The diagram on the left shows an oligopoly using a kinked demand curve.

Where the curve kinks is the price - but how does an oligopolist KNOW that that exact point is where a) price rises and demand is elastic b) price falls and demand is inelastic?

Where Average Revenue (demand) is inelastic we know that a price fall means a fall in total revenue. In which case, why isn't the Marginal Revenue curve negative after the kink in average revenue?

Also is this an example of a superior good - a good of ostentation:

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