11
Monopoly
Key Chapter issues
1. 2. 3. 4. 5. 6. 7. monopoly profit maximization: MR = MC market power monopoly welfare effects: p > MC o DWL cost advantages that create monopolies government actions that create monopolies government actions that reduce market power dominant firm and competitive fringe
Monopoly
monopoly: only supplier of a good for which there is no close substitute monopoly's output is the market output: q = Q monopoly's demand curve is market demand curve
its demand curve is downward sloping it doesn't lose all its sales if its raises its price
it is a price setter
Profit maximization
all firms maximize profits by choosing quantity such that marginal revenue = marginal cost MR(Q) = MC(Q)
Marginal revenue
firm's MR curve depends on its demand curve monopoly's MR curve
lies below its demand curve at any positive quantity because its demand curve is downward sloping
demand curve shows price, p, it receives for selling a given quantity, Q price = p = average revenue
Marginal revenue, MR
change in revenue from selling one more unit MR = K Q (Calculus: MR = dR(Q)/dQ) R/K if firm sells exactly one more unit, K = 1, Q
its marginal revenue is MR = K R KoR = R2 R1
MR < p at any given Q for a monopoly (but not for a competitive firm)
Figure 11.1a Average and Marginal Revenue
(a) Competitive Firm Price, p, $ per unit
R1 = A R2 = A + B oR = R2 R1 = B = p
Demand curve
1
p1
A
B
q q +1 Quantity,q, Units per year
Figure 11.1b Average and Marginal Revenue
(b) Monopoly Price, p, $ per unit
R1 = A + C R2 = A + B oR = R2 R1 = B C = p2 - C
p1 p2
C Demand curve A B
Q Q+1 Quantity, Q, Units per year
Deriving monopoly's MR curve
monopoly increases its output by K Q,
by lowering its price per unit by K Q (slope p/K of demand curve) so monopoly loses (K Q) Q on units p/K originally sold at higher price: area C but earns an additional p on extra output: area B
thus: MR = p + (K Q) Q p/K = p + a negative term < p
Calculus derivation
monopoly's revenue is R(Q) = p(Q)Q differentiating with respect to Q:
dR (Q) dp (Q ) MR = = p (Q) + Q dQ dQ
thus: MR = p + a negative term < p
Figure 11.2 Elasticity of Demand and Total, Average, and Marginal Revenue
p, $ per unit 24 Perfectly elastic
Elastic, < 1 MR = 2 Q = 1 12 p = 1 Q=1 = 1
Inelastic, 1 < < 0
Demand ( p = 24 Q)
Perfectly inelastic 24 Q, Units per day
0
12 MR = 24 2Q
Linear MR curve
for all linear demand curves, p = a - bQ MR curve is a straight line, MR = a - 2bQ
MR curve hits vertical (price) axis where demand curve does slope of MR curve = 2 slope of demand curve MR curve hits horizontal axis at half the quantity as the demand curve
In our example
p = 24 Q
so a = 24 and b = 1 K K /K = -1 p Q
hence MR = p + (K Q) Q p/K = (24 Q) + (-1) Q = 24 2Q
Using calculus
R(Q) = p(Q)Q if linear: R(Q) = [a - bQ]Q = aQ - bQ2 MR = dR/dQ = a - 2bQ
MR and elasticity of demand
MR at any given quantity depends on
demand curve's height (price) demand curve's shape (elasticity)
thus, it depends on its elasticity
Derive MR/elasticity formula
demand elasticity: K = (K Q/Q)/(K p/p) = (K Q/op)(p/Q) MR = p + (K Q) Q p/K 1 = p + (K Q)(Q/p)p = p 1 + p/K
MR and price
1 MR = p 1 +
MR closer to p the more elastic is demand
where demand curve hits price axis (Q = 0), demand curve is perfectly elastic KMR = p MR = 0 where demand elasticity is K= -1 MR < 0 where demand is inelastic: 0 K K > -1
Table 11.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Curve p=24-Q
Figure 11.2 Elasticity of Demand and Total, Average, and Marginal Revenue
p, $ per unit 24 Perfectly elastic
Elastic, < 1 MR = 2 Q = 1 12 p = 1 Q=1 = 1
Inelastic, 1 < < 0
Demand ( p = 24 Q)
Perfectly inelastic 24 Q, Units per day
0
12 MR = 24 2Q
Choosing price or quantity
monopoly can set p or Q to maximize its profit, K monopoly is constrained by market demand curve
