Regulation Policy and Economics of Regulation
Class No. 5 (file 5): Natural Monopoly
Objectives of Today’s Class(1) To recollect the discussion on monopoly(2) To understand a concept of natural monopoly(3) To understand the relationship between naturalmonopoly and a price regulation

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Outline of Class No
No. 55-1
5
1 E
Economy off SScalel
5-2 Natural Monopoly
5-3
5
3 Marginal Cost Pricing
5-4 Average Cost Pricing
5-5 Problems of Price Regulations
5-6 Price Cap
5-7 Price Regulations under Incomplete Information
5 8 Public
5-8P bli E
Enterpriseti

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2Economy of Scale(a) Merit of scale→ Average cost declines as production quantity increases
increases.
(b) Subadditivity of cost function→ Production by a single firm costs less compared to oneby plural firms (dividing up the same quantity).

If (a),(a) itit’ss (b).
(b) (The reverse is not truetrue.))

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E
Economyoff SScalel
AC

ＡＣ0

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Ｙ4S b ddi i i off Cost
Subadditivity
CFunctionFi

ACBounds ofmeaningfulproduction
d iＡＣ0REGULATION POLICY & ECONOMICS OF REGULATION

Ｙ*Ｙ5

Economy of Scale: Examples
・Industries requiring huge setup costs（E.g.） the steel industry, LNG receiving facilities
・Industries
Industries requiring huge R&D costs(E.g.) pharmaceutical, semiconductor, large aircraft
・Industries
Industries requiring network facilities（E.g.）telecommunications, electric power, city gas
・Markets where network externalities work strongly（E.g.）OS, computer game・Niche markets of a small market size

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6NNaturall MonopolyMlAC
Ｐ

ＤＡＣ
0

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Ｙ

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Question: Which is the production quantity amonopoly firm chooses?
ＰＤＡＣ
ＭＣ
ＭＲ
0

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Ｙ

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Question: The monopoly price?
Ｐ
ＤＡＣ
ＭＣ
ＭＲ
0

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9NNaturall Monopoly
MlＰ

ＤＡＣ
ＭＣ
ＭＲ
0ＹQuestion: Deadweight loss of welfare?
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10MarginalgCost Pricing
g Principlep
Ｐ
ＤＡＣＭＣＭＲ
ＰMC0ＹMCＹQuestion: Firm
Firm’ss deficit?
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Averageg Cost Pricing
g Principle
p
Ｐ
ＤＡＣＭＲ

ＭＣ

ＰAC
0ＹAC

ＹQuestion: Deadweight loss of welfare?
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Loss of Welfare by Average Cost Pricing Regulation
ＰＤＡＣＭＲ

