BCom 1st Year Modern Theory of Consumer Behaviour Notes Study Material
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BCom 1st Year Modern Theory of Consumer Behaviour Notes Study Material
The modern theory of consumer behaviour is based on ordinal utility approach. The main ordinal theories are (i) the indifference curve analysis and (ii) the revealed preference theory.
Origin of Indifference Curve Analysis
The analysis of consumer demand based on the notion of ordinal utility is called the indifference curve analysis of consumer demand.
The indifference curve is generally held to have been invented in 1881 by the English economist, F. Y. Edgeworth (1845-1926). It was carried to the continent of Europe where the Italian economist, Vilfredo Pareto (1848-1923), made extensive use of indifference curves in 1906.
Eugen Slutsky, the Russian economist and econometrician, argued that demand theory could be based on the concept of ordinal utility in an article published in 1915. In 1934 the two English economists, R. G. D. Allen (1906-1983) and J. R. Hicks (1904-1989) developed a full-fledged theory of consumer demand based on indifference curves. About the impact of Allen-Hicks consumer demand theory, it can be said,
“The attacks on the neo-classical cardinal utility concept early in the twentieth century were skirmishes on the outposts. But in the 1930s, heavy artillery was brought up and fired with apparently devastating results. The wreckage was swept away and ordinal utility was set on a throne consisting of a box of tools containing indifference curves.”
Indifference curve analysis is an alternative to the utility explanation of consumer behaviour. It eliminated the necessity of measuring utility and the principle of diminishing marginal utility. Without assuming that utility is measurable, a complete theory of consumer demand was constructed and this theory was as thorough going as Marshall’s.
Difference between Cardinal and Ordinal Utility
Cardinal and ordinal are terms borrowed from Mathematics. Number 1, 2, 3, 4, 5, etc. are cardinal numbers telling that number 4 is four times the size of number 1 and twice the size of number 2. Numbers 1st, 2nd, 3rd, 4th etc. are ordinal numbers. Such numbers are ordered or ranked and just from the ranking, the size relation of the numbers cannot be known. The ordinal numbers 1st, 2nd, 3rd and 4th could be 100, 300, 500 and 700 or 1, 100, 2,000 and 50,000.
To explain the difference between cardinal and ordinal utility more explicitly, let us take two combinations or baskets of goods A and B. Combination A may contain 6 apples, 3 oranges and 5 bananas, while B may have 8 apples, 2 oranges and 4 bananas.
In utility theory of consumer demand based on cardinal utility, the consumer is assumed to say that when his consumption basket changes, say, from A to B to C, he is better off or worse off and he can also say what is the magnitude of change. Thus he can not only say that C> B> A but also that C-B>B-A, that is, the change is utility in going from B to C exceeds the change in going from A to B.
In the case of ordinal utility he can only say that C > B > A which means that C is preferable to B and B is preferable to A, but cannot say by how much C is preferable to B and B is preferred to A. So he cannot say whether C – B is greater than, equal to or less than B – A. Indifference theory is based on “a much weaker assumption but it is all that is needed to develop demand theory.”
Since indifference curves are the main analytical tool of indifference curve analysis of consumer demand, we should begin with indifference curves. To understand indifference curves, it is better to begin with indifference schedules.
An indifference schedule is a tabular presentation of the combinations of two commodities which yield equal satisfaction to the consumer or among which the consumer is indifferent. Table contains two indifferent schedules:
Schedule A and Schedule B are schedules of two commodities X and Y. Each combination in schedule A is equally desirable and so the consumer gets equal satisfaction in having any one of the combinations 15X + 1Y, 11X + 2Y, 8X + 3Y or 6X + 4Y. Similarly, each one of the combinations in schedule B is equally desirable yielding the same satisfaction to the consumer. The consumer is, therefore, indifferent between them; he can have any one of 20X + 1Y, 15X + 2Y, 11X + 3Y or 8X + 4Y bundles.
An important point to note is that schedule B begins with 20 of X and 1 of Y. On the assumption that more of a commodity is preferable to less, any basket in B is preferred to any basket in schedule A.
We now go from indifference schedules to indifference curves, that is, from arithmetic to geometry. Indifference curves present a graphic picture of consumer preferences. An indifference curve shows the different combinations of commodities X and Y that yield equal satisfaction to the consumer, so he is indifferent among them.
In fig, horizontal axis measures physical units of commodity X and the vertical axis measures physical units of commodity Y. Thus both the axis measure quantity and any point in the field represents a combination of the two commodities X and Y.
