273

Monopoly Monopoly: one parrot.

9

273

A firm that creates a new drug may receive a patent that gives it the right to be the monopoly or sole producer of the drug for up to 20 years. As a result, the firm can charge a price much greater than its marginal cost of production. For example, one of the world’s best-selling drugs, the heart medication Plavix, sold for about $7 per pill but can be produced for about 3¢ per pill.

Prices for drugs used to treat rare diseases are often very high. Drugs used for certain rare types of anemia cost patients about $5,000 per year. As high as this price is, it pales in com-

parison with the price of over $400,000 per year for Soliris, a drug used to treat a rare blood disorder.1

Recently, firms have increased their prices substantially for specialty drugs in response to perceived changes in will- ingness to pay by consumers and their insurance companies. In 2008, the price of a crucial antiseizure drug, H.P. Acthar Gel, which is used to treat children with a rare and severe form of epilepsy, increased from $1,600 to $23,000 per vial. Two courses of Acthar treatment for a severely ill 3-year-old girl, Reegan Schwartz, cost her father’s health plan about $226,000. Steve Cartt, an execu- tive vice president at the drug’s manu- facturer, Questcor, explained that this price increase was based on a review of the prices of other specialty drugs and estimates of how much of the price insurers and employers would be willing to bear.

In 2013, 107 U.S. drug patents expired, including major products such as Cymbalta and OxyContin. When a patent for a highly profitable drug expires, many firms enter the market

1When asked to defend such prices, executives of pharmaceutical companies emphasize the high costs of drug development—in the hundreds of millions of dollars—that must be recouped from a relatively small number of patients with a given rare condition.

Brand-Name and Generic Drugs

Managerial Problem

274 CHAPTER 9 Monopoly

W hy can a firm with a patent-based monopoly charge a high price? Why might a brand-name pharmaceutical’s price rise after its patent expires? To answer these questions, we need to understand the decision-making process for a monopoly: the sole supplier of a good that has no close substitute.3

Monopolies have been common since ancient times. In the fifth century b.c., the Greek philosopher Thales gained control of most of the olive presses during a year of exceptionally productive harvests. The ancient Egyptian pharaohs controlled the sale of food. In England, until Parliament limited the practice in 1624, kings granted monopoly rights called royal charters to court favorites. Particularly valuable royal charters went to companies that controlled trade with North America, the Hudson Bay Company, and with India, the British East India Company.

In modern times, government actions continue to play an important role in creating monopolies. For example, governments grant patents that allow the inventor of a new product to be the sole supplier of that product for up to 20 years. Similarly, until 1999, the U.S. government gave one company the right to be the sole registrar of Internet domain names. Many public utilities are government-owned or government-protected monopolies.4

3Analogously, a monopsony is the only buyer of a good in a given market. 4Whether the law views a firm as a monopoly depends on how broadly the market is defined. Is the market limited to a particular drug or the pharmaceutical industry as a whole? The manufacturer of the drug is a monopoly in the former case, but just one of many firms in the latter case. Thus, defining a market is critical in legal cases. A market definition depends on whether other products are good substitutes for those in that market.

and sell generic (equivalent) versions of the brand-name drug.2 Generics account for nearly 70% of all U.S. prescriptions and half of Canadian prescriptions.

Congress, when it passed laws permitting generic drugs to quickly enter a market after a patent expires, expected that patent expiration would subsequently lead to sharp declines in drug prices. If consumers view the generic product and the brand-name product as perfect substitutes, both goods will sell for the same price, and entry by many firms will drive the price down to the competitive level. Even if consumers view the goods as imperfect substitutes, one might expect the price of the brand-name drug to fall.

However, the prices of many brand-name drugs have increased after their patents expired and generics entered the market. The generic drugs are relatively inexpensive, but the brand- name drugs often continue to enjoy a significant market share and sell for high prices. Even after the patent for what was then the world’s largest selling drug, Lipitor, expired in 2011, it continued to sell for high prices despite competition from generics selling at much lower prices. Indeed, Regan (2008), who studied the effects of generic entry on post-patent price competition for 18 prescription drugs, found an average 2% increase in brand-name prices. Studies based on older data have found up to a 7% average increase. Why do some brand- name prices rise after the entry of generic drugs?

2Under the 1984 Hatch-Waxman Act, the U.S. government allows a firm to sell a generic product after a brand-name drug’s patent expires if the generic-drug firm can prove that its product delivers the same amount of active ingredient or drug to the body in the same way as the brand-name product. Sometimes the same firm manufactures both a brand-name drug and an identical generic drug, so the two have identical ingredients. Generics produced by other firms usually differ in appearance and name from the original product and may have different nonactive ingredients but the same active ingredients.

2759.1 Monopoly Profit Maximization

Unlike a competitive firm, which is a price taker (Chapter 8), a monopoly can set its price. A monopoly’s output is the market output, and the demand curve a monopoly faces is the market demand curve. Because the market demand curve is downward sloping, the monopoly (unlike a competitive firm) doesn’t lose all its sales if it raises its price. As a consequence, a profit-maximizing monopoly sets its price above marginal cost, the price that would prevail in a competitive market. Consumers buy less at this relatively high monopoly price than they would at the competitive price.

In this chapter, we examine six main topics

Main Topics 1. Monopoly Profit Maximization: Like all firms, a monopoly maximizes profit by setting its output so that its marginal revenue equals marginal cost.

2. Market Power: A monopoly sets its price above the competitive level, which equals the marginal cost.

3. Market Failure Due to Monopoly Pricing: By setting its price above marginal cost, a monopoly creates a deadweight loss because the market fails to maximize total surplus.

4. Causes of Monopoly: Two important causes of monopoly are cost factors and government actions that restrict entry, such as patents.

5. Advertising: A monopoly advertises to shift its demand curve so as to increase its profit.

6. Networks, Dynamics, and Behavioral Economics: If its current sales affect a monopoly’s future demand curve, a monopoly may charge a low initial price so as to maximize its long-run profit.

9.1 Monopoly Profit Maximization All firms, including competitive firms and monopolies, maximize their profits by setting quantity such that marginal revenue equals marginal cost (Chapter 7). Chapter 6 demonstrates how to derive a marginal cost curve. We now derive the monopoly’s marginal revenue curve and then use the marginal revenue and marginal cost curves to examine how the manager of a monopoly sets quantity to maximize profit.

Marginal Revenue A firm’s marginal revenue curve depends on its demand curve. We will show that a monopoly’s marginal revenue curve lies below its demand curve at any positive quantity because its demand curve is downward sloping.

Marginal Revenue and Price. A firm’s demand curve shows the price, p, it receives for selling a given quantity, q. The price is the average revenue the firm receives, so a firm’s revenue is R = pq.

A firm’s marginal revenue, MR, is the change in its revenue from selling one more unit. A firm that earns ΔR more revenue when it sells Δq extra units of output has a marginal revenue of

MR = ΔR Δq

.

276 CHAPTER 9 Monopoly

If the firm sells exactly one more unit (Δq = 1), then its marginal revenue, MR, is ΔR (= ΔR/1).

The marginal revenue of a monopoly differs from that of a competitive firm because the monopoly faces a downward-sloping demand curve, unlike the com- petitive firm. The competitive firm in panel a of Figure 9.1 faces a horizontal demand curve at the market price, p1. Because its demand curve is horizontal, the competitive firm can sell another unit of output without reducing its price. As a result, the marginal revenue it receives from selling the last unit of output is the market price.

Initially, the competitive firm sells q units of output at the market price of p1, so its revenue, R1, is area A, which is a rectangle that is p1 * q. If the firm sells one more unit, its revenue is R2 = A + B, where area B is p1 * 1 = p1. The competitive firm’s marginal revenue equals the market price:

ΔR = R2 – R1 = (A + B) – A = B = p1.

A monopoly faces a downward-sloping market demand curve, as in panel b of Figure 9.1. (So far we have used q to represent the output of a single firm and Q to represent the combined market output of all firms in a market. Because a monopoly

FIGURE 9.1 Average and Marginal Revenue

p, $

p er

u ni

t

q q + 1 q, Units per year

p1

(a) Competitive Firm

Demand curve

A B

Q Q + 1 Q, Units per year

p1

p2

p, $

p er

u ni

t

(b) Monopoly

Demand curve

A B

C

Revenue with One More Unit,

R2 Initial Revenue,

R1 Marginal Revenue,

R2 – R1

Competition A A + B B = p1 Monopoly A + C A + B B − C = p2 − C

The demand curve shows the average revenue or price per unit of output sold. (a) The competitive firm’s mar- ginal revenue, area B, equals the market price, p1. (b) The

monopoly’s marginal revenue is less than the price p2 by area C, the revenue lost due to a lower price on the Q units originally sold.

2779.1 Monopoly Profit Maximization

is the only firm in the market, q and Q are identical, so we use Q to describe both the firm’s output and market output.

