# 15 Monopoly

## The Policy QuestionShould the Government Give Patent Protection to Companies That Make Life-Saving Drugs?

In 1993, Shionogi, a Japanese pharmaceutical company, received a patent for the anti-statin medication rosuvastatin calcium, better known by its brand name, Crestor. Crestor is used to treat high cholesterol and related heart and cardiovascular diseases. Crestor has become one of the best-selling drugs of all time. In 2016, the patent protection will expire, and AstraZeneca, the manufacturer of Crestor, will cease to be a monopolist, and generic versions of the drug will flood the market. The patent created a twenty-three-year monopoly in the Crestor market, for which AstraZeneca has enjoyed enormous profits; the company recorded $5 billion in Crestor sales in 2015 alone. Providing a company the exclusive rights to sell a popular and medically important drug creates the potential for enormous profits, which gives pharmaceutical companies a very strong incentive to invest in the research and development of new drugs. But it also creates a situation in which medically necessary drugs are very expensive for consumers. ## Exploring the Policy Question 1. Does the societal benefit from the advent of new drugs outweigh the cost to society from the creation of monopolies? 2. What other way could society promote the development of new medicines? ## Learning Objectives ### 15.1 Conditions for Monopoly Learning Objective 15.1: Explain the conditions that lead to monopolies. ### 15.2 Profit Maximization for Monopolists Learning Objective 15.2: Explain how monopolists maximize profits and solve for the optimal monopolist’s solution from a demand curve and a marginal cost curve. ### 15.3 Market Power and the Demand Curve Learning Objective 15.3: Describe the relationship between demand elasticity and a monopolist’s ability to price above marginal cost. ### 15.4 Monopoly and Welfare Learning Objective 15.4: Describe how monopolists create deadweight loss and explain how deadweight loss affects societal welfare. ### 15.5 Policy ExampleShould the Government Give Patent Protection to Companies That Make Life-Saving Drugs? Learning Objective 15.5: Explain the effect of patent protection on drug markets and the trade-off society makes to promote the development of new drugs. ## 15.1 Conditions for Monopoly Learning Objective 15.1: Explain the conditions that lead to monopolies. A monopoly is the sole supplier of a good for which there does not exist a close substitute. In the policy example above, a firm that makes the only drug with which to treat or cure a disease is a monopolist if there is no other drug available to treat or cure the disease or if the only other drugs are not nearly as effective. Many drug makers continue to hold on to their trademarked drug names even after the patents run out and generic drugs enter the market, but the presence of the generics means that the original companies are no longer monopolists in the market for that particular drug. As we learned in chapter 13, the characteristics of monopoly markets are a single firm, a unique product, and barriers to entry. But what are those barriers to entry, and where do they come from? There are two main sources of these barriers: (1) cost conditions that make it cheaper for one firm to produce and (2) government regulations that create legal barriers to entry that prevent other firms from competing in the same market. Cost advantages can come from a number of sources. A firm might control an essential input; for example, one company might control the only source of a rare earth element used in high-performance batteries for automobiles. A firm might have better technology for or a better method of producing a good or service that gives it a cost advantage. Of course, this advantage only lasts as long as the firm is the only one with the technology or method. For this reason, many firms keep their production processes a closely guarded secret. Another source of a monopoly is large fixed costs associated with production. If the fixed costs of production are large enough relative to the demand for a product, it may be true that only one firm can make non-negative economic profits. This is referred to as a natural monopoly—when one firm can supply the market more cheaply than two or more firms. For example, suppose an entrepreneur wants to start a concrete-pumping service in her isolated small town to provide concrete for difficult-to-reach places that normal concrete trucks are unable to access. Concrete-pumping trucks are very large and very expensive. The town might have enough demand to justify the cost of one such truck, and so the entrepreneur will attract enough business to cover the cost of the truck itself and the other accounting and opportunity costs of the business. But there might not be enough demand to justify the purchase of a second concrete-pumping truck if another business decided to start up. Thus the monopoly that results is a natural result of the large fixed cost relative to the limited demand. We can express the concrete-pumping example more formally with a simple model. Suppose the marginal cost of supplying pumped concrete is fixed at $c$ and the cost of the truck itself, the fixed cost, is $F$. The truck is a fixed cost because it costs $F$ to acquire the truck, and this does not depend on the amount of concrete sold, or $Q$. The firm’s total cost function is therefore $TC = cQ + F$. Average cost is $AC = c + F/Q$. This is the same for any firm that enters the market. Let’s say that the cost of the truck, $F$, is$500,000 per year, and the marginal cost is $1 per cubic foot of concrete, $Q$. Now suppose that the demand is such that at $MC = 1$, 100,000 cubic feet of concrete is sold per year. If there is one firm, the average cost of pumped concrete is $AC = 1 + 500,000/100,000$, or $AC = 6$. If there were two firms, the average cost of the industry would be $AC_IND = c + 2F/Q$. Note that at a constant $MC$, the cost of a single cubic foot of concrete is always $c$, no matter which company provides it; however, with two firms, there are two fixed costs because each one has to pay for a truck. So $AC = 1 + 1,000,000/100,000$, or $AC = 11$. If the maximum willingness to pay for concrete at 100,000 cubic feet a year in this town is$8, the town can only support one firm. One firm would make $2 in economic profit in this business, while two firms would each lose$3 in economic profit.

