Lecture 11: Applications of the Monopoly Model
Some Basic Topics
Comparison to Competitive Equilibrium
In the case of a competitive equilibrium, each firm will be producing where p
= MC. This implies economic efficiency, for marginal cost is ultimately measured in
terms of opportunity cost, which is referred to as the Marginal Rate of
Transformation (MRT).
Since, consumers choose between goods until the marginal rate of
substitution (MRS), or the rate at which they are willing to substitute one for the
other, equals the price ratio. This implies a measure of economic efficiency at MRS
= MRT.
Now consider a monopolist. If price is above marginal cost, a social loss
incurred. Since, there is an efficiency loss from monopoly pricing where p  MC.
For this reason, economists have stressed the virtues of competitive industry.
How a Monopolist Responds to Controls and Taxes
In the case of a competitive industry, we know that a tax falls on both the
producers and the consumers based on relative elasticities. For a monopolist, it
depends very much on just what kind of tax is imposed.
A tax on each unit of output – an excise tax
Suppose, there is a tax of $1 on each unit the monopolist sells, and that the
monopolist has the demand curve
q = 100- 2p
and marginal cost of 5. The effect will be to drive his marginal cost to 6. The
condition for profit maximization is still MR = MC, and
MR = 50 -q
Output will fall from 45 to 44 and the price will rise from 27.5 to 28. Again, the tax
will fall on both the consumer and producer. Other variables change as follows:
Price
Total Revenue
Total Costs
Profit
$28.00
$1232.00
$220.00
$1012.00
The monopolist bears only part of the cost; profit goes down by fifty cents.
Tax on Economic Profits
Next, suppose a tax is imposed on the firm’s economic profits (i.e., excluding
the opportunity costs of the resources). The firm’s maximization problem becomes
one of maximizing
 = (1-)(TR - TC)
The optimum solution is thus
' = (1-)(MR - MC) = 0
and we can quickly see that this requires that
MR - MC = 0
The solution is unchanged, with the exception of a fraction  of the profits going to
taxes.
A Maximum Price
Politicians are frequently suggesting that we impose maximum prices on
what a monopolist can charge. Here, prohibit the monopolist from charging no more
than pmax. Let qo be the quantity demanded at this price. When q  qo, demand is
infinitely elastic and MR = pmax. For q > qo, the old marginal revenue curve prevails.
Profit Maximization with a Price Ceiling
When the government imposes a price ceiling, the marginal
revenue curve changes. At the ceiling, MR=p. Now the marginal
revenue curve looks like the dashed line.
The Monopolist’s Supply Curve
The monopolist has no supply curve. The amount he supplies is a function of
demand conditions. (Of course, that does not stop instructors for asking you to
draw a supply curve on an exam: you can always catch one of two students who get
suckered in).
Creating a Monopoly
Suppose you see a potential for a new widget product, the Wudget. Others
see the market for the Fidget and the Pushit. Thus the race is on between:
 The Wudget
 The Fidget and
 The Pushit
Suppose further that the profits from catching on will be $X but it will cost
$I to develop it. They should stay in the race if
poX > Io
where p0 is the probability of winning monopoly rights.
How many firms will actually enter the race? That is a complicated
question. For example, if potential new widgets thought they had an equal chance
of winning,
N = X/Io
firms would enter. For example, suppose X is $500 million and Io is $50 million.
Our requirement for staying in is that poX > Io. In this case, if we assume there are
three equal firms already in the fourth firm will compute its chances of winning as
(1/4)$500 = $125 > $50
Once 10 equal firms have entered, then the odds will not look attractive for
an eleventh entrant. In fact, the handicapping is more complicated than that.
 Firms do not have an equal chance of winning
 Firms in the race may have a better chance
 Firms in the race want to dissuade other entrants.
The Future of the Monopoly
Suppose, your Wudget wins and becomes a hot item. Other designs flop. (If
you doubt this might happen, go back and read about VHS and Beta videotapes).
You will then have a monopoly. We know how you will price the product: you will
adopt the simple rule that
P
MC
1
1

Suppose the marginal cost of producing a Wudget is $500 and that the price
elasticity of demand is –1.625.
P = $500/(1+1/(-1.625) = $1,300.
