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Chapter 11
Monopoly and
Monopsony
Monopoly: one parrot.
Chapter 11 Outline
Challenge: Pricing Apple’s iPad
11.1 Monopoly Profit Maximization
11.2 Market Power and Welfare
11.3 Taxes and Monopoly
11.4 Causes of Monopolies
11.5 Government Actions that Reduce Market Power
11.6 Monopoly Decisions Over Time and Behavioral
Economics
11.7 Monopsony
Challenge Solution
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11-2
Challenge: Pricing Apple’s iPad
• Background:
• Apple started selling the iPad on April 3, 2010.
• People loved the original iPad. Even at $499 for the
basic model, Apple had a virtual monopoly on highend tablets in its first year. The company still has a
stronghold on the high-end tablet market.
• Questions:
• How did Apple set the price for the iPad when it was
essentially the only game in town? (See Solved
Problem 11.2)
• How did the presence of me-too rival products
produced by firms with higher marginal costs affect
Apple’s pricing more recently? (See Challenge
Solution)
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11.1 Monopoly Profit Maximization
• A monopoly is the only supplier of a good for which
there is no close substitute.
• Monopolies are not price takers like competitive firms
• Monopoly output is the market output
• Monopoly demand curve is the market demand curve
• Monopolists can set their own price given market
demand
• Because demand is downward sloping, monopolists set
price above marginal cost to maximize profit.
• Like all firms, monopolies maximize profits by setting
price or output so that marginal revenue (MR) equals
marginal cost (MC).
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11.1 Monopoly Profit Maximization
• Monopolies maximize profits by setting price or output
so that marginal revenue (MR) equals marginal cost
(MC).
• Profit function to be maximized by choosing output, Q:
• (Q) = R(Q) – C(Q), where
• R(Q) is the revenue function
• C(Q) is the cost function
• The necessary condition for profit maximization:
• The sufficient condition for profit maximization:
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11.1 Monopoly Profit Maximization
• If p(Q) is the inverse demand function, which shows the
price received for selling Q, then the marginal revenue
function is:
• Given a positive value of Q, MR(Q) lies below inverse
demand. MR(Q) < p(Q).
• Selling one more unit requires the monopolist to lower
the price
• Price is lowered on the marginal unit and all other units
sold
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11.1 Monopoly Profit Maximization
• Moving from Q to Q+1,
the monopoly’s
marginal revenue is
less than the price it
charges by an amount
equal to area C
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11.1 MR Curve and the Price
Elasticity of Demand
• We can rewrite MR function so that it is stated
in terms of elasticity:
• This makes the relationship between MR, D,
and elasticity quite clear.
• Where demand hits the vertical axis, MR=P and
demand is perfectly elastic.
• Everywhere that MR > 0, demand is elastic.
• The quantity at which MR = 0 corresponds to the
unitary elastic portion of the demand curve.
• Everywhere that MR < 0, demand is inelastic.
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11.1 MR Curve and the Price
Elasticity of Demand
• Relationship for inverse demand function of
and marginal revenue function of
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11.1 MR Curve and the Price
Elasticity of Demand
• Where would a monopolist produce? A quantity such
that
1. 𝜀 > 1. 2. 𝜀 = 1. 3. 𝜀 < 1.
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11.1 Monopoly Example
• Inverse demand function:
• Can be used to find the marginal revenue function:
• Quadratic SR cost function:
• Can be used to find the marginal cost function:
• Profit-maximizing output is obtained by producing Q*:
• Solving this expression reveals Q*=6
• The inverse demand function indicates that people are
willing to pay p = $18 for 6 units of output.
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11.1 Monopoly Example
• The monopolist’s
profit maximizing
choice of output is
found where MR=MC.
• At the profitmaximizing output,
set p according to
inverse demand.
