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REGULATION AND PROFIT MAXIMIZATION OF A NATURAL MONOPOLY

29TH NOVEMBER 2011

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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