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Monopoly Manual
Purpose of the Module
This module is designed to allow the user to practice running a firm in a monopoly
market. You will have to use information about the demand for the product and the firm’s
costs to maximize long run profits for the firm by choosing the best level of production.
In order to do a good job you will have to figure out how the firm’s costs change as its
level of production changes, how its revenues change as its production changes, and how
profits are affected by cost and revenue changes.
There are not many monopoly markets, especially natural monopolies with no
government control or regulation, but the principles governing successful profit
maximization that apply in other kinds of markets apply in this one. The most important
thing to remember is that you need to use marginal analysis. You do not start out by
thinking about whether you should do everything or nothing. That question may come up
eventually, but the more important questions are “Should I produce the next unit?” and
“Should I have produced the previous unit?” As long as you keep getting an affirmative
answers to these questions, you should continue to raise production.
The first part of this module will allow you to figure out how the unregulated monopoly
firm would act -- how much it would produce and what it would price it would charge.
Once you have that part done, you can see how two different forms of government
regulation could affect the firm’s output and price. You will need to compare the results
of regulation with the firm’s unregulated choices and consider who gains and who loses
from regulation.
The Model
This module features a firm in a monopoly market. To understand the firm’s problems
you need to understand how this kind of market works. First, some definitions of terms
that are important in understanding the model are provided. Next, an explanation of the
monopoly market and how it functions is given.
Price (P)
At a given moment in time the market price is the dollar amount that will be paid in the
market for one unit of the product. Every unit sold will be sold at this price (this is not a
discriminating monopoly).
Marginal Revenue
In a monopoly the firm must lower the price to sell additional units of the product. As a
result, when the firm sells another unit it does not get extra revenue equal to the price of
the last unit sold, it gets less. The firm gets the revenue from the price of the last unit, but
it loses revenue from each of the previous units that would have been sold at higher
prices. As a result the marginal revenue from selling another unit is less than the price of
the product. Note that when very small quantities are being sold the loss from selling
previous units is small (since there are few such units). In this module entry of quantities
smaller than 12 (thousand) gives results in which price looks as if it is equal to marginal
revenue, because the difference between the two is less than the rounding error (both are
reported to four decimal places).
Average Total Cost (ATC)
The average total cost of the product is the firm’s total cost (all costs regardless of type)
divided by the total number of units of the product produced. This is also referred to as
per unit cost. Since this module assumes that the monopoly firm is acting in the long run,
all costs are variable and there is are no fixed costs, so there is no distinction between
average total cost (ATC) and average variable cost (AVC). Thus, we will refer to the
average total cost (ATC) as simply average cost, or AC.
Entry Cost
This cost is the cost to the firm of being in the market at all. Its presence represents a
barrier to entry by new firms, which would start up at a low output level and, given the
entry cost, have a higher ATC than the larger, existing, firm. This entry cost, even in the
long run, plays a role similar to fixed cost. Examples of entry costs are initial advertising
to get a brand name seared into consumers’ minds, construction of a transmission
network to carry electricity, and a licensing fee to the government to get the right to
operate. Its presence is part of the explanation of the downward slope of the ATC curve,
and for the firm having a monopoly.
Marginal Cost (MC)
The firm’s marginal cost is the additional cost of producing an additional unit of the same
product. In this module marginal cost always gets smaller as the level of production
increases. That is a major reason for this firm being a monopoly.
Total (Economic) Profit
The firm’s total profit is its total revenue (TR) (price per unit multiplied by the total
quantity produced) minus its total cost (TC). In economics, the total costs include all of
the firm’s opportunity costs. The profit that remains after subtracting TC from TR is the
total “economic profit”. This “economic profit” is what the firm is earning over and
above what it could get using the same resources in some other way.
Equity
A firm’s equity is a measure of the value of the firm to its owners. If a firm makes a
profit and does not pay it out as dividend income to the owners, the profit is added to the
firm’s equity. If it makes a loss, that amount is subtracted from equity. A firm that has a
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zero or negative equity is a firm likely to find itself in bankruptcy court. The initial value
set in the module for owners equity is somewhat arbitrary, owners equity is shown so you
can see how much your decisions increase or decrease the wealth of the owners.
The Monopoly Market
A pure monopoly is a firm that is the only one in a given market. It produces a product
that has no close substitutes. The particular case used in this module is a firm that sells
electricity to final users (not distributors or wholesalers) in a particular geographical area.
Electricity has substitutes. You can cook on an electric stove, or a gas stove, or even a
wood stove. You can use gas for lighting, or candles. The assumption of this module is
that the alternatives are not close substitutes. (Technically, that means that the cross-price
elasticities with these alternatives are fairly small.) As a result, the demand for the
firm’s product is the same as the total market demand for the product.
Since the monopolist’s market demand obeys the “Law of Demand”, the more units the
firm wants to sell, the lower it has to set its price. It cannot have a high price and a large
quantity sold, it can’t make people buy the product -- they must be willing to buy at the
firm’s price, or it will have a bunch of leftover, unsold, products.