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Figure 11.3
Maximizing Profit
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11.1 Monopoly Example (setting p)
• Inverse demand function: 𝑄 𝑝 = 24 − 𝑝
• Can be used to find the marginal revenue function:
𝑀𝑅 𝑝 = 24 − 2𝑝
• 𝐶 𝑝 = 𝑄(𝑝)2 + 12 = 24 − 𝑝 2 + 12
• 𝑀𝐶 𝑝 = −2(24 − 𝑝)
• Profit-maximizing price is obtained by charging p*:
• 𝑀𝑅 𝑝∗ = 𝑀𝐶(𝑝∗ )
• Solving this expression reveals p*=18
• The demand function indicates that people are willing to
pay p = $18 for 6 units of output.
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11.1 Monopoly Example
• Should a profit-maximizing monopoly produce
at Q* or shut down?
• As with competitive firms, a monopoly should
shut down in the monopolist’s price is less than
its AVC.
• In our example, AVC at Q* of 6 is $6.
• Because p = $18 is clearly above $6, the
monopoly in this example should produce in
the SR.
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11.2 Market Power and Welfare
• Market power is the ability of a firm to charge a price above
marginal cost and earn a positive profit.
• Monopoly has market power; competitive firms do not.
• Market power is related to the price elasticity of demand
• Recall that
• Rewrite as
• The ratio of price to MC, from 1 to ∞, depends only on the
elasticity of demand at the profit maximizing quantity.
• The more elastic the demand curve, the less a monopoly can
raise its price without losing sales (and vice versa).
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11.2 Market Power and Welfare
• A monopolist sells to a market, p = Q1/ε, with a constant
elasticity of ε=-1.5. If its marginal cost is constant at $10, how
much will it charge for each unit?
• Recall
1.
2.
3.
4.
$10
$20
$25
$30
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11.2 Market Power
• The Lerner Index (or price markup) is another way to
examine the way in which elasticity affects a
monopoly’s price relative to its MC.
• The Lerner Index ranges from 0 to 1 for a profitmaximizing firm.
• Competitive firms have a Lerner Index of 0.
• The Lerner Index gets closer to 1 as a firm has more
market power (and faces less elastic demand).
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11.2 Market Power and Welfare
• A monopolist sells to a market, p = Q1/ε, with a constant
elasticity of ε=-1.5. If its marginal cost is constant at $10, the
price markup (Lerner Index) is
1.
2.
3.
4.
0
1/3
2/3
3/4
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11-19
11.2 Sources of Market Power
• Elasticity of the market demand curve depends on
consumers’ tastes and options.
• Demand becomes more elastic (which implies less
market power for the firm):
• as better substitutes for the firm’s product are
introduced
• as more firms enter the market selling a similar product
• as firms that provide the same service locate closer to
the firm
• As a profit-maximizing monopoly faces more elastic
demand, it has to lower its price.
• Examples: Xerox, USPS, McDonald’s
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11.2 Effects of Market Power on
Welfare
• Recall from Chapter 9 that competition maximizes
welfare, which is the sum of consumer surplus and
producer surplus, because price equals marginal cost.
• By contrast, a monopoly
• sets price above marginal cost (and above the
competitive price)
• causes consumers to buy less than the competitive
level of output
• generates deadweight loss
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11.2 Effects of Market Power on
Welfare
• The competitive
equilibrium, ec, has
no DWL, while the
monopoly
equilibrium, em, has
DWL = C+E.
– CS=18
– PS=72
• 𝜋=60
– DW=6
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11.2 Effects of Market Power on
Welfare
• How will a
government
regulate the
monopoly?
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11.3 Taxes and Monopoly
• Taxes (ad valorem and specific) affect monopoly
differently than a competitive industry:
1.Tax incidence on consumers (the change in the
consumers’ price divided by the change in the tax) can
exceed 100% in a monopoly market but not a
competitive market.
2.If tax rates α and τ are set so that the after-tax output
is the same with either type of tax, the government
raises the same amount of tax revenue in a competitive
market using either type of tax, but raises more
revenue using an ad valorem tax than a specific tax
under monopoly.
