<p>I have a problem where my answer does not seem to be right anywhere. For the following set up:</p>
<p>Budget constraint: <span class="math-container">$400=40x+20y$</span></p>
<p>Utility function: <span class="math-container">$u(x,y)=3x+y$</span></p>
<p>the problems asks to derive the demand function for <span class="math-container">$x$</span> (for the given <span class="math-container">$p_y$</span>). And I get to:</p>
<p><span class="math-container">$$x=f(p_x)= \begin{cases} 
      \frac{400}{p_x}\quad\quad &amp;if\quad p_x&lt;60\\
      0\quad\quad &amp;if\quad p_x&gt;60\\
      \left(0,\frac{400}{p_x}\right)\quad\quad &amp;if\quad p_x=60 
   \end{cases}
$$</span></p>
<p>When I graph this, I get the following chart:
<a href="https://i.sstatic.net/awuUE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/awuUE.png" alt="enter image description here" /></a></p>
<p>I was told that the step between 40 and 60 for <span class="math-container">$p_x$</span> should not be there, but I can not figure out why. Can someone please explain what am I missing?</p>

CC BY-SA 4.0
2021-05-28T05:26:28.900Z
1. Your description $$x=f(p_x)= \begin{cases} 
      \frac{400}{p_x}\quad\quad &if\quad p_x<60\\
      0\quad\quad &if\quad p_x>60\\
      \left(0,\frac{400}{p_x}\right)\quad\quad &if\quad p_x=60 
   \end{cases}
$$ has only three segments. How come your graph has four?
Giskard
CC BY-SA 4.0
2021-05-28T05:27:15.750Z
2. $\frac{400}{60}$ is not close to 10, but close to 7, so demand at $p_x =60$ should not stretch from 0 to ten-ish.
Giskard
<microeconomics><mathematical-economics>
Demand function for substitutes
alejandrogrrl
# Demand function for substitutes

(Asked by: username_0 on 2021-05-28)

I have a problem where my answer does not seem to be right anywhere. For the following set up:

Budget constraint: $400=40x+20y$

Utility function: $u(x,y)=3x+y$

the problems asks to derive the demand function for $x$ (for the given $p\_y$). And I get to:

$$x=f(p\_x)= \begin{cases}
\frac{400}{p\_x}\quad\quad &if\quad p\_x<60\\
0\quad\quad &if\quad p\_x>60\\
\left(0,\frac{400}{p\_x}\right)\quad\quad &if\quad p\_x=60
\end{cases}
$$

When I graph this, I get the following chart:
[![enter image description here](https://i.sstatic.net/awuUE.png)](https://i.sstatic.net/awuUE.png)

I was told that the step between 40 and 60 for $p\_x$ should not be there, but I can not figure out why. Can someone please explain what am I missing?

**Tags:** microeconomics, mathematical-economics
> **Comments:**
> **username_1**: 1. Your description $$x=f(p_x)= \begin{cases}        \frac{400}{p_x}\quad\quad &if\quad p_x<60\\       0\quad\quad &if\quad p_x>60\\       \left(0,\frac{400}{p_x}\right)\quad\quad &if\quad p_x=60     \end{cases} $$ has only three segments. How come your graph has four?  
> **username_1**: 2. $\frac{400}{60}$ is not close to 10, but close to 7, so demand at $p_x =60$ should not stretch from 0 to ten-ish.  

---

## 0 answers

