# Monopoly

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A monopoly describes a market in which there is only one firm and it does not face any competition. A monopolist is a firm that offers a unique product or service without close substitutes and therefore does not have any competitors. This means that the monopolist faces the entire market demand and each customer interested in buying the product can choose whether to buy from the monopolist at the respective price or not to buy at all. As consumers have no alternative to the monopolist´s product (except not buying) the monopolist, as opposed to a firm in perfect competition, can charge a price above marginal costs. Remember that in perfect competition there are so many buyers and sellers that no one can influence the price and the firms have to price at marginal costs. If a firm in perfect competition decides to price above marginal costs, it will not sell anything, because the consumers have plenty of other alternatives. The lack of alternatives for the consumers in a monopolized market allows the monopolist to charge a higher price, because there will still be consumers interested in buying the good even if the price is above marginal costs.

## The monopoly price

The monopolist is a profit-maximizing firm and will therefore charge a price that maximizes its profits given the market demand. How does the monopolist maximize profits? Profits are the difference between total revenue and total costs. When the monopoly decides how many units to sell it will compare the change in total revenue from selling one additional unit, i.e., the marginal revenue, to the increase in total costs, i.e. the marginal costs of this unit . The marginal revenue of a monopolist is lower than the market price, because to sell more units the monopolist has to reduce the price for all units. As long as the marginal revenue exceeds the marginal costs producing one additional unit will increase total revenue more than total costs which means that the profit increases. As soon as the marginal costs exceed the marginal revenue, the monopolist will reduce production as selling more units will decrease its profit. Consequently, the monopolist maximizes its profits at the quantity at which marginal costs are equal to marginal revenue. At this point it neither makes sense for the monopolist to increase nor to decrease the quantity.

Mathematically, the monopolist maximizes profits π with respect to its quantity, where Taking the derivate with respect to quantity q and setting the derivative equal to zero, we obtain the following first-order condition: The first two-terms on the left-hand side are the marginal revenue and the last term are the marginal costs of the monopolist. Therefore, we obtain the result that at the optimal quantity the marginal revenue (MR) has to be equal to the marginal costs (MC): Let us look at a simple example. Suppose that a monopolist produces at constant marginal costs equal to 2, i.e., C(q) = 2q and faces market demand q = 8 - p. The monopolist maximizes profits π = (8 - q)2q when marginal revenue, which is equal to MR = 8 - 2q, is equal to marginal costs. In this example, the optimal quantity of the monopolist is equal to 3 and the price (which we find by plugging back in into the demand function) is equal to 5. For any quantity below 3, the monopolist can increase its profit by increasing production. If the quantity exceeds 3, the profits again decrease as the quantity increases.

 P 0 1 2 3 4 5 6 7 8 Q 8 7 6 5 4 3 2 1 0 Profit π -16 -7 0 5 8 9 8 5 0

The price that the monopolist charges is higher than the market price in perfect competition (which is equal to marginal costs) and the monopoly quantity is lower than the quantity in a perfectly competitive market. This means that there are some customers who would be willing to buy the good at a price above marginal costs, but not at the monopoly price and therefore there are unrealized gains of trade. The consumer surplus is lower than the consumer surplus in a perfectly competitive market. This loss in consumer surplus is not fully compensated by an increase in profits, which means that there is a deadweight loss. In the figure the red triangle shows the efficiency loss (or deadweight loss) due to the monopoly for the case of a linear market demand and constant marginal costs. How much the monopoly price will be above marginal costs depends on the price elasticity of demand. If demand is inelastic, which means that a comparatively high increase in the price will only cause a small reduction in the quantity demanded, the monopolist can charge a higher mark-up. In the case of an elastic demand the monopolist loses many customers by increasing the price and therefore has less scope to charge a high mark-up. The possibility to charge a price above marginal costs is what we refer to when we talk about the market power of a monopoly. The market power of the monopolist depends can be measured by the Lerner index which is defined as Where ε is the price elasticity of demand. The Lerner index takes a value between 0 and 1, where 0 means that the firm has no market power and has to charge a price equal to marginal costs. The closer the Lerner index is to 1, the more market power the firm has. The higher the absolute value of the elasticity of demand (the more elastic the demand), the smaller the market power of the firm. This means that the monopolist will charge a higher mark-up in markets in which demand is less price-elastic.

## Why do monopolies exist?

There are several reasons why some markets are and remain monopolized. In some markets barriers to entry make it difficult for potential competitors to enter. For example, if one company controls the access to an essential resource, competitors without access to the resource cannot compete in the market. In some situations the government creates monopolies, as e.g. in the case of patents. A patent grants a temporary monopoly status to the patent holder. Besides this, the nature of production may be such that total costs of serving the customers are lower if only one firm takes care of it and not two or more firms. If this is the case we call the resulting monopoly also a natural monopoly.