We have now developed an indifference map consisting of three indifference curves. We could imagine a larger number of curves, each curve denoting a different level of utility.
4.3.1 The properties of indifference curves
Indifference curves possess the following properties:
They have a negative slope
levels of satisfaction So long as both goods are desirable to the consumer (i.e. goods as opposed to bads), obtaining more of one good without a compensating reduction in the other makes the consumer better off. To maintain the same level of utility, the consumer must therefore sacrifice units of one good if obtaining additional units of the other. An indifference curve must therefore be downward sloping.
Indifference curves are convex to the origin
Convexity implies that the slope of the indifference curve falls as we move down the curve from left to right. This follows from our assumption of a diminishing marginal rate of substitution (see Section 4.2.5 above). This principle can be again illustrated in Figure 4.4.
As we move down the indifference curve in Figure 4.4, the consumer is willing to sac- rifice fewer units of Y to obtain additional X.
The marginal rate of substitution of X for Y is defined as the number of units of Y that must be sacrificed to gain an extra unit of X when total utility remains constant. That is:
MRSXY
∆Y
–––
∆X