Consumer Preferences, Indifference Curves and Substitution

The previous section summarised the amounts of goods that the individual consumer is able to buy under the budget constraint defined by the consumer’s income and the prices of the goods. The next question is how to choose among the attainable bundles, how to find the most valuable bundle. To answer this question we have to find out how the consumer assesses the goods and bundles of goods, how useful and how preferred he/she thinks they are. The various products and services satisfy various wants and needs for the consumer, and under the conditions of scarcity the consumer must choose which needs he/she will satisfy by purchasing commodities, and which ones he/she will sacrifice. Of course the consumer will want to safisfy the needs and wants that are more important than the others, so he/she tries to rank these wants either consciously or in a subconscious, instinctive way. The individual ranking order of wants is called the consumer’s scale of preferences (Farkasné Fekete - Molnár, 2007). The consumer’s scale of preferences is an individual ranking, and it depends on the consumer’s tastes, habits, and reflects mainly the individual’s subjective opinion and value judgement, although the actual socio-economic environment may influence it, too. It is important to understand that the consumer’s preferences are not the same as the consumer’s choices, because preferences depend basically on the utility of the product for the consumer, which is independent of the price of the product, while the actual amount purchased strongly depends on the consumer’s budget constraint, including the price of the product. In the following section the consumer’s scale of preferences will be discussed, and the utilities and uses of commodity bundles or commodity combinations will be described.

Take our example introduced in section 3.1, and suppose that the bundles of scones and sandwiches are compared again – but this time not by their costs, but by the usefulness or satisfaction their consumption provides for the consumer. Assume an initial situation, when the consumer has 4 sandwiches and 8 scones to consume. All the other bundles will be compared to this initial bundle by their utilities. Suppose that the consumer likes both the sandwiches and the scones, then he/she will find it beneficial to have 8 scones and 5

9 The described simple version of two products for the budget constraint can be generalised for more products, as in reality consumers spend their incomes on a lot more than two goods (products, or services). In theory a multi-product budget constraint can be written as I = p₁× x1 + p₂× x2 +p₃× x3 +…+p_n× xn , where p_i is the price and x_i is the quantity of product i , but a more useful version for practical applications is the one in which the income is divided between a particular product x and all the other commodities that the consumer buys. For this version the equation of the budget constraint is: I = p_x× x + 1× y. Here x stands for the quantity of the particular product of interest, p_x is its price, y represents a fictitious product measuring the income left after buying product x (applying p_y=1 as its fictitious price).

sandwiches with it, instead of 4 ones. Similarly, higher utility, or satisfaction is attained from any bundle having more than 4 sandwiches with the 8 scones, because any such bundle contains the initial option of 8 scones and 4 sandwiches to consume, and offers some additional sandwiches to be used. The consumer may eat these additional sandwiches, or he/she can offer it to a friend in exchange for some favour, so the additional sandwiches can be used for some valuable purpose. The situation is similar when the bundle contains a fixed amount of 4 sandwiches and the amount of scones is increased from 8 units up. Summing up, the consumer prefers – that is, attributes higher use to - all the commodity bundles in which the amount of one commodity is the same as in the initial bundle, and the amount of the other commodity is higher. Of course, all bundles are preferred to the initial bundle, that contain larger amounts of both commodities.

Applying the same reasoning, when the consumer’s bundle contains the same amount of sandwiches as in the initial bundle of (4 sandwiches; 8 scones) and the amount of scones decreases, then these bundles become less valuable, less preferred. The situation is the same when the amount of scones is unchanged and the amount of sandwiches are decreased. The bundles with fewer scones and fewer sandwiches than in the initial bundle are also dispreferred.

Thus, compared to the initial consumer bundle of (4 sandwiches; 8 scones) clearly preferred and clearly dispreferred consumer bundles have been identified. We cannot decide the exact preference ranking of consumer bundles containing more than 4 sandwiches and less than 8 scones, or more than 8 scones and less than 4 sandwiches. The preference ranking of these bundles depend on how many scones the consumer is willing to exchange for one sandwich without experiencing a change in his/her well-being, that is, how many units of one commodity to sacrifice for one additional unit of the other product.

Figure 3.3 demonstrates the original consumer bundle (4 sandwiches and 8 scones), and the definitely preferred or dispreferred bundles. Clearly, the bundle of (4;8) divides the space of attainable bundles (the space of consumption) into 4 sections. The lower left section (dark grey area) contains bundles definitely dispreferred to the initial one, the upper right section (light grey area) contains the bundled definitely preferred to the initial one. However, it is not clear whether the bundles in the lower right and the upper left sections (white areas) are preferred or dispreferred compared to the initial bundle. In these areas some of the bundles are preferred, some others are dispreferred, and others are exactly as useful as the initial bundle. It is certain, however, that bundles of the same usefulness as the initial bundle must lie here, namely in the upper left and the lower right sections of the graph, and nowhere else.

Bundles representing the same level of satisfaction for the consumer as the initial bundle are called indifferent bundles for the consumer’s choice, compared to the original bundle. When plotting all these indifferent bundles, the resulting series of points is called indifference curve.

The indifference curve defines the consumer’s bundles (commodity combinations) in the consumption space that represent the same level of utility, to the consumer (Farkasné Fekete – Molnár, 2007).

Assuming the divisibility of commodities the indifferent product combinations are scattered infinitely densely in the consumption space and the indifference curve is a continuous curve. In the rest of the text we will assume this, although real-world situations are rarely like this. Still, this assumption leads to many useful results that can be applied to non-continuous situations in practice.

