# 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. – Giskard 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... – Fix.B. Jul 20 '16 at 23:20

How about constant elasticity demand: $Q(p)=p^a$, where $a<0$?
$$\eta=Q'(p)\frac{p}{q}=ap^{a-1}\frac{p}{p^a}=a.$$