question_answer

Explain why is an indifference curve (a) downward sloping and (b) convex.

Or

Explain the concept of 'Marginal Rate of Substitution' with the help of a numerical example. Also explain its behavior along an indifference curve.

 

Answer:

(a) Indifference curves are downward sloping from left to right. This reflects the fact that the consumer cannot simultaneously have more of both the goods. In other words, an increase in the quantity of one good is associated with the decrease in the quantity of the other good. This is in accordance with the assumption of monotonic preferences,
(b) Indifference curve is convex to the origin because as we move with the Indifference curve towards the right, the slope of IC (MRS) decreases. This is because as the consumer consumes more and more of one good, the marginal utility of the good falls. On the other hand, the marginal utility of the good sacrificed will rise. In other words, the consumer is willing to sacrifice less and less for each additional unit of the other good consumed. Thus, as we move down the 1C, MRS diminishes. This suggests the convex shape of indifference curve.
Or
Marginal rate of substitution refers to the rate at which a consumer is willing to substitute one good for each additional unit of other good.
Algebraically, it is represented as follows:
\[MRS={{\Delta }_{{{x}_{2}}}}/{{\Delta }_{{{x}_{1}}}}\]
This can be better understood with the help of the following numerical example.
Bundles	Good \[{{X}_{1}}\](units)	Good \[{{X}_{2}}\](units)
A	5	1
B	2	2
C	1	3
Now as we can see, a movement from Bundle A to Bundle B, in order to get one more units of Good\[{{X}_{2}}\], the consumer must sacrifice 3 units of Good\[{{X}_{1}}\]. This implies that MRS\[=\,3/1=\,3\].
As we move down along the Indifference curve to the right, Marginal Rate of Substitution decreases. This is because as the consumer consumes more and more of one good, the marginal utility of that good falls. On the other hand, the marginal utility of the good sacrificed will rise. In other words, the consumer is willing to sacrifice less and less for each additional unit of the other good consumed. Thus, as we move down the 1C, MRS diminishes. This suggests the convex shape of indifference curve. For instance, in the example given above, a further movement from bundle B to bundle C suggests that with one unit of increase in good 2, the consumer is willing to sacrifice good 1 falls to 1 unit. Thus, MRS falls.