The firm wants to set the production level, and the price, at its most profitable level. That
is where “marginal thinking” comes in. In Figure 1, at output QA the firm gets additional
revenue, MRA, from producing and selling an additional unit of the product. The way
this additional, or marginal, revenue is determined is this: the firm gains revenue equal to
the price it is paid when it sells that additional unit. However, that revenue is less than the
revenue it received from selling the previous unit since it must cut price to sell another
unit. For example: If the firm was selling 100 units at $10 each, to increase the number
of units sold to 101, it must cut its price to $9.95. The firm gains $9.95 in revenue from
selling the 101st unit. The firm loses $0.05 on each of the 100 units it was already selling
for $10 each since its only getting $9.95 each now. It loses 100 x $0.05 or $5 in revenue
this way. Overall, it gets extra revenue of $4.95 from selling one more unit.
Figure 1
Price
PE
MRA
MCA
Monopoly Price and Output Determination
D
e
m
a
n
d
MR
0
QA Q E
AC
MC
Quantity
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Notice that at output QA Marginal Revenue is higher than Marginal Cost (MCA). That
means that the extra revenue the firm receives from selling this unit is larger than the
extra cost of producing it -- so selling this unit would add to the firm’s total profit. The
firm should continue to increase sales until it equates MR with MC at QE. At QE the
firm maximizes total profit.
Figure 2
Monopoly Price and Output Determination
Price
PE
MCB
AC
MC
D
e
0
QE
QB
Quantity
m
a
In Figure 2, at output QB the firm gets less additional nrevenue (MRB) from the last unit it
sells than the additional cost of producing it (MCB).d It is bad idea to produce that last
unit because making and selling it reduces the firm’s total profit. At QB it would be
better if the firm cut production. The best place for the firm to produce is at Q E, where
MR equals MC and total profits are maximized.
MRB
MR
The remaining point to be made is that the downward sloping MC and AC curves are the
reason why this firm is a monopoly. This firm has lower costs the more it produces
(decreasing cost industry). If there were many firms in this market, each one would
produce a small fraction of the total and each would have higher marginal and average
costs than a single firm. In a case like that, if one firm were a little bigger than the others
it would have lower costs than the others. It would get the same price as all the others,
but with lower costs it would make more profit. This firm would use the extra profit to
grow even bigger, so it would have even lower costs, and in the end it would drive all the
others out of the market and it would grow into a monopoly. That process that must end
with the market controlled by one firm is what makes this a “natural” monopoly. It is
possible to have an artificial monopoly in a market where it would be possible to have a
number of competing firms, but only if there is some form of government intervention to
prevent competition. This module features a natural monopoly.
Regulation
When a firm achieves a monopoly the most likely result is that the government will be
called upon to regulate it and prevent it from using its monopoly power to make all the
profits it can make in the unregulated state. Consumers will not appreciate the higher
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prices (compared with costs) the firm is charging, and those who do not own stock in the
company will not appreciate the high profits the owners are receiving.
Even economists will object to the firm’s inefficiency. This inefficiency is not a matter
of the firm’s executives being sloppy in making decisions, or workers doing their jobs
poorly. This inefficiency is the consequence of the firm having a marginal cost which is
not equal to the price it is charging. (Note that for the monopoly, price is greater than
marginal revenue, and marginal revenue -- at the profit maximizing point -- equals
marginal cost. Thus price must be greater than marginal cost.)
The problem is this: efficiency in using resources requires that you use resources to the
point where the additional benefit of using them equals the additional cost of using them.
In the case of a monopoly, the additional benefit to society of producing another unit is
measured by the price people are willing to pay to get it. The MC measures the
additional cost to society. Since price is greater than MC, society would be better off if
production were increased because marginal benefits are greater than marginal costs. To
eliminate this inefficiency, economists sometimes recommend regulation.
Types of Regulation
There are three types of regulation that are commonly used when dealing with
monopolies: 1) anti-trust laws (break up the monopoly firm); 2) marginal cost price
regulation; and 3) average cost price regulation.
Anti-trust Laws
These kinds of laws are, in the simplest sense, designed to either prevent a monopoly
from forming, or to break up a big monopoly firm into a number of smaller firms if the
monopoly already exists. The results of anti-trust laws depend on why the monopoly
does (or might) exist. If the monopoly does -- or could -- exist because of decreasing
cost there is a problem with using anti-trust laws. Creating a number of smaller firms
instead of the one big firm might keep price from being greater than MC. Unfortunately,
the smaller firms are less efficient in producing the product (higher costs), so what is
gained in one respect is lost in the other. Consumers could wind up paying higher prices
and getting less production with several firms than with one. There are other causes for
monopoly for which anti-trust laws might offer greater efficiency, instead of lesser
efficiency.
In the real world breaking up a monopoly could lead to having a number of firms that
compete with each other (until the natural monopoly is eventually restored) in diverse
and complex ways. In this module this does not happen, anti-trust regulation is only used
jointly with other forms of regulation that do not permit real competition. That makes the
results of anti-trust regulation easier to figure out.
