BBA I Semester Managerial Economics Indifference Curves Analysis Study Material Notes

BBA I Semester Managerial Economics Indifference Curves Analysis Study Material Notes: Meaning of Infdefference Curve Law of diminishing Marginal Rate of Substitution ( DMRS ) Indifference Map Assumptions of the Indifference Curve Analysis   Properties of Indifference Curves Price Incom eLine or Budget Line Consumer Equilibrium Its Conditions Income Consumption curve and Inferior Goods The Substitution Effect The Price Effect Explanations Assumption separation substitution and Income Effects from the Price Effect :

MCom I Semester Business Environment GSTP GSP Counter Trade Study Material Notes

THE INDIFFERENCE CURVES ANALYSIS

INTRODUCTION

The indifference curve is a geometrical device developed by J.R. Hicks and R.G. D. Allen in an article “A Reconsideration of the Theory of Value”. It has been used to replace the neo-classical cardinal utility concept. Prof. Hicks presented its comprehensive version in his Value and Capital in 1939.

MEANING OF INDIFFERENCE CURVE

The indifference curve analysis measures utility ordinally. It explains consumer behaviour in terms of his preferences or rankings for different combinations of two goods, say X and Y. An indifference curve is drawn from the indifference schedule of the consumer. The latter shows the various combinations of the two commodities such that the consumer is indifferent to those combinations. “An indifference schedule is a list of combinations of two commodities, the list being so arranged that a consumer is indifferent to the combinations, preferring none of any other”. The following is an imaginary indifference schedule representing the various combinations of goods X and Y.

In the following schedule (Table 1) the consumer is indifferent whether he buys the first combination of units of 9Y+ 1 unit of X or the last combination of 3 units of Y+4 units of X or any other combination. All combinations give

him equal satisfaction. We have taken only one schedule, but any number of schedules can be taken for the two commodities. They may represent higher or lower satisfaction of the consumer.

If the various combinations are plotted on a diagram and are joined by a lines, this becomes an indifference curve, as I in the Figure 1. The indifference curve I, is the locus of the points L, M, N and P showing the combinations of the two goods X and Y between which the consumer is indifferent. “It is the locus of points representing pairs of quantities between which the individual is indifferent, so it is termed an indifference curve.”? It is, in fact, an iso-utility curve showing equal satisfaction at all its points.

Indifference Map

A single indifference curve concerns only one level of satisfaction. But there are a number of indifference curves as shown in Figure 2. The curves that are farther away from the origin represent higher levels of satisfaction as they have larger combinations of X and Y. Thus the indifference curve / indicates a higher level of satisfaction than I, which, in turn, is indicative of a higher level of satisfaction than I, and so on. Consumers would prefer to move in the direction indicated by the arrow in the figure. Such a diagram is known as an indifference map where each indifference curve corresponds to a different indifference schedule of the consumer. It is like a contour map showing the height of the land above sealevel where instead of height, each indifference curve rep- resents a level of satisfaction.

Assumptions of the Indifference Curve Analysis

The indifference curve analysis retains some of the assumptions of the cardinal theory, rejects others and formulates its own. The assumptions of the ordinal theory are the following:

1 The consumer acts rationally so as to maximize satisfaction.

2. There are two goods X and Y.

3. The consumer possesses complete information about the prices of the goods in the market.

4. The prices of the two goods are given.

5. The consumer’s tastes, habits and income remain the same throughout the analysis.

6. He prefers more of X to less of Y or more of Y to less of X.

7. An indifference curve is negatively inclined sloping downward.

8. An indifference curve is always convex to the origin.

9. An indifference curve is smooth and continuous which means that the two goods are highly divisible and that levels of satisfaction also change in a continuous manner.

10. The consumer arranges the two goods in a scale of preference which means that he has both preference’ and ‘indifference for the goods. He is supposed to rank them in his order of preference and can state if he prefers one combination to the other or is indifferent between them.

11. Both preference and indifference are transitive. It means that if combination A is preferable to B, and B to C, then A is preferable to C. Similarly, if the consumer is indifferent between combinations A and B and B and C, then he is different between A and C. This is an important assumption for making consistent choices among a large number of combinations.

12. The consumer is in a position to order all possible combinations of the two goods.

LAW OF DIMINISHING MARGINAL RATE OF SUBSTITUTION (DMRS)

The marginal rate of substitution is the rate of exchange between some units of goods X and Y which are equally preferred. The marginal rate of substitution of x for Y (MRS), is the amount of Y that will be given up for obtaining each additional unit of X. This rate is explained below in Table.2.

To have the second combination and yet to be at the same level of satisfaction, the consumer is prepared to forgo 3 units of Y for obtaining an extra unit ofx. The marginal rate of substitution of X for Y is 3:1. The rate of

Table 2. Marginal Rate of Substitution

substitution will then be the number of units of Y for which one unit of X is a substitute. As the consumer proceeds to have additional units of X, he is willing to give away less and less units of Y so that the marginal rate of substitution falls from 3:1 to 1:1 in the fourth combination (Col. 4).

