A positively sloped indifference curve, which slopes upward to the right, implies that even if both the goods are increased, satisfaction level remains unaltered (figure 7.4) All these possible shapes of indifference curve are unacceptable as these violate the assumption of non-satiety.

#### 2. Indifference curve never intersect each other

If two indifferent curves intersect, the assumption of non-satiety is violated. Consider two indifference curves IC1 and IC2 intersecting at point C (figure 7.5). Take two points A and B on indifference curves IC1 and IC2 respectively.

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Since A and C lie on the same indifference curve (IC1), both the bundles yield equal satisfaction. Again, B and C lie on IC2. So these two points also yield the same satisfaction level. Following the assumption of transitivity, we can say that A and B also yield same satisfaction.

But A and B represent different combinations of commodities. Bundle A contains ‘Ad’ quantity of commodity 2 along with ‘od’ quantity of commodity 1 and bundle B contains ‘Bd’ quantity of commodity 2 along with ‘od’ quantity of commodity 1.

So bundle A contains more of commodity 2 (by ‘AB’ quantity) than bundle B though both the bundles contain the same amount of commodity 1. Since it is assumed that the consumers believe ‘more is better’, bundle A will undoubtedly yield more satisfaction than bundle B. This contradicts the earlier conclusion that bundles A and B are equal in terms of satisfaction. So, because of this contradiction, indifference curves never intersect.

#### 3. Indifference Curves are Convex to the Origin:

Negative slope of indifference curves does not ensure its convexity to the origin. Because a concave to the origin curve, a convex to the origin curve and downward sloping straight line – all are negatively sloped. It is the assumption of diminishing MRS that ensures convexity of normal indifference curves.

Assume that a person consumes only pizza and cold drink and IC1 is one of his indifference curves. Consider the movement from point A to B in figure 7.6. If a consumer sacrifices 2 units of pizza and gets 1 extra unit of cold drink (i.e. MRS = 2), his level of utility remains unchanged.

Again, a movement from B to C implies that sacrificing 2 units of pizza calls for 2 extra bottles of cold drink (i.e. MRS = 1) to maintain the same level of satisfaction. It shows that, a movement from left to right along the indifference curve entails continuous decline in MRS.

It is interesting to note that when a customer possesses 6 pieces of pizza, he can maintain his level of utility by exchanging 2 pizzas for one bottle of cold drink [movement from point A to point B in figure 7.6].

But when he possesses only 4 pizzas, each piece of pizza becomes more valuable to him than the previous situation and hence he will demand 2 bottles of cold drink for sacrificing 2 pieces of pizzas to maintain the same utility level [movement from point B to point C in figure 7.6].

The economics behind diminishing MRS as follows: as the consumer goes down along the IC, the number of pizza in his possession decreases causing an increase in marginal satisfaction of each unit of pizza.

It is also true that downward movement of a consumer along an IC increases number of cold drinks in his possession causing a decline in marginal utility of cold drink. So, as the number of pizza in his possession reduces, more bottles of cold drink are required to compensate the loss caused by giving up one piece of pizza.

But for a concave indifference curve [figure 7.7], MRS is positive which violates the assumption of diminishing MRS. In case of a straight line indifference curve [figure 7.8], MRS is constant throughout the IC, which also goes against the assumption of diminishing MRS.

#### 4. Higher Indifference Curves Represent Higher Satisfaction:

Let us assume that a particular consumer consumes two products – pizza and cold drink. Two indifference curves IC1 and IC2 represent two different levels of satisfaction and IC2 lies above IC1.

Let us take two points ‘a’ and ‘b’ on indifference curves IC1 and IC2 respectively. Point ‘a’ represents a combination of 6 pizzas and 3 bottles of cold drink. Point ‘b’ represents a combination of 6 pizzas and 7 bottles of cold drink.

Since the combination represented by point ‘b’ contains 4 bottles more cold drink than the combination represented by point ‘a’, the former yields more satisfaction than the latter because it is assumed that more quantity yields more satisfaction (assumption of non-satiety).

Not only for the pair of points ‘a’ and ‘b’; it is also true for the pair of points ‘c’ and’d’, ‘e’ and ‘f’ and so on. Hence the line joining points ‘b’, ‘d’ and T (i.e., IC2) will yield more satisfaction than the line joining points ‘a’, ‘c’ and ‘e’ (i.e. IC1) which establishes the fact that higher indifference curve represents higher level of satisfaction. 