it cannot set both Q and p (cannot pick a point above demand curve) if monopoly sets p, demand curve determines Q if monopoly sets Q, demand curve determines p
because monopoly wants to maximize K it , chooses same profit-maximizing solution whether it sets p or Q
Profit maximization
all firms, including monopolies, use a two-step analysis 1. firm determines output, Q*, at which it makes highest K where ,
MR = MC in elastic portion of demand curve
2. firm decides whether to produce Q* or shut down: p o AVC
(a) Monopolized Market
Figure 11.3 Maximizing Profit
p, $ per unit
MC
24 e
AC AVC
18 = 60 12 8 6
Demand MR
0 (b) Profit, Revenue R, , $ 144
6
12
24 Q, Units per day
Revenue, R
108
60
Profit,
0
6
12
24 Q, Units per day
SR cost in our example
C(Q) = Q2 + 12 MC = dC(Q)/dQ = 2Q AVC = VC/Q = Q2/Q = Q AC = C/Q = (Q2 + 12)/Q = Q + 12/Q
Profit is maximized where
MR = 24 2Q = 2Q = MC KQ = 6 inverse demand: p = 24 Q = 24 6 = 18 AVC = Q = 6 < p = 18 so produce K K > 0 because AC = Q + 12/Q = 8 < p = 18
Market power
ability of a firm to charge a price above marginal cost profitably
No check on bank market power
banks exercise substantial market power on the rate for bounced checks although you had no idea that a check wouldn't clear, bank charges you an average of $4.75 to $7.50 (up to $10) large banks charge more than small ones bad check writer also pays an average of $15 to $19.50 (up to $30)
Bank costs
bank's handling fees for bad checks = $1.32 most checks eventually clear (check writer merely miscalculated balances) even including losses from fraud, total MC = $2.70 (Center for the Study of Responsive Law) thus, banks are exercising substantial market power: price > MC
Market power and shape of demand curve
market power depends on shape of demand curve (elasticity) at profit-maximizing quantity:
1 MR = p 1 + = MC
p 1 = MC 1 + ( 1/ )
Lerner index (price markup)
Lerner index is (p MC)/p if firm profit maximizes,
p - MC 1 =- p
Lerner index ranges from 0 to 1
p K MC 0 Kp MC o p 0 K(p MC)/p o p/p = 1
Causes of market power
monopoly's demand curve is relatively inelastic if consumers are willing to pay "virtually anything" for it no close substitutes for firm's product exist other firms can't enter market other similar firms are located far away other firms' products very different
Welfare effects of monopoly
welfare = consumer surplus + producer surplus W = CS + PS welfare is < under monopoly than under competition monopoly sets p > MC, causing deadweight loss (DWL)
Figure 11.5 Deadweight Loss of Monopoly
p, $ per unit 24 MC A = $18 B = $12 em C =$2 ec E= $4
pm = 18 p c = 16 MR =MC=12
D =$60
Demand MR 0 Q m = 6 Q c= 8 12 24 Q, Units per day
Solved problem
in our linear example, how does subjecting a monopoly to a specific tax of K = $8 per unit affect
monopoly optimum welfare of consumers, the monopoly, and society?
what is tax incidence on consumers?
Solved Problem 11.1
p, $ per unit 24 p 2 = 20 A B p1 = 18 D e2 C E e MC2 (after tax) = $8
1
MC 1 (before tax)
F
8
G MR Demand 24 Q, Units per day
0
Q2 = 4 Q 1= 6
12
Competitive vs. monopoly sugar tax incidence
incidence of a tax on consumers may be less for a monopolized than a competitive market in 1996, Florida voted on (and rejected) a one-cents-perpound excise tax on refined cane sugar in the Florida Everglades Agricultural Area given linear supply (or marginal cost) and demand curves the tax incidence on consumers from this tax is
70% if the market is competitive 41% if monopolistic
thus, a competitive Florida sugar industry passes on substantially more of the tax to demanders than it would if the industry were monopolized
Welfare effects of taxes
governments use ad valorem taxes (K per p unit) more often than specific taxes (K per unit) why? suppose both taxes cut output by the same amount which one raises the most government tax revenue?