In Fig. 3 above at point M on the indifference curve I, the consumer is willing to give up 3 units of Y to get an additional unit of X. Hence, MRS =3. As he moves along the curve from Mto N, MRS =2. When the consumer moves downwards along the indifference curve, he acquires more of X and less of y. The amount of Y he AY is prepared to give up to get additional units of X becomes smaller and smaller. The marginal rate of substitution of X for Y (MRS) is, in fact, the slope of the curve at a point on the indifference curve, such as points M, N or P

It means that the MRS is the ratio of change Good X in good Y to a given change in X. In the figure, there are three triangles on the I, curve whose vertical sides LA, MB and NC represent sy which diminish and the horizontal sides AM, BN and CP signify AX which remains the same. At point M MRS = LAIAM at Nit is MB/BN. This also shows that as the consumer moves downwards along the curve, he possesses additional units of X, and gives up lesser and lesser units of y, i.e., the MRS,,, diminishes. It is due to this law of diminishing MRS that an indifference curve is convex to the origin.

Exceptions of DMRS Law

However, this law is not applicable in the case of perfect substitutes and complementary goods. These are the exceptions of the DMRS law whereby an indifference curve is not convex to the origin but is a straight line and L-shaped.

1 Straight Line Indifference Curve. If MRS of X for Yor Y for Y is diminishing, the indifference curve must be convex to the origin. If it is constant, the indifference curve will be a straight line sloping downwards to the right at a 45° angle to either axis, as in Fig.4. This is the case of perfect substitute goods like Lux and 6 Godrej soap, Tata and Brooke Bond Tea, etc. When a consumer substitutes Lux for Godrej or vice versa, his satisfaction remains 0 the same. Thus MRS for perfect substitutes is constant, i.e.,

This is clear from equal triangles, Aabc= Acde, below

2. L-Shaped Indifference Curve. When two goods are used simultaneously in a constant ratio such as left shoe and right shoe, the indifference curve is L-Shaped or of 90° angle. Such a curve is for perfect complementary goods and their MRS_ is always zero: MRS =0. Figure 5 shows preferences of consumer for left and right shoes. Since shoes are perfect complementary, MB at point B of I curve an additional right shoe will not increase his satisfaction until he gets another left shoe of the same size. The Good X same is the case at point

A where he gets an additional left shoe without another right shoe. So the consumer will get full satisfaction at point M of the I curve where he purchases a left and right shoe of the same size and his MRS = 0. This is because he cannot substitute right and left shoes.

Indifference Curves Analysis

PROPERTIES OF INDIFFERENCE CURVES

From the assumptions described above the following properties of indifference curves can be deduced.

(1) A higher indifference curve to the right of another represents a higher level of satisfaction and a preferable combination of the two goods. In Figure 6, consider the indifference curves 1, and I, and combination N and A respectively on them. Since A is on a higher indifference curve and to the right of N, the consumer will be having more of both the goods X and Y, that is, Ox,+OY, in relation to OX+OY. Even if the two points on these curves are on the same plane as Mand A, the consumer will prefer the latter combination, because he will be more of good X though the quantity of good Y is the same.

(2) In between two indifference curves there can be a number of other indifference curves, one for every point in the space on the diagram.

(3) The numbers 1,1.,1..1…… etc. given to indifference curves are absolutely arbitrary. Any numbers can be given to indifference curves. The numbers can be in the ascending, order of 1, 2, 4, 6 or 2.3. 1.4 etc. Numbers have no importance in the indifference curve analysis.

(4) The slope of an indifference curve is negative, downward sloping, and from left to right. It means that the consumer to be indifferent to all the combinations on the indifference curves must leave less units of good Y in order to have more of good X. To prove this property, let us take indifference curves contrary to this assumption. In Figure 7 (A) combination B of Ox, + OY, is preferable to combination A which has a smaller amount of the two goods. Therefore, the indifference curve cannot slope upward from left to right. It is not an isoutility curve. Similarly, in Figure 7 (B) combination B is preferable to combination A for combination B has more of X and the same quantity of Y. So the indifference curve cannot be horizontal. In Figure 7 (C) the indifference curve is shown as vertical and again combination B is preferred to A as the consumer has more of Y and the same quantity of X. Therefore, the indifference curve cannot be vertical either. Consequently, the indifference curve will be of negative slope as shown in Figure 7 (D) where A and B combinations give equal satisfaction to the consumer. As he moves from combination A to B he gives up less quantity of Y in order to have more of x.

 (5) Indifference curves can neither touch nor intersect each other so that one indifference curve passes through only one point on an indifference map. What absurdity follows from such a situation can be shown with the help of Figure 8 (A) where the two curves I, and I, cut each other. Point A on the I, curve indicates a

A higher level of satisfaction than point B on the I, curve, as it lies farther away from the origin. But point C which lies on both the curves yields the same level of satisfaction as points A and B. Thus This is absurd because A is preferred to B, begin on a higher indifference curve Since each indifference curve represents a different level of satisfaction, indifference curves can never intersect at any point. The same reasoning applies if two indifference curves touch each other at point C in Panel (B) of the figure.

(6) An indifference curve cannot touch either axis. If it touches X-axis as I in Figure 9 at M, the consumer will be having OM quantity of good X and none of y. Similarly, if an indifference curve 1, touches the Y-axis at L the consumer will have only OL of Y good and no amount of X. Such curves are in contradiction to the assumption that the consumer buys two goods in combinations.

(7) An important property of indifference curves is that they are convex to the origin. The convexity rule implies that as the consumer substitutes X for Y the marginal rate of substitution diminishes. It means that as the amount X is increased by equal amounts that of Y diminishes by smaller amounts. The slope of the curve becomes smaller as we move to the right. To prove this, let us take a concave curve where the marginal rate of substitution of X for Y increases instead of diminishing, i.e., more of Y is given up to have additional units of X. As in Figure 10

(A) the consumer is giving up ab< cd ef units of Y for bc = de = fg units of X. But the indifference curve cannot be concave to the origin.