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11.3 Taxes and Monopoly
• Comparative Statics (of specific tax, τ)
• Before-tax cost function is C(Q)
• After-tax cost function is C(Q) + τQ
• Necessary condition for maximizing after-tax profit:
• Derivative (with respect to τ) of the sufficient condition for
maximizing after-tax profit:
• As the specific tax rises, the monopoly reduces its output.
• Downward sloping means the monopoly raises its price.
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11.3 Taxes and Monopoly
• Tax Incidence on Consumers
• Consumer price may rise by an amount greater than
the tax.
• Assume constant marginal cost, m, and inverse
demand function with constant elasticity, ε, p = Q1/ε
• Maximize profit by equating after-tax marginal cost and
marginal revenue:
• Substituting for Q in inverse demand yields the price set by
monopoly:
• dp/dτ>1 because monopoly operates on elastic portion
of demand curve.
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11.3 Taxes and Monopoly
• Governments
typically use an ad
valorem tax rather
than a specific tax
because the tax
revenue is greater.
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11.4 Taxes and Monopoly
• Comparing government tax revenues from the
monopoly facing inverse demand P(Q)=a-bQ and
constant marginal cost, c.
• specific tax τ.
– Monopolist maximizing 𝜋=[P(Q)- τ]Q-cQ
– F.O.C.: a-2bQ-τ =c.
• Ad valorem tax rate 𝛼.
– Monopolist maximizing 𝜋=(1-𝛼)P(Q)Q-cQ
– F.O.C.: (1-𝛼)[a-2bQ]=c.
• If two tax schemes result in the same optimal Q for the
monopolist (so Q are the same in both F.O.C.s)
– 1-𝛼=c/(c+τ) or 𝛼= τ /(c+τ)
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11.4 Taxes and Monopoly
• tax revenue under specific tax τ.
– τ from every unit sold.
• Ad valorem tax rate 𝛼 .
– 𝛼P(Q)=𝛼[a-bQ] from every unit sold.
– 𝛼P(Q)>𝛼[a-2bQ]= [τ /(c+τ)](c+τ)= τ. (from F.O.C. a-2bQ-τ=c)
• If two tax schemes result in the same optimal Q in the
monopoly, the governments collects a higher tax
revenue under ad valorem tax than a specific tax.
– The result holds for general P(Q) and C(Q) satisfying
assumptions required for F.O.C. and S.O.C.
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11.4 Taxes and Monopoly
• EX: P(Q)=120-2Q and constant marginal cost, c=20. If
the specific tax is $10 per unit, the monopolist sells at
quantity equal to
1.
2.
3.
4.
Q=20
Q=22.5
Q=25
Q=40
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11.4 Taxes and Monopoly
• EX: P(Q)=120-2Q and constant marginal cost, c=20.
For the monopolist to sell at quantity same as the
above, the ad valorem tax rate must be
1.
2.
3.
4.
τ =20%
τ =22.5%
τ =25%
τ =1/3
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11-31
11.4 Taxes and Monopoly
• EX: P(Q)=120-2Q and constant marginal cost,
c=20.
• The government collects under specific tax $10. a
total of 10*22.5=$225.
• The government collects under the ad valorem tax
rate of 1/3. a total of (1/3)*70*22.5=$525.
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11.4 Causes of Monopolies
• Why are some markets monopolized?
• Two key reasons:
• Cost advantage over other firms
• Government created monopoly
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11.4 Cost Advantages of Monopoly
• Sources of cost advantages:
1. Control of an essential facility, a scarce resource
that a rival firm needs to use to survive
•
Example: owning the only quarry in a region generates a cost
advantage in the production of gravel
2. Use of superior technology or a better way of
organizing production
•
Example:
Henry Ford’s assembly lines and standardization
3. Protection from imitation through patents or
informational secrets
•
Secrets are more common in new and improved processes;
patents more common with new products
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11.4 Cost Advantages of Monopoly
• A market has a natural monopoly if one firm can
produce the total output of the market at lower cost
than several firms could.