Figure 11.6 Ad Valorem Versus Specific Tax
p $ per unit ,
p2 p1 ps = p2 pa = (1 )p2 B
e1 A e2
MC Before-tax demand, D MR Ds Q2 Q1 MR s MR a Da Q Units per year ,
Why monopolies?
firm has cost advantage over others firms government created monopoly merger of several firms into a single firm firms act collectively: cartel strategies - such as threats of violence - that discourage other firms from entering market
Sources of cost advantages
firm controls a key input: essential facility: scarce resource that rival needs to use to survive
firm knows of superior technology, or has better way of organizing production
Natural monopoly
market has a natural monopoly if one firm can produce total market output at lower cost than could several firms if cost for Firm i to produces qi is C(qi), condition for a natural monopoly is C(Q) < C(q1) + C(q2) + ... + C(qn), where Q = q1 + q2 + .. + qn is sum of output of any n > 2 firms
Sufficient condition
natural monopoly if AC curve falls at any observed quantity for all firms economies of scale
Electricity example
F = $60 (build plant & connect houses) MC = m = $10 (constant) AC = m + F/Q = 10 + 60/Q, declines as output rises
Costs of producing Q = 12
# of firms 1 2 output 12 6 AC = 10+60/Q $15 $20 C $180 $240
having only one firm produce avoids a second fixed cost (MC doesn't vary with number of firms)
Figure 11.7 Natural Monopoly
AC, MC, $ per unit 40
20 15 10
AC = 10 + 60/Q
MC = 10
0
6
12 15 Q, Units per day
Public utilities
apparently believing they're natural monopolies, governments grant monopoly rights for essential good or service "public utilities" water gas electric power mail delivery
Electric power utilities
AC curve for U.S electric-power-producing firms in 1970
was U-shaped reached its minimum at 33 billion kWh per year
whether an electric power utility is a natural monopoly depends on demand it faces
Economies of scale
natural monopolies: most electric companies operated in regions of substantial economies of scale
Newport Electric produced 0.5 billion kWh/year Iowa Southern Utilities: 1.3 billion kWh/year
not natural monopolies: a few operated in upwardsloping section of AC curve
Southern produced 54 kWh/year 2 firms could produce that quantity at 3 less per thousand kWh than could a single firm
Application Electric Power Utilities
Cost, $ per thousand kWh 5.10 D
4.85 4.79 0 33
AC
66 Q, Billion kWh per year
Government created monopolies
barriers to entry (e.g, patents) own and manage many monopolies
postal services garbage collection utilities
electricity water gas phone services
Barriers to entry
governments prevent other firms from entering a market in 3 ways by making it difficult for new firms to obtain a license to operate by granting a firm rights to be a monopoly by auctioning rights to be a monopoly
Patents
an grants inventor right to be monopoly provider of good for a number of years stimulates research
Iceland's government creates genetic monopoly
starting in 874, Viking crews from western Norway grabbed young Celtic women from Ireland and took them to Iceland 11 centuries later, the descendents of these 10,000 to 15,000 pirates and their about five-times-as-many slave wives form an unusually isolated population with a relatively homogeneous gene pool Iceland has tissue samples dating back to the 1940s and meticulous records on every citizen since 1915 careful genealogic records have been kept that allows researchers to trace disease genes back more than 10 generations
deCODE Genetics
Dr. Kari Stefansson believed that the unique genetic dataset of the 286,000 current Icelanders (and their forbearers) would help pinpoint genetics of some serious common diseases he formed a firm, deCODE Genetics in 1998, deCODE acquired 12 years of monopoly rights to the genetic, medical, and genealogical records of Iceland for about $200 million the firm agreed to provide Icelanders for free with drugs and diagnostic tools stemming from their research the firm has collected voluntary blood samples from tens of thousands of people to augment their databases by 2002, deCODE announced findings for a number of diseases and had revenues of $13.4 million
Drug patent: Botox
Dr. Alan Scott turned a deadly poison, botulinum toxin, into a miracle drug to treat
strabismus, or cross-eyes, which affects about 4% of children blepharospasm, an uncontrollable closure of the eyes, which left about 25,000 Americans functionally blind before his discovery
his patented drug, Botox, is sold by Allergan Inc.
