INDIFFERENCE CURVES Course: Seminar on Micro Economics GROUP MEMBERS: ALKA SINGH MAHAK ARORA PARAS HANDA PRIMAL SHARMA
Cardinal versus ordinal utility Early economists assumed that people are able to assign meaningful utility numbers (utils) to their satisfaction in one situation vis-à-vis their satisfaction in an alternative situation. For example, the utils generated by each brownie you eat or book you read would be recorded as if you have utilometer imbedded in your system. Cardinal measurement of utility Satisfaction, like temperature or distance, is assumed measurable in meaningful, absolute numbers.
Ordinal Utility Genesis… Cardinal measures are possible when incremental units are constant and reasonably objective, but utility is roughly measurable at best. As there is no one born equipped with a utilometer to precisely measure satisfaction. In the 1930s, Nobel prize-winner Sir John Hicks followed the leads of Vilfredo Pareto and Francis Y. Edgeworth to develop indifference analysis, an underpinning for the theory of consumer behavior that dispenses with cardinally-measured utility. Hicks argued that ranking our preferences is the best we can do.
INDIFFERENCE CURVES The technique of indifference curves was originated by Francis Y. Edgeworth in England in 1881. It was then refined by Vilfredo Pareto, an Italian economist in 1906. This technique attained perfection and systematic application in demand analysis at the hands of Prof. John Richard Hicks and R.G.D. Allen in 1934. Hicks discarded the Marshallian assumption of cardinal measurement of utility and suggested ordinal measurement which implies comparison and ranking without quantification of the magnitude of satisfaction enjoyed by the consumer .
Assumptions: Rational behavior of the consumer Utility is ordinal Diminishing marginal rate of substitution Consistency in choice Transitivity in choice making Goods consumed are substitutable
Axioms of rational choice• Completeness – if A and B are any two situations, an individual can always specify exactly one of these possibilities: • A is preferred to B • B is preferred to A • A and B are equally attractive
Axioms of rational choice• Transitivity – if A is preferred to B, and B is preferred to C, then A is preferred to C – assumes that the individual’s choices are internally consistent
Axioms of rational choice• Continuity – if A is preferred to B, then situations suitably “close to” A must also be preferred to B – used to analyze individuals’ responses to relatively small changes in income and prices
Definition An indifference curve is the locus of points representing all the different combinations of two goods which yield equal level of utility to the consumer. Indifference schedule is a list of various combinations of commodities which are equally satisfactory to the consumer concerned.
Two Indifference Schedules SCHEDULE 1 SCHEDULE2Good X Good Y Good X Good Y1 12 2 142 8 3 103 5 4 74 3 5 55 2 6 4 In Schedule 2,consumer has initially 2 units of goods X and 14 units of Y.So questions arises how much of Y would consumer be ready to abandon for succesive additions of X in his stock so that satisfaction remains equal as compared to his intial one i.e 2X+14Y.
Schedule 1 or Schedule 2? Any combination in schedule 2 will give consumer more satisfaction than in schedule 1. The reason for this is that more of a commodity is preferable to less of it. In simple terms, greater quantity of a good gives an individual more satisfaction than the smaller quantity of it,the quantity of other goods with him remaining the same.
Indifference Curves An indifference curve shows a set of consumption among which the individual is indifferentQuantity of Y Combinations (X1, Y1) and (X2, Y2) provide the same level of utility Y1 Y2 U1 Quantity of X X1 X2
Shape of Indifference Curve Indifference curve slope down and to the right, and the slope becomes less steep the farther right you go (this shape is sometimes described as convex or convex to the origin). Why? The curves slope down to the right because any combination on the curve would yield equal satisfaction.
Indifference Curve An indifference curve shows various combinations of goods that yield the same utility, but different indifference curves show different levels of utility. For instance, the green indifference curve on the graph below indicates a higher level of utility than the red or the blue indifference curves. Economists assume that people want to attain the highest level of utility possible (I3 is better than I2 which is better than I1) There are an infinite number of indifference curves in the indifference map, and each person’s indifference map is unique to that person.
Indifference Curve Map• Each point must have an indifference curve through itQuantity of y Increasing utility U3 U1 < U2 < U3 U2 U1 Quantity of x
Utility Given these assumptions, it is possible to show that people are able to rank in order all possible situations from least desirable to most Economists call this ranking utility if A is preferred to B, then the utility assigned to A exceeds the utility assigned to B U(A) > U(B)
Utility is affected by the consumption of physical commodities, psychological attitudes, peer group pressures, personal experiences, and the general cultural environment Economists generally devote attention to quantifiable options while holding constant the other things that affect utility ceteris paribus assumption
Preferences and Utility• Marginal Rate of Substitution, MRSyx : The rate at which a consumer is willing to sacrifice one good (y) in return for more of another good (x).• Principle of Diminishing Marginal Rate of Substitution : A rule stating that, for any convex indifference curve, when moving down the curve from the top (northwest) to the bottom (southeast), the absolute value of that curve’s slope must be continuously declining
Marginal Rate of Substitution • MRS changes as x and y change – reflects the individual’s willingness to trade y for xQuantity of y At (x1, y1), the indifference curve is steeper. The person would be willing to give up more y to gain additional units of x At (x2, y2), the indifference curve is flatter. The person would be y1 willing to give up less y to gain additional units of x y2 U1 Quantity of x x1 x2
Marginal Rate of Substitution • The negative of the slope of the indifference curve at any point is called the marginal rate of substitution (MRS)Quantity of y dy MRS dx U U1 y1 y2 U1 Quantity of x x1 x2
Properties of Indifference Curves • Higher indifference curves are preferred to lower ones. • Indifference curves are downward sloping. • Indifference curves do not cross. • Indifference curves are bowed inward.