The monopoly, which initially sells Q units at p1, can sell one extra unit only if it lowers its price to p2 on all units. The monopoly’s initial revenue, p1 * Q, is R1 = A + C. When it sells the extra unit, its revenue, p2 * (Q + 1), is R2 = A + B. Thus, its marginal revenue is

ΔR = R2 – R1 = (A + B) – (A + C) = B – C.

The monopoly sells the extra unit of output at the new price, p2 , so its extra rev- enue is B = p2 * 1 = p2. The monopoly loses the difference between the new price and the original price, Δp = (p2 – p1), on the Q units it originally sold: C = Δp * Q. Therefore the monopoly’s marginal revenue, B – C = p2 – C, is less than the price it charges by an amount equal to area C.

Because the competitive firm in panel a can sell as many units as it wants at the market price, it does not have to cut its price to sell an extra unit, so it does not have to give up revenue such as Area C in panel b. It is the downward slope of the monopoly’s demand curve that causes its marginal revenue to be less than its price. For a monopoly to sell one more unit in a given period it must lower the price on all the units it sells that period, so its marginal revenue is less than the price obtained for the extra unit. The marginal revenue is this new price minus the loss in revenue arising from charging a lower price for all other units sold.

The Marginal Revenue Curve. Thus, the monopoly’s marginal revenue curve lies below a downward-sloping demand curve at every positive quantity. The relation- ship between the marginal revenue and demand curves depends on the shape of the demand curve.

For linear demand curves, the marginal revenue curve is a straight line that starts at the same point on the vertical (price) axis as the demand curve but has twice the slope. Therefore, the marginal revenue curve hits the horizontal (quantity) axis at half the quantity at which the demand curve hits the quantity axis. In Figure 9.2, the demand curve has a slope of -1 and hits the horizontal axis at 24 units, while the marginal revenue curve has a slope of -2 and hits the horizontal axis at 12 units.

We now derive an equation for the monopoly’s marginal revenue curve. For a monopoly to increase its output by one unit, the monopoly lowers its price per unit by an amount indicated by the demand curve, as panel b of Figure 9.1 illustrates. Specifically, output demanded rises by one unit if price falls by the slope of the demand curve, Δp/ΔQ. By lowering its price, the monopoly loses (Δp/ΔQ) * Q on the units it originally sold at the higher price (area C), but it earns an additional p on the extra output it now sells (area B). Thus, the monopoly’s marginal revenue is

MR = p + Δp ΔQ

Q. (9.1)

Because the slope of the monopoly’s demand curve, Δp/ΔQ, is negative, the last term in Equation 9.1, (Δp/ΔQ)Q, is negative. Equation 9.1 confirms that the price is greater than the marginal revenue, which equals p plus a negative term and must therefore be less than the price.

We now use Equation 9.1 to derive the marginal revenue curve when the monop- oly faces the linear inverse demand function (Chapter 3)

p = 24 – Q, (9.2)

278 CHAPTER 9 Monopoly

that Figure 9.2 illustrates. Equation 9.2 shows that the price consumers are willing to pay falls $1 if quantity increases by one unit. More generally, if quantity increases by ΔQ, price falls by Δp = -ΔQ. Thus, the slope of the demand curve is Δp/ΔQ = -1.

We obtain the marginal revenue function for this monopoly by substituting into Equation 9.1 the actual slope of the demand function, Δp/ΔQ = -1, and replacing p with 24 – Q (using Equation 9.2):

MR = p + Δp ΔQ

Q = (24 – Q) + (-1)Q = 24 – 2Q. (9.3)

Figure 9.2 shows a plot of Equation 9.3. The slope of this marginal revenue curve is ΔMR/ΔQ = -2, so the marginal revenue curve is twice as steep as the demand curve.

Using Calculus Using calculus, if a firm’s revenue function is R(Q), then its marginal revenue function is defined as

MR(Q) = dR(Q)

dQ .

For our example, where the inverse demand function is p = 24 – Q, the revenue function is

R(Q) = (24 – Q)Q = 24Q – Q2. (9.4)

Deriving a Monopoly’s Marginal Revenue Function

p, $

p er

u ni

t

Demand (p = 24 – Q )

Perfectly elastic, ε→ –∞

Perfectly inelastic, ε = 0

Elastic, ε < –1

Inelastic, –1 < ε < 0

ε = –1

Δp = –1

ΔQ = 1ΔQ = 1

ΔMR = –2

Q, Units per day

24

12

0 12 24

Marginal Revenue (MR = 24 – 2Q )

FIGURE 9.2 Elasticity of Demand and Total, Average, and Marginal Revenue

The demand curve (or average revenue curve), p = 24 – Q, lies above the marginal revenue curve, MR = 24 – 2Q. Where the marginal revenue equals

zero, Q = 12, the elasticity of demand is ε = -1. For larger quantities, the marginal revenue is negative, so the MR curve is below the horizontal axis.

2799.1 Monopoly Profit Maximization

Marginal Revenue and Price Elasticity of Demand. The marginal revenue at any given quantity depends on the demand curve’s height (the price) and shape. The shape of the demand curve at a particular quantity is described by the price elasticity of demand (Chapter 3), ε = (ΔQ/Q)/(Δp/p) 6 0, which tells us the percentage by which quantity demanded falls as the price increases by 1%.

At a given quantity, the marginal revenue equals the price times a term involving the elasticity of demand (Chapter 3):5

MR = p¢1 + 1 ε ≤. (9.5)

5By multiplying the last term in Equation 9.1 by p/p (=1) and using algebra, we can rewrite the expression as

MR = p + p Δp ΔQ

Q

p = pJ1 + 1

(ΔQ/Δp)(p/Q) R .

The last term in this expression is 1/ε, because ε = (ΔQ/Δp)(p/Q).

Q&A 9.1 Given a general linear inverse demand curve p(Q) = a – bQ, where a and b are posi- tive constants, use calculus to show that the marginal revenue curve is twice as steeply sloped as the inverse demand curve.

Answer

1. Differentiate a general inverse linear demand curve with respect to Q to determine its slope. The derivative of the linear inverse demand function with respect to Q is

dp(Q)

dQ =

d(a – bQ) dQ

= -b.

2. Differentiate the monopoly’s revenue function with respect to Q to obtain the mar- ginal revenue function, then differentiate the marginal revenue function with respect to Q to determine its slope. The monopoly’s revenue function is R(Q) = p(Q)Q = (a – bQ)Q = aQ – bQ2. Differentiating the revenue function with respect to quantity, we find that the marginal revenue function is linear,

MR(Q) = dR(Q)/dQ = a – 2bQ.

Thus, the slope of the marginal revenue curve,

dMR(Q) dQ

= -2b,

is twice that of the inverse demand curve, dp/dQ = -b. Comment: Note that the vertical axis intercept is a for both the inverse

demand and MR curves. Thus, if the demand curve is linear, its marginal revenue curve is twice as steep and intercepts the horizontal axis at half the quantity as does the demand curve.

By differentiating Equation  9.4 with respect to Q, we obtain the marginal revenue function, MR(Q) = dR(Q)/dQ = 24 – 2Q, which is the same as Equation 9.3.

280 CHAPTER 9 Monopoly

According to Equation 9.5, marginal revenue is closer to price as demand becomes more elastic. Where the demand curve hits the price axis (Q = 0), the demand curve is perfectly elastic, so the marginal revenue equals price: MR = p.6 Where the demand elasticity is unitary, ε = -1, marginal revenue is zero: MR = p[1 + 1/(-1)] = 0. Marginal revenue is negative where the demand curve is inelastic, -1 6 ε … 0.

With the demand function in Equation 9.2, ΔQ/Δp = -1, so the elasticity of demand is ε = (ΔQ/Δp)(p/Q) = -p/Q. Table 9.1 shows the relationship among quantity, price, marginal revenue, and elasticity of demand for this linear exam- ple. As Q approaches 24, ε approaches 0, and marginal revenue is negative. As Q approaches zero, the demand becomes increasingly elastic, and marginal revenue approaches the price.

Choosing Price or Quantity Any firm maximizes its profit by operating where its marginal revenue equals its marginal cost. Unlike a competitive firm, a monopoly can adjust its price, so it has a choice of setting its price or its quantity to maximize its profit. (A competitive firm sets its quantity to maximize profit because it cannot affect market price.)

6As ε approaches – ∞ (perfectly elastic demand), the 1/ε term approaches zero, so MR = p(1 + 1/ε) approaches p.

