# Can the demand curve be a rectangular hyperbola, but $E_D \neq 1$? [closed]

So, I am given the next table:

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!

• 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 Apr 26 at 9:37
• @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 Apr 26 at 9:54
• Point elasticity is only defined in points. – Giskard Apr 26 at 9:56
• @KennyLJ Income ($Y$) is different. – Giskard Apr 26 at 9:57
• @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 Apr 26 at 10:20

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 $$Q_D=900-10P$$.