Why is the demand curve for a monopolist downward sloping? How does this affect the monopolist's behavior?

The competitive firm faces a horizontal demand, because it is so small compared to the market that it cannot affect price. It simply takes the market-determined price as given. The monopolist, however, is the entire industry, and faces the industry demand curve for its product. Just as the industry demand curve for competition is downward sloping, the monopolist faces such a curve for itself.

As indicated in the chapter on elasticity, when the firm must cut price to increase unit sales, there will be a loss of revenue on the output that it has been selling, and a gain in revenue on the additional output. The marginal revenue in this case is less than the price the firm charges, and may even be negative. Therefore, the firm must be careful to charge a price high enough to keep marginal revenue positive. Further, the profit-maximizing firm should equate marginal revenue and marginal cost.