Post on 19-Jan-2023
A firm attains monopolistic power when it is impossible or
unprofitable for other firms to enter the market.
A natural monopoly is a firm with sub-additive cost functions
(i.e. production costs which are less if production is by a
single firm only), sustainability (thus it is not profitable
for other firms to enter the market) (Mosca,2007)
Richard Posner defined Natural Monopoly “…as a relationship between
demand and the technology of supply” instead of referring to “…the
actual number of sellers in a market…”
To Posner, other firms will be forced to merge with the least
cost producing firm or fail and leave the market to avoid
production inefficiencies, resulting in the existence of one
market. (Posner, 1969)
NATURAL MONOPOLY PRICING AND PROFIT MAXIMISATION
Company XYZ being a natural monopoly will be enjoying
economies of scale i.e. the ability to produce at a low cost
over a larger volume of goods. This will imply that the
average costs of XYZ will be decreasing and its marginal costs
will fall below the average costs as shown in figure 1 below.
Due to the fact that variable costs of a natural monopoly form
a minority portion of its total costs, both the average cost
curves and the marginal costs curves turn to be decreasing and
relatively stagnant over a large range of output level.(Nicholson, 1990)
As shown in figure 1 below, with a downward sloping demand
curve (D) which represent the prices consumers are willing and
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able to pay at a particular level of output and a decreasing
marginal cost curve (MC) which falls below its average cost
curve (AC) should XYZ fix it price (P) at N, i.e. MC = D = P,
it will be charging Price PL and producing a quantity level of
QL. Since PL fall below its AC, XYZ will operate at a loss of PL
PFIN.
An unregulated XYZ not charging any lump sum tariff i.e. a
meter rate will not charge PL because it will make a loss at a
price equated to it marginal cost. This is because its
decreasing costs results in its marginal cost always falling
below its average cost. To maximize profit XYZ will therefore
charge a per unit charge of PM and produce a quantity level of
QM, thus the highest price permissible by its demand curve
At QM , XYZ will not be producing efficiently as there will be a
deadweight loss represented by the area GNM between the D
curve and the MC. XYZ having the option of charging an annual
meter rate would use the two part tariff system to ensure
pareto optimality and maximize profit. “A two-part tariff is one in
which the consumer must pay a lump sum fee for the right to buy a product” (Oi,
1979)
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Under a two part tariff the customers of XYZ pay the annualmeter charge in addition to the price per units of electricitythey consumed. Mathematically the tariff structure (T) couldbe represented as follows
T (q) = a + pq
Where T (q) is the total tariffs/ revenue received,
a = the annual meter charge
p = per unit charge of electricity consumed
q= units of electricity consumed
From the above the average price (p*) paid by the consumers of XYZ will be
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P∗¿ Tq=aq
+p
To maximise profit XYZ will have to set a and p such that those
who pay a low average price, thus those who consume large q
cannot resell to those with high average price (i.e. lower
level of q). (Nicholson, 2005)
Therefore XYZ will have to set the price per unit consume p to
equal MC, thus p = PL and set a = the Consumer surplus per
consumer arose as a result of charging PL as shown in figure
2A below.
Where XYZ has a homogenous customer base i.e. customers with
the same demand for electricity it will set the annual rate
per customer as follows
a=csn Where,
cs = consumer surplus
n = total number of consumers,
XYZ maximum profits (π) will be as shown in below,
π=2a+(p−mc) (q ), as PL = MC, π=2a
Most likely XYZ has different customer base i.e. wholesale
customers (such as industries) and household customers. The
wholesale customers will have a lower average price as they
consume more than the households. The price choice PL will
maximize the consumer surplus for the wholesale customers and
a could be set equal to the consumer surplus of the households
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QL
MC
D
PL
a = total CS
CSHMC
DWDH
FIGURE 2A: HOMOGENEOUS CUSTOMER BASE
FIGURE 2B: HETEROGENEOUS CUSTOMER BASE
QW
CSW
QH
so as not to run them out of the market when using a uniform
tariff.
As shown in figure 2B, a uniform per unit price PL, will result in
a household surplus of CSH and a wholesale surplus of CSW where QH
and QW are units consumed by households and wholesale consumers
respectively, if CSW < CSH, then a = CSH .CSw is outstanding as a
single price will not be able to swipe up all consumer surpluses.
XYZ will maximize profit if it charges such that wholesale
customers are charge a different tariff from households. Thus
wholesale customers will be charged a higher price per unit as
their demand is more inelastic than that of the households and a
lower annual charge. Households with a more elastic demand will be
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willing to pay less for a unit, therefore they are charged lesser
per unit but their annual meter charge is higher. Mathematically,
W= Annual meter charge of Wholesale Consumers
H = Annual meter charge of Households
TH = Household Tariff
Tw = Wholesale Tariff
PW = Wholesale per unit price
PH = Household per unit price and = PL (MC), then XYZ’s tariff structure will be
TH + Tw
TH = CSH + PH (QH) and
Tw = CSw + Pw (Qw), where CSw<CSH and PH < PW (Joskow, 2005)
From the above XYZ, an unregulated natural monopoly with the
option of charging an annual meter charge will maximize profit
as follows:
1. Without the charge of an annual meter charge XYZ will not
equate its price to its marginal cost as this will result
in a loss, it will however maximize profit at the output
where marginal cost is equal to marginal revenue and will
charge the highest possible price as constrained by its
demand curve.