If we take a straight line indifference curve at an angle of 45° with either axis, the marginal rate of substitution between the two goods will be constant, as in Panel (B) where ab of Y = bc of X and c d of Y=de of X. Thus an indifference curve cannot be a straight line. Figure 10 (C) shows the indifference curve as convex to the origin. Here

the consumer is giving up less and less units of Y in order to have equal additional units of X i.e. abcdef of Y for bc = derfg of X. Thus an indifference curve is always convex to the origin because the marginal rate of substitution between the two goods declines.

(8) Indifference curves are not necessarily parallel to each other. Though they are falling, negatively inclined to the right, yet the rate of fall will not be the same for all indifference curves. In other words, the diminishing marginal rate of substitution between the two goods is essentially not the same in the case of all indifference schedules. The two curves and shown in figure 11 are not parallel to each other.

(9) In reality indifference curves are like bangles. But as a 6 matter of principle, their ‘effective region’ in the form of segments is shown in Figure 12. This is so because X Good x assumed to be negatively sloping and convex to the origin. An individual can move to higher indifference curves I, and I, until he reaches the saturation point S where his total utility is the maximum. If the consumer increases his consumption more than OX or OY, his total utility will fall. If he increases his consumption of X so as to reach the dotted portion of the I, curve horizontally from point S to N he gets negative utility. If to compensate himself for this loss of utility, he increases the consumption of Y, he may be again on the dotted portion of the curve, vertically from point Sto M. Thus the consumer may be on the concave portion of the circular curve. Since by moving to the dotted portion he gets negative utility, the effective region of the circular curve will be the convex portion.

Indifference Curves Analysis

PRICE-INCOME LINE OR BUDGET LINE

To study consumer equilibrium behavior, the knowledge of price- income line or budget line is necessary. An indifference map indicates preferences of the consumer only. But his actual selection of the two goods depends upon his income and their prices. According to Prof. Salvatore, “The budget line shows all the different combinations of the two commodities that a consumer can purchase, given his or her income and the price of the two commodities.”

We can explain a price or budget line with the help of a table. Suppose the monetary income of a consumer is Rs. 40 which he wants to spend on two goods X and Y. The price of good X is Rs. 2 per unit and that of good Y Re.I per unit. Given his income and prices of two goods, the alternative consumption or expenditure possibilities of a consumer are shown in Table 3.

It is obvious from the table that the consumer can spend on any of the alternative combinations of goods X and Y. However, if he spends his total income only on good X or Y, he can buy only 20 or 40 units respectively. But this is not possible because he has to buy only a combination of two goods. So he will buy any other combination.

Table 3: Alternative Consumption or Expenditure Possibilities

In Figure 13, the various combinations of the table are shown by the BL line. This is the price or budget line.* Given Rs 40 with the consumer, he can buy any one combination, R or S of goods X and Y. But he cannot obtain any point beyond this line such as combination A because it is out of reach of his income. On the other hand, he cannot obtain the combination even inside the BL line such as combination N because he can not spend all income (Rs.40) on both goods X

Thus consumer’s budget line is his budget limit or budget constraint line.

Changes in Price-Income Line

It is clear from the above analysis as to how many units of the two goods X and Y the consumer can purchase which depends upon his budget and the prices of both the goods. Now, we study as to how a consumer’s budget line will be affected by changes in price and income.

Indifference Curves Analysis

Change in Price

If the consumer’s income does not change but the prices of goods X and Y change, the slope of his budget line will change. Suppose that consumer’s income is Rs. 40 and the price of good Y (Re.1) remains constant and the price of good X falls from Rs. 2 to Re. 1, his budget line will rotate outwards from point B to the line L, He can now purchase the maximum 40 units of X as shown in Fig. 14. If the price of X increases from Rs. 2 to Rs. 4, his budget line will rotate inwards from point B to the line L, and he can purchase 10 units of X.

Take Figure 15, given the consumer’s income and price of X being constant, with a fall in the price of Y his budget line LB will rotate outwards from point L to LB,. This is because he buys more quantity of Y than before with the fall in its price. Conversely, with the increase in its price, his price income line LB will rotate to LB, because he purchases less quantity of Y than before.

The prices of X and Y remaining constant, if the consumer’s B income or budget increases or decreases, his income or budget line will also change. If income increases, the budget line will shift outwards as shown in Figure 16 where the BL line shifts to B, L,. On the other hand, if income falls, BL line will shift inwards to B,L,. Note that prices of goods X and Y being constant, there is no change in the slope of the budget line. There is a parallel inward or outward shift of the budget line.

CONSUMER’S EQUILIBRIUM

A consumer is in equilibrium when given his tastes, and prices of the two goods, he spends a given money income on the purchase of two goods in such a way as to get the maximum satisfaction.

Its Assumptions

The indifference curve analysis of consumer’s equilibrium is based on the following assumptions:

(1) The consumer’s indifference map for the two goods X and Y is based on his scale of preferences for them which does not change at all in this analysis.

(2) His money income is given and constant.

(3) Prices of the two goods X and Y are also given and constant.

(4) He has perfect knowledge about prices of two goods.

(5) The goods X and Y are homogeneous and divisible.

