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PED Equation = $ \frac{1}{0.4+0.00005Q}$

Demand Function is $$P = 920Q^{-0.4}e^{-0.00005Q},$$

$$ \epsilon_𝑑 = −1.89.$$

What is the price at the above level? And how would i see the quantity at that specific price?

I'm at a loss. I tried to make $-1.89$ equal to the PED equation, which ended up getting me a $Q$ value but obviously that is wrong as you would need to find the price before the quantity.

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  • $\begingroup$ I got something like $p=34.91$. $\endgroup$ Mar 24, 2018 at 13:32

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It is not true that "you would need to find the price before the quantity". The demand function is a bijection so you could solve for either one first. Starting with the information about the elasticity of demand you get $$-\frac{1}{0.4+0.00005Q}=-1.89 \;\Rightarrow Q=2582$$ Substituting this into the (inverse) demand function $$P = 920*2582^{-0.4}e^{-0.00005*2582}=34.909$$

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