<p>That type of demand is called an <a href="https://en.wikipedia.org/wiki/Isoelastic_function" rel="nofollow noreferrer">Isoelastic demand function</a>, because the elasticity of demand is constant, so it <strong>does not</strong> depend on prices.</p>

<p>You have not done any mistake. But you just need to move forward one more step. Notice that at the moment your derivative has both p and q in it. <strong>Try to get rid of q</strong>. This is, try to have $\epsilon=f(p)$, and not $\epsilon=f(p,q)$. This hint should be enough for you to solve the question.</p>

CC BY-SA 3.0
2017-04-20T08:53:00.557Z
2017-04-20T08:53:00.557Z
luchonacho
<p>I'm studying for a test I have this week and a practice question asks whether or not the price elasticity of demand for the demand function $\ q = Ap^{-x} $, where A and x are positive constants depends on the price <strong>p</strong>.</p>

<p>I've attempted to use the equation, $ \frac{dQ}{dP}*\frac{P}{Q} $ in order to solve the problem and I am getting the result,</p>

<p>$ \epsilon = \frac{-xA}{p^{x+1}}*\frac{p}{q} = \frac{-xA}{p^{x}q}$</p>

<p>Which would mean that the elasticity does  depend on <strong>p</strong>, however the answer in my practice exam says that it does not depend on <strong>p</strong>. Why is that the case/where did I go wrong? </p>

<elasticity>
Does this price elasticity depend on p?
Kyle
# Does this price elasticity depend on p?

(Asked by: username_0 on 2017-04-20)

I'm studying for a test I have this week and a practice question asks whether or not the price elasticity of demand for the demand function $\ q = Ap^{-x} $, where A and x are positive constants depends on the price **p**.

I've attempted to use the equation, $ \frac{dQ}{dP}\*\frac{P}{Q} $ in order to solve the problem and I am getting the result,

$ \epsilon = \frac{-xA}{p^{x+1}}\*\frac{p}{q} = \frac{-xA}{p^{x}q}$

Which would mean that the elasticity does depend on **p**, however the answer in my practice exam says that it does not depend on **p**. Why is that the case/where did I go wrong?

**Tags:** elasticity

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## 1 answers

### Answer by username_1 on 2017-04-20. Score: 1 | Accepted answer

That type of demand is called an [Isoelastic demand function](https://en.wikipedia.org/wiki/Isoelastic_function), because the elasticity of demand is constant, so it **does not** depend on prices.

You have not done any mistake. But you just need to move forward one more step. Notice that at the moment your derivative has both p and q in it. **Try to get rid of q**. This is, try to have $\epsilon=f(p)$, and not $\epsilon=f(p,q)$. This hint should be enough for you to solve the question.


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