Micro-economics, Indifference Curve, Properties of Indifference Curve: (3) Convexity:

3: Convexity:
The third property of indifference curve is that they are normally convex to the origin. The implication of this convexity have more and more units of goods x, and less and less of Y, the marginal rate of substitution of x for y goes on falling. This is the based on the law of diminishing marginal rate of substitution. The straight-line indifference curve and concave indifference curve do not follow the law. What absurdity follows when the curve is either concave or straight line. For the proof three graphs are illustrated. In figure(a), the indifference curve is convex to the origin. In figure (b) indifference curve is a straight line. In figure (c) indifference curve is concave to the origin.
Figure (a) shows that marginal rate of substitution of mangoes for apples falls. The convexity of indifference curve obeys the law of diminishing marginal rate of substitution.
Figure (b) shows that the marginal rate of substitution of mangoes for apples remains same which is against the behavior of the law of diminishing marginal rate of substitution.Figure (c) shows that the marginal rate of substitution of mangoes for apples increases which is opposite of the law of diminishing marginal rate of substitution.