In time, the learning curve will probably lower production costs. If a year
hence, production cost drops to $450, you will want to reduce the price to $1,170.
P = $450/(1+1/(-1.625) = $1,170.
That will not be then end of the story. If you succeed, other manufacturers
will begin competing. We will return to this subject in a later lecture, because your
profit projections must take this into account.
Competing for Monopoly Rights
There is another way to capture a monopoly: use lawyers and lobbyists to
achieve the objective.
Suppose you are on your local municipal board to award a cable franchise.
How should you award it? Consider two proposals:
Determine which firm is best.
 Award the franchise to the firm that offers the largest bid to the city.
 Award the franchise to the firm that offers to provide the service at the least
cost to subscribers.
First Proposal
Most economists would argue against the first one, as plausible as it seems.
Their fear is that the competition will then be one of expensive lobbying and bribes.
The monopolist would want to maximize his bid and that means maximizing his
profits before the bid. This is done by setting output where MR = MC, and then
offering the city any profits. In any event, the winning franchise bidder acts like a
monopolist. The only difference is that the city gets the revenue. In effect, the city
is acting as the monopolist, though it disguises that effect by putting the contract
out to bid.
Pricing When the Franchise is to be
Awarded to the High Bidder
The winning firm will offer to price at pm, the monopoly price
(where MR=MC). It will then offer a bid equal to the difference
between price and average cost. In essence the city will run the
serve as a monopoly, taking the profits for itself.
Second Proposal
The firm wants to enter the lowest bid consistent with zero profit. And that
means setting P = AC. The price is lower.
In this case, the city is forcing the winning bidder to act like a regulated
monopolist.
Pricing When the Franchise is to be
Awarded to the Low Bidder
The winning firm will offer to price at p*, where the average cost
curve intersects the demand curve. The demand will then be q*.
This will be a lower price and higher quantity than if the
franchise is awarded by a bid.
Managing a Monopoly
The Monopolist's Marginal Cost Curve with Many Plants
If a monopolist has many plants, the marginal cost curve will depend on the
individual plants. Consider a firm that currently runs N identical plants at the
minimum of their average cost curve.
The plant operates where MR = LRMC (presumably involving N plants).
Now suppose that there is an increase in the demand function. (Note: rotate the
MR curve around the point where it hits the y-axis). MR rises, and the short run
response is to move to where MR = SRMC. Clearly prices go up and demand goes
up. In the long run, the firm will build additional plants, and will move to the point
where MR = LRMC, making even more money, but at a lower price than the
intermediate solution.
Demand and LRMC Curves for a Monopolist with
Multiple Identical Plants
If the monopolist has many identical plants, his LRMC is simply
the minimum of their AC curves. The SRMC is the sum of the
marginal cost curves of the existing plants. When demand shifts
from D to D', the short run response is to move from point A
(where MR originally equaled LRMC) to B where MR=SRMC. In
time the firm will build additional plants ad move to point C
where MR once again equals LRMC
Application to Cost Innovation
Many conclude that monopolists are inefficient or that they have no incentive
to minimize costs. That is simply not true. Their profits are defined, like other
firms, as
 = TR - TC
and a monopolist can make more money by setting, for any given level of operations,
total cost as low as possible. There is the risk of a takeover bid for the monopoly if
he does not do so.
Does a monopoly have the incentive to be an innovator? While this is a
complicated issue, consider the case of manufacturing technologies.
A firm with N plants now at the minimum of their average cost curve, p1.
There is a LRMC curve equal to p1. Now suppose that it is possible to build new
plants with a minimum AC equal to po < p1. What the monopolist will do is operate
where MR = p1. He will operate existing plants to the point where MC = po, and
then build enough new plants to fill the rest of the output gap. In short, he will
introduce the optimal amount of new capacity.
Some would argue that efficiency requires the monopolist to abandon all of
his existing plants and build new ones. That is clearly not true. He should reduce
their scale of operation, but as long as they are operating where MC equals the
LRMC of new plants (and as long as MC is above AVC), it pays to operate the
existing plants.
Example: Suppose the monopolist is now operating where LRMC = $5. He is
making 100 units from each of his 10 existing plants. A new technology comes along.