Figure 3.3: Preferred and dispreferred bundles of goods

Source: Author’s own construction

The indifference curve belonging to the commodity bundle (4;8) is constructed as described above. Naturally, indifference curves may be constructed to any other initial bundle.

Thus, for example, after constructing the indifference curve of the initial bundle of (4; 10) we can declare, that this curve is preferred to the indifference curve of the bundle (4;8), -because the (4;10) bundle is preferred to the (4;8) bundle -, and lies above it in the consumption space. Similarly, the indifference curve of a dispreferred bundle will lie below the indifference curve of the initial bundle. This way an infinite number of indifference curves may be plotted in the consumption space. The diagram of these indifference curves is called indifference map, containing all combinations of two goods and the relevant indifference curves.

The indifference map is shown in the left panel of Figure 3.4. The figure demonstrates the most important properties of indifference curves. These are the following:

- Indifference curves are downward-sloping: This feature comes from the fact that when moving down along the same indifference curve, increasing the amount of product x the amount of product y must decrease to keep the utility of the bundle unchanged.

- Indifference curves running higher represent higher levels of utility: Taking commodity bundles with the same amount of product x, the more amount of y we have, the higher preference is attributed to the bundle; then the indifference curves containing such preferred bundles lie above the initial curve. The indifference curves (1), (2) and (3) in the left panel of Figure 3.4 demonstrate this property.

- Two different indifference curves cannot intersect: Assume that the indifference curves (3) and (4) in the left panel of Figure 3.4 are different, but intersect in point B. As they are different curves they must have different points, as point C in curve (3) and point A in

curve (4). Assume that points A and C represent commodity bundles in which the amounts of product x are the same, and the amounts of commodity y differ (higher for A than for C). This means that bundle A is preferred to bundle C. However, bundle A is indifferent to bundle B as both lie along the indifference curve (4). But bundle B is also indifferent to bundle C along the indifference curve (3). Therefore, as both bundle A and bundle C are indifferent to bundle B, then they must be indifferent to each other, too. This is a contradiction, as their y-amounts differ, while x-amounts are the same. This means that our initial assumption of the existence of an intersection point B was false.

- Indifference curves are convex: Instead of using the exact mathematical definition for convexity let’s take the intuitive geometrical interpretation: a curve is convex if connecting any two points of the curve the connecting line lies above the curve. This is illustrated in the right panel of Figure 3.4. The commodity bundle represented by point A contains a lot of commodity y, and only a little of commodity x. On the other hand bundle B contains only a small amount of y and a lot of x, therefore both A and B contains somewhat extreme combinations of the two goods. Let’s connect the two bundles A and B, and take the commodity bundle represented by point D in the connecting line. Bundle D contains less of y and more of x than bundle A, and more of y and less of x than bundle B, therefore its content is more balanced than either A or B. However, bundle D lies above the A-C-B indifference curve, so it is preferred to all of them (to A, B and C alike), its utility is higher than of those. Thus, convexity means, that the consumer prefers the balanced commodity bundles to any extreme bundle.

(1) (2)

(4)

(3) A

B C

A

C B D

Figure 3.4: Properties of the indifference curve and the indifference map

Source: Author’s own construction

Continuous indifference curves having the above properties are usually called ‘well-behaved’ indifference curves. Some consumers, or some goods may have specific properties that make the relevant indifference curves behave in a different way, but most of the consumers and most of the commodity bundles generally show the above characteristics. In the rest of the text – when it is not indicated otherwise – well-behaved indifference curves are assumed.

The negative slope of the indifference curve means that the consumer is willing to exchange any two bundles lying along the curve. In other words, for getting an additional unit of commodity x he/she is willing to give up a certain amount of commodity y, and the other way round, the consumer is willing to give up one unit of commodity x for getting some additional units of commodity y. This phenomenon is called substitution along the indifference curve, that is, the consumer substitutes a certain amount of commodity y for one additional unit of commodity x. The rate of the exchange between the two commodities is an

important property of the shape of the indifference curve. Naturally, the substitution depends on the actual amounts that the consumer owns of the two commodities, because having a lot of one of the commodities and a very small amount of the other, the consumer is willing to give up more of the first one for getting an additional unit of the second one.

Figure 3.5: Substitution along the indifference curve

Source: Author’s own construction

In Figure 3.5 the consumer is exchanging bundle A for bundle B, decreasing the amount of y for some additional amount of x. Then for giving up Δy of commodity y an additional amount of Δx is requested of commodity x as a compensation. The quotient of the absolute values of these two amounts is called the Rate of Substitution (RS).

The formula for computing the Rate of Substitution is: RS = |y / x | = - y / x, and this formula measures the absolute value of the slope of the line connecting points A and B. It is easy to see that this slope depends on the positions and the distance of A and B along the indifference curve. When point A is moved towards point B along the curve, the absolute value of the slope of the connecting line decreases, as well as the Rate of Substitution. For this reason an additional term is introduced: the Marginal Rate of Substitution (MRS) measures the amount of commodity y that the consumer is willing to give up for an infinitely small additional unit of commodity x, assuming that the utility of the new bundle remains the same as that of the initial bundle.

The formula for the Marginal Rate of Substitution is: MRS = |lim y/x| = |dy /dx |

= - dy / dx. The Marginal Rate of Substitution gives the absolute value of the slope of the tangent line of the indifference curve at point B (that is equal to the first derivative of the curve by x).