Another important source of monopoly power is government. The government itself owns and manages monopolies; for example, the federal government runs the US Postal Service, and local governments are often the sole provider of utilities such as water and sewer services. The government also provides protection from competition for individual firms, guaranteeing their monopoly status. The most common protection the government offers is patent protection, but the government can also require licenses to operate businesses—for example, a local hospital—and issue only one per market. The government can also grant a firm the right to operate as a monopoly; for example, a municipality might grant one company the right to collect residential trash.

A patent is an exclusive right to an invention that excludes others from making, using, selling, or importing it into the country for a limited time. In other words, the inventor is granted protection from any direct competition for a period of time, generally twenty years from the time an application is filed, and in exchange, the invention becomes public knowledge when the patent is granted. Why does the government offer patent protection? As we will see in the next section, being a monopolist often allows companies to collect positive economic profits—a better-than-normal return on investment. So patents give companies a reward for investing in new technologies, new drugs, and new methods that are valuable to society as an incentive.

## 15.2 Profit Maximization for Monopolists

Learning Objective 15.2: Explain how monopolists maximize profits and solve for the optimal monopolist’s solution from a demand curve and a marginal cost curve.

All profit maximizing firms, regardless of the structure of the markets in which they sell, maximize profits by setting the output so that marginal revenue equals marginal cost, as we learned in chapter 9. Chapter 8 demonstrated how to find a marginal cost curve from the firm’s total cost curve. What is different in the case of a monopoly is the marginal revenue curve. Perfectly competitive firms take prices as given; their output decisions do not change market prices, and so the marginal revenue for a perfectly competitive firm is simply the market price. Monopolists, on the other hand, are “price makers” in the sense that they can set their prices by picking a point on the demand curve. Note that they are not free of constraint; the demand curve dictates the maximum price they can charge for every quantity level. The task for the profit maximizing monopolist is to determine which point on the demand curve maximizes their profits. A downward-sloping demand curve will mean that the firm faces a trade-off: they can sell more but must lower their price to do so. This means that the marginal revenue of a monopolist will depend on their output decision.

The total revenue for a firm is the number of goods they sell, $Q$, multiplied by the price at which they sell the goods, $p$. Note that $Q$ is both the firm’s output and the market output, as there is only one firm supplying the market.

$TR=pQ$

The firm’s marginal revenue is the change in total revenue from the sale of one more unit of its output. Thus in a firm that earns $\Delta TR$ extra revenue from the sale of $\Delta Q$, more units have a marginal revenue of

$MR=\frac{\Delta TR}{\Delta Q}$.

Therefore, if the firm sells one more unit, $\Delta Q=1$ and $MR=\Delta TR$.

