (2x) + (6x2) = 20 (1x) + (8x2) = 20 (0x) + ( x2) = 20 Slope of the Budget Line We know, the slope of a curve is calculated as a change in variable on the vertical or Y-axis divided by change in variable on the horizontal or X-axis. Slope of the budget line will be number of units of bananas, that the consumer is willing to sacrifice for an additional unit of apple. Units of Bananas (B)willing to Sacrific Slope of Budget Line = = B Units of Apples (A) willing to Gain A 11 Contact No. 77930-11198
Budget Constraint Budget line shown the budget constraint (i). Income of the consumer. (ii). Prices of both the goods. Properties of Budget Line 1. Budget line is left to right down ward sloping It is because a consumer can buy extra units of one commodity only by sacrificing some units of the other commodity as the income is constant. 2. Budget line is a straight line Slope of budget line is straight because it is based in two assumptions (a) Consumer has a fixed income. (b) Prices of two goods are given. Change in Budget Line 1. Due to change in Price:- (A) If price of X good Increases or Decreases (B) If price of Y good Increases or Decreases (A) If price of Good 1 rises so a budget line rotate to left ON to ON2.If price of Good 1 falls then budget line rotate to right ON to ON1 (B) If price of Good 2 rises then budget line rotate downward from OM to OM 2. If price of Good 2 falls then budget line rotate upward from OM to OM1. 2. Due to change in Income:- I If income of the buyer Increases II If income of the buyer Decreases If income of the buyer increases than budget line shifted right ward from OA- OB to OA1 - OB1 If income of the buyer decreases than budget line shifted left ward from OA -OB to OA2 - OB2 12 Contact No. 77930-11198
Consumer Equilibrium by Indifference Curve Analysis Consumer equilibrium refers to a situation, in which a consumer derives maximum satisfaction, with no intention to change it and subject to given prices and his given income. The point of maximum satisfaction is achieved by studying indifference map and budget line together. On an indifference map, higher indifference curve represents a higher level of satisfaction than any lower indifference curve, So, a consumer always tries to remain at the highest possible indifference curve, subject to his budget constraint. Conditions of Consumer s Equilibrium The consumer s equilibrium under the indifference curve theory must meet the following two conditions: (i) MRSXY = Ratio of prices or If MRSXY, it means that the consumer is willing to consume more of X. As a result, MRS falls till it becomes equal to the ratio of prices and the equilibrium is established. If MRSXY, it means that the consumer is willing to pay less for X than the price prevailing in the market. It induces the consumer to buy less of X and more of Y. As a result, MRS rises till it becomes equal to the ratio of prices and the equilibrium is established. (ii) MRS continuously falls. The second condition for consumer s equilibrium is that MRS must be diminishing at the point of equilibrium, i.e. the indifference curve must be convex to the origin at the point of equilibrium. Unless MRS continuously falls, the equilibrium cannot be established. Thus, both the conditions need to be fulfilled for a consumer to be in a equilibrium. The budget line is tangent to indifference curve IC2 at point E. This is the point of consumer equilibrium, where the consumer purchases OM quantity of commodity X and ON quantity of commodity Y. Both the conditions of consumer s equilibrium are satisfied: (i) (ii) MRS = Ratio of prices or : MRS continuously falls. The second condition is also satisfied at point E as MRS is diminishing at point E, i.e. IC2 is convex to the origin at point E. 13 Contact No. 77930-11198
In the above diagram AB is budget line which shows consumers purchasing power (MRE) Market Rate Exchange. IC1, IC2, IC3 are showing consumers preference. The slope of IC and slope of budget line are equal at point E. this is consumer s equilibrium. MRSXY = It is the number of units of Y the consumer s is willing to sacrifice to obtain an extra unit of X. Initially when the consumer starts purchase, MRSXY > (MRE) it means To obtain one extra unit of X the consumer is willing to sacrifice more than he has to sacrifice actually. He starts purchasing more of X commodity. Therefore Marginal Utility of X goes an declining. Consumer is willing to sacrifice less & less units of Y good. Therefore MRS xy fall till it become equal to so MRS XY =. If consumer, attempts of obtain more units of X good beyond the equilibrium level P MRSXY < X Therefore total utility start falling. So he will not try to obtain more of X units, rather he will reduce the consumption of X good till. Note :- The consumer cannot get satisfaction level higher than IC2 because his income doesn t permit him to move above the budget line AB.Therefore, the equilibrium choice is only at the tangency point E. Consumer s Equilibrium (Ordinal Approach) According to ordinal approach a consumer is in equilibrium situation where an indifference curve becomes tangent to Budget line. Difference between cardinal and ordinal approach of consumer behavior Basis of Difference Cardinal Approach/ Utility Ordinal Approach/ Analysis Indifference Analysis Cardinal numbers are used to Ordinal numbers (order of Measurement of utility measure utility preference ) are used to express utility. Basic concept Marginal utility Marginal Rate of Substitution Goods One commodity and multi Only applicable in two commodity cases commodity cases Propounded by Alfred Marshall (1890) J.R. Hicks and R.G.D. Allen Concept about utility Utility is measurable and it is objective concept (because satisfaction laying in the goods and services) (193) Utility is not measurable and it is subjective concept (because satisfaction laying in the mind of the consumer) 1 Contact No. 77930-11198