For a monopolist, both marginal revenue and demand are downward-sloping curves. Marginal revenue will always be less than demand for a given quantity. This is because a monopolist's demand curve is the same as its average revenue curve, and for a monopolist, both average and marginal revenue will decrease as quantity increases.

Demand Curves

A demand curve is a representation of how much of a given good or service customers want to buy at each possible price. It is charted on a graph of quantity against price. Because customers prefer to buy more of a good when it is cheap and less when it is expensive, the demand curve slopes downward. A monopolist can set its price and automatically sell to every customer who is willing to buy at that price, because a monopolist has no competition. On one hand, this means the monopolist can make significant profits, but on the other hand the monopolist is at the mercy of consumers when it comes to determining price and quantity -- the monopolist picks only one, and the customers determine the other.

Average Revenue

For any company, average revenue is the total revenue of the company divided by the quantity of goods sold -- this can be interpreted as revenue per unit. For a monopolist, this is the same as the demand curve. Average revenue for a monopolist consists of the price per unit, because a monopolist captures the entire market at a given level of output. The monopolist must decrease prices if it wants to sell any more of its goods, because at any level of prices it has already sold to every customer willing to buy. The only new customers in the market who have not bought the product are those farther down the demand curve, who only buy when the price is lower.

Marginal Revenue

The marginal revenue of a company is the revenue of its last unit sold. For a monopolist, this is always decreasing -- producing more units means producing at a lower price, and therefore making more units leads to less marginal revenue due to that reduced price. The marginal revenue curve for a monopolist is always located below its demand curve. Total revenue will increase as production increases, but marginal revenue declines.

Shifts in Demand

Because marginal revenue, average revenue and demand for a monopolist are so closely related, any event that shifts the demand curve has a corresponding effect on marginal revenue. For example, if demand for the monopolist's good increases because a news story reveals that the good is very fashionable, demand will increase at every level of output, and the monopolist can sell more at any given price. The relationships will not change -- marginal revenue will stay below demand -- but the curves will move to reflect the increased consumer preference for the good.