Quantity, Q

Price, p

Marginal Revenue, MR

Elasticity of Demand, ε = -p/Q

0 24 24 – ∞

1 23 22 -23

2 22 20 -11

3 21 18 -7

4 20 16 -5

5 19 14 -3.8

6 18 12 -3

7 17 10 -2.43

8 16 8 -2

9 15 6 -1.67

10 14 4 -1.4

11 13 2 -1.18

12 12 0 -1

13 11 -2 -0.85 f f f f

23 1 -22 -0.043

24 0 -24 0

TABLE 9.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Function p = 24 – Q

m or

e el

as ti

c S

d le

ss e

la st

ic

2819.1 Monopoly Profit Maximization

Whether the monopoly sets its price or its quantity, the other variable is deter- mined by the market demand curve. Because the demand curve slopes down, the monopoly faces a trade-off between a higher price and a lower quantity or a lower price and a higher quantity. A profit-maximizing monopoly chooses the point on the demand curve that maximizes its profit. Unfortunately for the monopoly, it cannot set both its quantity and its price, such as a point that lies above its demand curve. If it could do so, the monopoly would choose an extremely high price and an extremely large output and would earn a very high profit. However, the monopoly cannot choose a point that lies above the demand curve.

If the monopoly sets its price, the demand curve determines how much output it sells. If the monopoly picks an output level, the demand curve determines the price. Because the monopoly wants to operate at the price and output at which its profit is maximized, it chooses the same profit-maximizing solution whether it sets the price or output. Thus, setting price and setting quantity are equivalent for a monopoly. In the following discussion, we assume that the monopoly sets quantity.

Two Steps to Maximizing Profit All profit-maximizing firms, including monopolies, use a two-step analysis to deter- mine the output level that maximizes their profit (Chapter 7). First, the firm deter- mines the output, Q*, at which it makes the highest possible profit (or minimizes its loss). Second, the firm decides whether to produce Q* or shut down.

Profit-Maximizing Output. In Chapter 7, we saw that profit is maximized where marginal profit equals zero. Equivalently, because marginal profit equals marginal revenue minus marginal cost (Chapter 7), marginal profit is zero where marginal revenue equals marginal cost.

To illustrate how a monopoly chooses its output to maximize its profit, we use the same linear demand and marginal revenue curves as above and add a linear marginal cost curve in panel a of Figure 9.3. Panel b shows the corresponding profit curve.

The marginal revenue curve, MR, intersects the marginal cost curve, MC, at 6 units in panel a. The corresponding price, 18, is the height of the demand curve, point e, at 6 units. The profit, π, is the gold rectangle. The height of this rectangle is the average profit per unit, p – AC = 18 – 8 = 10. The length of the rectangle is 6 units. Thus, the area of the rectangle is the average profit per unit times the number of units, which is the profit, π = 60.

The profit at 6 units is the maximum possible profit: The profit curve in panel b reaches its peak, 60, at 6 units. At the peak of the profit curve, the marginal profit is zero, which is consistent with the marginal revenue equaling the marginal cost.

Why does the monopoly maximize its profit by producing where its marginal revenue equals its marginal cost? At smaller quantities, the monopoly’s marginal revenue is greater than its marginal cost, so its marginal profit is positive—the profit curve is upward sloping. By increasing its output, the monopoly raises its profit. Similarly, at quantities greater than 6 units, the monopoly’s marginal cost is greater than its marginal revenue, so its marginal profit is negative, and the monopoly can increase its profit by reducing its output.

As Figure 9.2 illustrates, the marginal revenue curve is positive where the elastic- ity of demand is elastic, is zero at the quantity where the demand curve has a unitary

282 CHAPTER 9 Monopoly

elasticity, and is negative at larger quantities where the demand curve is inelastic. Because the marginal cost curve is never negative, the marginal revenue curve can only intersect the marginal cost curve where the marginal revenue curve is positive, in the range in which the demand curve is elastic. That is, a monopoly’s profit is maxi- mized in the elastic portion of the demand curve. In our example, profit is maximized at Q = 6, where the elasticity of demand is -3. A profit-maximizing monopoly never operates in the inelastic portion of its demand curve.

The Shutdown Decision. A monopoly shuts down to avoid making a loss in the short run if its price is below its average variable cost at its profit-maximizing (or loss-minimizing) quantity (Chapter 7). In the long run, the monopoly shuts down if the price is less than its average cost.

In the short-run example in Figure 9.3, the average variable cost, AVC = 6, is less than the price, p = 18, at the profit-maximizing output, Q = 6, so the firm chooses to produce. Price is also above average cost at Q = 6, so the average profit per unit, p – AC is positive (the height of the gold profit rectangle), so the monopoly makes a positive profit.

12

18

24

8

6

60

60 12 24

π, $

0 126

AC

AVC e

Demand

π = 60

MC

MR

Q, Units per day

Profit, π

Q, Units per day

p, $

p er

u ni

t

(a) Monopolized Market

(b) Profit

FIGURE 9.3 Maximizing Profit

(a) At Q = 6, where marginal revenue, MR, equals marginal cost, MC, profit is maximized. The rect- angle shows that the profit is $60, where the height of the rectangle is the average profit per unit, p – AC = $18 – $8 = $10, and the length is the number of units, 6. (b) Profit is maximized at Q = 6 (where marginal revenue equals marginal cost).

2839.1 Monopoly Profit Maximization

Effects of a Shift of the Demand Curve Shifts in the demand curve or marginal cost curve affect the profit-maximizing monopoly price and quantity and can have a wider variety of effects with a monopoly than with a competitive market. In a competitive market, the effect of a shift in demand on a competitive firm’s output depends only on the shape of the

Using Calculus We can also solve for the profit-maximizing quantity mathematically. We already know the demand and marginal revenue functions for this monopoly. We need to determine its cost curves.

The monopoly’s cost is a function of its output, C(Q). In Figure 9.3, we assume that the monopoly faces a short-run cost function of

C(Q) = 12 + Q2, (9.6)

where Q2 is the monopoly’s variable cost as a function of output and 12 is its fixed cost. Given this cost function, Equation 9.6, the monopoly’s marginal cost function is

dC(Q) dQ

= MC(Q) = 2Q. (9.7)

This marginal cost curve in panel a is a straight line through the origin with a slope of 2. The average variable cost is AVC = Q2/Q = Q, so it is a straight line through the ori- gin with a slope of 1. The average cost is AC = C/Q = (12 + Q2)/Q = 12/Q + Q, which is U-shaped.

Using Equations 9.4 and 9.6, we can write the monopoly’s profit as

π(Q) = R(Q) – C(Q) = (24Q – Q2) – (12 + Q2).

By setting the derivative of this profit function with respect to Q equal to zero, we have an equation that determines the profit-maximizing output:

dπ(Q) dQ

= dR(Q)

dQ –

dC(Q) dQ

= MR – MC = (24 – 2Q) – 2Q = 0.

That is, MR = 24 – 2Q = 2Q = MC. To determine the profit-maximizing out- put, we solve this equation and find that Q = 6. Substituting Q = 6 into the inverse demand function (Equation 9.2), we learn that the profit-maximizing price is

p = 24 – Q = 24 – 6 = 18.

Should the monopoly operate at Q = 6? At that quantity, average variable cost is AVC = Q2/Q = 6, which is less than the price, so the firm does not shut down. The average cost is AC = (6 + 12/6) = 8, which is less than the price, so the firm makes a profit.

Solving for the Profit-Maximizing Output

284 CHAPTER 9 Monopoly

marginal cost curve. In contrast, the effect of a shift in demand on a monopoly’s output depends on the shapes of both the marginal cost curve and the demand curve.

As we saw in Chapter 8, a competitive firm’s marginal cost curve tells us every- thing we need to know about the amount that the firm is willing to supply at any given market price. The competitive firm’s supply curve is its upward-sloping mar- ginal cost curve above its minimum average variable cost. A competitive firm’s sup- ply behavior does not depend on the shape of the market demand curve because it always faces a horizontal demand curve at the market price. Thus, if we know a competitive firm’s marginal cost curve, we can predict how much that firm will produce at any given market price.

In contrast, a monopoly’s output decision depends on the shapes of its marginal cost curve and its demand curve. Unlike a competitive firm, a monopoly does not have a supply curve. Knowing the monopoly’s marginal cost curve is not enough for us to predict how much a monopoly will sell at any given price.

Figure 9.4 illustrates that the relationship between price and quantity is unique in a competitive market but not in a monopolistic market. If the market is competitive, the initial equilibrium is e1 in panel a, where the original demand curve D1 intersects the supply curve, MC, which is the sum of the marginal cost curves of a large number of competitive firms. When the demand curve shifts to D2, the new competitive equi- librium, e2, has a higher price and quantity. A shift of the demand curve maps out competitive equilibria along the marginal cost curve, so every equilibrium quantity has a single corresponding equilibrium price.

For the monopoly in panel b, as the demand curve shifts from D1 to D2, the profit-maximizing monopoly outcome shifts from E1 to E2, so the price rises but the quantity stays constant, Q1 = Q2. Thus, a given quantity can correspond to more than one profit-maximizing price, depending on the position of the demand curve. A shift in

p, $

p er

u ni

t

Q, Units per year

p1 p2

Q2Q1

(a) Competition

MC, Supply curve

e2

e1

D1D2

Q, Units per year

p1

p2

Q2Q1=

p, $

p er

u ni

t

(b) Monopoly

MC

D1D2

MR1

E2

E1

MR2

FIGURE 9.4 Effects of a Shift of the Demand Curve

(a) A shift of the demand curve from D1 to D2 causes the competitive equilibrium to move from e1 to e2 along the supply curve (which is the horizontal sum of the marginal cost curves of all the competitive firms). Because the com- petitive equilibrium lies on the supply curve, each quan- tity (such as Q1 and Q2) corresponds to only one possible equilibrium price. (b) With a monopoly, this same shift of

demand causes the monopoly optimum to change from E1 to E2. The monopoly quantity stays the same, but the monopoly price rises. Thus, a shift in demand does not map out a unique relationship between price and quantity in a monopolized market. The same quantity, Q1 = Q2, is associated with two different prices, p1 and p2.

