<p>Your Lagrangian has a <span class="math-container">$p_i$</span> in the first term that shouldn't be there.</p>

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2023-02-13T12:55:42.833Z
2023-02-13T12:55:42.833Z
VARulle
<p>the pictures outline the situation and my problem. The only thing I dont understand, is why the inverse of the price elasticity is equal to the negative elasticity of substitution? (price elasticity is equal to negative elasticity of substitution?). I realize that there is a hint in the footnote, on how to derive this, but I failed.</p>
<p><a href="https://i.sstatic.net/oBY29.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oBY29.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/ZHoh2.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZHoh2.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/X28n0.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/X28n0.jpg" alt="enter image description here" /></a></p>
<p>Source: Ding Dong, Notes on Krugman (1991)</p>
<p>This is how I think this should be done, but something is missing or im doing something wrong... :</p>
<p><a href="https://i.sstatic.net/f0f7i.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/f0f7i.jpg" alt="enter image description here" /></a></p>

<elasticity><elasticity-of-substitution>
Krugman Model: Profit Maximization (relation price elasticity of demand and elasticity of substitution)
Paul Herrmann
# Krugman Model: Profit Maximization (relation price elasticity of demand and elasticity of substitution)

(Asked by: username_0 on 2023-02-11)

the pictures outline the situation and my problem. The only thing I dont understand, is why the inverse of the price elasticity is equal to the negative elasticity of substitution? (price elasticity is equal to negative elasticity of substitution?). I realize that there is a hint in the footnote, on how to derive this, but I failed.

[![enter image description here](https://i.sstatic.net/oBY29.jpg)](https://i.sstatic.net/oBY29.jpg)

[![enter image description here](https://i.sstatic.net/ZHoh2.jpg)](https://i.sstatic.net/ZHoh2.jpg)

[![enter image description here](https://i.sstatic.net/X28n0.jpg)](https://i.sstatic.net/X28n0.jpg)

Source: Ding Dong, Notes on Krugman (1991)

This is how I think this should be done, but something is missing or im doing something wrong... :

[![enter image description here](https://i.sstatic.net/f0f7i.jpg)](https://i.sstatic.net/f0f7i.jpg)

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


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## 1 answers

### Answer by username_1 on 2023-02-13. Score: 2

Your Lagrangian has a $p\_i$ in the first term that shouldn't be there.


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