Other uses
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 Boxtox into the facial muscles of actors, models, and other people to smooth out their wrinkles ideally for Allergan, the treatment is only temporary, lasting up to 120 days, so repeated injections are necessary
Profits
Allergan had expected to sell $400 million worth of Botox in 2002 however, in April 2002, the FDA approved Botox for cosmetic purposes--allows Allegran to advertise the drug widely The firm expects Botox to eventually earn a $1 billion a year (becoming another Viagra)
Compare
Mattel sold $1.4 billion worth of Barbie dolls over 37 years
Justification
patent monopoly profits spur new research people benefit greatly from many inventions (new drugs)
Botox profit maximization
Dr. Scott can produce a vial of Botox in his lab for about $25 Allergan sells a vtal to doctors for about $400 assuming that the firm is setting its price to maximize its short-run profit, the elasticity of demand for Botox is determined by:
p 400 =- = - p - MC 400 - 25
-1.067.
thus, demand it faces is only slightly elastic
Linear demand
if the demand curve is linear and elasticity of demand is 1.067 at 2002 monopoly optimum (1 million vials sold at $400 each), Allergan's inverse demand function is p = 775 375Q. demand curve:
slope is -375 hits price axis at $775 hits quantity axis at 2.07 million vials per year
corresponding marginal revenue curve is MR = 775 750Q,
strikes the price axis at $775 has twice the slope, -750, as the demand curve
Monopoly optimum
intersection of the marginal revenue and marginal cost curves, MR = 775 750Q = 25 = MC, determines the monopoly equilibrium at the profit-maximizing quantity of 1 million vials per year and a price of $400 per vial
p , $ per vial 775
A = $187.5 million 400 e
m
B = $375 million 25 1
Demand C = $187.5 million e Q , Millions vials of Botox per year 2
c
MC = AVC 2.07
MR
Botox Benefits
SR relief from eye problems and wrinkles (CS at monopoly price): A = $187.5 million per year LR CS after patent expired (buy at MC): A + B + C = $750 million per year Patent monopoly profit (ignoring fixed costs): B = $375 million per year
Auctions
Oakland cable TV SF auctioned monopoly rights to store cars towed for illegal parking
monopoly, City Tow, collects $40 per car, of which $15.03 goes to the city losing company's bid promised the city only $7.50
ASUC tried to create a bookstore monopoly without holding an auction
Government actions that reduce market power
antitrust laws prohibit monopolization, price fixing, and so forth regulations prevent monopolies from exercising all of their market power
Optimal price regulation
price regulation may eliminate DWL regulation is optimal if it leads to "competitive" outcome
Figure 11.8 Optimal Price Regulation
p , $ per unit 24 A B D MR MR r MC Market demand em C E eo Regulated demand
18 16
0
6
8
12
24 Q , Units per day
Nonoptimal price regulation
welfare is reduced if government does not set price optimally if regulated p is < minimum of monopoly's AVC, monopoly shuts down if regulated price is between shut-down point and monopoly price but not equal to competitive price
too little is produced welfare is below competitive level
Figure 11.9 Regulating an Electric Utility
p, Yen ( ) per hundred KWH 53
MC 30.3 26.9 22.3 21.9 19.5 e1 A e2 B e3 AC
Demand
MR 0 23 31 34 54 Q, Billion kWh per year
Solved problem 11.3
What's the effect of a price regulation on a monopoly that is below the competitive price?
Solved Problem 11.3
p, $ per unit Market demand MC
A p1 p2 C D
B e1 Regulated demand
e2 E MR
MR r
Q 2 Q1
Qd
Q, Units per day
Excess demand
Creation and destruction of an aluminum monopoly
cost advantages and government actions gave Aluminum Company of America (Alcoa) a U.S. monopoly in aluminum monopoly lasted for decades
Alcoa becomes a monopoly
Alfred Hall invented and patented a new process in 1893 allowed his firm, Pittsburgh Reduction (which became Alcoa) to produce aluminum at much lower cost than competitors this firm controlled most domestic and many international sources of bauxite ore K KAlcoa was only American producer of aluminum
WWI to WWII
Alcoa faced some competition from foreign producers, but U.S. established high tariffs on aluminum imports during WWI, when foreign competitors were unable to effectively produce and sell in other countries, Alcoa became an exporter Alcoa continued to export after war between WWI and WWII, Alcoa remained only aluminum smelter (producer) in U.S. due to its technological advantages and economies of scale
WWII
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