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Why is marginal revenue always less than price for a monopolist but equal to price for a perfectly competitive firm? Will a profit maximizing monopolist charge whatever price it desires for its output? If a monopolist is able to price discriminate will a consumer with highly elastic demand pay a higher price than a consumer with very inelastic demand?

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Why is marginal revenue always less than price for a monopolist but equal to price for a perfectly competitive firm?

Will a profit maximizing monopolist charge whatever price it desires for its output?

If a monopolist is able to price discriminate will a consumer with highly elastic demand pay a higher price than a consumer with very inelastic demand?