For what kind of company or companies—a perfectly competitive firm, a monopolistically competitive firm, and/or a monopolist—is negative marginal revenue possible at some quantities (though never at the quantity at which the firm actually produces)? What must be true of the demand curve over the range where marginal revenue is negative? Explain

Under monopoly and monopolistic competitive firm, marginal revenue can be negative under some quantitites.

It is not so in perfect competition because in perfect competition constant price is charged through out.

However in monopoly and monopolistic competition, if a firm cuts price it may be able to sell larger quantiies but it loses revenue of those gathered by selling smaller amount of quantiies at a higher price.

We have

MR = P(1 + 1/Ed)

If Ed is greater than -1, Marginal revenue will be negative.

Ed > -1 , refers that the demand is inelastic.

Hence in the range where MR is negative, the demand curve is said to be inelastic.

A monopolist or a monopolistically competitive firm will never produce on the inelastic portion of the demand curve.