### Calculus

Marginal revenue can be found from total revenue by taking the derivative:

$MR=\frac{dTR}{dQ}$

Because of the price-quantity trade-off from the demand curve, the marginal revenue of a monopolist will depend on its output. Unlike a perfectly competitive firm whose product sells for a constant price and therefore has a constant price for its marginal revenue, a monopolist who wants to sell one more unit must lower its price to do so. Thus a monopolist’s marginal revenue is a constantly declining function. It also declines at a rate greater than the demand curve because to sell more, the monopolist must lower the price of all its goods. Figure 15.2.1 demonstrates the marginal revenue trade-off.

At price $p_1$, the total revenue is $p_1Q_1$, which is represented by the areas $A+B$. At price $p_2$, the total revenue is $p_2Q_2$, which is represented by the areas $A+C$. Area $A$ is the same for both, so the marginal revenue is the difference between $B$ and $C$, or $C-B$.

Note that area $C$ is the price, $p_2$, times the change in quantity, $Q_2-Q_1$, or $p \Delta Q$, and area $B$ is the quantity, $Q_1$, times the change in price, $p_2-p_1$, or $\Delta pQ$. Since $p_2-p_1$ is negative, the change in total revenue is $C-B$, or

$\Delta TR=p \Delta Q+ \Delta pQ$.

Dividing both sides by $\Delta Q$ gives us an expression for marginal revenue:

(15.1) $MR=\frac{\Delta TR}{\Delta Q}=p+Q\frac{\Delta p}{\Delta Q}$

This expression has an intuitive interpretation. The first part, $p$, is the extra revenue the firm gets from selling an extra unit of the good. The second part, $Q\frac{\Delta p}{\Delta Q}$, which is negative, is the decrease in revenue from the fact that increasing output marginally lowers the price the firm receives for all of its output. Since the second part is negative, we know that the $MR$ curve is below the demand curve for every $Q$, since the demand curve relates price and quantity.

Figure 15.2.2 shows the relationship between a linear demand curve and the marginal revenue curve in the top panel and the total revenue in the bottom panel.

Since marginal revenue is the rate of change in total revenue for a marginal increase in quantity, when marginal revenue is positive, the total revenue curve has a positive slope, and when marginal revenue is negative, the total revenue curve has a negative slope. Note that this means the total revenue is maximized at the point where marginal revenue is zero.

A profit maximizing firm chooses an output so that the marginal cost of producing that output exactly matches the marginal revenue it gets from selling that output. Now that we have the marginal revenue, all that remains is to add the marginal cost. Figure 15.2.3 shows that the optimal output for the monopolist is where marginal revenue and marginal cost intersect.

The intersection of the marginal revenue and marginal cost curves occurs at point $Q^M$, and the highest price at which the monopolist can sell exactly $Q^M$ is $p^M$. At $Q^M$, the total revenue is simply $(p^M) \times (Q^M)$, and total cost is $(AC) \times (Q^M)$, since $AC$ is just $TC/Q$. Therefore, the shaded area is the difference between total revenue and total cost or profit.

Mathematically, profit maximization for a monopolist is the same as for any firm: find the output level for which marginal revenue equals marginal cost. Let’s start with a general example. Suppose the demand for a good produced by a monopolist is $p=A=BQ$. Note that this is an inverse demand curve, a demand curve written with price as a function of quantity. We could easily solve it for $Q$ to get it back in normal form: $Q = A/B—p/B$. We can find the marginal revenue curve by first noting that $TR = p \times Q$. Thus $TR = (A—BQ) \times Q$, or $TR = AQ—BQ^2$.

### Calculus

If $TR = AQ—BQ^2$, then

$MR=\partial TR \partial Q=A-2BQ$

The marginal revenue from a linear demand curve is a curve with the same vertical intercept as the demand curve (in this case, $A$) and a slope twice as steep (in this case, $−2B$). In other words, for an inverse demand curve, $p = A—BQ$, and the marginal revenue curve is $MR = A − 2BQ$.

Let’s consider a specific example: suppose that Tesla is a monopolist in the manufacture of luxury electric cars. For its electric Model S cars, let’s say it faces an annual demand curve of $Q = 200 − 2p$ (in thousands). Its marginal cost of producing a Model S is $MC = Q$ (also in thousands).