ＭＣ

ＰAC
0ＹAC

Ｙ

Question: Which average cost pricing yields bigger
deadweight loss of welfare, the regulated or non-regulated?
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Problems with Price Regulation
Problem with a regulation
gbased on the pprinciple
p of marginal
gcost pricing
・Deficit being incurred ← Required to be covered withsubsidy
・Difficult to grasp accounting marginal costs sometimes
Problem with a regulation based on the principle of average
cost pricing
・Welfare loss being incurred
Problem common with both regulations
・No inducement for cost reduction
・Real costs being unclear sometimes→ It’s unclear if accounting costs are truly necessary ones.
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Price CapTo set up the upper-limit price, and change it as per a certain
rule:l P
P=f(x)-g(t)f( ) (t)g(t) to signify the time factor; e.g., a rule to reduce 1% everyyear (the part to take technological innovation and such intoaccount)f(x) being the part to incorporate various economic factors（Examples of those factors） price increase rate, factor price(e.g., petroleum price: adjustments of fuel costs/raw materialcosts）, interest rate, quality of supply products～ Factors unrelated to one’s own effort on cuttingg costs→ Not to impair inducements to cut costs
Similar system:
ythe fuel cost/raw/material cost adjustment
jsystem（Class No. 7, 8）
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Problems with Price Cap(1) Welfare loss being incurred: Prices not to come down withth reduction
thed ti iin costst → theth didisparity
it off marginali l costs
tand prices(2) It’s difficult to obtain a commitment not to reduce theupper limit price even if costs go down.
→ One makes a big profit
profit. → It becomes clear that one’sone scosts are low. → The inducement for one to revise its priceoccurs ex ppost facto.
⇒ As a practical matter, a long-term commitment is difficult tocome by. In many cases, the practice is to fix the rule for aterm of X years (some 3-5 years in a large number ofinstances), and to have another look after X years.
～To result in shrinking inducements to cut costs
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Example 1
No cost with no production. For production, the setup cost
being 100100, and another 20 as the cost per a single unit ofproduction: the demand function being P=100-Y
A monopoly firm engages in production in this market; thegovernment establishes the pricing and subsidy S. (If S isnegative, it means imposition of taxes.)
The firm
fdoes not produce unless its profit
f should benonnegative.
Aggregate surplus ＝CS（consumer surplus）＋PS（producersurplus）－ S
The ggovernment settles on the ppricingg and subsidy
y so as tomaximize the aggregate surplus.
Question: What are the price the government sets and thenecessary subsidy？
b id ？
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17Excess Burden of Tax・Expenditure
Editffor ttax collectionll ti
・Excess burden of tax accompanying tax collection（E ） excess burden（E.g.）anb d off 10%
A subsidy of 10 billion yen to the business enterprise sector ⇒the cost at 1 billion yen

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Example 2
No cost with no production. For production, the setup costb i 100
being
100, andd anotherth 20 as th
the costt per a singlei l unit
it offproduction: the demand function being P=100-Y
A monopoly firm engages in production in this market; thegovernment establishes the pricing and subsidy S. (If S isnegative, it means imposition of taxes.)
The firm does not produce unless its profit should benonnegative.
Aggregate surplus ＝CS（consumer surplus）＋PS（producersurplus）－ (1+λ)S : λ being a positive constant
The government settles on the pricing and subsidy so as tomaximize the aggregate surplus.
Question: What are the price the government sets and thenecessary subsidy？
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19Example 2Question: What are the price
Qpthe ggovernment sets and thenecessary subsidy？
To set S to attain PS=0
W=CS － (1+λ)SREGULATION POLICY & ECONOMICS OF REGULATION

20Consumer Surplus
100P200Ｙ

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Ｙ21

例２To set S to attain PS=0
W=CS － (1+λ)SQuestion: What is CS?（Express as P’s functionfunction.))

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Example 2To set S to attain PS=0
W=CS － (1+λ)SQuestion: What is (1+λ)S?（Express as P’s function.）

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Example 2
To set S to attain PS=0
W=CS － (1+λ)SQuestion: What is (1+λ)S?（Express as P’s function.）
Answer: (1+λ)(100-(P-20)(100-P))

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Example 2Question: What is the price the government sets?
To set S to attain PS=0
W=CS － (1+λ)SREGULATION POLICY & ECONOMICS OF REGULATION

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Example 3
No cost with no production. For production, the setup costb i 100
being
100, andd anotherth 20 as ththe costt per a singlei l unit
it offproduction: the demand function being P=100-Y
A monopoly firm engages in production in this market; thegovernment establishes the pricing and subsidy S. (If S isnegative, it means imposition of taxes.)
The firm does not produce unless its profit should benonnegative.
Aggregate surplus ＝CS（consumer surplus）＋PS（producersurplus）－ (1+λ)S : λ being a positive constant
The government settles on the pricing and subsidy so as tomaximize the aggregate surplus.
government sets?
Question: What is the price the g
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Real Costs being Unclear