2859.2 Market Power

the demand curve may cause the profit-maximizing price to stay constant while the quantity changes. More commonly, both the profit-maximizing price and quantity would change.

9.2 Market Power A monopoly has market power, which is the ability to significantly affect the market price. In contrast, no single competitive firm can significantly affect the market price.

A profit-maximizing monopoly charges a price that exceeds its marginal cost. The extent to which the monopoly price exceeds marginal cost depends on the shape of the demand curve.

Market Power and the Shape of the Demand Curve If the monopoly faces a highly elastic—nearly flat—demand curve at the profit- maximizing quantity, it would lose substantial sales if it raised its price by even a small amount. Conversely, if the demand curve is not very elastic (relatively steep) at that quantity, the monopoly would lose fewer sales from raising its price by the same amount.

We can derive the relationship between markup of price over marginal cost and the elasticity of demand at the profit-maximizing quantity using the expression for marginal revenue in Equation 9.5 and the firm’s profit-maximizing condition that marginal revenue equals marginal cost:

MR = p¢1 + 1 ε ≤ = MC. (9.8)

By rearranging terms, we see that a profit-maximizing manager chooses quantity such that

p

MC =

1 1 + (1/ε)

. (9.9)

In our linear demand example in panel a of Figure 9.3, the elasticity of demand is ε = -3 at the monopoly optimum where Q = 6. As a result, the ratio of price to marginal cost is p/MC = 1/[1 + 1/(-3)] = 1.5, or p = 1.5MC. The profit-maximizing price, $18, in panel a is 1.5 times the marginal cost of $12.

Table  9.2 illustrates how the ratio of price to marginal cost varies with the elasticity of demand. When the elasticity is -1.01, only slightly elastic, the monopoly’s profit-maximizing price is 101 times larger than its marginal cost: p/MC = 1/[1 + 1/(-1.01)] ≈ 101. As the elasticity of demand approaches nega- tive infinity (becomes perfectly elastic), the ratio of price to marginal cost shrinks to p/MC = 1.7 Thus, even in the absence of rivals, the shape of the demand curve constrains the monopolist’s ability to exercise market power.

7As the elasticity approaches negative infinity, 1/ε approaches zero, so 1/(1 + 1/ε) approaches 1/1 = 1.

286 CHAPTER 9 Monopoly

A manager can use this last result to determine whether the firm is maximiz- ing its profit. Typically a monopoly knows its costs accurately, but is somewhat uncertain about the demand curve it faces and hence what price (or quantity) to set. Many private firms—such as ACNielsen, IRI, and IMS Health—and industry groups collect data on quantities and prices in a wide variety of industries includ- ing automobiles, foods and beverages, drugs, and many services. Firms can use these data to estimate the firm’s demand curve (Chapter 3). More commonly, firms hire consulting firms (often the same firms that collect data) to estimate the elasticity of demand facing their firm.

A manager can use the estimated elasticity of demand to check whether the firm is maximizing profit. If the p/MC ratio does not approximately equal 1/(1 + 1/ε), as required by Equation 9.9, then the manager knows that the firm is not setting its price to maximize its profit. Of course, the manager can also check whether the firm is maximizing profit by varying its price or quantity. However, often such experiments may be more costly than using statistical techniques to estimate the elasticity of demand.

Checking Whether the Firm Is Maximizing Profit

Managerial Implication

Mini-Case Since San Francisco’s cable car system started operating in 1873, it has been one of the city’s main tourist attractions. In 2005, the cash-strapped Municipal Railway raised the one-way fare by two-thirds from $3 to $5. Not surprisingly, the number of riders dropped substantially, and many in the city called for a rate reduction.

The rate increase prompted many locals to switch to buses or other forms of transportation, but most tourists have a relatively inelastic demand curve for cable car rides. Frank Bernstein of Arizona, who visited San Francisco with his wife, two children, and mother-in-law, said they would not visit San Francisco without riding a cable car: “That’s what you do when you’re here.” But the round-trip $50 cost for his family to ride a cable car from the Powell Street turn- around to Fisherman’s Wharf and back “is a lot of money for our family. We’ll do it once, but we won’t do it again.”

Cable Cars and Profit Maximization

Elasticity of Demand, ε

Price/Marginal Cost Ratio, p/MC = 1/[1 + (1/ε)]

Lerner Index, (p – MC)/p = -1/ε

-1.01 101 0.99

-1.1 11 0.91

-2 2 0.5

-3 1.5 0.33

-5 1.25 0.2

-10 1.11 0.1

-100 1.01 0.01

– ∞ 1 0

TABLE 9.2 Elasticity of Demand, Price, and Marginal Cost

le ss

el as

ti c S

d m

or e

el as

ti c

2879.2 Market Power

If the city ran the cable car system like a profit-maximizing monopoly, the decision to raise fares would be clear. The 67% rate hike resulted in a 23% increase in revenue to $9,045,792 in the 2005–2006 fiscal year. Given that the revenue increased when the price rose, the city must have been operating in the inelas- tic portion of its demand curve (ε 7 -1), where MR = p(1 + 1/ε) 6 0 prior to the fare increase.8 With fewer riders, costs stayed con- stant (they would have fallen if the city had decided to run fewer than its traditional 40 cars), so the city’s profit increased given the increase in revenue. Presumably the profit-

maximizing price is even higher in the elastic portion of the demand curve. However, the city may not be interested in maximizing its profit on the

cable cars. At the time, then-Mayor Gavin Newsom said that having fewer riders “was my biggest fear when we raised the fare. I think we’re right at the cusp of losing visitors who come to San Francisco and want to enjoy a ride on a cable car.” The mayor said that he believed keeping the price of a cable car ride relatively low helps attract tourists to the city, thereby ben- efiting many local businesses. Newsom observed, “Cable cars are so funda- mental to the lifeblood of the city, and they represent so much more than the revenue they bring in.” The mayor decided to continue to run the cable cars at a price below the profit-maximizing level. The fare stayed at $5 for six years, then rose to $6 in 2011 and has stayed there through at least the first half of 2013.

8The marginal revenue is the slope of the revenue function. Thus, if a reduction in quantity causes the revenue to increase, the marginal revenue must be negative. As Figure 9.2 illustrates, marginal revenue is negative in the inelastic portion of the demand curve.

The Lerner Index Another way to show how the elasticity of demand affects a monopoly’s price rela- tive to its marginal cost is to look at the firm’s Lerner Index (or price markup)—the ratio of the difference between price and marginal cost to the price: (p – MC)/p. This index can be calculated for any firm, whether or not the firm is a monopoly. The Lerner Index is zero for a competitive firm because a competitive firm pro- duces where marginal cost equals price. The Lerner Index measures a firm’s market power: the larger the difference between price and marginal cost, the larger the Lerner Index.

If the firm is maximizing its profit, we can express the Lerner Index in terms of the elasticity of demand by rearranging Equation 9.9:

p – MC p

= – 1 ε

. (9.10)

288 CHAPTER 9 Monopoly

The Lerner Index ranges between 0 and 1 for a profit-maximizing monopoly.9

Equation 9.10 confirms that a competitive firm has a Lerner Index of zero because its demand curve is perfectly elastic.10 As Table 9.2 illustrates, the Lerner Index for a monopoly increases as the demand becomes less elastic. If ε = -5, the monopoly’s markup (Lerner Index) is 1/5 = 0.2; if ε = -2, the markup is 1/2 = 0.5; and if ε = -1.01, the markup is 0.99. Monopolies that face demand curves that are only slightly elastic set prices that are multiples of their marginal cost and have Lerner Indexes close to 1.

9For the Lerner Index to be above 1 in Equation 9.10, ε would have to be a negative fraction, indicat- ing that the demand curve was inelastic at the monopoly’s output choice. However, as we’ve already seen, a profit-maximizing monopoly never operates in the inelastic portion of its demand curve. 10As the elasticity of demand approaches negative infinity, the Lerner Index, -1/ε, approaches zero.

Mini-Case Apple started selling the iPad on April 3, 2010. The iPad was not the first tablet. Indeed, it wasn’t Apple’s first tablet: Apple sold another tablet, the Newton, from 1993–1998. But it was the most elegant one, and the first one large numbers of consumers wanted to own. Users interact with the iPad using Apple’s multi- touch, finger-sensitive touchscreen (rather than a pressure-triggered stylus that most previous tablets used) and a virtual onscreen keyboard (rather than a physical one). Most importantly, the iPad offered an intuitive interface and was very well integrated with Apple’s iTunes, eBooks, and various application programs.

