<p>The total market demand is given by the sum of the two destinations (<span class="math-container">$e$</span> and <span class="math-container">$f$</span>) given to the product.</p>
<p>Given these conditions:</p>
<ul>
<li><p>Demand: <span class="math-container">$d(p) = e(p) + f(p)$</span> where:</p>
<ul>
<li><span class="math-container">$d(p) &gt; 0$</span>, <span class="math-container">$d'(p) \leq 0$</span>;</li>
<li><span class="math-container">$e(p) &gt; 0$</span>, <span class="math-container">$e'(p) \leq 0$</span>;</li>
<li><span class="math-container">$f(p) &gt; 0$</span>, <span class="math-container">$f'(p) \leq 0$</span>;</li>
</ul>
</li>
<li><p>Supply: <span class="math-container">$s(p)$</span> where <span class="math-container">$s(p) &gt; 0$</span> and <span class="math-container">$s'(p) \geq 0$</span>;</p>
</li>
<li><p>Equilibrium: <span class="math-container">$d(p) = s(p)$</span>;</p>
</li>
</ul>
<p><strong>How can the condition below be interpreted?</strong></p>
<ul>
<li><span class="math-container">$\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}&gt; \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}$</span></li>
</ul>
<p>It may be helpfull to see that's possible to multiply by <span class="math-container">$p$</span> and get some elasticities:</p>
<p><span class="math-container">$p*\big(\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}&gt; \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}\big) \Rightarrow$</span>
<span class="math-container">$\varepsilon_{f}-\varepsilon_{d} &gt; \frac{e(p)}{f(p)}\varepsilon_{s}$</span></p>
<p>This is a simplification of the whole situation from the The Ethanol-subsidy Multiplier  <a href="http://models.economicreasoning.com/EthanolSubsidyMultiplier.pdf" rel="nofollow noreferrer">example</a> (or <a href="http://models.economicreasoning.com/EthanolSubsidyMultiplier.nb" rel="nofollow noreferrer">notebook file</a>).</p>

CC BY-SA 4.0
2021-01-10T22:29:50.360Z
Well i dont see how you postulate d(p)=s(p) with d(p)<0 and s(p)>0.
Levittstyle
CC BY-SA 4.0
2021-01-11T15:33:50.533Z
Indeed, @Armenthus. There was was a typo, although that relation was still possible (at least for a p*).
Rodrigo Remedio
<microeconomics><mathematical-economics><supply-and-demand><price-theory>
Interpretation of market condition given by relation between elasticities
Rodrigo Remedio
# Interpretation of market condition given by relation between elasticities

(Asked by: username_0 on 2021-01-10)

The total market demand is given by the sum of the two destinations ($e$ and $f$) given to the product.

Given these conditions:

* Demand: $d(p) = e(p) + f(p)$ where:

  + $d(p) > 0$, $d'(p) \leq 0$;
  + $e(p) > 0$, $e'(p) \leq 0$;
  + $f(p) > 0$, $f'(p) \leq 0$;
* Supply: $s(p)$ where $s(p) > 0$ and $s'(p) \geq 0$;
* Equilibrium: $d(p) = s(p)$;

**How can the condition below be interpreted?**

* $\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}> \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}$

It may be helpfull to see that's possible to multiply by $p$ and get some elasticities:

$p\*\big(\frac{f'(p)}{f(p)}-\frac{d'(p)}{d(p)}> \frac{e(p)}{f(p)}\frac{s'(p)}{s(p)}\big) \Rightarrow$
$\varepsilon\_{f}-\varepsilon\_{d} > \frac{e(p)}{f(p)}\varepsilon\_{s}$

This is a simplification of the whole situation from the The Ethanol-subsidy Multiplier [example](http://models.economicreasoning.com/EthanolSubsidyMultiplier.pdf) (or [notebook file](http://models.economicreasoning.com/EthanolSubsidyMultiplier.nb)).

**Tags:** microeconomics, mathematical-economics, supply-and-demand, price-theory

> **Comments:**
> **username_1**: Well i dont see how you postulate d(p)=s(p) with d(p)<0 and s(p)>0.  
> **username_0**: Indeed, @Armenthus. There was was a typo, although that relation was still possible (at least for a p*).  

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## 0 answers