Property 1: Higher indifference curves are preferred to lower ones.• Consumers usually prefer more of something to less of it.• Higher indifference curves represent larger quantities of goods than do lower indifference curves.
Property 2: Indifference curves are downward sloping. • A consumer is willing to give up one good only if he or she gets more of the other good in order to remain equally happy. • If the quantity of one good is reduced, the quantity of the other good must increase. • For this reason, most indifference curves slope downward.
Property 3: Indifference curves do not cross.Quantityof Pepsi C A B 0 Quantity of Pizza
Property 4: Indifference curves are bowed inward. People are more willing toQuantityof Pepsi trade away goods that they have in abundance and less 14 willing to trade away goods of MRS = 6 which they have little. 8 A 1 4 MRS = 1 B 3 Indifference 1 curve 0 2 3 6 7 Quantity of Pizza
Budget Line or Budget Constraint Essential for understanding the theory of consumer’s equilibrium. The budget line shows all the different combinations of two goods that a consumer can purchase given his money income and price of two commodities When a consumer attempts to maximize his satisfaction, there are two constraints: Paying the prices for the goods Limited money income
Budget Equation Px*X + Py*Y=MM := Income of the consumerPx := Price of good XPy := Price of good YX := Quantity of good XY := Quantity of good Y
A budget line 30 a Units of Units of Point on good X good Y budget line 0 30 a bUnits of good Y 20 5 20 b 10 10 15 0 10 Assumptions PX = £2 PY = £1 Budget = £30 0 0 5 10 15 20 Units of good X
Budget Line Continued… Budget line graphically shows the budget constraint. The combination of commodities lying to the right of the budget line are unattainable because income of the consumer is not sufficient to buy those combinations. The combinations of goods lying to the left of the budget line are attainable.
Budget Space A set of all combinations of the two commodities that can be purchased by spending the whole or a part of the given income.
Changes in Price and Shift in Budget Line At the lower price of X, the given income purchases OL’ of X which is greater than OL. At the higher price of X, the given income purchases OL” of X which is less than OL.
Changes in Income and Shift in Budget Line BL initial budget line If consumer’s income increases while prices of both X and Y remain unaltered, the price line shifts upwards i.e. B’L’ and is parallel to BL. Similarly it will shift downward i.e. B”L”, if income decreases.
Slope of Budget Line and Prices of two goodsSlope of budget line BL is equal to the ratio ofprices of two goods. Slope of budget line = OB/OL = Px / Py
Consumer Equilibrium It refers to a situation in which a consumer with given income and given prices purchases such a combination of goods which gives him maximum satisfaction and he is not willing to make any change in it. Assumptions: 1) The consumer has a given indifference map exhibiting his scale of preferences for various combinations of two goods, X and Y. 2) Fixed amount of money to spend and has to spend whole of his money on two goods. 3) Prices of goods are given and constant for him. He cannot influence those prices. 4) Goods are homogeneous and divisible.
There are three indifference curves IC1, IC2 and IC3. The price line PT is tangent to the indifference curve IC2 at point C. The consumer gets the maximum satisfaction or is in equilibrium at point C by purchasing OE units of good Y and OH units of good X with the given money income. The consumer cannot be in equilibrium at any other point on indifference curves. For instance, point R and S lie on lower indifference curve IC1 but yield less satisfaction. As regards point U on indifference curve IC3, the consumer no doubt gets higher satisfaction but that is outside the budget line and hence not achievable to the consumer.
Conditions A given price line must be tangent to an indifference curve or marginal rate of satisfaction of good X for good Y (MRSxy) must be equal to the price ratio of the two goods. i.e. MRSxy = Px / Py The second order condition is that indifference curve must be convex to the origin at the point of tangency.