2. With the option of an annual meter charge of its choice,
XYZ will equate price to marginal cost and maximize
profits only when the annual meter charge is equal to the
resulting consumer surplus.
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PRICING AND OUTPUT LEVELS OF A REGULATED NATURAL MONOPOLY.
The arguments of anti-monopolists can be sum up to the fact
that monopolist earn super normal profits while using
resources inefficiently at the expense of the society. To them
government regulations of such firms is needed to ensure the
better good of society.
Government regulations do turn to be problematic if there’s
asymmetric information.
As stated due to negative economic profits, XYZ does not have
the luxury of marginal cost pricing. Therefore a prohibition
of its annual rate will cause it to fail if it maintains price
at the marginal cost.
Assuming the a government has symmetric knowledge of the
market, it could subsidize XYZ to the point where all its
losses are covered i.e. the subsidy provided equals to its
average cost. In that instance XYZ breaks even and can stay
afloat and continue to produce at the same level QL and
maintain price level PL as shown in figure 1.
On the other hand, in lieu of subsidizing, XYZ’s per unit
charge could be regulated such that XYZ charges a “fair –
price” i.e. a price equal to its average cost, then it will
continue to produce. Under this regulation the price per unit
of electricity will increase from PL to PF and output reduces
to QF. XYZ being regulated will have this level of output and
price as its profit maximization level. It must be said that
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FIGURE 3: PRICE DISCRIMINATION OF HETEROGENEOUS CUSTOMERS
QH QW
PM
PH MC
DWDH
PRICE
QUANTITY
this is not the most efficient level of production as at this
level a dead weight loss exists although not as extensive as
when XYZ charges PM.
Should the government allow XYZ to fix per unit charges which
discount consumers willing to pay it a normal profit or more,
because total consumer’s surplus cannot be captured with a
single price then XYZ will maximize profit by price
discrimination. Thus to ensure allocation efficiency XYZ will
price such that consumers are charged per the elasticity of
their demand. (Posner, 1969)
According to Posner “… price discrimination is the profit-maximizing strategy
of a monopolist.” He believed that to maximize profits, the
monopolist will charge each consumer what they are willing to
pay so far as that charge earns profit.
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From the above households will consume less at a price above PH
(=MC) whereas wholesale consumers are willing to more for
additional units of electricity.
Therefore with XYZ being a natural monopoly with
heterogeneous consumer base and the resale of electric power
not possible, it will be better off to third-degree price
discriminate by charging different unit prices to different
consumers i.e. households are charged differently from
wholesale consumers.
This pricing structure is known as the Ramsey – Boiteux
Pricing which embroils third-degree price discrimination that
results in prices lying between marginal cost pricing (PL) and
prices that would be set by a pure monopoly (PM) as shown
below:
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PM
PL MCD
PRICE
QUANTITY
In discriminating price the losses incur at marginal cost
pricing will be compensated for by revenues gained at charging
higher prices.
From above price discrimination may be the only viable price
structure for the natural monopolist consistent with efficient
allocation of resources and maximization of profit.
Therefore, XYZ to maximize profit after the restriction of its
meter charge will price discriminate and provide output
consistent with its discriminated prices.
BIBLIOGRAPHY
Begg, D., & al, e. (2011). Economics (10th ed.). Maidenhead: Mcgraw - Hill Education.
Brown, D. J., & et, a. (1992, June). Two Part Tariff, MarginalCost Pricing Equilibria: Existence And Efficiency. Journal Of Economic Theory, 57(1), 52-72.
Friedman, D. D. (1990). Price Theory: An Intermediate Text (2nd ed.). South - Western Publishing co.
Joskow, P. L. (2005). Regualtions Of Natural Monopolies(05-008 WP). CENTER FOR ENERGY AND ENVIRONMENTAL POLICY RESEARCH.
Mosca, M. (WP 92/45 2007). On The Origin Of Natural Monopoly. UNIVERSITA DI LECCE.
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Neufeld, J. L. (1987, September). Price Discrmination And The Adoption Of Electric Demand Charge. The Journal of Economic History, 47(No. 3), 693-709.
Nicholson, W. (1990). Intermediate Microeconomics And Its Application (5th ed.).
Nicholson, W. (2005). Microeconomic Theory: Basic Principles And Extensions(9th ed.). Thomson South Western.
Oi, W. Y. (1979, February). A Disneyland Dilemma: Two - Part Tariffs For A Mickey Mouse Monopoly. The Quaterly Journal Of Economics, 85(1), 77-96.
Posner, R. A. (1969, February). Natural Monopoly And It's Regulation. Standford Law Review,, 21(3), 548 - 643.
Sloman, J., & Wride, A. (2009). Economics (7th ed.). Harlow: Pearson Education Ltd.
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