A monopoly price is set by a
monopoly
A monopoly (from Greek language, Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situati ...
.
[Roger LeRoy Miller, ''Intermediate Microeconomics Theory Issues Applications, Third Edition'', New York: McGraw-Hill, Inc, 1982.][Tirole, Jean, "The Theory of Industrial Organization", Cambridge, Massachusetts: The MIT Press, 1988.] A monopoly occurs when a firm lacks any viable
competition
Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indivi ...
and is the sole producer of the industry's product.
Because a monopoly faces no competition, it has absolute
market power
In economics, market power refers to the ability of a firm to influence the price at which it sells a product or service by manipulating either the supply or demand of the product or service to increase economic profit. In other words, market powe ...
and can set a price above the firm's
marginal cost
In economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it r ...
.
Since marginal cost is the increment in
total cost
In economics, total cost (TC) is the minimum dollar cost of producing some quantity of output. This is the total economic cost of production and is made up of variable cost, which varies according to the quantity of a good produced and includes ...
required to produce an additional unit of the product, the firm can make a positive economic profit if it produces a greater quantity of the product and sells it at a lower price.
The monopoly ensures a monopoly price exists when it establishes the quantity of the product.
As the sole supplier of the product within the market, its sales establish the entire industry's
supply
Supply may refer to:
*The amount of a resource that is available
**Supply (economics), the amount of a product which is available to customers
**Materiel, the goods and equipment for a military unit to fulfill its mission
*Supply, as in confidenc ...
within the market, and the monopoly's production and sales decisions can establish a single price for the industry without any influence from competing firms.
[John Black, "Oxford Dictionary of Economics", New York: Oxford University Press, 2003.] The monopoly always considers the
demand
In economics, demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given time. The relationship between price and quantity demand is also called the demand curve. Demand for a specific item ...
for its product as it considers what price is appropriate, such that it chooses a production supply and price combination that ensures a maximum
economic profit
In economics, profit is the difference between the revenue that an economic entity has received from its outputs and the total cost of its inputs. It is equal to total revenue minus total cost, including both explicit and implicit costs.
It i ...
,
which is determined by ensuring that the marginal cost (determined by the firm's technical limitations that form its cost structure) is the same as the
marginal revenue
Marginal revenue (or marginal benefit) is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit.Bradley R. chiller, "Essentials of Economics", New York: McGraw-Hill, Inc., ...
(MR) (as determined by the impact a change in the price of the product will impact the quantity demanded) at the quantity it decides to sell.
The marginal revenue is solely determined by the demand for the product within the industry and is the change in revenue that will occur by lowering the price just enough to ensure a single additional unit is sold.
The marginal revenue is positive, but it is lower than its associated price because lowering the price will increase the demand for its product and increase the firm's sales revenue, and lower the price paid by those who are willing to buy the product at the higher price, which ensures a lower sales revenue on the product sales than those willing to pay the higher price.
Marginal revenue can be calculated as
, where
.
![MarginalRevenue](https://upload.wikimedia.org/wikipedia/commons/c/c8/MarginalRevenue.jpg)
Marginal cost (MC) relates to the firm's technical cost structure within production, and indicates the rise in total cost that must occur for an additional unit to be supplied to the market by the firm.
The marginal cost is higher than the average cost because of
diminishing marginal product in the short run.
It can be calculated as
, where
.
[Henderson, James M., and Richard E. Quandt, "Micro Economic Theory, A Mathematical Approach. 3rd Edition", New York: McGraw-Hill Book Company, 1980. Glenview, Illinois: Scott, Foresmand and Company, 1988.
Usually, in many textbooks, ]economic cost Economic cost is the combination of losses of any goods that have a value attached to them by any one individual. Economic cost is used mainly by economists as means to compare the prudence of one course of action with that of another. The comparis ...
, here presented by , is divided into two categories; labor costs and capital costs:
, where
* = labor
Labour or labor may refer to:
* Childbirth, the delivery of a baby
* Labour (human activity), or work
** Manual labour, physical work
** Wage labour, a socioeconomic relationship between a worker and an employer
** Organized labour and the labour ...
hired,
* = wage
A wage is payment made by an employer to an employee for work done in a specific period of time. Some examples of wage payments include compensatory payments such as ''minimum wage'', ''prevailing wage'', and ''yearly bonuses,'' and remuner ...
rate,
* = total amount of capital
Capital may refer to:
Common uses
* Capital city, a municipality of primary status
** List of national capital cities
* Capital letter, an upper-case letter Economics and social sciences
* Capital (economics), the durable produced goods used f ...
financed by both debt
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, which differentiates it from an immediate purchase. The ...
and equity
Equity may refer to:
Finance, accounting and ownership
* Equity (finance), ownership of assets that have liabilities attached to them
** Stock, equity based on original contributions of cash or other value to a business
** Home equity, the dif ...
,
* = cost of capital, including both interest expense and the minimum required rate of return on equity
* = = a function of the quantity of labor and capital employed in production![Per Unit Economic Costs for a Firm - Short Run with a Fixed Cost](https://upload.wikimedia.org/wikipedia/commons/0/0d/Per_Unit_Economic_Costs_for_a_Firm_-_Short_Run_with_a_Fixed_Cost.jpg)
Samuelson indicates this point on the consumer demand curve is where the price is equal to one over one plus the
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of the
price elasticity of demand
A good's price elasticity of demand (E_d, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elastici ...