People loved the original iPad. Even at $499 for the basic model, Apple had a virtual monopoly in its first year. According to the research firm IDC, Apple’s share of the 2010 tablet market was 87%. Moreover, the other tablets available in 2010 were not viewed by most consumers as close substitutes. Apple reported that it sold 25 million iPads worldwide in its first full year, 2010–2011. Accord- ing to one estimate, the basic iPad’s marginal cost was MC = $220, so its Lerner Index was (p – MC)/p = (499 – 220)/499 = 0.56.

Within a year of the iPad’s introduction, over a hundred iPad want-to-be tablets were launched. To maintain its dominance, Apple replaced the original iPad with the feature-rich iPad 2 in 2011, added the enhanced iPad 3 in 2012, and cut the price of the iPad 2 by $100 in 2012. According to court documents Apple filed in 2012, its Lerner Index fell to between 0.23 and 0.32.

Industry experts believe that Apple can produce tablets at far lower cost than most if not all of its competitors. Apple has formed strategic partnerships with other companies to buy large supplies of components, securing a lower price from suppliers than its competitors. Using its own patents, Apple avoids paying as many licensing fees as do other firms.

Copycat competitors with 10″ screens have gained some market share from Apple. More basic tablets with smaller 7″ screens that are little more than e-readers have sold a substantial number of units, so that the iPad’s share of the total tablet market was 68% in the first quarter of 2012.

Apple’s iPad

2899.2 Market Power

Q&A 9.2 When the iPad was introduced, Apple’s constant marginal cost of producing this iPad was about $220. We estimate that Apple’s inverse demand function for the iPad was p = 770 – 11Q, where Q is the millions of iPads purchased.11 What was Apple’s marginal revenue function? What were its profit-maximizing price and quantity? Given that the Lerner Index for the iPad was (p – MC)/p = 0.56 (see the “Apple’s iPad” Mini-Case), what was the elasticity of demand at the profit-maximizing level?

Answer

1. Derive Apple’s marginal revenue function using the information about its demand function. Given that Apple’s inverse demand function was linear, p = 770 – 11Q, its marginal revenue function has the same intercept and twice the slope: MR = 770 – 22Q.12

2. Derive Apple’s profit-maximizing quantity and price by equating the marginal rev- enue and marginal cost functions and solving. Apple maximized its profit where MR = MC:

770 – 22Q = 220.

Solving this equation for the profit-maximizing output, we find that Q = 25 million iPads. By substituting this quantity into the inverse demand function, we determine that the profit-maximizing price was p = $495 per unit.

3. Use Equation 9.10 to infer Apple’s demand elasticity based on its Lerner Index. We can write Equation  9.10 as (p – MC)/p = 0.56 = -1/ε. Solving this last equality for ε, we find that ε ≈ -1.79. (Of course, we could also calculate the demand elasticity by using the demand function.)

11See the Sources for “Pricing Apple’s iPad” for details on these estimates.

12Alternatively, we can use calculus to derive the marginal revenue curve. Multiplying the inverse demand function by Q to obtain Apple’s revenue function, R = 770Q – 11Q2. Then, we derive the marginal revenue function by differentiating the revenue with respect to quantity: MR = dR/dQ = 770 – 22Q.

Sources of Market Power What factors cause a monopoly to face a relatively elastic demand curve and hence have little market power? Ultimately, the elasticity of demand of the market demand curve depends on consumers’ tastes and options. The more consumers want a good—the more willing they are to pay “virtually anything” for it—the less elastic is the demand curve.

Other things equal, the demand curve a firm (not necessarily a monopoly) faces becomes more elastic as (1) better substitutes for the firm’s product are introduced, (2) more firms enter the market selling the same product, or (3) firms that provide the same service locate closer to this firm. The demand curves for Xerox, the U.S. Postal Service, and McDonald’s have become more elastic in recent decades for these three reasons.

When Xerox started selling its plain-paper copier, no other firm sold a close sub- stitute. Other companies’ machines produced copies on special heat-sensitive paper

290 CHAPTER 9 Monopoly

that yellowed quickly. As other firms developed plain-paper copiers, the demand curve that Xerox faced became more elastic.

In the past, the U.S. Postal Service (USPS) had a monopoly in overnight delivery services. Now FedEx, United Parcel Service, and many other firms compete with the USPS in providing overnight deliveries. Because of these increases in competition, the USPS’s share of business and personal correspondence fell from 77% in 1988 to 59% in 1996. Its total mail volume fell 40% from 2006 to 2010. Its overnight market fell to 15% by 2010.13 Compared to when it was a monopoly, the USPS’s demand curves for first-class mail and package delivery have shifted downward and become more elastic.

As you drive down a highway, you may notice that McDonald’s restaurants are located miles apart. The purpose of this spacing is to reduce the likelihood that two McDonald’s outlets will com- pete for the same customer. Although McDonald’s can prevent its own restaurants from competing with each other, it cannot prevent Wendy’s or

Burger King from locating near its restaurants. As other fast-food restaurants open near a McDonald’s, that restaurant faces a more elastic demand. What happens as a profit-maximizing monopoly faces more elastic demand? It has to lower its price.

9.3 Market Failure Due to Monopoly Pricing Unlike perfect competition, which achieves economic efficiency—that is, maximizes total surplus, TS (= consumer surplus + producer surplus = CS + PS)—a profit- maximizing monopoly is economically inefficient because it wastes potential sur- plus, resulting in a deadweight loss. The inefficiency of monopoly pricing is an example of a market failure: a non-optimal allocation of goods and services such that a market does not achieve economic efficiency. Market failure often occurs because the price differs from the marginal cost, as with a monopoly. This eco- nomic inefficiency creates a rationale for governments to intervene, as we discuss in Chapter 16.

Total surplus (Chapter 8) is lower under monopoly than under competition. That is, monopoly destroys some of the potential gains from trade. Chapter 8 showed that competition maximizes total surplus because price equals marginal cost. By setting its price above its marginal cost, a monopoly causes consumers to buy less than the competitive level of the good, so society suffers a deadweight loss.

If the monopoly were to act like a competitive market, it would produce where the marginal cost curve cuts the demand curve—the output where price equals marginal

13Peter Passell, “Battered by Its Rivals,” New York Times, May 15, 1997, C1; Grace Wyler, “11 Things You Should Know about the U.S. Postal Service Before It Goes Bankrupt,” Business Insider, May 31, 2011; “The U.S. Postal Service Nears Collapse,” BloombergBusinessweek, May 26, 2011; www .economicfreedom.org/2012/12/12/stamping-out-waste.

2919.3 Market Failure Due to Monopoly Pricing

cost. For example, using the demand curve given by Equation 9.2 and the marginal cost curve given by Equation 9.7,

p = 24 – Q = 2Q = MC.

Solving this equation, we find that the competitive quantity, Qc, would be 8 units and the price would be $16, as Figure 9.5 shows. At this competitive price, consumer surplus is area A + B + C and producer surplus is D + E.

If instead the firm acts like a profit-maximizing monopoly and operates where its marginal revenue equals its marginal cost, the monopoly output Qm is only 6 units and the monopoly price is $18. Consumer surplus is only A. Part of the lost consumer surplus, B, goes to the monopoly, but the rest, C, is lost. The benefit of being a monopoly is that it allows the firm to extract some consumer surplus from consumers and convert it to profit.

By charging the monopoly price of $18 instead of the competitive price of $16, the monopoly receives $2 more per unit and earns an extra profit of area B = $12 on the

p, $

p er

u ni

t

Demand

Q, Units per day

MR

MC

pc = 16 B = $12

D = $60

C = $2

MR = MC = 12

pm = 18

24

Qm = 6 Qc = 8 240

em

ec

Competition Monopoly Change

Consumer Surplus, CS A + B + C −B − C = ΔCS Producer Surplus, PS D + E B − E = ΔPS

A + B + C + D + E

A B + D

A + B + D −C − E = ΔTS = DWL

A = $18

E = $4

12

Total Surplus, TS = CS + PS

FIGURE 9.5 Deadweight Loss of Monopoly

A competitive market would produce Qc = 8 at pc = $16, where the demand curve intersects the marginal cost (supply) curve. A monopoly produces only Qm = 6 at pm = $18, where the marginal revenue curve intersects

the marginal cost curve. Under monopoly, consumer sur- plus is A, producer surplus is B + D, and the inefficiency or deadweight loss of monopoly is -C – E.

292 CHAPTER 9 Monopoly

Qm = 6 units it sells. The monopoly loses area E, however, because it sells less than the competitive output. Consequently, the monopoly’s producer surplus increases by B – E over the competitive level. Monopoly pricing increases producer surplus relative to competition.

