<p>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 <strong>SAME AMOUNT OF SATISFACTION</strong>. Now that we have these two extreme points, we can be sure that they <em>lie on the same indifference curve</em>. </p>

<p>Now, the convexity assumption kicks in. A bundle <span class="math-container">$X$</span> that is a linear combination of the two extreme bundles gives the consumer greater utility, and so will lie on a higher indifference curve. </p>

<p>That is to say, suppose the two extreme bundles are <span class="math-container">$Y$</span> and <span class="math-container">$Z$</span>, and <span class="math-container">$U(Y)$</span>=<span class="math-container">$U(Z)$</span>.
Then, for <span class="math-container">$t{\epsilon} [0,1]$</span>, </p>

<p><span class="math-container">$U[(1-t)Y+tZ]&gt;U(Y),U(Z)$</span></p>

<p>Thus, along the same Indifference Curve, the level of utility is a constant.</p>

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

<p>Hope it helps!</p>

CC BY-SA 4.0
2019-09-15T13:33:52.843Z
2019-09-15T13:33:52.843Z
Ananya
<p>Why are averages preferred to extremes on the same indifference curve? Doesn't everything along an indifference curve have the same preference?</p>

<microeconomics><consumer-theory>
Indifference Curves and Preferences
econstudent
# Indifference Curves and Preferences

(Asked by: username_0 on 2019-09-12)

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

**Tags:** microeconomics, consumer-theory


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## 1 answers

### Answer by username_1 on 2019-09-15. Score: 0

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!


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