Pure Monopolies and Natural Monopolies

Pure Monopolies

A pure monopoly is a firm that satisfies the following conditions:

1. It is the only supplier in the market.
2. There is no close substitute to the output good.
3. There is no threat of competition.

In practice, pure monopolies are very rare. For instance, a supermarket may be the only food supplier in a particular town, but if it raises its prices and retains too much of a profit, a competitor may enter the space. Even the threat of serious competition entering the market forces the existing firm to act conscionably, and differently from how it would act otherwise. A train company may be the only carrier in a particular station, but if cars are also available in the area, there exists a close substitute to the output good.

Natural Monopoly

A natural monopoly is a firm with such extreme economies of scale that once it begins creating a certain level of output, it can produce more at a far lower cost than any smaller competitor. Natural monopolies exist far more frequently than pure monopolies, mainly because the requirements are not as stringent.

Natural monopolies occur when, for whatever reason, the average cost curves decline over a relevant span of output quantities. A firm with high fixed costs relative to its marginal costs will have declining average costs for a significant span of quantities. A firm with a decreasing marginal cost structure will also have declining average costs. For example, utilities and software are two industries where natural monopolies occur often.

An Example

A monopoly differs from competitive firms in that it is not a price taker. Because it is the only supplier in the market, it faces a downward sloping demand curve, the market demand curve. As a result, the monopoly is free to choose its price and quantity according to market demand.

Monopolies are still profit maximizing firms and are thus going to satisfy the profit maximizing condition that marginal cost equal marginal revenue. The key to understanding monopolies and monopoly power is the marginal revenue calculation. In a perfectly competitive market, there exists a market price. Marginal revenue is simply equal to price in this market; every additional unit that is sold brings the market price. In a monopoly, however, every quantity is associated with a different price. The marginal revenue is not simply the price.

For example, I may be able to sell 10 guitars at 100 each,butinordertose ll11guitars,Iwillhavetoofferapriceof 95. Unfortunately, it's very difficult to sell 10 guitars at100andthensellthelastoneat 95. In our model of a monopoly, there can only be one price for a good. If I choose to sell 11 units, I make95revenueonthe11thguitar, butIlose 5 revenue on each of the first 10 guitars. If it costs me 50toproduceaguitar, mymarginalrevenueisthen 95 - 50 = 45.

Let's generalize. Assume that a monopolistic firm faces a linear, downward- sloping market demand curve, described as follows:

Q = 100 - P

Let's further assume its marginal cost curve is constant at a value of 10.

MC = 10

Our firm naturally wants to maximize profits and will therefore aim to satisfy the profit maximizing condition, MC = MR . Marginal costs are constant at ten, so half of our equation is easy. To find our marginal revenue, we first look at the total revenue. Total revenue is simply:

R = P * Q

Because the monopolist faces the entire market demand curve, price and quantity have a one-to-one relationship. That is, P = 100 - Q . We can rewrite our total revenue as:

R = (100 - Q) * Q = 100 * Q - Q^2

The marginal revenue is simply the first derivative of the total revenue with respect to Q .

MR = 100 - 2 * Q

If you don't feel comfortable with derivatives, you can convince yourself this MR is correct by analyzing its components.

MR = (100 - Q) - Q

(100 - Q) is the price according to our market demand curve. This 100 - Qrepresents the marginal revenue brought in by selling the next unit. However, in order to sell the next unit, we had to lower the price by 1 for all units sold (the demand curve has a slope of -1, so the tradeoff between Q and P is 1 for 1). Therefore, on the margin, we lost 1 unit of revenue for all Q units sold. The marginal revenue is then (100 - Q) - Q = 100 - 2*Q .

To solve for the monopolistic equilibrium, we find the quantity at which MR = MC . Solving:

100 - 2 * Q = 10 => Q = 45

At this quantity, the market price would be 100 - 45 = 55 . Assuming no fixed costs, the profits for this firm would be 45*(55 - 10) = 2025 . Naturally, this is a vast improvement for the firm over the competitive outcome of zero profits.