<p>Price elasticity of demand is defined as:</p>
<p><span class="math-container">$$e=\frac{dQ}{dP} \frac{P}{Q}$$</span></p>
<p>For demand curve <span class="math-container">$y=x^{-b}$</span> elasticity of demand is given by</p>
<p><span class="math-container">$$e=-b$$</span></p>

CC BY-SA 4.0
2022-05-04T23:56:58.827Z
2022-05-04T23:56:58.827Z
1muflon1
<p>I have a demand curve <span class="math-container">$y(x) = x^{-b}$</span> where <span class="math-container">$b &gt; 1$</span>.</p>
<p>I'm trying to figure <em>the price elasticity of demand</em>, but I'm not familiar with finding price elasticity without having some sort of numbers.</p>
<p>Normally, I would go about this by taking the partial derivative of the demand curve, but the format is throwing me off?</p>
<p>I think the partial derivative in question <span class="math-container">$-b*x^{-b-1}$</span>, but I'm having trouble here.</p>
<p>Does anyone have thoughts on this?</p>

CC BY-SA 4.0
2022-05-05T10:52:03.103Z
Which trouble? That's correct so far (except that "partial" is not needed). Since the $x$-elasticity of $y$ is defined as $\epsilon=\frac{dy}{dx}\frac{x}{y}$, you just substitute your derivative in this expression, replace $y$ by $x^{-b}$, and simplify.
VARulle
<microeconomics><elasticity>
Trying to figure out the price elasticity of demand
Edward Peterson
# Trying to figure out the price elasticity of demand

(Asked by: username_0 on 2022-05-04)

I have a demand curve $y(x) = x^{-b}$ where $b > 1$.

I'm trying to figure *the price elasticity of demand*, but I'm not familiar with finding price elasticity without having some sort of numbers.

Normally, I would go about this by taking the partial derivative of the demand curve, but the format is throwing me off?

I think the partial derivative in question $-b\*x^{-b-1}$, but I'm having trouble here.

Does anyone have thoughts on this?

**Tags:** microeconomics, elasticity
> **Comments:**
> **username_1**: Which trouble? That's correct so far (except that "partial" is not needed). Since the $x$-elasticity of $y$ is defined as $\epsilon=\frac{dy}{dx}\frac{x}{y}$, you just substitute your derivative in this expression, replace $y$ by $x^{-b}$, and simplify.  

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## 1 answers

### Answer by username_2 on 2022-05-04. Score: 1

Price elasticity of demand is defined as:

$$e=\frac{dQ}{dP} \frac{P}{Q}$$

For demand curve $y=x^{-b}$ elasticity of demand is given by

$$e=-b$$


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