• where Q = q1 + q2 +… + qn for n > 1 firms
• Examples: public utilities such as water, gas, electric,
and mail delivery
• Natural monopolies may have high fixed costs, but low
and fairly constant marginal costs.
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11.4 Cost Advantages of Monopoly
• A natural monopoly has economies of scale at all levels
of output, so average costs fall as output increases.
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11.5 Government Actions that
Create Monopolies
• Governments typically create monopolies in 1 of 3
ways:
1. By making it difficult for new firms to obtain a license
to operate
•
Example: U.S. cities require new hospitals to secure a
certificate of need to demonstrate the need for a new facility
2. By granting a firm the rights to be a monopoly
•
Example: public utilities operated by private company
3. By auctioning the rights to be a monopoly
•
Example: selling government monopolies to private firms
(privatization)
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11.5 Government Actions that
Reduce Market Power
• Governments limit monopolies’ market power in various
ways:
1.Optimal Price Regulation: government regulates the
monopoly by imposing a price ceiling that is equal to
the competitive price, which eliminates DWL.
2.Nonoptimal Price Regulation: government-imposed
price ceiling is not set at the competitive level, which
reduces but does not eliminate DWL.
3.Increasing Competition: allowing/encouraging
market entry by new domestic firms and ending import
bans that kept out international firms.
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11.5 Government Actions that
Reduce Market Power
• With optimal price
regulation, the
government
imposes a price
ceiling that is equal
to the competitive
price.
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11.4 Cost Advantages of Monopoly
• How will the government regulate the natural
monopoly?
𝑝(𝑄)
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11.6 Monopoly Decisions Over Time
and Behavioral Economics
• In some markets, today’s decisions affect demand or
cost in the future.
• Some monopoly decisions may maximize LR profit but
not SR profit.
• Example: low introductory pricing to build up
customers
• Why would consumers’ demand in the future depend on
a monopoly’s actions in the present?
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11-41
11.6 Monopoly Decisions Over Time
and Behavioral Economics
• A good has a network externality if one person’s demand
depends on the consumption of a good by others.
• With a positive network externality, value to the consumer grows as
the number of units sold increases (e.g. telephones, ATMs)
• With a negative network externality, value to the consumer grows
as fewer people possess the good (e.g. numbered paintings)
• A bandwagon effect is a popularity-based explanation for a
positive network externality (e.g. iPod, UGG boots).
• A snob effect is an explanation for a negative network
externality (e.g. original painting by an unknown artist).
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11.7 Monopsony
• A monopsony is a single buyer in a market, much like
a monopoly is a single seller in a market.
• A monopsony exercises its market power by buying at a
price below the price that competitive buyers would pay.
• Examples: professional baseball teams, university in a
college town, mining in a “company town”
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11.7 Monopsony
• Suppose that a firm is the sole employer in town and
uses only one factor, L, to produce a final good.
• The monopsony’s total expenditure is E = w(L)L, where
w(L) is the wage given by the market labor supply
curve.
• The firm’s marginal expenditure is then:
• ME is upward sloping and greater than w(L), the labor
supply curve.
• The firm hires labor until the marginal value of the last
worker hired equals the firm’s marginal expenditure.
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11.7 Monopsony
• Equilibrium is determined by the intersection of
marginal expenditure and demand.
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11.7 Monopsony with Calculus
• Assume the firm is a price taker in the output market
• Maximize profit by choosing L given production function,
Q(L):
• FOC:
• The firm hires labor until the value of the output
produced by the last worker equals the marginal
expenditure on the last worker.
• The markup of ME over the wage is inversely
proportional to the elasticity of supply,  :
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11.7 Welfare Effects of Monopsony
• Monopsony
results in
welfare loss of
C+E relative to
competition.
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Challenge Solution
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