# why is diamond an inelastic good?

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?

• 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)... Feb 13 at 11:32
• I suspect that if diamonds were cheap, fewer people would want to buy them. They are (probably) a Veblen good Feb 13 at 13:26
• @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 Feb 13 at 14:20
• An argument that diamonds are price-inelastic (ie elasticity < 1) at least in some circumstances is made here. Feb 13 at 19:48
• @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." jewellermagazine.com/Article2/8353/… And a theoretical argument for unit-elasticity is made in jstor.org/stable/1806737. Feb 14 at 14:00

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

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

• As far as I know, "anelastic" is only used in physics. Typo? Feb 14 at 13:04
• 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. Feb 14 at 14:32