Income Effect : Income Consumption Curve The income effect means the change in consumer’s preferences of the goods as a result of a change in his money income. Income consumption curve traces out the income effect on the quantity consumed of the goods. Income effect for a good is said to be positive when with the increase in income of the consumer, his consumption of good also increases. (Normal Goods) Income effect for a good is said to be negative when with the increase in income of the consumer, his consumption of good decreases. (Inferior Goods)
Continued… With the given budget line P1L1, the consumer is initially in equilibrium at point Q1 on the indifference curve IC1 and is having OM1 of X and ON1 of Y. As income increases budget line shifts upwards i.e. from P1L1 to P1L2 to P3L3 and so on. With budget line P2L2, equilibrium is at Q2 on IC2. Similarly it changes with next budget lines. If now various points Q1, Q2, Q3 and Q4 showing consumer’s equilibrium at various levels of income are joined together, we will gwt Income Consumption Curve.
Income Consumption Curve in Case of Good X being Inferior Good
Income Consumption Curve in Case of Good Y being Inferior Good
Engel curve An Engel curve describes how household expenditure on a particular good or service varies with household income. There are two varieties of Engel Curves. Budget share Engel Curves describe how the proportion of household income spent on a good varies with income. Alternatively, Engel curves can also describe how real expenditure varies with household income. They are named after the German statistician Ernst Engel (1821– 1896) who was the first to investigate this relationship between goods expenditure and income systematically in 1857. The best-known single result from the article is Engel’s Law which states that the poorer a family is, the larger the budget share it spends on nourishment.
The Shape of Engel Curves The shape of Engel curves depend on many demographic variables and other consumer characteristics. A good’s Engel curve reflects its income elasticity and indicates whether the good is an inferior, normal, or luxury good. Empirical Engel curves are close to linear for some goods, and highly nonlinear for others. Graphically, the Engel curve is represented in the first- quadrant of the Cartesian coordinate system. Income is shown on the Y-axis and the quantity demanded for the selected good or service is shown on the X-axis.
The Shape of Engel Curves (Contd.) For normal goods, the Engel curve has a positive gradient. That is, as income increases, the quantity demanded increases. Amongst normal goods, there are two possibilities. Although the Engel curve remains upward sloping in both cases, it bends toward the y-axis for necessities and towards the x- axis for luxury goods.
The Shape of Engel Curves (Contd.) For inferior goods, the Engel curve has a negative gradient. That means that as the consumer has more income, they will buy less of the inferior good because they are able to purchase better goods.
Applications Of Engel Curves In microeconomics Engel curves are used for equivalence scale calculations and related welfare comparisons, and determine properties of demand systems such as aggregability and rank. Engel curves have also been used to study how the changing industrial composition of growing economies are linked to the changes in the composition of household demand In trade theory, one explanation inter-industry trade has been the hypothesis that countries with similar income levels possess similar preferences for goods and services (the Lindner hypothesis), which suggests that understanding how the composition of household demand changes with income may play an important role in determining global trade patterns. Engel curves are also of great relevance in the measurement of inflation and tax policy
Substitution Effect It is the change in the quantity of good. purchased due to change in their relative prices alone, while real income of the consumer remains the same.
Substitution Effect (Contd.) In this diagram the consumer with given money income and given prices of two goods represented by price line PL is in equilibrium at point Q on the indifference curve IC. He buys ON quantity of good Y and OM of good X. We suppose now that the price of good X has fallen and the price of good Y remains the same. With the fall in the price line shifts from PL to PL/. Consumer’s real income is raised because commodity X is cheaper now. This increase in the real income of the consumer is to be wiped out for finding out the substitution effect. The reduction in the money income of the consumer is to be made by so much amount which keeps him on the same indifference curve IC.
Indifference Curve Analysis - Price Effect When there is no change in the income of the consumer, no change in the price of one commodity, and there is a change in the price of another commodity, there will be a change in the consumption made by the consumer. This change in consumption is known as the Price Effect. Though money income does not increase, the real income increases, generating more purchasing power.
Indifference Curve Analysis - Price Effect (Contd.) Under the Price Effect, there will be a change in the equilibrium position of the consumer. This can be shown in the following diagram. In this diagram PCC is the Price Consumption Curve. It is sloping downwards to the right. Any point on the Price Consumption Curve will indicate the equilibrium position of the consumer under the Price Effect. In this diagram when the price of X falls, the consumer purchases more of X and less of Y.
Indifference Curve Analysis - Price Effect (Contd.) Shapes of Price Consumption Curve With a fall in the price of one commodity there will be some extra income with the consumer. It can distribute this real extra income on the two commodities in different ways. So the Price Consumption Curve will have different shapes. Below we draw the different shapes of the Price Consumption Curve.
Indifference Curve Analysis - Price Effect (Contd.) In the above diagram PCC is the price consumption curve. It is a horizontal straight line. It indicates that with a fall in the price of X, the consumer purchases more of X and the same quantity of Y
Indifference Curve Analysis - Price Effect (Contd.) In the above diagram PCC, the price consumption curve, is sloping upwards to the right. This indicates that with a fall in the price of X the consumer purchases more of X and more of Y.
Indifference Curve Analysis - Price Effect (Contd.) In this diagram the price consumption curve is sloping upwards to the left. This indicates that with a fall in the price of X, the consumer purchases less of X. This is applicable in case of Giffen goods.