Would it be safe to associate price inelasticity of demand with monopoly while expecting an oligopoly to be price elastic?

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In general, the more competition there is, the more the demand for any one firm's product will be price elastic.  In that sense, it is safe to say that the product of a monopolist will be more price inelastic than that of an oligopolist.  

If a monopolist raises prices, the consumer has two choices.  They can pay the higher price or they can buy less of the product.  By contrast, the consumer in an oligopoly has more choices.  Let us assume the airline market is an oligopoly.  If one airline raises its prices, a consumer can simply buy air travel from a different airline.  This would mean that air travel would be relatively price elastic.  

All other things being equal, more competition means demand for any one firm's products will be more price elastic.  Therefore, it is generally safe to associate monopolies with more inelastic demand and oligopolies with more elastic demand.

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