<p>Premise of your question is simply false. You state (emphasis mine):</p>
<blockquote>
<p>Price elasticity of demand <span class="math-container">$\mathrm{e_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^*}}$</span> <strong>clearly depends on the levels of price and quantity</strong>.</p>
</blockquote>
<p>Incorrect. Consider trivial counter example. A perfectly reasonable demand can be given by:</p>
<p><span class="math-container">$$ Q  = A p^{-\epsilon} $$</span></p>
<p>where <span class="math-container">$Q$</span> is quantity, <span class="math-container">$p$</span> price and <span class="math-container">$A$</span> and <span class="math-container">$\epsilon$</span> are constant parameters.</p>
<p>Hence the price elasticity of demand <span class="math-container">$e$</span>  will be given by:</p>
<p><span class="math-container">$$e = \frac{dQ}{dp} \cdot \frac{p}{Q} = -\epsilon  A p^{-\epsilon-1} \frac{p}{ A p^{-\epsilon}} = -\epsilon $$</span></p>
<p>Consequently, <strong>clearly</strong> elasticity <strong>does not</strong> <em>always</em> depend on the levels of price and quantity and can be completely constant.</p>
<blockquote>
<p>Then why is everywhere (research papers, textbooks etc.) a constant estimate provided?</p>
</blockquote>
<p>Again false premise, in several textbooks and papers you will find elasticity being expressed as a function of price and quantity. Since you made statement about <strong>everywhere</strong> it is enough to show one example to the contrary which would be Varian Microeconomic Analysis, where there are several examples where elasticity in a model won't be constant.</p>
<p>In empirical papers elasticity will be most often estimated as a single number, but this is due to the way how empirical models are set up. It is too broad to discuss all empirical models in a single question, but typically coefficients estimated by model are values that hold on average. For example, in a regression <span class="math-container">$y_i = \beta_0 + \beta_1 E_i + e_i$</span> where <span class="math-container">$y$</span> would be income and <span class="math-container">$E$</span> years of education, the <span class="math-container">$\beta_1$</span> would tell us how much on average <span class="math-container">$y$</span> increases with education, it would not tell us what happen to every individual kids. That is if <span class="math-container">$\beta_1=10$</span> that does not mean that if your kid stays in school one more year they are guaranteed that their income will increase by 10. That is just a value we would expect for average kid.  Similarly, even if researcher assumes elasticity is not constant because they are using linear demand, they might be forced to estimate elasticity at a point rather than as a whole function and convention is to estimate point elasticity at average quantity and price (see discussion in <a href="https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/97WR00571" rel="nofollow noreferrer">Espey  Espey  &amp; Shaw (1997)</a>.</p>

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2021-05-07T10:13:42.903Z
2021-05-07T20:30:44.190Z
2021-05-07T20:30:44.190Z
1muflon1
<p>Price elasticity of demand <span class="math-container">$\mathrm{e_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^*}}$</span> clearly depends on the levels of price and quantity.</p>
<p>Then why is everywhere (research papers, textbooks etc.)  a constant estimate provided?</p>
<p>Also, doesn't the non-constancy of the price elasticity render the comparative statics <span class="math-container">$e_{P^*,\alpha} = \dfrac{e_{D,\alpha}}{e_{S,P}- e_{D,P}}$</span> invalid?</p>

<supply-and-demand><elasticity><price><demand>
Why are constant price elasticities reported?
reasonStore
# Why are constant price elasticities reported?

(Asked by: username_0 on 2021-05-07)

Price elasticity of demand $\mathrm{e\_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^\*}}$ clearly depends on the levels of price and quantity.

Then why is everywhere (research papers, textbooks etc.) a constant estimate provided?

Also, doesn't the non-constancy of the price elasticity render the comparative statics $e\_{P^\*,\alpha} = \dfrac{e\_{D,\alpha}}{e\_{S,P}- e\_{D,P}}$ invalid?

**Tags:** supply-and-demand, elasticity, price, demand

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## 1 answers

### Answer by username_1 on 2021-05-07. Score: 2 | Accepted answer

Premise of your question is simply false. You state (emphasis mine):

> Price elasticity of demand $\mathrm{e\_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^\*}}$ **clearly depends on the levels of price and quantity**.

Incorrect. Consider trivial counter example. A perfectly reasonable demand can be given by:

$$ Q = A p^{-\epsilon} $$

where $Q$ is quantity, $p$ price and $A$ and $\epsilon$ are constant parameters.

Hence the price elasticity of demand $e$ will be given by:

$$e = \frac{dQ}{dp} \cdot \frac{p}{Q} = -\epsilon A p^{-\epsilon-1} \frac{p}{ A p^{-\epsilon}} = -\epsilon $$

Consequently, **clearly** elasticity **does not** *always* depend on the levels of price and quantity and can be completely constant.

> Then why is everywhere (research papers, textbooks etc.) a constant estimate provided?

Again false premise, in several textbooks and papers you will find elasticity being expressed as a function of price and quantity. Since you made statement about **everywhere** it is enough to show one example to the contrary which would be Varian Microeconomic Analysis, where there are several examples where elasticity in a model won't be constant.

In empirical papers elasticity will be most often estimated as a single number, but this is due to the way how empirical models are set up. It is too broad to discuss all empirical models in a single question, but typically coefficients estimated by model are values that hold on average. For example, in a regression $y\_i = \beta\_0 + \beta\_1 E\_i + e\_i$ where $y$ would be income and $E$ years of education, the $\beta\_1$ would tell us how much on average $y$ increases with education, it would not tell us what happen to every individual kids. That is if $\beta\_1=10$ that does not mean that if your kid stays in school one more year they are guaranteed that their income will increase by 10. That is just a value we would expect for average kid. Similarly, even if researcher assumes elasticity is not constant because they are using linear demand, they might be forced to estimate elasticity at a point rather than as a whole function and convention is to estimate point elasticity at average quantity and price (see discussion in [Espey Espey & Shaw (1997)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/97WR00571).


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