At its profit maximizing output a pure nondiscriminating monopolist achieves

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.