<p>If the other good is inferior, the indifference curve would be shift to the left and budget constraint shift to the right when there is an increase in income. That would make the consumer have no utility maximization point. cmiiw</p>

CC BY-SA 4.0
2019-05-13T06:05:07.453Z
This answer contains false claims.
Giskard
CC BY-SA 4.0
2019-05-13T03:52:48.800Z
2019-05-13T03:52:48.800Z
Thoriq Akbar
<p>Reason: <strong>Both goods cannot be inferior.</strong></p>

<p>Let's say originally you consume <span class="math-container">$x$</span> and <span class="math-container">$y$</span>. So your budget constraint looks like</p>

<p><span class="math-container">$$p_x x + p_y y = I.$$</span></p>

<p>If both X and Y are inferior, when income goes down from <span class="math-container">$I_0$</span> to <span class="math-container">$I'$</span>, the quantity demanded for both has to go up (by definition) from <span class="math-container">$x$</span> to <span class="math-container">$x'$</span> and <span class="math-container">$y$</span> to <span class="math-container">$y'$</span>. This implies</p>

<p><span class="math-container">$$p_x x' + p_y y' = I' &lt; I = p_x x + p_y y.$$</span></p>

<p>This is a contradiction, since <span class="math-container">$x' &gt; x$</span> and <span class="math-container">$y' &gt; y$</span>.</p>

<p>Your question is a bit more specific. But since a Giffen good must be inferior, this answers your question as well.</p>

CC BY-SA 4.0
2019-05-13T06:38:22.477Z
2019-05-13T06:38:22.477Z
Art
<p>While going through some problems as part of self-study I encountered the following True/False question:  </p>

<p>Q. Steven only consumes two goods: <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>. If <span class="math-container">$X$</span> is a Giffen good for Steven, then <span class="math-container">$Y$</span> must be a normal good for Steven.</p>

<p>The given answer is True.</p>

<p>I am unable to understand why it is necessary for the other good to be normal. Why can't it be inferior/Giffen?</p>

<microeconomics><elasticity><elasticity-of-substitution>
If $X$ is a Giffen good then $Y$ must be a normal good
Vizag
# If $X$ is a Giffen good then $Y$ must be a normal good

(Asked by: username_0 on 2019-05-12)

While going through some problems as part of self-study I encountered the following True/False question:

Q. Steven only consumes two goods: $X$ and $Y$. If $X$ is a Giffen good for Steven, then $Y$ must be a normal good for Steven.

The given answer is True.

I am unable to understand why it is necessary for the other good to be normal. Why can't it be inferior/Giffen?

**Tags:** microeconomics, elasticity, elasticity-of-substitution


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## 2 answers

### Answer by username_3 on 2019-05-13. Score: 5 | Accepted answer

Reason: **Both goods cannot be inferior.**

Let's say originally you consume $x$ and $y$. So your budget constraint looks like

$$p\_x x + p\_y y = I.$$

If both X and Y are inferior, when income goes down from $I\_0$ to $I'$, the quantity demanded for both has to go up (by definition) from $x$ to $x'$ and $y$ to $y'$. This implies

$$p\_x x' + p\_y y' = I' < I = p\_x x + p\_y y.$$

This is a contradiction, since $x' > x$ and $y' > y$.

Your question is a bit more specific. But since a Giffen good must be inferior, this answers your question as well.


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### Answer by username_1 on 2019-05-13. Score: -3

If the other good is inferior, the indifference curve would be shift to the left and budget constraint shift to the right when there is an increase in income. That would make the consumer have no utility maximization point. cmiiw

> **Comments:**
> **username_2**: This answer contains false claims.  

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