How to show the two Exceptions to the Convex Shape of Indifference Curves.

An indifference curve is a locus of combinations of two commodities that yield the same level of satisfaction to the consumer. In general, they are convex to the origin implying the decreasing slope or the diminishing marginal rate of substitution (MRSx,y) between two commodities x and y. However, there x, y may be exceptions to the convex shape of indifference curve as shown below:

L-shaped Indifference curves: In case the two goods under consideration are perfect complements to each other for example left shoe and right shoe, then the indifference curve will be L- shaped showing the strict complementary of the two goods. The MRSx,y is zero along the horizontal segment and infinite along the vertical segment for the Indifference curves in this case.

Negatively sloped straight line Indifference curves : In case the two goods are perfect substitutes to each other, then we have downward sloping straight line Indifference curve. The MRS will be constant for the two commodities such x, y as Pepsi and Coke as shown in the following diagram.