Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

66 CONSUMER DEMAND THEORY [CHAP. 4
EXAMPLE 6. In moving from point C to point D on indifference curve I in Fig. 4-2, the individual gives up 5 units of Y in
exchange for one additional unit of X. Thus, the MRS xy ¼ 5. Similarly, from point D to point F on indifference curve I, the
MRS xy ¼ 2. On moving down the indifference curve, the individual is willing to give up less and less of Y in order to gain
each additional unit of X (i.e., the MRS xy diminishes). This is so because the less of Y and the more of X the individual has
(i.e., the lower the point on the indifference curve), the more valuable is each remaining unit of Y and the less valuable is
each additional unit of X to the individual. Therefore, the individual is willing to give up less and less of Y to get each
additional unit of X, and the MRS xy diminishes.
EXAMPLE 7. Table 4.4 shows the MRS xy between the various points on indifference curves I, II, and III given in
Table 4.3. It should be noted that the MRS xy between two points on the same indifference curve is nothing else than the
absolute (or positive value of the) slope of the chord between the two points. Thus, the MRS xy between point C and
point D on indifference curve I is equal to the absolute slope of chord CD (which is equal to 5, see Fig. 4-2). Also, as
the distance between two points on an indifference curve decreases and approaches zero in the limit, the MRS xy approaches
the absolute slope of the indifference curve at a point. Thus, as point C approaches point D on indifference curve I, the
MRS xy approaches the absolute slope of the indifference curve at point D.
Table 4.4
Indifference Curve I Indifference Curve II Indifference Curve III
Q x Q y MRS xy Q x Q y MRS xy Q x Q y MRS xy
1 10 .. 3 10 .. 5 12 ..
2 5 5 4 7 3 6 9 3
3 3 2 5 5 2 7 7 2
4 2.3 0.7 6 4.2 0.8 8 6.2 0.8
5 1.7 0.6 7 3.5 0.7 9 5.5 0.7
6 1.2 0.5 8 3.2 0.3 10 5.2 0.3
7 0.8 0.4 9 3 0.2 11 5 0.2
8 0.5 0.3 10 2.9 0.1 12 4.9 0.1
9 0.3 0.2
10 0.2 0.1
4.5 CHARACTERISTICS OF INDIFFERENCE CURVES
Indifference curves exhibit three basic characteritics: they are negatively sloped, they are convex to the
origin, and they cannot intersect.
EXAMPLE 8. Since we are dealing with economic (i.e., scarce) goods, if consuming more of X, the individual must
consume less of Y to remain at the same level of satisfaction (i.e., on the same indifference curve). Therefore, an indifference
curve must be negatively sloped. It is also convex to the origin (see Fig. 4-2) because it exhibits diminishing MRS xy (see
Examples 6 and 7).
EXAMPLE 9. We can prove that indifference curves cannot intersect by looking at Fig. 4-3, which assumes the contrary.
G and H are two points on indifference curve I, and as such they yield equal satisfaction to the consumer. In addition, G and J
are two points on indifference curve II and they also yield equal satisfaction to the consumer. It follows that H and J are
points of equal satisfaction, so that, by definition, they lie on the same indifference curve (and not on two different
curves as assumed). Thus, it is impossible for indifference curves to intersect.