If we assume that both the commodities can be divided into very small parts, we can draw a smooth indifference curve. This has been done in fig. IC1 and IC2 are two indifference curves corresponding to two schedules of Table. On IC1, we take a point A which presents OX1 + OY1 combination of the two commodities. Point A’ on IC2 presents another combination OX1 + OY2 of the two commodities.
When we compare points A and A’, we notice that both contain the same amount of X(= OX1), but different quantities of Y. A contains OY1 of Y, while A’ has OY2 of Y such that OY2 > OY1 by the quantity Y1Y2. Since more units of a commodity yields greater satisfaction, point A’ is preferable to A.
But points like C, B, A, D and E lie on the same indifference curve IC1, which means that they represent the same level of satisfaction. So the consumer is indifferent between them. These points represent such combinations of X and Y that if there are more units of one commodity, then there are less units of the other commodity.
As against points C, B, A, D and E on IC1, points like C’, B’, A’, D’, and E’ on IC2 make such combinations of X and Y, each of which contains more units of both the commodities or at least of one commodity. So all of them are preferable to points on IC1. Hence it is said that IC2 is a higher indifference curve which means higher level of satisfaction. IC1 is a lower indifference curve representing lower level of satisfaction.
“An indifference curve is the locus of points-particular combinations or bundles of goods—which yield the same utility (level of satisfaction) to the consumer, so that he is indifferent as to the particular combination he consumes.” An indifference curve presents a graphic picture of consumer tastes and preferences such that every point on it shows different combinations of X and Y that yield equal satisfaction to the consumer.
All definitions of an indifference curve are similar. According to Macmillan Dictionary of Modern Economics, an indifference curve is a “curve showing the locus of combinations of the amounts of two goods, say X and Y, such that the individual is indifferent between any combination on that curve.”
In deciding that combinations C, B, A, D and E are equally desirable to him and so lie on the same indifference curve, the consumer has considered only quantities of the two commodities, X and Y; no question of price has been raised at all. When price is also considered, our consumer may find that through all the above combinations give equal satisfaction, he cannot buy all combinations with his given money income.
Since the field in the diagram between the two axes contains infinite number of points and since an indifference curve passes through every point, there can be drawn a set of indifference curves which completely fill the space between the two axes. This set of indifference curves is known as the indifference map, as shown in fig. An indifference map presents a complete description of a consumer’s preferences for two commodities corresponding to an entire system of indifference schedules.
Each curve shows different combinations of the two commodities, X and Y that yield equal satisfaction to the consumer. Any curve that lies to the right of another curve is said to be a higher one.
Any combination of the two commodities on a higher curve is preferred to any combination on a lower curve. It is so because a combination on a higher curve contains more units of both the commodities (or at least of one commodity and same units of another) than that on a lower curve.
But any combination of the two commodities on a single indifference curve contains more of one commodity and less of another commodity than another combination and so the consumer is indifferent between them. “Indifference, therefore, means sliding back and forth on any one curve, and preference means moving north-east on the map,” as shown by the arrow in fig.
Characteristics or Properties of Indifference Curves
A system of indifference curves shows the following characteristics:
(i) Negative slope: An indifference curve has a negative slope. In other words, it slopes downwards to the right. It is for the reason that, in order to stay on the same level of satisfaction, if the quantity of one commodity (say, Y) decreases, the quantity of the other (X) must increase.
(ii) Convexity: An indifference curve is convex to the origin. In order to understand this property of the curve, we have to introduce the concept of the marginal rate of substitution. The marginal rate of substitution of X for Y (MRSXY) is defined as the amount of Y that must be given up in exchange to get an additional unit of X so that the consumer maintains the same level of satisfaction. In the case of Indifference Schedule A, the consumer takes 15 units of X and 1 unit of Y.
In order to obtain an additional unit of Y, he is willing to give up 4 units of X. Thus the marginal rate of substitution of X for Y is 4. In order to get yet another unit of Y, the consumer will not be prepared to sacrifice 4 units of X, but something less because more units he has of Y, it becomes less important for him and less he has of X, more important it becomes to him. Thus in the case of a combination in which there are only 8 units of X and 3 units of Y, the MRSXY is only 3. In a combination of 6X + 4Y, the MRSXY is only 2.
Similarly in Schedule B of Table, the MRSXY goes no declining from 5 to 4 to 3.