(6) There is no change in the tastes and habits of the consumer through out the analysis.

(7) The consumer can spend in small quantities.

(8) The consumer is rational and thus maximises his satisfaction from the purchase of the two goods.

(9) There is perfect competition in the market.

Its Conditions

There are two conditions for consumer’s equilibrium:

(1) The Budget Line should be Tangent to the Indifference Curve. Given these assumptions, the first condition for consumer’s equilibrium is that his budget line should be tangent to the highest possible indifference curve, as shown in Fig. 17. According to Prof. A. Koutsoyiannis, “Given the indifference map of the consumer and his budget line, the equilibrium is defined by the point of tangency of the budget line with the highest possible indifference curve.”

In Fig. 17, the consumer wants to be at I, consumption curve but it is not possible because it is beyond the reach of his given income and prices of X and Y goods which is clear from the price-income (budget) line BL. He can consume them at both or S points of /curve but none of these points is an optimum point. Such a point can be only one on his budget! Line BL and above the curve. This is the point E where the BL line is tangent to the highest possible I. curve and the consumer gets maximum satisfaction by purchasing OX units of X and OY units of Y. When the budget line is tangent to the indifference curve, it means that at the point of equilibrium, the slope of the indifference curve and of the budget line should be equal:

The slope of budget line = PIP

The slope of the indifference curve = MRS… Thus P. IP. – MRS at point E in Fig. 17. This is a necessary but not a sufficient condition for consumer’s equilibrium.

(2) Indifference Curve should be Convex to the Origin. 0 Therefore, the last condition is that at the point of equilibrium, the marginal rate of substitution of X for Y must be falling for equilibrium to be stable. It means that the indifference curve must be convex to the origin at the equilibrium point. If the indifference curve, 1,, is concave to the origin at the point R, the MRS increases. The consumer is at the minimum point of satisfaction at Ron Fig. 18.

A movement away from R toward either axis along PO would lead him to a higher indifference curve. Point S on the curve 1, is, in fact, the point of maximum satisfaction and of stable equilibrium. Thus for equilibrium to be stable at any point on an indifference curve, the marginal rate of substitution between any two goods must be diminishing and be equal to their price ratio, i.e., MRS. = P./P. fore, the indifference curve must be convex to the origin at the point of tangency with the budget line.

Indifference Curves Analysis

INCOME EFFECT

In the above analysis of the consumer’s equilibrium it was assumed that the income of the consumer remains constant, given the prices of the goods X and Y. Given the tastes and preferences of the consumer and the prices of the two goods, if the income of the consumer changes, the effect it will have on his purchases is known as the Income Effect. If the income of the consumer increases, his budget line shifts upward to the right, parallel to the original budget line. On the contrary, a fall in the income will shift the budget line inward to the left. The budget lines are parallel to each other because relative prices remain unchanged.

Assumptions

This analysis has the following assumptions:

1 There is no change in the tastes and preferences of consumer.

2.The relative prices of the goods X and Y are given.

3. The consumer’s income increases.

Explanation

In Figure 19, when the budget line is PQ, the equilibrium point is R where it touches the indifference curve I,. If now the income of the consumer increases, PQ will move to the right as the budget line P, Q, and the new equilibrium point is S where it touches the indifference curvel. As income increases further, P,Q, becomes the budget line with Tas its equilibrium noint The locus of these equilibrium points R, S and I traces out a curve which is called the the income effect of changes in consumer’s income on the

Normal Goods purchases of the two goods, given their relative prices. Р. Normally, when the income of the consumer increases, ICC he purchases larger quantities of two goods. In Figure:19, he buys OY of Y and OX of X at the equilibrium point Ron the budget line PQ. As his income increases, he buys Oy of Y Yand Ox, of X at the equilibrium point Son P,Q, budget line and still more of the two goods Oy, of Y and Ox of X, on the budget line P,Q,. Usually, the income-consumption curve slopes upwards to the right as shown in Figure 19.

Income Consumption Curve and Inferior Goods.

Normally, the slope of ICC curve is positive.

Such a slope is for both X and Y goods when they are normal or superior, as shown in Fig 19. But if either X good or 12 Y good is normal and the other is inferior, the slope of Inferior curve is negative. Inferior good is that whose consumption falls when the income of the consumer increases beyond a certain level and he replaces it by the superior substitute. He may replace coarse grains by wheat or rice, and coarse cloth by a fine variety. In Fig. 20 good y is inferior and good X is normal (superior). When the income of consumer is PQ, he is in equilibrium at point R on the / Curve. The slope of ICC 0 X XQ Q, XQ, curve is positive upto point Rand beyond that it is negatively Good X inclined as the income of consumer increases to P, Q, and P,Q,

Fig. 20 That is why, the quantity of inferior good purchased by a consumer becomes less from RX to SX, and TX, with the increase in his income while the amount of good X increases from OX to XX, and X,X,

On the other hand in Fig 21, X is inferior good and Y is normal (superior) good. Beyond point R, when the income of consumer increases from PQ to P, Q, and P,Q,, the purchased amount of good X decreases from OX to Ox, and OX, while quantity of good Y increases from RX to SX, and TX, Thus beyond point R, the ICC curve slopes backward to the left and the income effect is negative.

We can also show three ICC curves in a single diagram. In Fig. 22, ICC, shows the positive income effect when both X and Y goods are normal. ICC, curve shows negative income effect when Y is inferior good and X is normal (superior) good and ICC, curve also indicates negative income effect when X is inferior good and Y is normal good.