Total surplus is less under monopoly than under competition. The deadweight loss of monopoly is -C – E, which represents the potential surplus that is wasted because less than the competitive output is produced. The deadweight loss is due to the gap between price and marginal cost at the monopoly output. At Qm = 6, the price, $18, is above the marginal cost, $12, so consumers are willing to pay more for the last unit of output than it costs to produce it.

Q&A 9.3 In the linear example in panel a of Figure 9.3, how does charging the monopoly a specific tax of τ = $8 per unit affect the profit-maximizing price and quantity and the well-being of consumers, the monopoly, and society (where total surplus includes the tax revenue)? What is the tax incidence on consumers (the increase in the price they pay as a fraction of the tax)?

Answer

1. Determine how imposing the tax affects the monopoly price and quantity. In the accompanying graph, the intersection of the marginal revenue curve, MR, and the before-tax marginal cost curve, MC1, determines the monopoly quantity, Q1 = 6. At the before-tax solution, e1, the price is p1 = 18. The specific tax causes the monopoly’s before-tax marginal cost curve, MC1 = 2Q, to shift upward by 8 to MC2 = MC1 + 8 = 2Q + 8. After the tax is applied, the monopoly operates where MR = 24 – 2Q = 2Q + 8 = MC2. In the after- tax monopoly solution, e2, the quantity is Q2 = 4 and the price is p2 = 20. Thus, output falls by ΔQ = 6 – 4 = 2 units and the price increases by Δp = 20 – 18 = 2.

2. Calculate the change in the various surplus measures. The graph shows how the surplus measures change. Area G is the tax revenue collected by the govern- ment, τQ = 32, because its height is the distance between the two marginal cost curves, τ = 8, and its width is the output the monopoly produces after the tax is imposed, Q = 4. The tax reduces consumer and producer surplus and increases the deadweight loss. We know that producer surplus falls because (a) the monopoly could have produced this reduced output level in the absence of the tax but did not because it was not the profit-maximizing output, so its before-tax profit falls, and (b) the monopoly must now pay taxes. The before- tax deadweight loss from monopoly is -F. The after-tax deadweight loss is -C – E – F, so the increase in deadweight loss due to the tax is -C – E. The table below the graph shows that consumer surplus changes by -B – C and producer surplus by B – E – G.

3. Calculate the incidence of the tax on consumers. Because the tax goes from 0 to 8, the change in the tax is Δτ = 8. Because the change in the price that the consumer pays is Δp = 2, the share of the tax paid by consumers is Δp/Δτ = 2/8 = 14. Thus, the monopoly absorbs $6 of the tax and passes on only $2.

2939.4 Causes of Monopoly

Monopoly Before Tax Monopoly After Tax Change

Consumer Surplus, CS A + B + C A -B – C = ΔCS

Producer Surplus, PS D + E + G B + D B – E – G = ΔPS

Tax Revenues, T = τQ 0 G G = ΔT

T o t a l S u r p l u s , TS = CS + PS + T

A + B + C + D + E + G A + B + D + G -C – E = ΔTS

Deadweight Loss, DWL -F -C – E – F -C – E = ΔDWL

p, $

p er

u ni

t

Demand

Q, Units per day

MR

MC1 (before tax)

MC2 (after tax)

p1 = 18

D E

C

F

G

B

A τ = $8

0

8

p2 = 20

24

Q2 = 4 Q1 = 6 2412

e1

e2

Monopoly Before Tax Monopoly After Tax Change

Consumer Surplus, CS A + B + C A −B − C = ΔCS Producer Surplus, PS D + E + G B + D B − E − G = ΔPS Tax Revenues, T = τQ 0 G G = ΔT

A + B + C + D + E + G A + B + D + G −C − E = ΔTS Deadweight Loss, DWL −F −C − E − F −C − E = ΔDWL Total Surplus, TS = CS + PS + T

9.4 Causes of Monopoly Why are some markets monopolized? The two most important reasons are cost considerations and government policy.14

14In later chapters, we discuss other means by which monopolies are created. One method is the merger of several firms into a single firm. This method creates a monopoly if new firms fail to enter the market. A second method is for a monopoly to use strategies that discourage other firms from entering the market. A third possibility is that firms coordinate their activities and set their prices as a monopoly would. Firms that act collectively in this way are called a cartel rather than a monopoly.

294 CHAPTER 9 Monopoly

Cost-Based Monopoly Certain cost structures may facilitate the creation of a monopoly. One possibility is that a firm may have substantially lower costs than potential rivals. A second pos- sibility is that the firms in an industry have cost functions such that one firm can produce any given output at a lower cost than two or more firms can.

Cost Advantages. If a low-cost firm profitably sells at a price so low that other potential competitors with higher costs would lose money, no other firms enter the market. Thus, the low-cost firm is a monopoly. A firm can have a cost advantage over potential rivals for several reasons. It may have a superior technology or a better way of organizing production.15 For example, Henry Ford’s methods of organizing production using assembly lines and standardization allowed him to produce cars at substantially lower cost than rival firms until they copied his organizational techniques.

If a firm controls an essential facility or a scarce resource that is needed to produce a particular output, no other firm can produce at all—at least not at a reasonable cost. For example, a firm that owns the only quarry in a region is the only firm that can profitably sell gravel to local construction firms.

Natural Monopoly. A market has a natural monopoly if one firm can produce the total output of the market at lower cost than two or more firms could. A firm can be a natural monopoly even if it does not have a cost advantage over rivals provided that average cost is lower if only one firm operates. Specifically, if the cost for any firm to produce q is C(q), the condition for a natural monopoly is

C(Q) 6 C(q1) + C(q2) + g + C(qn), (9.11)

where Q = q1 + q2 + g + qn is the sum of the output of any n firms where n Ú 2 firms.

If a firm has economies of scale at all levels of output, its average cost curve falls as output increases for any observed level of output. If all potential firms have the same strictly declining average cost curve, this market is a natural monopoly, as we now illustrate.16

A company that supplies water to homes incurs a high fixed cost, F, to build a plant and connect houses to the plant. The firm’s marginal cost, m, of supply- ing water is constant, so its marginal cost curve is horizontal and its average cost, AC = m + F/Q, declines as output rises.

Figure 9.6 shows such marginal and average cost curves where m = 10 and F = 60. If the market output is 12 units per day, one firm produces that output

15When a firm develops a better production method that provides it with a cost advantage, it is important for the firm to either keep the information secret or obtain a patent, whereby the government protects it from having its innovation imitated. Thus, both secrecy and patents facilitate cost-based monopolies. 16A firm may be a natural monopoly even if its cost curve does not fall at all levels of output. If a U-shaped average cost curve reaches its minimum at 100 units of output, it may be less costly for only one firm to produce an output of 101 units even though average cost is rising at that output. Thus, a cost function with economies of scale everywhere is a sufficient but not a necessary condition for a natural monopoly.

2959.4 Causes of Monopoly

at an average cost of 15, or a total cost of 180 (= 15 * 12). If two firms each pro- duce 6 units, the average cost is 20 and the cost of producing the market output is 240 (= 20 * 12), which is greater than the cost with a single firm.

If the two firms divided total production in any other way, their cost of produc- tion would still exceed the cost of a single firm (as the following question asks you to prove). The reason is that the marginal cost per unit is the same no matter how many firms produce, but each additional firm adds a fixed cost, which raises the cost of producing a given quantity. If only one firm provides water, the cost of building a second plant and a second set of pipes is avoided.

In an industry with a natural monopoly cost structure, having just one firm is the cheapest way to produce any given output level. Governments often use a natural monopoly argument to justify their granting the right to be a monopoly to public utilities, which provide essential goods or services such as water, gas, electric power, or mail delivery.

Q&A 9.4 A firm that delivers Q units of water to households has a total cost of C(Q) = mQ + F. If any entrant would have the same cost, does this market have a natural monopoly?

Answer Determine whether costs rise if two firms produce a given quantity. Let q1 be the output of Firm 1 and q2 be the output of Firm 2. The combined cost of these two firms producing Q = q1 + q2 is

C(q1) + C(q2) = (mq1 + F) + (mq2 + F) = m(q1 + q2) + 2F = mQ + 2F.

If a single firm produces Q, its cost is C(Q) = mQ + F. Thus, the cost of pro- ducing any given Q is greater with two firms than with one firm (the condition in Equation 9.11), so this market is a natural monopoly.

15

20

40

10

60 12 15

AC = 10 + 60/Q

MC = 10

Q, Units per day

A C

,M C

, $ p

er u

ni t

FIGURE 9.6 Natural Monopoly

This natural monopoly has a strictly declining average cost, AC = 10 + 60/Q.

296 CHAPTER 9 Monopoly

Government Creation of Monopoly Governments have created many monopolies. Sometimes governments own and manage such monopolies. In the United States, as in most countries, first class mail delivery is a government monopoly. Many local governments own and operate pub- lic utility monopolies that provide garbage collection, electricity, water, gas, phone services, and other utilities.