Decreasing marginal rate of substitution means that the indifference curve must be convex toward the origin. Diminishing MRSXY and the convexity of indifference curve are shown in fig.
We start with a combination at point A in which there is a large quantity of Y, OY’ and a small quantity of X, OX’. In order to get one more unit of X, the consumer is willing to give up ∆Y1. At point B, the consumer has a larger amount of X compared to point A.
So he is willing to sacrifice a smaller quantity of Y, ∆Y2< ∆Y1, in order to get yet another unit of X, ∆X2(=∆X1). At point C, there is plenty of X, but a small quantity of Y. So in order to get another unit of X(=∆X3), the amount of Y given up is much smaller-only ∆Y3. Thus the marginal rate of substitution goes on diminishing—∆Y1 > ∆Y2 > ∆Y3.
At any point on the indifference curve, the marginal rate of substitution of X for Y is given by the slope of the indifference curve at that point. Thus
MRSXY = slope of indifference curve = -∆Y/∆X
In the indifference curve analysis, the assumption of the principle of diminishing marginal utility of cardinal utility is substituted by the assumption of the convexity of the indifference curve which implies diminishing marginal rate of substitution of the commodities.
(iii) Indifference curves do not intersect or touch: If indifference curves intersect, the point of their intersection would imply two different levels of satisfaction, which is impossible. Fig. would help to explain this point.
In the diagram there are two indifference curves IC1 and IC2; IC2 is a higher indifference curve, while IC1 is a lower curve. A and B are two points on IC1 which represent the following two combinations of X and Y yielding same utility. Quantity of X
OX2 + OY1 = OX1 + OY2 …(1)
Similarly, two points A and C lie on IC2 representing the following two combinations of X and Y which yield the same level of satisfaction:
OX2 + OY1 = OX1 + OY3 …(2)
A close look at equations (1) and (2) will show that OX2 + OY1 is common for both, so
OX1 + OY2 = OX1 + OY3 …(3)
Equation (3) cannot be correct. OX1 is common on both sides, so OY2 should be equal to OY3. But this is not correct because OY3 > OY2, as given in figure. So the conclusion is that indifference curve cannot intersect. IC1 and IC2 touch at A. This leads to the same result. Indifference curves, therefore, cannot touch either.
(iv) Indifference curves are drawn as continuous curves, having no gaps or breaks: This is based on the assumption expressed as a willingness of the consumer always to accept some quantity of one good in exact compensation for a reduction, however small or large, in amount of the other good. This is the assumption of continuity.
Complementary and Substitute Goods
Convex indifference curves are based on the assumption that the commodities are substitutes of one another, but are not perfect substitutes. If the commodities are perfect substitutes the indifference curves are straight lines with negative slopes. The slopes of the lines indicate the rate at which one good can be substitute for the other.
Lipsey and Chrystal give the example of drawing pins. Red packages of 100 pins would be perfect substitutes for identical pins that come in green packages of 100. A consumer would be willing to substitute one type of package for the other at a rate of one for one.
If the commodities are perfect complements, like the right hand socks and left hand socks, indifference curves take the shape of right angle, i.e., they are L-shaped.
It is not always correct to say, however, that commodities are either substitutes or complements. In fig, the indifference curve IC1 is a curve where within the range of AB one commodity is a substitute for the other. But above point A and to the right of point B, they become complementary. Hot dog buns and wieners, according to Leftwich, are examples of such commodities.
In fig, indifference curves for a product that yields zero satisfaction have been presented. They run parallel to the axis yielding zero satisfaction.
Take the case of a vegetarian. For him meat gives no satisfaction at all. So he would not be willing to sacrifice even the smallest amount of vegetables to obtain any quantity of meat.
Equilibrium of the Consumer
Under consumer’s equilibrium is explained how a consumer reaches the position of maximum satisfaction. This is done with the help of indifference map. Several assumptions are usually mentioned as being required for consumer demand theory (consumer’s equilibrium) based on indifference curve analysis.
These assumptions are:
(i) Completeness: Simply stated, this assumption means that the consumer is able to order all combinations of goods according to his preferences. In other words, every consumer has a set of preferences for the commodities that he can purchase in the market. These preferences are given in the sense that they are not affected by a change in his income or a change in the price of any commodity. This assumption is necessary to ensure the predictability of the consumer behaviour.