Indifference Curves Analysis

THE SUBSTITUTION EFFECT

The substitution effect relates to the change in the quantity demanded resulting from a change in the price of a good due to the substitution of a relatively cheaper good for a dearer one, while keeping the price of the other good and real income and tastes of the consumer as constant.

Prof. Hicks has explained the substitution effect independent of the income effect through compensating variation in income. The substitution effect is the increase in the quantity bought as the price of the commodity falls, after ‘adjusting income so as to keep the real purchasing power of the consumer the same as before. This adjustment in income is called compensating variation and is shown graphically by a parallel shift of the new budget line until it becomes tangent to the initial indifference curve. Thus on the basis of the method of compensating variation, the substitution effect measures the effect of the change in the relative price of a good with real income constant. The increase in the real income of the consumer as a result of fall in the price of, say, good X is so withdrawn that he is neither better off nor worse off that before.

Assumptions

The substitution effect is based on the following assumptions:

1 The relative prices of X and Y goods change thereby X and Y become costly.

2. The money income of the consumer changes in such a way that he is neither better off nor worse off than before.

3. The real income of the consumer remains constant.

4. Tastes of the consumer remain constant.

Explanation

Given these assumptions, the substitution effect is explained in Figure 23 where the original budget line is PQ with equilibrium at point on the indifference curve 1,. At R, the consumer is buying OB of X and BR of Y. Suppose the price of X falls so that his new budget lines is PQ,. With the fall in the price of X, the real income of the consumer increases.

To make the compensating variation in income or to keep the consumer’s real income constant, take away the increase in his income equal to PM of good Y or ON of good X so that his budget line PQ, shifts to the left as MN and is parallel to it. At the same time, MN is tangent to the original indifference curvel, but at point H where the consumer buys OD of X and DH of Y. Thus PM of Y or Q.N of X represents the compensating variation in income, by the line MN being tangent to the curve I at point H. Now the consumer substitutes Y and moves from point R to H or the horizontal distance from B to D. This movement called the substitution effect. The substitution effect is always negative because when the price of a good falls (or rises), more or less) of it would be purchased, real income and price of the other good remaining constant. In other words, the relation between price and quantity demanded being inverse, the substitution effect is negative.

THE PRICE EFFECT

Effect of change in Price on Consumer’s Equilibrium.

The price effect shows the effect of a change in the price of a commodity on its quantity purchased by the consumer, when the price of other commodity and consumer’s income remain constant.

We study the effect of fall in the price of good X on consumer’s equilibrium.

Assumptions

This analysis is based on the following assumptions:

1 Consumer wants to buy two goods X and Y.

2. Of these goods, the price of good X falls.

3. The price of good Y is given and constant.

4. Consumer income remains constant.

5. There is no change in tastes and preferences of the consumer.

Indifference Curves Analysis

Explanation

Given these assumptions, the price effect is shown in Fig 24. When the price of good X falls, the consumer’s budget line PQ will extend further out to the right as PQ, showing that the consumer will buy more X than before as X has become cheaper. The budget line PQ, shows a further fall in the price of X. Each of the budget lines fanning out from P is a tangent to an indifference curve I, 1, and I, at R, S and I respectively. The curve PCC connecting the locus of these equilibrium points is called the price-consumption curve or PCC. PCC curve is difined as the locus of optimum combination of X and Y that result from a change in relative prices, holding money income constant.

In Fig. 24, the PCC curve slopes downward. As the price of X falls, the consumer buys more of X and less of Y. Thus at point on the PCC curve, he purchases OB of X and OM of Y instead of OA of X and OL of Y at point R. A downward sloping price consumption curve thus shows that the two goods X and Y substitutes for one another. If the PCC slopes upward as shown in Fig. 25, X and Y are complementary goods. The consumer purchases larger quantities AB and MN of both the goods at points R and 7 respectively.

SEPARATION OF SUBSTITUTION AND INCOME EFFECTS FROM THE PRICE EFFECT

We saw that a fall in the price of good X, given the price of y, increases its demand. This is the price effect which has dual effects: a substitution effect and an income effect. The substitution effect relates to the increase in the quantity demand of X when its price falls while keeping the real income of the consumer constant. The consumer substitutes the cheaper good X for the relatively dearer good Y. The income effect is the increase in the quantity demanded of X when the real income of the consumer increases as a result of the fall in the price of X’while the price of Y is held constant. Thus Price Effect Substitution Effect +Income Effect

Hicks has separated the substitution effect and the income effect from the price effect through compensating variation in income by changing the relative price of a good while keeping the real income of the consumer constant.

Suppose initially the consumer is in equilibrium at point R on the budget line PM PQ where the indifference curve I, is tangent to it in Figure 26. Let the price of good X fall. As a result, his budget line M V rotates outward to PQ, where the consumer is in equilibrium at point T on the higher Effect indifference curve I,. The movement from Rto Tor B to E on the horizontal axis is the price effect of the fall in price of X. With Income the fall in the price of X, the consumer’s

Effect real income increases. To make the compensating variation in income and to a isolate the substitution effect, the money income is reduced equivalent N of X by drawing the budget line MN parallel to PQ, so that it is tangent to the original indifference curvel, at point H. The movement from Rto H on the I, curve is the substitution effect whereby the consumer increases his purchases of X from OB to OD by substituting X for Y because it is cheaper. It may be noted that when there is a fall (or rise) in the price of X, the substitution effect always leads to an increase (or decrease) in its quantity demanded. Thus the relation between price and quantity demanded being inverse, the substitution effect of a price change is always negative.

