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

The perfectly competitive firm faces a horizontal demand curve because it is one among many, and has to take the price offered by the market.

The monopoly firm is the only firm, therefore they face the industry downward sloping demand curve determined by the market. If the monopolist wants to sell more, the price has to come down.

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

The monopolist can set the price or the quantity, but not both. The other variable is determined by the market demand curve.

• 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?

No, the consumer with inelastic demand will pay more, because that consumer wants or needs the product almost regardless of price. Insulin for a diabetic would be an example.