<blockquote>
<p>it is elastic when the price drops?</p>
</blockquote>
<p>It could be so.</p>
<p>Elasticity is a <strong>local, pointwise notion,</strong> or relative to a <strong>specific</strong> <strong>interval</strong>, that is the elasticity of a curve in general varies from point to point of the curve and from portion to portion of the curve.</p>
<p>We must remember the <strong>formula that defines elasticity,</strong> in our case, elasticity of the demand of a good with respect to its price.</p>
<p>Elasticity of demand <span class="math-container">$Q$</span> with respect to price <span class="math-container">$p$</span> is defined, if <span class="math-container">$\Delta p$</span> and <span class="math-container">$\Delta Q$</span> are finite differences, as:</p>
<p><span class="math-container">$$\epsilon= |\frac {\Delta Q} {\Delta p} \frac {p} {Q}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (1)$$</span></p>
<p>or</p>
<p><span class="math-container">$$\epsilon = |\frac {dQ} {dp} \frac {p} {Q}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (2)$$</span></p>
<p>if <span class="math-container">$Q$</span> and <span class="math-container">$p$</span> are continuous variables and the change is ‘infinitesimal’, where <span class="math-container">$\frac {dQ} {dp}$</span> is the derivative of the demand function with respect to price<span class="math-container">$^1$</span>.</p>
<p><span class="math-container">$\frac {dQ} {dp}$</span> and <span class="math-container">$\frac {\Delta Q} {\Delta p}$</span> can vary from point to point of the function, and also  <span class="math-container">$\frac {p} {Q}$</span> can vary from point to point.</p>
<p>Therefore, when speaking of elasticity, <strong>we must specify the point</strong> in which we are considering the elasticity or, in case of finite changes of the variables as in <span class="math-container">$(1)$</span>, <strong>the interval</strong> we are referring to.</p>
<p>Also in the case of the simplest form of a demand function, a <strong>linear demand function</strong>, the elasticity of demand is different at each point, and we have a section of the demand curve that is elastic and a section of the curve which is anelastic.</p>
<p>This  can be easily shown using a graph for a linear demand function</p>
<p><span class="math-container">$$Q= a-bp \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;a&gt;0,  b&gt;0 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (3)$$</span>.</p>
<p><a href="https://i.sstatic.net/Lb7g6.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Lb7g6.png" alt="enter image description here" /></a></p>
<p>The slope of the demand curve in the above picture is, in absolute value, 1/b<span class="math-container">$,  ^2$</span> and it is a constant for each point of the demand curve. The ratio <span class="math-container">$p/Q$</span> is represented by the red lines. As you can see, their slope decreases as we go toward the right part of the demand curve.  Therefore, there is a point where  <span class="math-container">$\epsilon =1$</span> (when the line <span class="math-container">$p/Q$</span> is perpendicular to the demand curve),  on the right of it we have  <span class="math-container">$\epsilon &lt;1$</span>, (the demand is <em>anelastic</em>) and on the left <span class="math-container">$\epsilon &gt;1$</span> (the demand is <em>elastic</em>).<span class="math-container">$^3$</span>.</p>
<p>A similar, but opposite,  situation can occur for other forms, not linear,  of demand curves, as in the picture below.</p>
<p><a href="https://i.sstatic.net/XqMkU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XqMkU.png" alt="enter image description here" /></a></p>
<p>Therefore, it is possible that the demand of a good is elastic for some range of the price, and not elastic for another range: in the picture, is anelastic for a price <span class="math-container">$P&gt;P_0$</span> and elastic for <span class="math-container">$P&lt;P_0$</span>.</p>
<p>A similar situation can hold for the demand of diamonds.</p>
<p>Until now, I spoke  of elasticity at <strong>one</strong> point.</p>
<p>If, as you argue, we have a <strong>huge decrease of the diamond price,</strong> we have to speak of elasticity in an interval, that is a <strong>finite change</strong> of the price <span class="math-container">$\Delta P$</span>.</p>
<p>Sometimes, when we are confronted with a big change of the variable <span class="math-container">$p$</span>, economists use the concept of <em><strong>arc elasticity</strong></em>, a convention that can be used to avoid some ambiguities about the assessment of the elasticity on an interval.  Arc elasticity is based on an average of initial and final values of quantity and price, <span class="math-container">$Q_0, Q_1, P_0, P_1$</span>, and the formula becomes:</p>
<p><span class="math-container">$$\epsilon= |\frac {\Delta Q} {\Delta p} \frac {p_0+p_1} {Q_0+Q_1}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (4)$$</span></p>
<p><span class="math-container">$$***$$</span></p>
<p>Of course, what in practice happens in the market of diamonds, if demand is elastic or not, and for which intervals of the price,  is an empirical matter, that cannot be resolved by the above formulas.</p>
<hr />
<p><span class="math-container">$^1$</span> Notice that in <span class="math-container">$(1)$</span> and <span class="math-container">$(2)$</span> we are taking the absolute value, this is the usual convention, because it is more comfortable to avoid to keep the minus sign before any formula.</p>
<p><span class="math-container">$^2$</span> We must remember that in the graph we have the <em>inverse demand function,</em> that is <span class="math-container">$p= a/b-1/b Q$</span>, as we have <span class="math-container">$P$</span> on the ordinate axis and <span class="math-container">$Q$</span> on the abscissa axis.</p>
<p><span class="math-container">$^3$</span> By definition, if <span class="math-container">$\epsilon &gt;1$</span>, the demand is said <em>elastic</em>, if <span class="math-container">$\epsilon &lt;1$</span> the demand is said <em>anelastic</em>.</p>

