The shape of the indifference curve and the marginal rate of substitution

The shape of the indifference curve and the marginal rate of substitution

Indifference curve is convex to the origin.
The marginal rate of substitution is the amount of one good (i.e. Good A) that has to be given up if the consumer is to obtain one extra unit of the other good (Good B).

The marginal rate of substitution (MRS) = change in good X / change in good Y

Using Figure 1, the marginal rate of substitution between point A and Point B is;

MRS = -6 / 2 = -3 = 3 (Note, the convention is to ignore the sign).

Combinations	Units of A	Units of B	Units of A given up to get few more units of B	MRTS=A/B
A	12	2	-
B	6	4	6 units of A to get 2 units of B	=-6/2= -3
C	4	6	2 units of A to get 2 units of B	=-2/2= -1
D	3	8	1 units of A to get 2 units of B	=-1/2 =-0.5

· The shape of the indifference curve is not a straight line. The indifference curve is convex to the origin.This is due to the concept of the diminishing marginal rate of substitution between the two goods.

· The marginal rate of substitution is the amount of one good (i.e. Good A) that has to be given up if the consumer is to obtain one extra unit of the other good (Good B).

· The slope of the curve represents the marginal rate of substitution, (MRS)

The reason why the marginal rate of substitution diminishes is due to the principle of diminishing marginal utility. Where this principle states that the more units of a good are consumed, then additional units will provide less additional satisfaction than the previous units. Therefore, as a person consumes more of one good (i.e. work) then they will receive diminishing utility for that extra unit (satisfaction), hence, they will be willing to give up less of their leisure to obtain one more unit of work.

The relationship between marginal utility and the marginal rate of substitution is often summarised with the following equation;

MRS = Mux / Muy