<p>Let's try a linear demand function, so <span class="math-container">$Q=a-bP$</span>. Then <span class="math-container">$\epsilon_A=\frac{\partial Q}{\partial P}\frac{P_A}{Q_A}=-b\frac{P_A}{Q_A}$</span>, so <span class="math-container">$b=-\epsilon_A\frac{Q_A}{P_A}=0.8\frac{500}{40}=10$</span>. Then <span class="math-container">$a=Q_A+bP_A=500+10\cdot 40=900$</span>. Thus, your table is compatible with the demand function <span class="math-container">$Q_D=900-10P$</span>.</p>

CC BY-SA 4.0
2020-04-26T13:43:06.073Z
This was the exact way I solved it in the first place, but my according to my professor this is wrong. I will ask for more insight on this question however, and I will keep you updated!
george.zrs
CC BY-SA 4.0
2020-04-27T10:43:27.520Z
Your professor is obviously wrong and should admit that. You cannot use two data points to reconstruct a complete curve, but his suggestion (the rectangular hyperbola) is even worse since it is not compatible with the given elasticity, as you correctly observed.
VARulle
CC BY-SA 4.0
2020-04-26T13:07:42.370Z
2020-04-26T13:07:42.370Z
VARulle
<p>So, I am given the next table:
<a href="https://i.sstatic.net/Vyqxp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Vyqxp.png" alt="enter image description here"></a></p>

<p>I am asked to find <span class="math-container">$Q_D$</span>.
So the prerequisites to find <span class="math-container">$Q_D$</span> is that the price must change, and all other factors of demand must be steady. So, I can find the <span class="math-container">$Q_D$</span> between A and C. Our professor stated that, as <span class="math-container">$P_A Q_A= P_C Q_C =20000$</span> , the demand curve is a rectangular hyperbola and <span class="math-container">$Q_D = \frac{20.000}{P}$</span>. However, in the rectangular hyperbola, <span class="math-container">$E_D=-1$</span> in every point of the demand curve, but here we have that <span class="math-container">$E_{D}=-0,8$</span>. Is there something I am missing? Does <span class="math-container">$E_D=-0.8  \neq -1$</span> imply that the curve is a line or not? Thanks!</p>

CC BY-SA 4.0
2020-04-26T09:37:42.520Z
Perhaps $E_D$ does not denote point elasticity, but this is unclear. This a valid question, but it is between you and your professor, you should raise it with her.
Giskard
CC BY-SA 4.0
2020-04-26T09:54:22.487Z
@Giskard Ok, thanks for the recommendation, I will ask my professor for more insight. If the elasticity was $E_{D_{A \rightarrow C}}$, then would that make sense? I mean, we know that the point elasticity equals 1 in any given point, but what about when we go from A to C? Does the same rule still apply?
george.zrs
CC BY-SA 4.0
2020-04-26T09:56:41.427Z
Point elasticity is only defined in points.
Giskard
CC BY-SA 4.0
2020-04-26T09:57:11.090Z
@KennyLJ Income ($Y$) is different.
Giskard
CC BY-SA 4.0
2020-04-26T10:00:41.993Z
@Giskard Ok, so if it was $E_{D_{A \rightarrow C}}$, then we don't have any problem right? Because as you mentioned $E_D=1$, only in points, and not when moving between them? I am sorry, for asking again, but that's a very vague point for me.
george.zrs
CC BY-SA 4.0
2020-04-26T10:20:17.927Z
@george.zrs I don't really understand your question. Please raise it with your professor, this discussion should really happen between the two of you.
Giskard
<supply-and-demand><elasticity><price><demand>
Can the demand curve be a rectangular hyperbola, but $E_D \neq 1$?
george.zrs
# Can the demand curve be a rectangular hyperbola, but $E_D \neq 1$?

(Asked by: username_0 on 2020-04-26)

So, I am given the next table:
[![enter image description here](https://i.sstatic.net/Vyqxp.png)](https://i.sstatic.net/Vyqxp.png)

I am asked to find $Q\_D$.
So the prerequisites to find $Q\_D$ is that the price must change, and all other factors of demand must be steady. So, I can find the $Q\_D$ between A and C. Our professor stated that, as $P\_A Q\_A= P\_C Q\_C =20000$ , the demand curve is a rectangular hyperbola and $Q\_D = \frac{20.000}{P}$. However, in the rectangular hyperbola, $E\_D=-1$ in every point of the demand curve, but here we have that $E\_{D}=-0,8$. Is there something I am missing? Does $E\_D=-0.8 \neq -1$ imply that the curve is a line or not? Thanks!

**Tags:** supply-and-demand, elasticity, price, demand

> **Comments:**
> **username_1**: Perhaps $E_D$ does not denote point elasticity, but this is unclear. This a valid question, but it is between you and your professor, you should raise it with her.  
> **username_0**: @username_1 Ok, thanks for the recommendation, I will ask my professor for more insight. If the elasticity was $E_{D_{A \rightarrow C}}$, then would that make sense? I mean, we know that the point elasticity equals 1 in any given point, but what about when we go from A to C? Does the same rule still apply?  
> **username_1**: Point elasticity is only defined in points.  
> **username_1**: @KennyLJ Income ($Y$) is different.  
> **username_0**: @username_1 Ok, so if it was $E_{D_{A \rightarrow C}}$, then we don't have any problem right? Because as you mentioned $E_D=1$, only in points, and not when moving between them? I am sorry, for asking again, but that's a very vague point for me.  
> **username_1**: @username_0 I don't really understand your question. Please raise it with your professor, this discussion should really happen between the two of you.  

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## 1 answers

### Answer by username_2 on 2020-04-26. Score: 1

Let's try a linear demand function, so $Q=a-bP$. Then $\epsilon\_A=\frac{\partial Q}{\partial P}\frac{P\_A}{Q\_A}=-b\frac{P\_A}{Q\_A}$, so $b=-\epsilon\_A\frac{Q\_A}{P\_A}=0.8\frac{500}{40}=10$. Then $a=Q\_A+bP\_A=500+10\cdot 40=900$. Thus, your table is compatible with the demand function $Q\_D=900-10P$.

> **Comments:**
> **username_0**: This was the exact way I solved it in the first place, but my according to my professor this is wrong. I will ask for more insight on this question however, and I will keep you updated!  
> **username_2**: Your professor is obviously wrong and should admit that. You cannot use two data points to reconstruct a complete curve, but his suggestion (the rectangular hyperbola) is even worse since it is not compatible with the given elasticity, as you correctly observed.  

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