First, we will solve for the monopolist’s profit maximizing level of output and the profit maximizing price. Second, we will graph the solution.

To solve the problem, we need to proceed in four steps: (1) find the inverse demand curve; (2) find the marginal revenue curve; (3) set marginal revenue equal to marginal cost and solve for $Q^M$, the monopolist’s profit maximizing output level; (4) find $p^M$, the monopolist’s profit maximizing price.

1. Find the inverse demand curve by solving for demand curve for $p$:
2. $Q = 200 − 2p$
$2p = 200 − Q$
$p = 100 − \frac{1}{2} Q$
3. Find the marginal revenue curve by doubling the slope coefficient ($B$):
4. $MR = 100 − (2) \times (\frac{1}{2}) Q$
$MR = 100 − Q$
5. Set MR equal to $MC$ and solve for $Q$:
6. $MR = MC$
$100 − Q = Q$
$100 = 2Q$
$Q^M = 50$ or
$Q^M = 50,000$
7. Find $p^M$ from the inverse demand curve:
8. $p = 100 − \frac{1}{2} Q$
$p = 100 − frac{1}{2} (50)$
$p = 100 − 25$
$p^M = 75$ or
$p^M = 75,000$

## 15.5 Policy ExampleShould the Government Give Patent Protection to Companies That Make Life-Saving Drugs?

Learning Objective 15.5: Explain the effect of patent protection on drug markets and the trade-off society makes to promote the development of new drugs.

Providing companies like AstraZeneca patent protection for drugs like Crestor gives them a profit incentive to invest in the research and development of new, medically important drugs. However, from section 15.4, we also know that monopoly power creates deadweight loss. Figure 15.5.1 shows the deadweight loss that results from monopoly power, but it is important to understand what the deadweight loss represents: this is the loss to society that results from the reduction in output of these medically important drugs. By restricting output, monopolies keep prices high and, in so doing, exclude a segment of consumers who would purchase the drugs if the price were at marginal cost, as would be the case in a perfectly competitive market.

However, there would be an even larger deadweight loss if the drug was never discovered and the market never created. The total surplus, the combination of the red- and green-shaded areas in figure 15.5.1, would be lost.

The most basic policy question is therefore whether the benefit to society is greater than the deadweight loss. Given the diagram in figure 15.5.1, the answer is almost certainly yes. Another policy question is whether there is an alternate policy that could achieve the same objective of developing new medicines at a lower societal cost—the most obvious is to fund the research of new medicines directly by the government and then allow new discoveries to be produced by many firms. This would lead to more production and lower costs of new drugs but might not be as efficient at promoting new discoveries. A final question is whether the patent protections promote the discovery of only the most profitable drugs, such as those often associated with aging in high-income countries. Malaria, a disease that remains one of the most lethal in the world, has not generated a lot of funding for the creation of a new drug to combat it, and many critics believe this is because it is a disease most commonly found in low-income countries and thus the potential profits are low because the market could not support high prices. Supporters of the current system like the fact that it is private enterprise, not the government, that decides in which areas to invest resources, thus ensuring that the drugs with the highest expected benefits are invested in most heavily.

## REVIEW: Topics and Related Learning Outcomes

### 15.1 Conditions for Monopoly

Learning Objective 15.1: Explain the conditions that lead to monopolies.

### 15.2 Profit Maximization for Monopolists

Learning Objective 15.2: Explain how monopolists maximize profits and solve for the optimal monopolist’s solution from a demand curve and a marginal cost curve.

### 15.3 Market Power and the Demand Curve

Learning Objective 15.3: Describe the relationship between demand elasticity and a monopolist’s ability to price above marginal cost.

### 15.4 Monopoly and Welfare

Learning Objective 15.4: Describe how monopolists create deadweight loss and explain how deadweight loss affects societal welfare.

### 15.5 Policy ExampleShould the Government Give Patent Protection to Companies That Make Life-Saving Drugs?

Learning Objective 15.5: Explain the effect of patent protection on drug markets and the trade-off society makes to promote the development of new drugs.