It s unclear whether the firm’sIt’sfirm s cost structure is high or lowlow.
Setting up the regulation price low by making a rush
jjudgmentgthat a firm’s cost is low would cause the firm
really with a high cost structure to make an exit.
⇒ To have the firm declare its own cost
～ Requirment for inducements to declare correct costs
Self-selection

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Example 4
No cost with no production. For production, the setup cost
being 100, and another 20 or 10 as the cost per a single unitof production. The government does not know whether thefirm’s production cost is 20 or 10: the demand function being
P=100-Y.
P=100-Y
A monopoly firm engages in production in this market; thegovernment establishes the pricing and subsidy S. (If S isnegative,ti
it means iimposition
iti off ttaxes.))
The firm does not produce unless its profit should benonnegative.
Aggregate surplus ＝CS（consumer surplus）＋PS（producersurplus）－ S
The government settles on the pricing and subsidy so as tomaximize the aggregate surplus.
Question: What is the price the government sets? And thesubsidy？
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Example 4
Question: What is the price the government sets? And thesubsidy？
Answers: to present the two schedules of
Ｐ＝20 Subsidy＝100
Ｐ＝10 Subsidy ＝180
Choose the former if the firm’s cost is 20, an the latter if it is 10.

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Imperfect information (No Excess Burden of Tax)
ＰAble to gain this much of profit bylying that cost are highCHCＬ0

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Deadweight loss ofwelfare when tellingliesＹHＹＬＹ30Examplep 5
No cost with no production. For production, the setup cost
being 100
100, and another 20 or 10 as the cost per a single unitof production. The government does not know whether thefirm’s production cost is 20 or 10; the probability of 20 being
q: theth ddemandd ffunction
ti b
beingi P
P=100-Y.
100 Y A monopolyl fifirm
engages in production in this market; the government
establishes the ppricing
g and subsidyy S. ((If S is negative,g, itmeans imposition of taxes.) The firm does not produce
unless its profit should be nonnegative.
AAggregatet surplus
l ＝CS（consumerCS（surplus）＋PS（producerl ）＋PS（ dsurplus）－ (1+λ)S : λ being a positive constant
The government settles on the pricing and subsidy so as tomaximize the aggregate surplus.
Question: What is the pprice the ggovernment sets? And thesubsidy？
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Examplep 5
The government’s choice:(1) TTo presentt a single
i l schedule,h d l andd if ththe fifirm iis a ttype H(having high cost), then approve of the situation for the firm
to discontinue production→ To be reasonable when λ is positive and q is close to 0
In this casecase, it is a combination of the price and subsidy derived
in the example 3.

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Examplep 5(2) To present the two schedules, and have the firm produce
whichever type it belongs to (pH, SH) (pL, SL)
Inducement for a firm of the type L (having a low cost) tooverreport its cost
When the type-L firm has selected the schedule designed forthe type H, it is necessary to pay a subsidy to the typetype-L
L firmso that it can obtain at least the same amount of profit.
(pH-20)(100-p)(pH))-100+SH ≧0 ((binding)g)(pL-10)(100-pL)-100+SL ≧0 (non-binding)(pL-10)(100-p)(pL))-100+SL ≧ (pH-10)(100-p)(pH))-100+SH ((binding)g)

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Examplep 5
SH=- (pH-20)(100-pH)+100
SL= 10(100-p10(100 H)) (p( L-10)(100-p10)(100 L)+) 100
W=q{(100W{(100 pH)2/2 - (1+λ)(100(1(1+λ)(100λ)(100- (p( H-20)(100-p20)(100 H))}H)+ 100+(1-q){(100- pL)2/2 - (1+λ)(10(100-p(1+λ)(100-- (pL-20)(100-pL))}
Question (1): Is pL either higher than, or lower than, or thesame withith th
the regulationl ti pricei underd perfectf t iinformation?
fti ?
(2) Is pH either higher than, lower than, or the same with theregulation price under perfect information?

