# What is a good way te represent analytically two markets with different price elasticities of demand?

It seems that two linear demand curves with different slopes would be a good way to do it, but linear demand curves are hard to work with otherwise.

• Further details are needed. Also linear demand curves with different slopes do not necessarily imply different price elasticities, even with identical prices. Jul 20 '16 at 3:45
• Ok, I see, yes, you are right. The idea is that you want to build a model of f irma that maximizes profits, by selling into different markets, all while the environment is changing in terms of costs, etc. So, I'd like something that leads to analytically tractable expressions. Linear demands don't really work well in that sense... Jul 20 '16 at 23:20

## 1 Answer

How about constant elasticity demand: $Q(p)=p^a$, where $a<0$?

Such functions, as their name implies, have the advantage that the price elasticity of demand is constant along their entire length:

$$\eta=Q'(p)\frac{p}{q}=ap^{a-1}\frac{p}{p^a}=a.$$

Since the elasticity of the demand function is directly controlled with a single parameter, such functions are often convenient when performing comparative statics exercises in which the objective is to show the effect of varying the elasticity of demand upon equilibrium.

• that doesn't look right. Derivative of p with respect to q multiplied by q/p I think. The unit doesn't even match. Apr 4 '18 at 4:33
• Oh I see. It's derivative of q with respect to p multiplied by p/q Apr 4 '18 at 4:34