Barriers to Entry. Frequently governments create monopolies by preventing competing firms from entering a market occupied by an existing incumbent firm. Several countries, such as China, maintain a tobacco monopoly. Similarly, most gov- ernments grant patents that limit entry and allow the patent-holding firm to earn a monopoly profit from an invention—a reward for developing the new product that acts as an incentive for research and development.

By preventing other firms from entering a market, governments create monopo- lies. Typically, governments create monopolies either by making it difficult for new firms to obtain a license to operate or by explicitly granting a monopoly right to one firm, thereby excluding other firms. By auctioning a monopoly right to a private firm, a government can capture the future value of monopoly earnings.17

Frequently, firms need government licenses to operate. If one initial incumbent has a license and governments make it difficult for new firms to obtain licenses, the incumbent firm may maintain its monopoly for a substantial period. Until recently, many U.S. cities required that new hospitals or other inpatient facilities demonstrate the need for a new facility to obtain a certificate of need, which allowed them to enter the market.

Government grants of monopoly rights have been common for public utilities. Instead of running a public utility itself, a government might give a private sector company the monopoly rights to operate the utility. A government may capture some of the monopoly profits by charging the firm in some way for its monopoly rights. In many countries or other political jurisdictions, such a system is an inducement to bribery as public officials may be bribed by firms seeking monopoly privileges.

Governments around the world have privatized many state-owned monopolies in the past several decades. By selling cable television, garbage collection, phone service, towing, and other monopolies to private firms, a government can capture the value of future monopoly earnings today. However, for political or other reasons, governments frequently sell at a lower price that does not capture all future profits.

Patents. If an innovating firm cannot prevent imitation by keeping its discoveries secret, it may try to obtain government protection to prevent other firms from dupli- cating its discovery and entering the market. Most countries provide such protec- tion through patents. A patent is an exclusive right granted to the inventor of a new and useful product, process, substance, or design for a specified length of time. The length of a patent varies across countries, although it is now 20 years in the United States and in most other countries.

This right allows the patent holder to be the exclusive seller or user of the new invention.18 Patents often give rise to monopoly, but not always. For example,

17Alternatively, a government could auction the rights to the firm that offers to charge the lowest price, so as to maximize total surplus.

18Owners of patents may sell or grant the right to use a patented process or produce a patented product to other firms. This practice is called licensing.

2979.4 Causes of Monopoly

Mini-Case Ophthalmologist Dr. Alan Scott turned the deadly poison botulinum toxin into a miracle drug to treat two eye conditions: strabismus, which affects about 4% of children, and blepharospasm, an uncontrollable closure of the eyes. Blepha- rospasm left about 25,000 Americans functionally blind before Scott’s discovery. His patented drug, Botox, is sold by Allergan, Inc.

Dr. Scott has been amused to see several of the unintended beneficiaries of his research at the Academy Awards. Even before it was explicitly approved for cosmetic use, many doctors were injecting Botox into the facial muscles of actors, models, and others to smooth out their wrinkles. (The drug paralyzes the muscles, so those injected with it also lose the ability to frown—and, some would say, to act.) The treatment is only temporary, lasting up to 120 days, so repeated injections are necessary. Allergan had expected to sell $400 million worth of Botox in 2002. However, in April of that year, the U.S. Food and Drug Administration approved the use of Botox for cosmetic purposes, a ruling that allows the company to advertise the drug widely.

Allergan had Botox sales of $800 million in 2004 and about $1.8 billion in 2012. Allergan has a near-monopoly in the treatment of wrinkles, although plastic surgery and collagen, Restylane, hyaluronic acids, and other filler injections provide limited competition. Between 2002 and 2004, the number of facelifts dropped 3% to about 114,000 according to the American Society of Plastic Surgeons, while the number of Botox injections skyrocketed 166% to nearly 3 million.

Dr. Scott says that he can produce a vial of Botox in his lab for about $25. Allergan then sells the potion to doctors for about $400. Assuming that the firm is setting its price to maximize its short-run profit, we can rearrange Equa- tion 9.10 to determine the elasticity of demand for Botox:

ε = – p

p – MC = –

400 400 – 25

≈ -1.067.

Thus, the demand that Allergan faces is only slightly elastic: A 1% increase in price causes quantity to fall by only a little more than 1%.

If we assume that the demand curve is linear and that the elasticity of demand is -1.067 at the 2002 monopoly optimum, em (one million vials sold at $400 each, producing revenue of $400 million), then Allergan’s inverse demand function is

p = 775 – 375Q.

This demand curve (see graph) has a slope of -375 and hits the price axis at $775 and the quantity axis at about 2.07 million vials per year. The corresponding marginal revenue curve,

MR = 775 – 750Q,

intersects the price axis at $775 and has twice the slope, -750, as the demand curve.

Botox

although a patent may grant a firm the exclusive right to use a particular process in producing a product, other firms may be able to produce the same product using different processes. In Chapter 16, we discuss the reasons why governments grant patents.

298 CHAPTER 9 Monopoly

9.5 Advertising You can fool all the people all the time if the advertising is right and the budget is big enough. —Joseph E. Levine (film producer)

In addition to setting prices or quantities and choosing investments, firms engage in many other strategic actions to boost their profits. One of the most important is advertising. By advertising, a monopoly can shift its demand curve, which may allow it to sell more units at a higher price. In contrast, a competitive firm has no incentive to advertise as it can sell as many units as it wants at the going price with- out advertising.

Advertising is only one way to promote a product. Other promotional activities include providing free samples and using sales agents. Some promotional tactics are subtle. For example, grocery stores place sugary breakfast cereals on lower shelves so that they are at children’s eye level. According to a survey of 27 supermarkets nationwide by the Center for Science in the Public Interest, the average position of 10 child-appealing brands (44% sugar) was on the next-to-bottom shelf, while the average position of 10 adult brands (10% sugar) was on the next-to-top shelf.

A monopoly advertises to raise its profit. A successful advertising campaign shifts the market demand curve by changing consumers’ tastes or informing them about new products. The monopoly may be able to change the tastes of some consumers

At the point where the MR and MC curves inter- sect, MR = MC. Therefore,

775 – 750Q = 25.

We can then solve for the profit-maximizing quantity of 1 million vials per year and the associated price of $400 per vial.

Were the company to sell Botox at a price equal to its marginal cost of $25 (as a competitive industry would), consumer surplus would equal areas A + B + C = $750 million per year. At the higher monopoly price of $400, the consumer sur- plus is A = $187.5 million. Compared to the competi-

tive solution, ec, buyers lose consumer surplus of B + C = $562.5 million per year. Part of this loss, B = $375 million per year, is transferred from consumers to Allergan. The rest, C = $187.5 million per year, is the deadweight loss from monopoly pricing. Allergan’s profit is its producer surplus, B, minus its fixed costs.

p, $

p er

v ia

l

2 2.07

A ≈ $187.5 million

C ≈ $187.5 million

B ≈ $375 million Demand

Q, Million vials of Botox per year

400

25

0

es

ec MC = AVC MR

775

1

2999.5 Advertising

by telling them that a famous athlete or performer uses the product. Children and teenagers are frequently the targets of such advertising. If the advertising convinces some consumers that they can’t live without the product, the monopoly’s demand curve may shift outward and become less elastic at the new equilibrium, at which the firm charges a higher price for its product.

If a firm informs potential consumers about a new use for the product, the demand curve shifts to the right. For example, a 1927 Heinz advertisement suggested that putting its baked beans on toast was a good way to eat beans for breakfast as well as dinner. By so doing, it created a British national dish and shifted the demand curve for its product to the right.

Deciding Whether to Advertise I have always believed that writing advertisements is the second most profitable form of writing. The first, of course, is ransom notes. . . . —Philip Dusenberry (advertising executive)

Even if advertising succeeds in shifting demand, it may not pay for the firm to adver- tise. If advertising shifts demand outward or makes it less elastic, the firm’s gross profit, ignoring the cost of advertising, must rise. The firm undertakes this advertis- ing campaign, however, only if it expects its net profit (gross profit minus the cost of advertising) to increase.

We illustrate a monopoly’s decision making about advertising in Figure 9.7. If the monopoly does not advertise, it faces the demand curve D1. If it advertises, its demand curve shifts from D1 to D2.

The monopoly’s marginal cost, MC, is constant and equals its average cost, AC. Before advertising, the monopoly chooses its output, Q1, where its marginal cost hits its marginal revenue curve, MR1, that corresponds to demand curve, D1. The profit-maximizing equilibrium is e1, and the monopoly charges a price of p1. The monopoly’s profit, π1, is a box whose height is the difference between the price and the average cost and whose length is the quantity, Q1.

After its advertising campaign shifts its demand curve to D2, the monopoly chooses a higher quantity, Q2 (7Q1), where the MR2 and MC curves intersect. In this new equilibrium, e2, the monopoly charges p2. Despite this higher price, the monopoly sells more units after advertising because of the outward shift of its demand curve.