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Imperfect information (Excess Burden of Taxin Existence)
ＰPHNecessary SubsidyPHCHPLCＬ0ＹH ＹH

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Stranded Cost
Setup costs are sunk costs, as a firm has already invested.
Normally to be recovered through fare receipts
Monopoly to date; the firm has intended to recover with theregulation price under noncompetition over a long term.
⇒Abrupt liberalization or a change in the regulatory regime,
making certain costs irrecoverable
Costs that have become uncollectible due to a change in thefframework
k ~ StrandedSt d d costt
How to recover this is a big problem.

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Allocation of Common Cost
To have plural monopoly sectors, and/or a monopoly sector anda competitive
titi sectort att theth same timeti（E.g.）
・Partially liberalized market (electric power, city gas)
・Simultaneous management of an essential facilities sector anda competitive
titi sectort (telecommunications,(t li tielectricl t i power, cityitgas)
・ Business having a reserved area (the postal business in eachcountry)
・Simultaneously
Simultaneously management of a universal service sector anda competitive sector (telecommunications, electric power, citygas, pg
postal service))
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Allocation of Common Cost
To have plural monopoly sectors, and/or a monopoly sector
and a competitive sector at the same time ~ There are
expenses to be borne commonly.
（（E.g.）・Personnel）
expenses of employees administeringboth sectors
・Expenses
Eforf accounting
ti andd taxation
tti businessb i・Power station to be used for the ancillary service andgeneration of electricity
・Facilities to be used for the ancillary service and gas supply
・PowerPower transmission cable and gas pipeline to be used bothfor regulated and liberalized fields
How should these be distributed among various sectors?
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Allocation of Common Cost
To have a monopoly sector and a competitive sector at thesame time ~ There are expenses to be borne commonly.
How should theyy be distributed between these sectors?
(1) To distribute common expenses to both sectors as per adefinite rule
(E.g.)
・Distribute personnel expenses by estimating how much workhas been done for which sector in practice (ABCaccounting).
・Distribute customer expenses (costs of metering and such)in accordance with the number of customers.
・DistributeDi t ib t power transmission
ti i ((conduits)
d it ) expenses iin
proportion to the ratio of the maximum amount used.
39
REGULATION POLICY & ECONOMICS OF REGULATIONDistribution of Expenses
pof Installed Capacitypy
Usage
To distribute UH /(UH＋ UL) muchto H market

UHUＬ
0

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Time40Distribution of Expenses of Installed Capacity
Usage

To distribute UH /(UH＋ UL) muchto H market
But actually, UH /(UH＋ UL*) muchshould be distributed to H market.

UHUＬUＬ＊
0

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Allocation of Common Cost
To have a monopoly sector and a competitive sector at thesame timeti~ ThThere are expenses tto beb bborne commonly.
l H
Howshould they be distributed between these sectors?
(2) To distribute common expenses to the competitive sector
To calculate how much expenses would be if it were thepsector alone
competitive→ Deduct these from the entire expenses, and calculate ones forthe monopoly (regulated) sector.
～To distribute the whole economic profit in the confines to themonopoly (regulated) sector⇒ An inducement to spin off the competitive sector (ascompared to the other rules)～Risks thata eeven
e aan ooriginallyg a y desdesirable
ab e integrationeg a o might
g be sp
split
off
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Allocation of Common Cost
To have a monopoly sector and a competitive sector at the sametime ~ There are expenses to be borne commonly. How
should they be distributed between these sectors?
(3) To distribute common expenses to the monopoly (regulated)sector
To calculate expenses for the monopoly (regulated) sector alone→ Deduct these from the entire expenses, and calculate ones
f theforth competitive
titi sector.
t ～ ToT distributedi t ib t th
the wholeh l economici
profit in the confines to the competitive sector⇒To distort competition ～ Normally this kind of rule does not
get adopted. But which can be discussed as the upper limitprice for the monopoly
pp y ((regulated)g) sector.
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