### 8.3 Indifference curve

On the last two pages it became clear which combinations of goods the consumer can afford. However, which of these combinations the consumer finally chooses, depends not only on his financial possibilities but also on his preferences. If, for example, he is offered 2 different purchasable bundles of goods to choose from, only his taste decides which one he prefers. If, on the other hand, he prefers neither one of the bundles, we say the consumer is indifferent between the two. Let us assume that the bundles of goods A and B are completely equivalent for the consumer. Now we give him another bundle C to choose from and he is just as indifferent to it as he is to A and B, so it doesn’t matter which one of these three bundles of goods he receives (of course, there are many other combinations that satisfy the household just as much as A, B and C). If we enter all these points into the above coordinate system, here as an example only A, B and C, they lie on a curve, the so-called indifference curve, here I1.
Thus, an indifference curve is the location of all combinations of goods that provide a household with the same benefit. For points B and C, for example, we can observe that more of Good 1 is consumed in point C than in B. Because of the idea that this household is equally happy with both combinations, it follows that more of Good 2 must be consumed in point B. By moving point A from B to C, the following can be observed: less consumption of Good 1 is balanced by additional consumption of Good 2 . Mathematically speaking, this means that the slope of the indifference curve is negative: more of a good in the direction of one axis leads to less of a good in the direction of the other axis. The ratio in which Good 1 is exchanged for Good 2 is called the marginal rate of substitution (MRS). Usually, this rate is not constant on an indifference curve, because if you already have a lot of Good 2 , you are much more likely to exchange some of it for Good 1 . The slope of the indifference curve indicates the value of the willingness to exchange one good for the other at each point of the curve.
Um To illustrate this, we can depict the marginal rate of substitution in the above graph. Moving point A close to point B, the MRS is approximately 5. Here, the consumer is willing to exchange 5 units of Good 2 for one unit of Good 1 without feeling worse off. Close to point C, however, the MRS is only about 0.1, or in other words: at this point the household would only exchange one unit of Good 2 for 10 units of Good 1 . As mentioned above, this makes sense because if you have a lot of Good 2 , you are willing to give up more of it to receive one unit of Good 1 . If we move point A from left to right on the indifference curve, we can see that the MRS or the slope of the indifference curve decreases steadily. Curves with a negative and simultaneously, in absolute value, decreasing slope are called convex. Indifference curves are therefore convex curves, because of the above consideration that the willingness to exchange – expressed by the slope in the respective points – decreases.
But what about point D? If we compare A and D in the starting position, we see that in point D more Good 1 and more Good 2 is consumed, so the household always prefers bundle D over bundle A. So D lies on a indifference curve, where the household prefers the bundles of goods to those on I1. If we move D, this shows all these equivalent combinations of goods (the same applies to point A). The level of consumption at I2 is higher than at I1, and higher-lying indifference curves are thus preferred to lower-lying indifference curves. One can imagine this like the contour lines on a map: if one moves along a contour line, one neither climbs up nor down, the same is true for a movement on an indifference curve: the consumer satisfaction level remains the same. However, if you move from one indifference curve to a higher one, the level of consumption and thus the degree of satisfaction increases. As in a map, not all contour lines are shown in the above graphic, but one can imagine them as a cohort.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de