## LEARN: KEY TOPICS

### Terms

Monopoly

The sole supplier of a good for which there does not exist a close substitute.

Natural monopoly

When one firm can supply the market more cheaply than two or more firms.

Patent

An exclusive right to an invention that excludes others from making, using, selling, or importing it into the country for a limited time.

Inverse demand curve

A demand curve written with price as a function of quantity. See figure 15.2.3.

Markup

The percentage of the price above marginal cost.

Market power

The ability to choose a price above marginal cost.

The Lerner index

Measures the firm’s optimal markup. This is also a measure of market power, as firms with more market power are more able to charge prices above marginal cost.

$\frac{p-MC}{p}=-\frac{1}{\varepsilon}$

### Graphs

Monopoly, revenue, and marginal revenue
Demand, marginal revenue, and total revenue
Profit maximization for a monopolist
Solution to Tesla’s profit maximization problem
The markup and shape of the demand curve

### Equations

Marginal revenue

$MR=\frac{\Delta TR}{\Delta Q}=p+Q\frac{\Delta p}{\Delta Q}$

The Lerner index

Measures the firm’s optimal markup. Also measures market power, as firms with more market power are more able to charge prices above marginal cost.

$\frac{p-MC}{p}=-\frac{1}{\varepsilon}$

Marginal revenue curve produced by an inverse demand curve

The marginal revenue from a linear demand curve is a curve with the same vertical intercept as the demand curve and a slope twice as steep. The demand for a particular good is (or the inverse demand curve, or the demand curve solved as a function of price):

$p=A-BQ$

The marginal revenue curve is found by first noting that:

$TR = p \times Q$[/p>

Total revenue equals profit times output, and therefore,

$TR = (A—BQ) \times Q$
or $TR = AQ—BQ^2$

and if $TR = AQ—BQ^2$, then

$MR=\partial TR \partial Q=A-2BQ$

In other words, for an inverse demand curve of

$p = A—BQ$

the marginal revenue curve is

$MR = A − 2BQ$

The Tesla example

Optimizing a monopolist’s output and profit is a two-part process. The first part is solving for the monopolist’s profit maximizing level and the second is solving for their profit maximizing price. The results are usually graphed afterwards.

#### Solving for the monopolist’s profit maximizing level of output

A four step process.

##### I. Find the inverse demand curve

Find the inverse demand curve by solving for the demand curve for $p$

$Q = 200 − 2p$
$2p = 200 − Q$
$p = 100 − \frac{1}{2} Q$

##### II. Find the marginal revenue curve

Find the marginal revenue curve by doubling the slope coefficient $(B)$

$MR = 100 − (2) \times (\frac{1}{2}) Q$
$MR = 100 − Q$

##### III. Solve for Q

Set marginal revenue $(MR)$ equal to $(MC)$ and solve for $Q$

$MR = MC$
$100 − Q = Q$
$100 = 2Q$
$Q^M = 50$
or
$Q^M = 50,000$

##### IV. Find $p^M$

Find $p^M$ from the inverse demand curve

$p = 100 − \frac{1}{2} Q$
$p = 100 − frac{1}{2} (50)$
$p = 100 − 25$
$p^M = 75$
or
$p^M = 75,000$

#### Solving for Tesla’s profit maximizing price

Requires the total cost function. A theoretical total cost equation for Tesla:

$TC = \frac{1}{2} Q^2$

Previously defined variables $p^M$ ($75) and $Q^M$ ($50) are now substituted into Tesla’s total cost function and the total revenue equation:

$TR=75\times 50=3,750$
$TC = \frac{1}{2} (50)^2 = 1,250$

This defines the variables of total cost $(TC)$ and total revenue $(TR)$ as $1,250 and$3,750, respectively. Substituting into the profit equation:

$p=TR—TC$

gives us $p=3750-1250$, or 2,500; in this case, we have sliced zeroes off for ease of calculation, so the exact total is \$2.5 million.

The graphed solution to the Tesla example