Plants built with the new technology have a minimum of their LRAC at $4. In
terms of pricing the product, his LRMC is now reduced to $4. He will want to lower
price. When he does, demand will increase from 1,000 to 1,400. At the same time
he will want to reduce the scale of operations at his existing plants to where their
MC = $4. Suppose, that this requires reducing production at each of the 10 plants
to 80 units each. He will then be getting 800 units of production from his existing
plants, and he will want to build enough plants of the new design to meet the last
600 units of demand.
A Change in Monopoly Production with New Efficient
Plants
The minimum of the AC function for new plants is p 1. The MC
curve is the horizontal sum of the MC curves for existing plants.
They are operated to the point where MC = p1, and additional
production comes from the new plants. The LRMC is thus the
dashed line in this figure.
Should he abandon the old plants? Assuredly not, as long as the MC is above
LRVC. For instance, suppose that when MC = $4, LRVC is $3. His total cost of
producing the first 800 units is actually $2,400. Only variable cost counts, because
the fixed costs of the plant have already been incurred. He could meet this demand
with new plants, but at a cost of $4 a unit for a total of $3,200. In short, were he to
abandon the plants, he would drive up costs by $800.
New Technologies
A similar argument applies when a monopolist is considering introducing a
new innovation. Suppose a monopolist is selling a computer program, such as a
word processor. There are five customers. Unfortunately the monopolist cannot
charge each customer a different price for the software. Since the marginal cost of
producing another copy of the software is essentially zero, the best price for the
monopolist to charge is $30. He picks up three customers and makes $90. Any
other price would make less money for him.
Willingness to pay for a Word Processing Program
Smith
$10
Jones
$20
Wilson
$30
Green
$40
Brown
$50
Sales at Different Prices
Price
Sales
Total Sales
$10
5
$50
$20
4
$80
$30
3
$90
$40
2
$80
$50
1
$50
Now suppose the monopolist has sold the word processing program to
Wilson, Green and Brown. He now can develop a new version of the software
package for which everyone would be willing to pay an additional $10. The cost of
producing the software package is $25.
The monopolist will have an incentive to do so. He can offer the package as
an "upgrade" option to Wilson, Green and Brown and as a new package to Jones for
$30.1 He will gross $60. This is part of a very complicated story, but it does
illustrate a key point: monopolists will innovate if there is a profit opportunity.
You will notice that we are letting the monopolist charge customers different prices for the
same package. We will have more to say about this in a later lecture.
1
The Durability Issue
The monopolist has a demand curve for lots in a housing development. The
marginal cost is zero up until the capacity of the lots.
Why not sell q1 units at a much higher price and then try to sell the rest at a
different price? In this case, he would face a new demand curve, and the process
would start over. Clearly he could make more money by doing so.
Example, suppose a monopolist has developed 60 lots. The demand for the
lots is 100 - p, and there is no marginal cost to handling the lots. If the lots were
sold in a competitive auction, the market-clearing price is $40. The total revenue
would then be $2400. The monopolist can maximize his revenues by selling 50 lots
at $50, for $2500. The remaining lots would then have a demand curve of 50 – p,
and the monopolist could then make another $200 by selling the remaining lots at
$10 each.
Once that happened, the market price for lots would all drop to $40.
Therein lies the problem with this solution. The potential buyers of the first
50 lots know about this scam. They will not buy until this risk has been removed.
Thus the monopolist’s ability to engage in profit maximization above and beyond
that of the competitive firm is limited.
To get $2500 for the first fifty lots, the developer must assure buyers that
this will not happen. In this case he could donate the lots to a park, making an
irrevocable commitment that the lots will not be sold.
How a Monopolist Wants to Sell a Durable Product
The MC curve hits zero (marginal cost) at q1. In theory, the
monopolist could make profits by selling q 1 units at p1. The MR
curve for the remaining unmet demand is shown by the dashed
line, which hits zero at q2. In theory the monopolist could then
sell another q2-q1 units at p2 and make even more money. Alas,
for the scheming monopolist, consumers are smart and will
demand production against this scam.
Some applications of this principle
This principle comes up all the time in business transactions.
Apartment/condominium developers have this problem.
IBM faced this problem in the heyday of rapid technology of new computers.