(ii) Transitivity: This assumption states that if some combination of goods A is preferred to another combination B, and B is preferred to C then (by transitivity) A is preferred to C. Symbolically,
If A > B, and B > C, then A> C.
(iii) Selection: It means that the consumer aims for his most preferred state, that is, optimum satisfaction.
(iv) Dominance: The consumer prefers more goods to less. It is also known the assumption of non-satiation.
(v) Consistency: It is assumed that the consumer’s choices are consist If in one period he chooses combination A over B, he will not choose B over A another period if both combinations are available to him.
(vi) Given Income: The consumer has a given amount of money to so and he spends the whole amount on the two commodities. Thus he acts under budget constraint.
(vii) Given Prices: The consumer is one of the many buyers and knows the prices of all goods which are given and constant and makes no saving at all.
(viii) Homogeneity: All goods are homogeneous and divisible.
(ix) Convexity: The indifference curve is convex to the origin. It means that the marginal rate of substitution diminishes.
Keeping the above assumptions in mind, we can now consider consumer’s equilibrium. We start by assuming that our consumer has a given money income which he spends on two commodities X and Y whose prices are given in the market.
In fig. it has been shown that his money income in terms of X is OM or in terms of Y it is ON. In other words, if the consumer spends his whole income on X, the maximum quantity of X that can be bought is OM (the price of X is given).
Similarly, if he spends his whole income on Y, with the given price of Y, the maximum of Y that he can purchase is ON. By joining points M and N, we get a line MN which is called the price line or the budget line. The slope of MN shows the ratio of the prices of these two commodities and its position to the size of the Consumer’s money income.
The triangle OMN is the consumer’s choice triangle, given money income and commodity prices. Any point within the triangle or on the line MN is within his limits. If he takes any point within the triangle, he is not spending his entire income.
A number of indifference curves can pass through the price line MN. They will generally cut the line at two points. In the figure, IC1 cuts MN at A & B and IC2 at C and D. These are not equilibrium (maximum satisfaction) points because by moving up or down from these points on the budget line, the consumer can move to higher indifference curves, that is, to higher levels of satisfaction. By moving up from B on IC1, for instance, on the budge line, he comes to point D which lies on the higher indifference curve IC2 where his satisfaction is higher.
The consumer is in equilibrium at point P where the IC3 touches, i.e., is tangent to, the budget line. By moving up or down along the budget line from point P, the consumer comes to a lower indifference curve—the lower level of satisfaction. So IC3 is the highest attainable indifference curve for the consumer. Combination OX1 of X and OY1 of Y is the most preferred attainable bundle of these two goods.
In fig, a higher indifference, IC4, has also been drawn. Any combination of X and Y on this curve is preferable to any bundle of these two goods made on IC3. But, with the given income and prices of the two goods, IC4 is not attainable.
At the point of equilibrium, the indifference curve is tangent to the budget line. It means that at the tangent point, the slope of the indifference curve and that of the budget line are equal. This equality of slopes has an economic meaning. The slope of the indifference curve is ∆Y/∆X, that is, a change in Y divided by a change in X. It is the marginal rate of substitution (MRS). The slope of the budget line is , PX/PY where PX = price of X and PY = price of Y.
In terms of the indifference curve analysis, the condition of consumer equilibrium is ∆Y/∆X = PX/PY, that is, the marginal rate of substitution is equal to the ratio of the two prices.
But this is only the first condition of equilibrium. It is a necessary but not a sufficient condition for equilibrium. The second condition is that the indifference curves are convex to the origin, i.e., the marginal rate of substitution diminishes.
The indifference curve analysis does not require the cardinal utility approach. But the concept of marginal utility is implicit in the definition of the slope of the indifference curve. The slope of the indifference, ∆Y/∆X or MRS means a small loss of Y divided by a small gain in X. Between any two combinations of X and Y on any indifference curve, the consumer is indifferent because they yield equal satisfaction.
So the utility of loss of Y is equal to that of gain in X, that is,
∆Y x MUY = ∆X x MUX
where MUX = marginal utility of X and MUY = marginal utility of Y.
∆Y/∆X = MUX/MUY,
i.e., the slope of the curve is equal to the ratio of the marginal utilities. The slope of the budget line is PX/PY. At the point of equilibrium, therefore,
MRS = ∆Y/∆X = MUX/MUY = PX/PY
So MUX/MUY = PX/PY
Or MUX/PX = MUY/PY
The last equation is the condition of consumer’s equilibrium of the new classical cardinal utility analysis.