# Does elasticity make sense for different levels of prices? If not, how can we fix that?

Let's say we know that our customers can't make sense of a raise in 5% of the price. It's too little for them to notice. However, an increase above 10% is easily noticed. If this is true, different level of prices impacts the customers in different ways and the formula we learned at college is not enough for real-world problems. Additionally, 10% of increase in something that costs 10 dollars is different than 10% of increase in something that costs 100 dollars, right?

So, how can we deal with this type of problem? How can we deal with price in real-world? How can we get elasticity in this situation?

The standard elasticity still makes sense. Elasticity is not necessarily constant. Also, I am not sure what sort of formula you learned at your college but elasticity is rigorously defined (and also taught at college level for econ majors) as $$EL = \frac{df(x)}{dx}\frac{x}{f(x)}$$ for some function $$f(x)$$ (see Essential Mathematics for Economic Analysis by Sydsæter, Hammond & StrØm - which is an undergraduate textbook used at many econ departments).

For example, for demand function given by: $$Q= a - bp$$ the elasticity will be given by:

$$\epsilon = \frac{dQ}{dp}\frac{p}{Q}= -b \frac{p}{a-bp}$$

so for $$a=100$$ and $$b=10$$ it will be:

$$\epsilon = - \frac{p}{100 - 10p}$$

So for example at price 5 dollars the elasticity (in its absolute value) will be 0.1 at price 9 dollars elasticity will be 0.9 and so on. Hence, elasticity can change when prices change and you don't need any new concepts. There is a special type of demand functions where elasticity will always be constant but then there are infinite number of possible demand functions and in most of them it will change with price.

• What is 'a' and 'b'? – dummyds Feb 22 at 13:11
• @dummyds some parameters of demand function. Here $a$ would be the maximum quantity demanded by market at price = 0 and $b$ would be slope of the demand function – 1muflon1 Feb 22 at 13:13

Elasticity of demand is normally considered in relation to market demand for a good, that is, the sum of individual customer demands. Different customers will probably respond in different ways to a price increase. If the increase is 5%, especially on a low value item, very likely many customers will not notice, some will notice but not change their buying behaviour, and perhaps a few will change their behaviour and no longer buy the good, or reduce the quantity they buy. If the increase is 10%, probably more will notice, and of those more will change their buying behaviour.

For each customer, there may be a different minimum price increase that would result in a reduction in their purchases of the good. Their behaviour is "jumpy" in the sense that their behaviour suddenly changes at that price increase. But different customers can be expected to behave differently for various reasons, eg differences in income, preferences, awareness of substitute goods. Given such differences, jumpy behaviour by individual customers can aggregate to a relatively smooth market demand curve to which the concept of elasticity of demand is readily applicable.