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.
How about constant elasticity demand: $Q(p)=p^a$, where $a&lt;0$?

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.