To isolate the income effect from the price effect, return the income which was taken way from the consumer so that he goes back to the budget line PQ, and is again in ibrium at point on the curve /,. The movement from point Hon the lower indifference is the income effect of the fall in the price curve /, to point Ton the higher indifference curve 7, is the income effect of the the method of compensating variation in income, the real income of the good X. By the method of the consumer has increased as a result of the fall in the price of X . The Consumer Purchases More of this cheaper good X thus moving on the horizontal axis from D to E. This is the effect of the fall in the price of a normal good X. The income effect with respect to the price change for a normal good is negative. Thus the relation between price and quantity demanded is inverse. That is why, the income effect is negative.

Substitution and Income Effects for an Inferior Good

If X is an inferior good, the income effect of a fall in the price of X will be positive because as the real income of the consumer increases, less quantity of X will be demanded. This is so because price and quantity demanded move in the same direction. On the other hand, the negative substitution effect will increase the quantity demanded of X. The negative substitution effect is stronger than the positive income effect in the case of inferior goods so that the total price effect is negative. It means that when the price of the inferior good falls, the consumer Inferior Good purchases more of it due to compensating variation in PIN income. The case of X as an inferior good is illustrated in Figure 27. Initially, the consumer is in equilibrium at MKRN point where the budget line PQ is tangent to the fall in the price of X, he moves to on the budget line PQ, at the higher indifference: curve I,.

His movement from R to T or from B to Eon axis is the price effect. By compensating variation in income, he is in equilibrium at point Hon the new budget line MN along the original curve I, The movement from R to H on the I, curve is the substitution effect measured horizontally by BD of X. To isolate the income effect, return the increased real income to the consumer which was taken from him so that he is again at point T of the equality of PQ, line and the curve I,. The movement from H to T is the income effect of the fall in the price of X and is measured by DE. This income effect is positive because the fall in the price of the inferior good X leads, to the decrease in its quantity demanded by DE. When the relation between price and quantity demanded is direct the income effect is always positive.

Indifference Curves Analysis

Substitution and Income Effects for a Geffen Good

A strongly inferior good is a Giffen good, after Sir Robert Giffen who found that potatoes were an indispensable food item for the poor peasants of Ireland. He observed that in the famine of 1848, a rise in the price of potatoes led to an increase in their quantity demanded. Thereafter, a fall in their price led to a reduction in their quantity demanded. This direct relation between price and quantity demanded in relation to essential food items is called the Giffen paradox. The reason for such a paradoxical tendency is that when the price of some food acticle like bread of mass consumption rises, this is tantamount to a fall in the real income of the consumers who reduce their expenses on more expensive food items, as a result the demand for the bread increases. Similarly, a fall in the price of bread raises the real income of consumers who substitute expensive food items for bread thereby reducing the demand for bread.

In the case of a Giffen good, the positive income effect is stronger than the negative substitution effect so that the consumer buys less of it when its price falls. This is illustrated in figure 28. Suppose X is a Giffen good and the initial equilibrium point is R where the budget line PQ is tangent to the indifference curve I. Now the price of X falls and the consumer moves to point T of the Income tangency between the budget line PQ Effect and the curve I,. His movement from point R to T’ is the price effect whereby Substitution he reduces his consumption of x by To isolate the substitution effect, the increased real income due to the

Good X fall in the price of X is withdrawn from Price Effect Fig. 28 the consumer by drawing the budget line MN parallel to PQ, and tangent to the original curve I, at point H. As a result, he moves from point Rto Halong the I, curve. This is the negative substitution effect which leads him to buy BD more of X with the fall in its price. To isolate the income effect, when the income that was taken away from the consumer is returned to him, he moves from point H to T so that he reduces the consumption of X by a very large quantity DE. This is the positive income effect because with the fall in the price of the Giffen good X, its quantity demanded is reduced by DE. Thus in the case of a Giffen good, the positive income effect DE is stronger than the negative substitution effect BD so that the total price effect is positive.

According to Hicks, a Giffen good must satisfy the following conditions: (i) the consumer must spend a large part of his income on it; (ii) it must be an inferior good with strong income effect; and (iii) the substitution effect must be weak. But Giffen goods are very rare which may satisfy these conditions.

Indifference Curves Analysis

TO DERIVE DEMAND CURVE FROM PRICE-CONSUMPTION CURVE

The price-consumption curve (PCC) indicates the various amounts of a commodity bought by a consumer when its price changes. The Marshallian demand curve also shows the different amounts of a good demanded by the consumer at various prices, other things remaining the same. Given the consumer’s money income and his indifference map, it is possible to draw his demand curve for any commodity from the PCC. The conventional demand curve is easy to draw from a given price-demand schedule for a commodity, whereas the drawing of a demand curve from the PCC is somewhat complicated. But the latter method has an edge over the former. It arrives at the same results without making the dubious assumptions of measurability of utility and constant marginal utility of money. The derivation of demand curve from the PCC also explains the income and substitution effects of a given fall or rise in the price of a good which the Marshalling demand curve fails to explain. Thus the ordinal technique of deriving a demand curve is better than the Marshalling method.

