<p>I'm trying to figure out the elasticity of substitution between input <span class="math-container">$s$</span> and input <span class="math-container">$v$</span>. I know that the marginal rate of substitution between these two inputs are <span class="math-container">$\frac{v^2}{s(v+k)}$</span>, where <span class="math-container">$k$</span> is another input. </p>

<p>Then, the elasticity of substitution is,</p>

<p><span class="math-container">$$E_{sv}=\dfrac{dln\big(v/s\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}$$</span></p>

<p><span class="math-container">$$=\dfrac{dln\big(v\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}-\dfrac{dln\big(s\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}$$</span></p>

<p>But I'm not sure how to proceed to get the input elasticity of substitution between factors <span class="math-container">$s$</span> and <span class="math-container">$v$</span>? Do I need to know the prices of both? </p>

CC BY-SA 4.0
2018-09-24T16:11:24.600Z
Sorry the $x$ was a mistake, it should not have been there. Yes, I'm having mathematical difficulties w.r.t. differentiation. Also, conceptually, I'm not sure whether I can even proceed without having the relative prices of both $v$ and $s$.
pafnuti
CC BY-SA 4.0
2018-09-24T17:43:38.913Z
@denesp, sorry about the mistake.
pafnuti
<microeconomics><elasticity>
Elasticity of Substitution between 2 factors, without knowing relative prices
pafnuti
# Elasticity of Substitution between 2 factors, without knowing relative prices

(Asked by: username_0 on 2018-09-24)

I'm trying to figure out the elasticity of substitution between input $s$ and input $v$. I know that the marginal rate of substitution between these two inputs are $\frac{v^2}{s(v+k)}$, where $k$ is another input.

Then, the elasticity of substitution is,

$$E\_{sv}=\dfrac{dln\big(v/s\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}$$

$$=\dfrac{dln\big(v\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}-\dfrac{dln\big(s\big)}{dln\bigg(\frac{v^2}{s(v+k)}\bigg)}$$

But I'm not sure how to proceed to get the input elasticity of substitution between factors $s$ and $v$? Do I need to know the prices of both?

**Tags:** microeconomics, elasticity

> **Comments:**
> **username_0**: Sorry the $x$ was a mistake, it should not have been there. Yes, I'm having mathematical difficulties w.r.t. differentiation. Also, conceptually, I'm not sure whether I can even proceed without having the relative prices of both $v$ and $s$.  
> **username_0**: @denesp, sorry about the mistake.  

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## 0 answers