As a consequence, the monopoly’s gross profit rises. Its new gross profit is the rectangle π1 + B, where the height of the rectangle is the new price minus the aver- age cost, and the length is the quantity, Q2. Thus, the benefit, B, to the monopoly from advertising at this level is the increase in its gross profit. If its cost of advertising is less than B, its net profit rises, and it pays for the monopoly to advertise at this level rather than not to advertise at all.

How Much to Advertise The man who stops advertising to save money is like the man who stops the clock to save time.

How much should a monopoly advertise to maximize its net profit? The rule for setting the profit-maximizing amount of advertising is the same as that for setting the profit-maximizing amount of output: Set advertising or quantity where the marginal benefit (the extra gross profit from one more unit of advertising or the marginal revenue from one more unit of output) equals its marginal cost.

300 CHAPTER 9 Monopoly

Using Calculus We can derive this marginal rule for optimal advertising using calculus. A monopoly’s inverse demand function is p = p(Q, A), which says that the price it must charge to clear the market depends on the number of units it chooses to sell, Q, and on the level of its advertising, A. As a result, the firm’s revenue func- tion is R(Q, A) = p(Q, A)Q. The firm’s cost function is C(Q) + A, where C(Q) is the cost of manufacturing Q units and A is the cost of advertising, because each unit of advertising costs $1 (by choosing the units of measure appropriately). The monopoly’s profit is

π(Q, A) = R(Q, A) – C(Q) – A. (9.12)

Optimal Advertising

Consider what happens if the monopoly raises or lowers its advertising expenditures by $1, which is its marginal cost of an additional unit of advertising. If a monopoly spends one more dollar on advertising—its marginal cost of advertising— and its gross profit rises by more than $1, its net profit rises, so the extra advertising pays. A profit-maximizing monopoly keeps increasing its advertising until the last dollar of advertising raises its gross profit by exactly $1. If it were to advertise more, its profit would fall.

p ,

$ pe

r un

it

B

Q, Units per yearQ2Q1

MR1 MR2 D2D1

p2 p1

e2

e1

π 1

MC = AC

FIGURE 9.7 Advertising

If the monopoly does not advertise, its demand curve is D1. At its actual level of advertising, its demand curve is D2. Advertising increases the monopoly’s gross profit (ignoring the cost of advertising) from π1 to π2 = π1 + B.

Thus, if the cost of advertising is less than the benefits from advertising, B, the monopoly’s net profit (gross profit minus the cost of advertising) rises.

3019.5 Advertising

Q&A 9.5 A monopoly’s inverse demand function is p = 800 – 4Q + 0.2A 0.5, where Q is its

quantity, p is its price, and A is the level of advertising. Its marginal cost of production is 2, and its cost of a unit of advertising is 1. What are the firm’s profit-maximizing price, quantity, and level of advertising?

Answer

1. Write the firm’s profit function using its inverse demand function. The monopoly’s profit is

π = (800 – 4Q + 0.2A0.5)Q – 2Q – A

= 798Q – 4Q2 + 0.2A0.5Q – A. (9.15)

2. Set the partial derivatives of the profit function in Equation 9.15 with respect to Q and A to zero to obtain the equations that determine the profit-maximizing levels, as in Equations 9.13 and 9.14. The first-order conditions are

0π 0Q

= 798 – 8Q + 0.2A0.5 = 0, (9.16)

0π 0A

= 0.1A-0.5Q – 1 = 0. (9.17)

3. Solve Equations 9.16 and 9.17 for the profit-maximizing levels of Q and A. We can rearrange Equation 9.17 to show that A0.5 = 0.1Q. Substituting this expres- sion into the Equation 9.16, we find that 798 – 8Q + 0.02Q = 0, or Q = 100. Thus, A0.5 = 0.1Q = 10, so A = 100.

The monopoly maximizes its profit by choosing Q and A. Its first-order conditions to maximize its profit are found by partially differentiating the profit function in Equation 9.12 with respect to Q and A in turn:

0π(Q, A) 0Q

= 0R(Q, A)

0Q –

dC(Q) dQ

= 0, (9.13)

0π(Q, A) 0A

= 0R(Q, A)

0A – 1 = 0. (9.14)

The profit-maximizing output and advertising levels are the Q and A that simultaneously satisfy Equations  9.13 and 9.14. Equation  9.13 says that the monopoly should set its output so that the marginal revenue from one more unit of output, 0R/0Q, equals the marginal cost, dC/dQ, which is the same condition that we previously derived before considering advertising. According to Equation 9.14, the monopoly should advertise to the point where its marginal revenue or marginal benefit from the last unit of advertising, 0R/0A, equals the marginal cost of the last unit of advertising, $1.

Mini-Case Super Bowl commercials are the most expensive commercials on U.S. television. A 30-second spot during the Super Bowl averaged over $3.8 million in 2013. A high price for these commercials is not surprising because the cost of commer- cials generally increases with the number of viewers (eyeballs in industry jargon),

Super Bowl Commercials

302 CHAPTER 9 Monopoly

9.6 Networks, Dynamics, and Behavioral Economics We have examined how a monopoly behaves in the current period, ignoring the future. For many markets, such an analysis is appropriate as each period can be treated separately. However, in some markets, decisions today affect demand or cost in a future period, creating a need for a dynamic analysis, in which managers explicitly consider relationships between different periods.

In such markets, the monopoly may maximize its long-run profit by making a decision today that does not maximize its short-run profit. For example, frequently a firm introduces a new product—such as a new type of candy bar—by initially charg- ing a low price or giving away free samples to generate word-of-mouth publicity or to let customers learn about its quality in hopes of getting their future business. We now consider an important reason why consumers’ demand in the future may depend on a monopoly’s actions in the present.

Network Externalities The number of customers a firm has today may affect the demand curve it faces in the future. A good has a network externality if one person’s demand depends on the consumption of the good by others.19 If a good has a positive network externality, its value to a consumer grows as the number of units sold increases.

19In Chapter 16, we discuss the more general case of an externality, which occurs when a person’s well-being or a firm’s production capability is directly affected by the actions of other consumers or firms rather than indirectly through changes in prices. The following discussion on network externalities is based on Leibenstein (1950), Rohlfs (1974), Katz and Shapiro (1994), Economides (1996), Shapiro and Varian (1999), and Rohlfs (2001).

and the Super Bowl is the most widely watched show, with over 108 million viewers in 2013. What is surprising is that Super Bowl advertising costs 2.5 times as much per viewer as other TV commercials.

However, a Super Bowl commercial is much more likely to influence viewers than commercials on other shows. The Super Bowl is not only a premier sports event; it showcases the most memorable commercials of the year, such as Apple’s classic 1984 Macintosh ad, which is still discussed today. Indeed, many Super Bowl viewers are not even football fans—they watch to see these superior ads. Moreover, Super Bowl commercials receive extra exposure because these ads often go viral on the Internet.

Given that Super Bowl ads are more likely to be remembered by viewers, are these commercials worth the extra price? Obviously many advertisers believe so, as their demand for these ads has bid up the price. Kim (2011) found that immediately after a Super Bowl commercial airs, the advertising firm’s stock value rises. Thus, investors apparently believe that Super Bowl commercials raise a firm’s profits despite the high cost of the commercial. Ho et al. (2009) found that, for the typical movie with a substantial advertising budget, a Super Bowl commercial advertising the movie raises theater revenues by more than the same expenditure on other television advertising. They also concluded that movie firms’ advertising during the Super Bowl was at (or close to) the profit-maximizing amount.

3039.6 Networks, Dynamics, and Behavioral Economics

When a firm introduces a new good with a network externality, it faces a chicken- and-egg problem: It can’t get Max to buy the good unless Sofia will buy it, but it can’t get Sofia to buy it unless Max will. The firm wants its customers to coordinate or to make their purchase decisions simultaneously.

The telephone provides a classic example of a positive network externality. When the phone was introduced, potential adopters had no reason to get phone service unless their family and friends did. Why buy a phone if there’s no one to call? For Bell’s phone network to succeed, it had to achieve a critical mass of users— enough adopters that others wanted to join. Had it failed to achieve this critical mass, demand would have withered and the network would have died. Similarly, the market for fax machines grew very slowly until a critical mass was achieved where many firms had them.

Direct Size Effects. Many industries exhibit positive network externalities where the customer gets a direct benefit from a larger network. The larger an auto- mated teller machine (ATM) network, such as the Plus network, the greater the odds that you will find an ATM when you want one, so the more likely it is that you will want to use that network. The more people who use a particular computer program, the more attractive it is to someone who wants to exchange files with other users.

Indirect Effects. In some markets, positive network externalities are indirect and stem from complementary goods that are offered when a product has a critical mass of users. The more applications (apps) available for a smart phone, the more people want to buy that smart phone. However, many of these extra apps will be written only if a critical mass of customers buys the smart phone. Similarly, the more people who drive diesel-powered cars, the more likely it is that gas stations will sell diesel fuel; and the more stations that sell the fuel, the more likely it is that someone will want to drive a diesel car. As a final example, o