.
[Samuelson; Marks (2003). p.104] This rule does not apply to
competitive firms, as they are price takers and do not have the
market power
In economics, market power refers to the ability of a firm to influence the price at which it sells a product or service by manipulating either the supply or demand of the product or service to increase economic profit. In other words, market powe ...
to control either prices or industry-wide sales.
Although the term
''markup'' is sometimes used in economics to refer to the difference between a monopoly price and the monopoly's MC,
[Nicholson, Walter and Christopher Snyder, ''Microeconomic Theory: Basic Principles and Extensions'', Mason, OH: Thomson/South-Western, 2008.] it is frequently used in American accounting and finance to define the difference between the price of the product and its per unit accounting cost. Accepted neo-classical micro-economic theory indicates the American accounting and finance definition of markup, as it exists in most
competitive markets
In economics, competition is a scenario where different economic firmsThis article follows the general economic convention of referring to all actors as firms; examples in include individuals and brands or divisions within the same (legal) firm ...
, ensures an accounting profit that is just enough to solely compensate the equity owners of a competitive firm within a competitive market for the economic cost (
opportunity cost
In microeconomic theory, the opportunity cost of a particular activity is the value or benefit given up by engaging in that activity, relative to engaging in an alternative activity. More effective it means if you chose one activity (for example ...
) they must bear if they hold on to the firm's equity.
The economic cost of holding onto equity at its
present value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has inte ...
is the opportunity cost the investor must bear when giving up the interest earnings on
debt
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, which differentiates it from an immediate purchase. The ...
of similar present value (they hold onto equity instead of the debt).
Economists would indicate that a markup rule on economic cost used by a monopoly to set a monopoly price that will maximize its profit is excessive markup that leads to inefficiencies within an economic system.
[Henderson, James M., and Richard E. Quandt, "Micro Economic Theory, A Mathematical Approach. 3rd Edition", New York: McGraw-Hill Book Company, 1980. Glenview, Illinois: Scott, Foresmand and Company, 1988.][Bradley R. chiller, "Essentials of Economics", New York: McGraw-Hill, Inc., 1991.]
Mathematical derivation: how a monopoly sets the monopoly price
Mathematically, the general rule a monopoly uses to maximize monopoly profit can be derived through simple calculus. The basic equation for economic profit, in which the total economic cost varies directly with the quantity produced, can be expressed as
, where
*
= quantity sold,
*
=
inverse demand function In economics, an inverse demand function is the inverse function of a demand function. The inverse demand function views price as a function of quantity.
Quantity demanded, ''Q'', is a function f (the demand function) of price; the inverse demand f ...
; the price at which
can be sold given the existing demand
*
= total cost of producing
.
*
= economic profit
This is done by equating the derivative of
with respect to
to 0. The profit of a firm is given by total revenue (price times quantity sold) minus total cost:
, where
*
= quantity sold,
*
= the
partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
of the inverse demand function, and the price at which
can be sold given the existing demand
*
= marginal cost, or the partial derivative of the total cost of producing
which yields
where marginal revenue equals marginal cost. This is usually called the first order conditions for a profit maximum.
![MonopolyPower3-Wiki](https://upload.wikimedia.org/wikipedia/commons/1/16/MonopolyPower3-Wiki.JPG)
According to Samuelson,
By definition,
is the reciprocal of the price elasticity of demand (or
), or
This gives the markup rule:
or, letting
be the reciprocal of the price elasticity of demand,
Thus the monopolistic firm chooses the quantity at which the demand price satisfies this rule. Since
for a price setting firm, it means that a firm with market power will charge a price above marginal cost and earn a
monopoly rent
In economics, economic rent is any payment (in the context of a market transaction) to the owner of a factor of production in excess of the cost needed to bring that factor into production. In classical economics, economic rent is any payment m ...
. On the other hand, a competitive firm by definition faces a perfectly elastic demand,
, which means that it sets price equal to marginal cost.
The rule also implies that, absent
menu cost In economics, the menu cost is a cost that a firm incurs due to changing its prices. It is one microeconomic explanation of the price-stickiness of the macroeconomy put by New Keynesian economists. The term originated from the cost when restaurants ...
s, a monopolistic firm will never choose a point on the
inelastic
In economics, elasticity measures the percentage change of one economic variable in response to a percentage change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the demand quantity to fall ...
portion of its demand curve. For an
equilibrium to exist in a monopoly or in an
oligopoly
An oligopoly (from Greek ὀλίγος, ''oligos'' "few" and πωλεῖν, ''polein'' "to sell") is a market structure in which a market or industry is dominated by a small number of large sellers or producers. Oligopolies often result from ...
market, the price elasticity of demand must be less than negative one (
), for marginal revenue to be positive.
The mathematical profit maximization conditions ("first order conditions") ensure the price elasticity of demand must be less than negative one,
since no rational firm that attempts to maximize its profit would incur additional cost (a positive marginal cost) in order to reduce revenue (when MR < 0).
References
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Financial economics