So, I am given the next table: enter image description here

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!

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    $\begingroup$ 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. $\endgroup$ – Giskard Apr 26 '20 at 9:37
  • $\begingroup$ @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? $\endgroup$ – george.zrs Apr 26 '20 at 9:54
  • $\begingroup$ Point elasticity is only defined in points. $\endgroup$ – Giskard Apr 26 '20 at 9:56
  • $\begingroup$ @KennyLJ Income ($Y$) is different. $\endgroup$ – Giskard Apr 26 '20 at 9:57
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    $\begingroup$ @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. $\endgroup$ – Giskard Apr 26 '20 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 $Q_D=900-10P$.

  • $\begingroup$ 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! $\endgroup$ – george.zrs Apr 26 '20 at 13:43
  • $\begingroup$ 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. $\endgroup$ – VARulle Apr 27 '20 at 10:43

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