<p>In order to know the exact bundle for that maximizes utility, you need to know what the consumer's preferences are. Nevertheless, if you knew that good <span class="math-container">$z$</span> is an inferior good for this particular consumer at <strong>her current income level</strong>, you should still be able to draw this diagram. The only thing you need is to recall the definition of an inferior good: a good is said to be inferior if as income increases its consumption decreases. This alone implies that <span class="math-container">$z_3&lt;z_2.$</span> Observe that in the diagram the budget constraint is drawn for three income levels. As income increases from <span class="math-container">$m_1$</span> to <span class="math-container">$m_2,$</span> consumption of goes from <span class="math-container">$z_1$</span> to <span class="math-container">$z_2,$</span> implying that <span class="math-container">$z$</span> is an inferior good. If income increases further to <span class="math-container">$m_3,$</span> consumption needs to reduce relative to <span class="math-container">$z_2.$</span></p>

<p>Note that it could have been the case that as income grew from <span class="math-container">$m_1$</span> to <span class="math-container">$m_2$</span> consumtion of <span class="math-container">$z$</span> increased, but from <span class="math-container">$m_2$</span> to <span class="math-container">$m_3$</span> it decreased. This is why I emphasized the role of consumer income: a given good may be normal at some income levels and then inferior for other, presumably larger, income levels.</p>

CC BY-SA 4.0
2019-01-21T08:12:51.427Z
2019-01-21T08:12:51.427Z
Patricio
<p>In Consumer Choice, we frequently encounter budget lines and indifference curves. For a given budget line, the optimization point is at the point where the indifference curve is just tangent to the budget line. For example, here is a graph used to illustrate how inferior goods behave with increases in income:</p>

<p><a href="https://i.sstatic.net/vNt0w.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vNt0w.png" alt="enter image description here"></a></p>

<p>Here, as the budget line shifts to <span class="math-container">$ I_3 $</span>, we're shown that consumption of <span class="math-container">$ z $</span>, an inferior good, decreases. My question is: what's stopping me from drawing the indifference curve elsewhere? Why can't I draw the indifference curve tangent to <span class="math-container">$ I_3 $</span>, just right of <span class="math-container">$ z_1 $</span> so that <span class="math-container">$ z_3 &gt; z_1 $</span>? </p>

<p>Sure, the MRS should be equal to the ratio of the price of the goods, but we can show that anywhere along the budget line, right? </p>

<p>Also, I understand that we can't draw the IC in a way that they intersect. So, I can't draw the IC for <span class="math-container">$ I_3 $</span> towards the end of <span class="math-container">$ I_3 $</span> (near the x-axis) because it'll intersect other indifference curves -- but how do we know where to draw the IC? </p>

<p>In other words, I can only reproduce this diagram for inferior goods because I've seen it. If I had to graphically represent this without having seen it earlier, there is no way I'd have figured that <span class="math-container">$ z_3 $</span> is lesser than <span class="math-container">$ z_1 $</span>. </p>

CC BY-SA 4.0
2019-01-20T15:27:02.360Z
Please let me know if I can improve my question.
WorldGov
CC BY-SA 4.0
2019-01-20T22:52:17.223Z
You have answered the question. The ratio of the prices is equal to the MRS.
superhulk
<consumer-theory>
Budget lines and Indifference curves: How do you figure where exactly you should draw the IC tangent to a budget line?
WorldGov
# Budget lines and Indifference curves: How do you figure where exactly you should draw the IC tangent to a budget line?

(Asked by: username_0 on 2019-01-20)

In Consumer Choice, we frequently encounter budget lines and indifference curves. For a given budget line, the optimization point is at the point where the indifference curve is just tangent to the budget line. For example, here is a graph used to illustrate how inferior goods behave with increases in income:

[![enter image description here](https://i.sstatic.net/vNt0w.png)](https://i.sstatic.net/vNt0w.png)

Here, as the budget line shifts to $ I\_3 $, we're shown that consumption of $ z $, an inferior good, decreases. My question is: what's stopping me from drawing the indifference curve elsewhere? Why can't I draw the indifference curve tangent to $ I\_3 $, just right of $ z\_1 $ so that $ z\_3 > z\_1 $?

Sure, the MRS should be equal to the ratio of the price of the goods, but we can show that anywhere along the budget line, right?

Also, I understand that we can't draw the IC in a way that they intersect. So, I can't draw the IC for $ I\_3 $ towards the end of $ I\_3 $ (near the x-axis) because it'll intersect other indifference curves -- but how do we know where to draw the IC?

In other words, I can only reproduce this diagram for inferior goods because I've seen it. If I had to graphically represent this without having seen it earlier, there is no way I'd have figured that $ z\_3 $ is lesser than $ z\_1 $.

**Tags:** consumer-theory

> **Comments:**
> **username_0**: Please let me know if I can improve my question.  
> **username_1**: You have answered the question. The ratio of the prices is equal to the MRS.  

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## 1 answers

### Answer by username_2 on 2019-01-21. Score: 0

In order to know the exact bundle for that maximizes utility, you need to know what the consumer's preferences are. Nevertheless, if you knew that good $z$ is an inferior good for this particular consumer at **her current income level**, you should still be able to draw this diagram. The only thing you need is to recall the definition of an inferior good: a good is said to be inferior if as income increases its consumption decreases. This alone implies that $z\_3 Observe that in the diagram the budget constraint is drawn for three income levels. As income increases from $m\_1$ to $m\_2,$ consumption of goes from $z\_1$ to $z\_2,$ implying that $z$ is an inferior good. If income increases further to $m\_3,$ consumption needs to reduce relative to $z\_2.$

Note that it could have been the case that as income grew from $m\_1$ to $m\_2$ consumtion of $z$ increased, but from $m\_2$ to $m\_3$ it decreased. This is why I emphasized the role of consumer income: a given good may be normal at some income levels and then inferior for other, presumably larger, income levels.


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