In a market with perfect competition, the demand curve will be perfectly elastic. That is, the quantity supplied or demanded doesn’t affect the price per se. Additionally, the marginal cost is the price of the product.
Under monopolistic conditions, there is one supplier, and so the marginal revenue does not equal the marginal return. The supplier can raise prices without losing customers. As the supplier increases output, the marginal return decreases because the additional cost of producing the extra product does not fall when price does. This phenomenon results in a downward-facing demand curve. The marginal revenue curve, therefore, lies below the demand curve for a monopoly.
The reason for this less-than-intuitive behavior of the demand curve is that a monopoly can set the price it wants, rather than sell at the market price. A consequence of this is that the marginal revenue decreases as output increases.