# The Elasticity Conjecture

**Posted:**December 10, 2009

**Filed under:**Uncategorized 1 Comment

If you know economists, you probably have noticed that when they discuss microeconomics, they almost certainly end up talking about *elasticity. *In fact, I have summed up this simple observation in my very own conjecture:

The longer a discussion about microeconomics between two economists is, the probability that elasticity is mentionned exponentially approaches 1.

Of course, if you are not acquainted with this notion, it may seem far-fetched to talk about the elasticty of a curve and discard the comments about the demand for insulin being perfectly inelastic as yet another surrealistic comment about the strange nature of markets. Well, not really.

But what *exactly *is elasticty ? Let . We define an operator which we call *-elasticty of parameter * as:

Simply put, it is the product of the partial derivative in regard to parameter and the ratio of and , which, you probably have noticed, means elasticity has *no unit *and is exactly the reason why its use is so widespread in economics. Elasticity is the measure of the *relative *effect the change in a variable has on another variable, regardless of the units employed. The elasticity of a parameter is classified in the following categories:

- : perfectly inelastic: a change in the parameter has no effect on the other
- : inelastic: a change in the parameter has a small effect on the other
- : unit elastic: a change in the parameter has a proportional effect on the other
- : elastic: a change in the parameter has a more than proportional effect on the other
- : perfectly elastic: a change in the parameter nullifies the other

To better illustrate the notion, let us take a very straightforward, thus bogus but instructive exemple. Let us imagine the demand for wheat is described by the following demand curve:

We can calculate the price elasticity of demand:

Thus, at point , elasticity is:

Which means that the demand is quite inelastic at this point, *i.e. *that a change in price will only have a small effect on the demanded quantity. Insulin is a very good example of an almost inelastic good: whatever the price, someone with diabetes will pay this much to get his dose, as it is of vital importance to him. *In contrario*, an example of a very elastic price demand is the demand for leisure goods, such as DVDs and books.

Microeconomists study many kinds of demand elasticities (*e.g. *income elasticty of demand, cross-price elasticity of demand, *etc.*) and it is of peculiar interest to observe the empirical measures of such elasticities. In a future blog post, I will introduce you to a selected collection of elasticity data taken from litterature.

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