Assumptions

This analysis assumes that

(a) The money to be spent by the consumer is given and constant. It is Rs. 10.

(b) The price of good X falls.

(C) Prices of other related goods do not change.

(d) Consumer’s tastes and preferences remain constant. Explanation

If in the double storey Figure 29 money is taken on the vertical axis in rupees and good X on the horizontal axis. PQ, PQ, and PQ, are the budget lines of the consumer on which R, S and 7, are the equilibrium positions forming the PCC curve. He buys OA, OB and OC units of X respectively at these points on the PCC curve. If the total money income of the consumer is divided by the number of goods to be bought with it, we get per unit price of the good. For OA units of X, he pays OP/OQ price; for OB units, OP/OQ, price; and for OC units, OP/OQ, This is, in fact, the consumer’s price-demand schedule for good X which is shown in the tabular form in Table 4.

Indifference Curves Analysis

Table 4: Price-Demand Schedule for Good X

The price-demand schedule of the consumer for good X shows that given his money income OP (Rs 10) when he spends his income in buying OQ quantity (2 units), it means that the price of X is OP/ PQ (Rs. 5) as per budget line PQ at which the consumer buys OA (one unit) of good X. This is shown by point R on the I, curve. When the price of good X as determined by the budget line PQ, is OP/PQ, (Rs 2), the price-consumption curve shows that he buys OB (4 units) of X. This is shown by point Son the curve I, When the price of good X is determined as OP/OQ, (=Re 1) on the budget line PQ, and the curvel, at point T, the consumer buys OC (7 units) of X. Points R, S and T on the PCC curve show pricequantity relationships for good X.

These points are plotted on the lower diagram in Figure 29. The prices of X are taken on the vertical axis and quantity demanded on the horizontal axis. To draw the demand curve from the PCC, draw a perpendicular on the lower figure from point R in the upper portion of Fig. Pure 29 which should pass through point A. Then draw a line from point P, (=5) on the price axis (lower figure) which should cut the perpendicular at point F. The points G and Hare drawn in a similar fashion. They are joined by a line to form the demand curve D.

This curve shows the amount of X demanded by the consumer at various prices. With the fall in the price of X the consumer buys more units of it and the demand curve D slopes downward to the right. i Good X Curve. If the demand curves of a number of individuals are derived from this price-consumption curve for a good and then added together we get the market demand curve for that good. Thus in Figure (A) the demand for good X at the price OP, is Quantity Demanded of X on the part of consumer A. Consumer  demands of X at the same price and C consumer as shown in Panels (B) and (C). These quantities g. 9, and Q are added sideways in Panel (D), where OQ=2, +2, +Q The slope of the demand curves of all the individuals and hence for the market is the same.

Like the individual demand curve, the market demand curve will slope downward to the right. It will not, however, slope to the left even if the good happens to be inferior for some individuals. There will be other consumers demanding it at a lower price to whom it may not appear an inferior good. For the market as a whole a good is not likely to be inferior at all, there being always a sufficient number of buyers over the same price range. Hence the market demand curve will always slope downward to the right.

Indifference Curves Analysis

SUPERIORITY OF INDIFFERENCE CURVE TECHNIQUE OVER UTILITY ANALYSIS

The indifference curve technique, as developed by Professor Allen and Hicks, is regarded as an improvement over the Marshallian utility analysis because it is based on fewer and more realistic assumptions.

(1) It Dispenses with Cardinal Measurement of Utility. The entire utility analysis assumes that utility is a cardinally measurable quantity which can be assigned weights called ‘utils’. If the utility of an apple is 10 utils, of a banana it is 20 utils and of a cherry 40 utils, then the utility of a banana is twice that of an apple and of a cherry four times that of apple and twice that of banana. This is cardinal measurement of utility. In fact, the utility which a commodity possesses for a consumer is something subjective and psychological and therefore cannot be measured quantitatively. The indifference approach is superior to the utility analysis because it measures utility ordinally. The consumer arranges the various combinations of goods in a scale of preference marked as first second, third etc. He can tell whether he prefers the first to the second or the second to the first or he is indifferent between them. But he cannot tell by how much he prefers one to the other. The ordinal method makes this technique more realistic.

(2) It studies Combinations of two Goods instead of one Good. The utility approach is a single-commodity analysis in which the utility of one commodity is regarded independent of the other. Marshall avoided the discussion of substitutes and complementary goods by grouping them together as one commodity. This assumption is far from reality because a consumer buys not one but combinations of goods at a time. The indifference curve technique is a two commodity model which discusses consumer behavior in the case of substitutes, complementariness and unrelated goods. It is thus superior to the utility analysis.

(3) It explains the Law of Diminishing Marginal Utility without the Unrealistic Assumptions of the Utility Analysis. The utility analysis explains the law of diminishing marginal utility which is applicable to all types of goods, including money. Since this law is based on the cardinal measurement, it possesses all the defects inherent in the later. In the preference theory, this law has been replaced by the principle of diminishing marginal rate of substitution. It is scientific and is free from the quantitative measurement of utility.

(4) It is Free from the Assumption of Constant Marginal Utility of Money. This assumption makes the utility theory unrealistic. It is applicable to a single-commodity model. It fails to use money as the measuring rod of an individual’s satisfaction derived from the consumption of various goods. On the other hand, the indifference curve technique analyses the income effect when the income of the consumer changes.

