In moving from point a to point b on Figure 4.4, 5 units of Y must be exchanged for an extra unit of X. MRSXY therefore equals 5. If we then move from point b to point c, and then from point c to point d, the marginal rate of substitution declines.
In moving up the indifference curve, the marginal rate of substitution of Y for X (MRSYX) similarly declines.
MRSXY can be seen geometrically in Figure 4.4 as the slope of a line (or chord) between point a and point b. The slope of such chords diminishes as we move down the curve. The marginal rate of substitution is therefore determined by the slope of the
indifference curve. At a single point on an indifference curve, the marginal rate of substi- tution would be represented by the slope of a tangent to the curve at that point. Such a tangent is shown at point b. As we move down the curve, the slope of corresponding tangents declines.
The marginal rate of substitution changes if there is a shift in consumer preferences between the goods. For example, referring again to Figure 4.4, if the consumer were to develop an increased desire for X over Y, the slope of the indifference curve would increase, illustrating the willingness of the consumer to sacrifice larger amounts of Y to obtain additional units of X. A shift in preference towards Y would cause the indifference curve to become more shallow.
We have noted the principle of diminishing marginal rate of substitution to be consis- tent with diminishing marginal utility. We may now show that MRSXY (the slope of the indifference curve) is equal to the ratio of the marginal utilities of the corresponding goods at that point on the indifference curve.
Recall that:
MRSXY
∆Y
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