CC BY-SA 4.0
2023-02-14T13:04:15.227Z
As far as I know, "anelastic" is only used in physics. Typo?
VARulle
CC BY-SA 4.0
2023-02-14T14:32:26.633Z
I I've read both inelastic and anelastic in English books, as synonymous.  I think it's the same, but you may be right, I'm not a native speaker. I found 'inelastic' also in physics, 'anelastic' in mechanics only. In economics both.  Also in my language, Italian, we use 'anelastico in mechanics, 'inelastic or 'anelastico' indifferently in other contexts. But I may change, if you think that 'inelastic' in economics is more usual.
BakerStreet
CC BY-SA 4.0
2023-02-13T15:56:22.297Z
2023-02-13T23:36:20.753Z
2023-02-13T23:36:20.753Z
BakerStreet
<p>I understand that since diamonds are valued as rare, high-value items in society, even when the price for them increases, the quantity demanded remains the same. That is, people are willing to pay high prices for diamonds.</p>
<p>This makes diamonds an inelastic good.</p>
<p>However, let's say the price of diamonds dropped significantly. If it was an inelastic good, according to the graph, the quantity demanded of it would not change by much.</p>
<p>Yet if something like a diamond, so valued in society, was to become cheaper, wouldn't everyone want to buy it now that it is affordable? In this way, it is not an inelastic good—it is elastic when the price drops?</p>

CC BY-SA 4.0
2023-02-13T11:32:23.733Z
Who told you that the demand for diamonds is inelastic? And even if this were the case, "inelastic" doesn't necessarily mean "perfectly inelastic" (elasticity of zero)...
VARulle
CC BY-SA 4.0
2023-02-13T14:20:39.827Z
@user253751 there is a market for imitation diamonds based on sparkly looks alone.  Presumably if the price was low enough, people would buy diamonds for that reason
Henry
CC BY-SA 4.0
2023-02-13T19:48:19.320Z
An argument that diamonds are price-inelastic (ie elasticity < 1) at least in some circumstances is made [here](http://economicspoliticsanthropology.blogspot.com/2010/11/economic-analysis-of-rise-in-prices-of.html).
Adam Bailey
CC BY-SA 4.0
2023-02-14T14:00:10.640Z
@AdamBailey, there seem to be a variety of views out there. 'Jeweller' magazine says "Like other luxury goods, diamond prices are highly elastic, which means any changes in price have a direct impact on demand." https://www.jewellermagazine.com/Article2/8353/The-white-diamond-report-Evolution-and-Survival And a theoretical argument for unit-elasticity is made in https://www.jstor.org/stable/1806737.
VARulle
CC BY-SA 4.0
2023-02-14T18:32:10.213Z
@VARulle  Agreed (that there are a variety of views).  I posted the link as an example of a case that diamonds are price-inelastic, and wasn't particularly endorsing the conclusion.
Adam Bailey
<microeconomics><elasticity>
why is diamond an inelastic good?
Susanoo D Ace
# why is diamond an inelastic good?

(Asked by: username_0 on 2023-02-12)

I understand that since diamonds are valued as rare, high-value items in society, even when the price for them increases, the quantity demanded remains the same. That is, people are willing to pay high prices for diamonds.

This makes diamonds an inelastic good.

However, let's say the price of diamonds dropped significantly. If it was an inelastic good, according to the graph, the quantity demanded of it would not change by much.

Yet if something like a diamond, so valued in society, was to become cheaper, wouldn't everyone want to buy it now that it is affordable? In this way, it is not an inelastic good—it is elastic when the price drops?

**Tags:** microeconomics, elasticity
> **Comments:**
> **username_1**: Who told you that the demand for diamonds is inelastic? And even if this were the case, "inelastic" doesn't necessarily mean "perfectly inelastic" (elasticity of zero)...  
> **username_2**: @user253751 there is a market for imitation diamonds based on sparkly looks alone.  Presumably if the price was low enough, people would buy diamonds for that reason  
> **username_3**: An argument that diamonds are price-inelastic (ie elasticity < 1) at least in some circumstances is made [here](http://economicspoliticsanthropology.blogspot.com/2010/11/economic-analysis-of-rise-in-prices-of.html).  
> **username_1**: @AdamBailey, there seem to be a variety of views out there. 'Jeweller' magazine says "Like other luxury goods, diamond prices are highly elastic, which means any changes in price have a direct impact on demand." https://www.jewellermagazine.com/Article2/8353/The-white-diamond-report-Evolution-and-Survival And a theoretical argument for unit-elasticity is made in https://www.jstor.org/stable/1806737.  
> **username_3**: @VARulle  Agreed (that there are a variety of views).  I posted the link as an example of a case that diamonds are price-inelastic, and wasn't particularly endorsing the conclusion.  

