<p>My guess is that the ''elasticity of substitution'' means something like$$\frac{\%\Delta K}{\% \Delta L}=\mathrm{mrs} \times\frac lk, $$ but that is dependant on what point you are at (i.e. a coordinate $(l, k)$). To get $\mathrm{mrs} $, find $\frac {\mathrm d k} {\mathrm d l} $, and even that is dependent on the value of $f$. </p>

CC BY-SA 3.0
2017-04-28T19:58:35.687Z
2017-04-28T19:58:35.687Z
ahorn
<p>Elasticity of subsitution ($\sigma$) can be found by using this formula</p>

<p>$$\sigma=\frac{dln(\frac{x_1}{x_2})}{dln(MRS)}$$</p>

<p>alternatively you can use:
$$\sigma=\frac{e(x)f(x)f_1(x)f_2(x)}{x_1x_2|BH|}$$</p>

<p>where $x=x_1,x_2......x_n$ and $e(x)$ is  elasticity of scale. You can use this information to solve your problem.</p>

CC BY-SA 4.0
2022-10-24T21:34:48.827Z
Could you elaborate further what is |BH|, please?
Athaeneus
CC BY-SA 4.0
2022-10-25T01:36:12.897Z
@Athaeneus its been a while but if id guess, |BH| is the determinant  of the boardered hessian.
EconJohn
CC BY-SA 3.0
2017-04-28T20:21:24.380Z
2017-04-28T20:21:24.380Z
EconJohn
<p>The motive of my post is in search of some help in order to understand the correct way to find the elasticity of substitution by means of calculating the following function. </p>

<p>$$f(K, L)=\frac{K^{2}L^{2}}{K+L} $$</p>

<microeconomics><elasticity-of-substitution>
How do find elasticity of substitution for this function
user76838
# How do find elasticity of substitution for this function

(Asked by: username_0 on 2017-04-28)

The motive of my post is in search of some help in order to understand the correct way to find the elasticity of substitution by means of calculating the following function.

$$f(K, L)=\frac{K^{2}L^{2}}{K+L} $$

**Tags:** microeconomics, elasticity-of-substitution

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## 2 answers

### Answer by username_1 on 2017-04-28. Score: -2 | Accepted answer

My guess is that the ''elasticity of substitution'' means something like$$\frac{\%\Delta K}{\% \Delta L}=\mathrm{mrs} \times\frac lk, $$ but that is dependant on what point you are at (i.e. a coordinate $(l, k)$). To get $\mathrm{mrs} $, find $\frac {\mathrm d k} {\mathrm d l} $, and even that is dependent on the value of $f$.


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### Answer by username_2 on 2017-04-28. Score: 1

Elasticity of subsitution ($\sigma$) can be found by using this formula

$$\sigma=\frac{dln(\frac{x\_1}{x\_2})}{dln(MRS)}$$

alternatively you can use:
$$\sigma=\frac{e(x)f(x)f\_1(x)f\_2(x)}{x\_1x\_2|BH|}$$

where $x=x\_1,x\_2......x\_n$ and $e(x)$ is elasticity of scale. You can use this information to solve your problem.

> **Comments:**
> **username_3**: Could you elaborate further what is |BH|, please?  
> **username_2**: @Athaeneus its been a while but if id guess, |BH| is the determinant  of the boardered hessian.  

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