(5) This Analysis explains the Dual Effect of the Price Effect. One of the main defects in the utility analysis is that it fails to analyze the income and substitution effects of a price change. In the indifference curve technique when the price of a good falls, the real income of the consumer increases. This is the income effect. Secondly, with the fall in price, the good becomes cheaper. The consumer substitutes it for some other good. This is the substitution effect.

(6) It rehabilitates the Concept of Consumer’s Surplus. Hicks has explained the concept of consumer’s surplus without the unrealistic assumption of the constancy of the marginal utility of money.

(7) It explains the Law of Demand more Realistically. The indifference curve technique explains the law of demand in a more realistic manner. It removes the assumptions of the utility analysis. It explains the effect of the fall in the price of an inferior good on consumer’s demand. Giffen goods have been also explained with the help of this technique.

Indifference Curves Analysis

CISMS OF INDIFFERENCE CURVE ANALYSIS

The indifference curve analysis has been criticized on the following grounds:

(1) Old Wine in New Bottles. Professor Robertson does not find anything new in the indifference curve technique and regards it simply ‘the old wine in a new bottle’. It substitutes the concept of preference for utility. It replaces cardinals by ordinals: instead of the cardinal numbers such as 1, 2, 3, etc., ordinal numbers 1, II, III etc. are used. It substitutes marginal utility by marginal rate of substitution and the law of diminishing marginal utility by the principle of diminishing marginal rate of substitution. Instead of Marshall’s proportionality rule to explain consumer’s equilibrium, the indifference curve technique equates the marginal rate of substitution to the price ratio of the two goods. Thus it merely gives new names to the old concept.

(2) Unrealistic. The indifference curve analysis is based on the assumption that the consumer is familiar with inumerable possible combinations of goods and his relative preferences for them. This is unrealistic.

(3) Absurd Combinations. Since the combinations of two goods are made without any regard of the nature of goods, they often become absurd. How many of us buy 10 pairs of shoes and 8 pants, 6 radios and 5 watches, 4 scooters and 3 cars? Such combinations do not possess any significance for the consumer.

(4) Two-Goods Model Unrealistic. The indifference curve analysis is a two-goods model. It analyses the consumer behavior with respect to two goods only and studies the equilibrium of one consumer. When more than two goods are involved and for studying group behavior indicating the choice of a region or country or town, it will not be possible to draw indifference curves.

(5) Ignores Market Behavior. It considers only the prices of two goods and ignores changes in prices of other goods.

(6) Consumers not Rational. The indifference curve assumes that the consumers are rational. They are calculating machines carrying innumerable combinations of different commodities in their head. This is really too much to expect from them.

(7) Based on Unrealistic Assumption of Perfect Competition. This analysis is based on perfect competition and homogeneity of goods, whereas in reality the consumer is confronted with differentiated products and monopolistic competition.

(8) All Commodities are not Divisible. The indifference curve analysis becomes ridiculous when it is assumed that goods are divisible in small units. Goods like watches, cars, radios, etc., are indivisible. To have 372 watches, or 212 cars or 12 radios in any combination is unrealistic. Indivisible goods cannot be substituted without dividing them. Thus the consumer cannot get maximum satisfaction from the use of indivisible goods.

(9) Fails to Explain Choices involving Risk or Uncertainty. It fails to explain consumer behavior when the individual is faced with choices involving risk or uncertainty of expectation.

(10) Indifference Curves not Transitive and Continuous. The assumptions of transitivity and continuity are not applicable to the real world. The real world exhibits discontinuity. According to Armstrong, the consumer is indifferent between the combinations of two goods because of his inability to judge the difference between alternative combinations.

(11) Tastes not Constant. This analysis assumes that consumers’ tastes remain constant over a period of time. This is not correct because tastes do change with the passage of time.

(12) Midway House. Indifference curves are hypothetical because they are not subject to direct measurement. Though consumer choices are grouped in combinations on an ordinal scale, no operational method has been devised so far to measure the exact shape of the indifferences curve. Prof. Schumpeter calls it a midway house because it lacks scientific approach.

(13) Introspective Behavior. Samuelson points out that this analysis is made on the ground of imaginarily drawn indifference curves regarding the behavior of the consumer. Hence it is introspective in nature.

(14) Weak Ordering Hypothesis. The indifference curve analysis is based on weak ordering hypothesis. This means that the consumer does not make definite preference or strong ordering while choosing one combination in relation to the other combination.

(15) Neglects Some Other Factors of Consumer Behaviour. This analysis neglects such important factors concerning consumer behaviour as speculative demand, demonstration effect, conspicous consumption, advertisement, etc.

Indifference Curves Analysis

EXERCISES

1What is the indifference curve ? Give its properties.

2. Explain the law of diminishing marginal rate of substitution in indifference curve analysis.

3. Explain the consumer’s equilibrium in terms of indifference curves.

4. Explain price effect in terms of indifference curves.

5. With the help of the indifference curve technique, explain income effect and substitution effect.

6. Differentiate between income effect and substitution effect caused by changes in the price of a commodity.

7. Explain the law of demand in terms of indifference curve.

8. Explain Income Consumption Curve.

9. Explain the budget line. How change in price and change in income effect consumer’s equilibrium?

10. Distinguish between (i) a normal and inferior good, (ii) inferior good and Giffen good in terms of indifference curves.

11. Explain the significance of indifference curve analysis.

12. Discuss the weaknesses of indifference curve analysis.

Indifference Curves Analysis