According to conventional wisdom, if a monopolist operates in two separate markets whose respective demand functions can be ordered by elasticity, he will charge more on the market with the less elastic demand. In this paper we debunk the widespread canard that this follows from the first order profit maximization conditions. It is shown that, on the other hand, an inverse relationship between price and elasticity follows--with some qualifications--from the properties of the star partial ordering applied to the two demand functions. A number of related results are also given.