---

## 1 answers

### Answer by username_4 on 2023-02-13. Score: 2

> it is elastic when the price drops?

It could be so.

Elasticity is a **local, pointwise notion,** or relative to a **specific** **interval**, that is the elasticity of a curve in general varies from point to point of the curve and from portion to portion of the curve.

We must remember the **formula that defines elasticity,** in our case, elasticity of the demand of a good with respect to its price.

Elasticity of demand $Q$ with respect to price $p$ is defined, if $\Delta p$ and $\Delta Q$ are finite differences, as:

$$\epsilon= |\frac {\Delta Q} {\Delta p} \frac {p} {Q}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (1)$$

or

$$\epsilon = |\frac {dQ} {dp} \frac {p} {Q}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (2)$$

if $Q$ and $p$ are continuous variables and the change is ‘infinitesimal’, where $\frac {dQ} {dp}$ is the derivative of the demand function with respect to price$^1$.

$\frac {dQ} {dp}$ and $\frac {\Delta Q} {\Delta p}$ can vary from point to point of the function, and also $\frac {p} {Q}$ can vary from point to point.

Therefore, when speaking of elasticity, **we must specify the point** in which we are considering the elasticity or, in case of finite changes of the variables as in $(1)$, **the interval** we are referring to.

Also in the case of the simplest form of a demand function, a **linear demand function**, the elasticity of demand is different at each point, and we have a section of the demand curve that is elastic and a section of the curve which is anelastic.

This can be easily shown using a graph for a linear demand function

$$Q= a-bp \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;a>0, b>0 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (3)$$.

[![enter image description here](https://i.sstatic.net/Lb7g6.png)](https://i.sstatic.net/Lb7g6.png)

The slope of the demand curve in the above picture is, in absolute value, 1/b$, ^2$ and it is a constant for each point of the demand curve. The ratio $p/Q$ is represented by the red lines. As you can see, their slope decreases as we go toward the right part of the demand curve. Therefore, there is a point where $\epsilon =1$ (when the line $p/Q$ is perpendicular to the demand curve), on the right of it we have $\epsilon <1$, (the demand is *anelastic*) and on the left $\epsilon >1$ (the demand is *elastic*).$^3$.

A similar, but opposite, situation can occur for other forms, not linear, of demand curves, as in the picture below.

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

Therefore, it is possible that the demand of a good is elastic for some range of the price, and not elastic for another range: in the picture, is anelastic for a price $P>P\_0$ and elastic for $P.

A similar situation can hold for the demand of diamonds.

Until now, I spoke of elasticity at **one** point.

If, as you argue, we have a **huge decrease of the diamond price,** we have to speak of elasticity in an interval, that is a **finite change** of the price $\Delta P$.

Sometimes, when we are confronted with a big change of the variable $p$, economists use the concept of ***arc elasticity***, a convention that can be used to avoid some ambiguities about the assessment of the elasticity on an interval. Arc elasticity is based on an average of initial and final values of quantity and price, $Q\_0, Q\_1, P\_0, P\_1$, and the formula becomes:

$$\epsilon= |\frac {\Delta Q} {\Delta p} \frac {p\_0+p\_1} {Q\_0+Q\_1}| \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; (4)$$

$$\*\*\*$$

Of course, what in practice happens in the market of diamonds, if demand is elastic or not, and for which intervals of the price, is an empirical matter, that cannot be resolved by the above formulas.

---

$^1$ Notice that in $(1)$ and $(2)$ we are taking the absolute value, this is the usual convention, because it is more comfortable to avoid to keep the minus sign before any formula.

$^2$ We must remember that in the graph we have the *inverse demand function,* that is $p= a/b-1/b Q$, as we have $P$ on the ordinate axis and $Q$ on the abscissa axis.

$^3$ By definition, if $\epsilon >1$, the demand is said *elastic*, if $\epsilon <1$ the demand is said *anelastic*.

> **Comments:**
> **username_1**: As far as I know, "anelastic" is only used in physics. Typo?  
> **username_4**: I I've read both inelastic and anelastic in English books, as synonymous.  I think it's the same, but you may be right, I'm not a native speaker. I found 'inelastic' also in physics, 'anelastic' in mechanics only. In economics both.  Also in my language, Italian, we use 'anelastico in mechanics, 'inelastic or 'anelastico' indifferently in other contexts. But I may change, if you think that 'inelastic' in economics is more usual.  

---

