# Indifference Curves and Preferences

Why are averages preferred to extremes on the same indifference curve? Doesn't everything along an indifference curve have the same preference?

## 2 Answers

Why are averages preferred to extremes on the same indifference curve?

That is false. Whoever told you this is mistaken.

Or it could also be that you misheard/misread and are confusing this with the idea that the bundle of 100 apples + 100 oranges is (usually) preferred to the bundle of 200 apples or the bundle of 200 oranges.

Doesn't everything along an indifference curve have the same preference?

Yes.

• This should have been a comment for clarification. The “averages” to “extremes” point is indeed a misinterpretation but you dont answer the point. What OP is talking about is convexity of indifference curves—the tendency to prefer variety or a mixture of two goods as opposed to consuming just one. – Brennan Sep 13 '19 at 0:34
• @brennan IMO this answer is spot on. – Giskard Sep 13 '19 at 2:31
• @Brennan: I think I did exactly answer to the point. There were exactly two questions posed. My answers were that (1) the premise of the first question was false (I also suggested how the false premise/confusion might have arisen); and (2) the answer to the second question was in the affirmative. – user23102 Sep 13 '19 at 2:38
• Ok thats fair, i just figured the wording in the question was incorrect and hence false (in agreement with your answer) and what OP was actually meaning was that a combination of two goods is preferred to an extreme. I dont see the whole averages and extremes statement to be consistent with consumer theory either. – Brennan Sep 13 '19 at 5:37

Averages are preferred to extremes is an assumption we make while drawing our indifference curves. However, while using this assumption to draw our ICs, we do not consider any two arbitrary extreme points. We consider 2 arbitrary extreme points that give the consumer the SAME AMOUNT OF SATISFACTION. Now that we have these two extreme points, we can be sure that they lie on the same indifference curve.

Now, the convexity assumption kicks in. A bundle $$X$$ that is a linear combination of the two extreme bundles gives the consumer greater utility, and so will lie on a higher indifference curve.

That is to say, suppose the two extreme bundles are $$Y$$ and $$Z$$, and $$U(Y)$$=$$U(Z)$$. Then, for $$t{\epsilon} [0,1]$$,

$$U[(1-t)Y+tZ]>U(Y),U(Z)$$

Thus, along the same Indifference Curve, the level of utility is a constant.

The convexity assumption ensures that the set all bundles that are weakly preferred to the bundles of the indifference curve is a convex set.

Hope it helps!