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Marginal Cost Pricing
The government can set up a regulatory body to order the firm to produce amounts, and
charge prices, other than the ones the firm would like. In many states a body called the
Public Utilities Commission (PUC) does exactly that for local telephone companies,
electric power companies, privately owned water companies and similar monopoly firms.
One type of regulation the PUC can try to use is marginal cost pricing. The PUC would
get information about the firm’s marginal cost and demand for the product, and order the
firm to set its output-price combination where the marginal cost line is equal to demand.
In Figure 3, this would be at point QR1, PR1.
If you compare the firm’s average cost (AC) at this output with this price you might
notice that the firm’s unit cost is higher than its revenue per unit. That means its profit per
unit is negative -- and so are its total profits. To see the problem with this form of
regulation, see how long could the firm continue to operate at this point before it went
broke and could not buy the resources needed to produce this amount of the product.
This result is obtained because this is a natural monopoly -- with a downward sloping
marginal cost curve. If this were an “artificial” monopoly (costs do not decrease)
marginal cost pricing would not have that effect.
D
Figure 3
Price
PE
AC
PR1
0
MC
QE
QR1
Quantity
Average Cost Pricing
A Public Utilities Commission can also use cost and demand information to order the
firm to produce where average cost is equal to demand. In Figure 4 the PUC directs the
firm to produce the combination PR2, QR2. At this point, the firm would be making a
zero economic profit. The efficiency problem would remain to some degree, since price
would still be above marginal cost, but it isn’t as far from marginal cost as it would be if
the firm was allowed to maximize profit without regulation.
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Price
Figure 4
D
PE
PR2
AC
MC
MR
0
QE
QR2
Quantity
Running the Module
You will be given some information about the firm’s initial conditions and you will have
the opportunity to set the firm’s entry cost level. The default level for this is $10,000.
You cannot set it any lower than that but you can raise it to as much as $1 million. The
point of this is to allow you to observe what difference changes in entry cost makes for
the firm’s results. It is probably best to run the module at least once with the default
value, before making any changes.
You have the option at this point of getting more information about the firm’s costs
different output levels, and about the market demand for the product. (See “Instructions”
in the toolbar). The first time you run the module you should look at this information, and
possibly print it out for easy reference. You can also proceed directly to making
decisions by selecting “Make Decisions” from the toolbar. The decision you need to
make is the output level for the firm. Once you set the output level, the module will
determine the highest price the firm can get from selling that amount using the demand
information. After you have made your decision click on “Results” to see how well the
firm did under your management. You will not be allowed to set a zero or a negative
output, nor will you be allowed to set an output level so large that the firm would have to
pay people to haul the stuff away (a negative price).
After getting the numerical results of your decision (costs, revenues, profit, the firm’s
equity) you can look at the graphical display of your decision by selecting “See Graph.”
You can go back and set a new output level (“New Output”), or you can continue on to
the second part of the module (“Regulation”).
If you select “Regulation”, you can see what would happen if the Public Utilities
Commission left the firm stay a monopoly (number of firms = 1) and regulated it with
either marginal cost or average cost price controls. The first time you do this part of the
module, you should see what these regulations do first without breaking up the
monopoly. Subsequently, you might want to see what happens if the PUC breaks up the
firm into 2, 3 or more firms and compare the prices, quantities, and costs with one firm
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and a given regulation with the values you get with multiple firms and the same
regulation.
Mathematical Model
In this module the firm’s Total Cost is:
TC = ec + (0.1 * Q) + (2 * (Q ^ 0.6))
Where ec is the entry cost determined by the user at the beginning of the module. Its
default value is $10.
Average cost is defined as usual, TC/Q, so:
AC = (ec/Q) + 0.1 + (2*(Q^-0.4))
Marginal cost is:
MC = 0.1 + 1.2*(Q^-0.4)
Knowledge of calculus is required to show that the slopes of AC and MC are both
negative—the larger the value of Q, the smaller AC and MC will be.
The market demand curve (holding income, preferences, and all other prices constant) is:
price = 190 - (0.009 * Q)
Marginal revenue is:
MR = 190 - (0.018 * Q)
Profit Maximizing Output and Output Under Regulation
For the monopoly in this market marginal revenue is equal to marginal cost if:
MR = 190 - (0.018 * Q) = MC = 0.1 + 1.2*(Q^-0.4)
Solving an equation of this form, where Q has an exponent of –0.4 requires advanced
methods (algebra won’t do it). The simplest way involves “numerical methods,” e.g.,
enter a value for Q and see if the value it gives MR is more than the value it gives MC, if
it is put in a bigger value for Q. This is very slow and hard to manage by hand or even
with a good scientific calculator. Fortunately, computers can be programmed to find the
answer very quickly.
Similar equations are needed to find the Q for which Demand equals AC and where
Demand equals MC in the regulatory section of the module. In that section the computer
does find the right value (or pretty close to it) for you. (Even a computer can take awhile.
You might notice that when getting the average cost regulation result there is a
perceptible pause before the results come up -- unless you are using a very fast computer.
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That is because the computer is actually doing thousands of numerical operations to get
the answers.) As to finding the best answer for the regulated firm—you are on your own
(except for the clues offered by MR and MC).
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