<p>It does not really mater, as you will get the same numerical values eventually. You may choose whatever is more convenient in each particular situation. Convention is, however, to replase $q$ with $q(p)$ to derive a formula for elasticity as a function of the price only.</p>

CC BY-SA 3.0
2015-01-18T06:23:19.753Z
2015-01-18T06:23:19.753Z
Nikita Toropov
<p>The problem I am considering involves a firm that is a price-taker and sells its good at price $p$. From the production function, I calculated the cost function and the profit-maximizing level of output. This allowed me to define my quantity supplied in terms of price. I got </p>

<p>\begin{equation}
q(p) = \frac{p}{2c}
\end{equation} </p>

<p>where $c$ is a constant. </p>

<p>I want to calculate price elasticity of supply. </p>

<p>\begin{equation}
E_s = \frac{dq}{dp}\frac{p}{q}
\end{equation} </p>

<p>Thus, I got 
\begin{equation}
\frac{dq(p)}{dp} = \frac{1}{2c}
\end{equation} 
Here's where I am confused: </p>

<p>Can I now just multiply that derivative by $\frac{p}{q}$ to get the price elasticity of supply? <strong>My confusion is that $q(p)$ is a function of $p$. So am I supposed to merely multiply by  $\frac{p}{q}$ or $\frac{p}{q(p)}$?</strong></p>

<elasticity>
Am I using quantity and price correctly in trying to calculate price elasticity of supply?
Stan Shunpike
# Am I using quantity and price correctly in trying to calculate price elasticity of supply?

(Asked by: username_0 on 2015-01-18)

The problem I am considering involves a firm that is a price-taker and sells its good at price $p$. From the production function, I calculated the cost function and the profit-maximizing level of output. This allowed me to define my quantity supplied in terms of price. I got

\begin{equation}
q(p) = \frac{p}{2c}
\end{equation}

where $c$ is a constant.

I want to calculate price elasticity of supply.

\begin{equation}
E\_s = \frac{dq}{dp}\frac{p}{q}
\end{equation}

Thus, I got
\begin{equation}
\frac{dq(p)}{dp} = \frac{1}{2c}
\end{equation}
Here's where I am confused:

Can I now just multiply that derivative by $\frac{p}{q}$ to get the price elasticity of supply? **My confusion is that $q(p)$ is a function of $p$. So am I supposed to merely multiply by $\frac{p}{q}$ or $\frac{p}{q(p)}$?**

**Tags:** elasticity

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## 1 answers

### Answer by username_1 on 2015-01-18. Score: 1

It does not really mater, as you will get the same numerical values eventually. You may choose whatever is more convenient in each particular situation. Convention is, however, to replase $q$ with $q(p)$ to derive a formula for elasticity as a function of the price only.


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