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Sustainable Energy Systems

Theory of Regulation

PhD, DFA

M. Victor M. Martins

Semester 22008/2009

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SustainableEnergySystems


2. 1 Natural monopoly regulation

2. 1 Natural monopoly regulation: efficient pricing, linear, non linear pricing and Ramsey pricing.

Bibliography:( VVH) Chap 11Baumol W. J. and D. F. Bradford, 1970, "Optimal Departures from Marginal Cost Pricing," American Economic Review, Vol. 60, No. 3, pp. 265-83.

Ramsey, 1927, "A Contribution to the Theory of Taxation," Economic Journal, Vol. 37, No. 1, pp. 47-61.

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2. 1 Natural monopoly regulation: definitions

The natural monopoly problem

An industry is a natural monopoly if the productionof a particular good or service ( or all combinationsof outputs in the multiple output case ) by a singlefirm minimizes cost

It used to be that natural monopoly was simply defined as existing when the AC curve is everywhere downward-sloping relative to market demand ( economies of scale )( Baumol et al., 1970 ) introduced formally the notion of subadditive costs as a characteristic of natural monopoly

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Economies of scale: definition

Economies of scale are said to be present in production when unit (average) cost decreases as output increases. There are various explanations for the presence of economies of scale, such as:

The existence of substantial fixed costs;Opportunities for specialization in the deployment of resources andA strong market position of factor inputs

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Subadditivity: definitionConsider a market for a homogeneous product where each of k firms produces output qi and total output is given byEach firm has an identical cost function C(qi)Acording to technological or cost based definition, a natural monopoly will exist when:

Since it is less costly to supply output with a single firm. Firm costfunctions that have this attribute are said to be subadditive atoutput level QWhen firm cost functions for all values of Q, consistent withdemand Q=D(q), then the cost function is said to be globallysubadditive

ik

Q q= ∑

1 2 kC(Q) C(q ) C(q ) ... C(q )< + + +

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According to this definition assume that firms i´s cost function isdefined as Ci=F+cqi

Than the firm´s average cost of production ACi= (F/ qi )+c declines continuosly as its output expands.

PriceCost

Quantity

ACi=(F/ qi )+c

c

P=D(Q)

Q=q1+...+qn

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Economies of scale: definition

When a firm´s average cost of production declines as its output expands its production technology is characterized by economies of scale

In a single product case, economies of scale up to qi=Q is a sufficient condition but not a necessary condition for subadditivityover this range or, by technological definition, for natural monopoly

It may still be less costly for output to be produced in a single firm rather than multiple firms even if output of a single firm has expanded beyond the point where there are economies of scale

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Subadditivity and economies of scaleOne firm Two firms

PriceCost

Quantity

AC

MC

P=D(Q)

q1 q2

PriceCost

€

Q

AC1 AC2

Q1 Q2Q*

Fig. 11.4 VVH

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Economies of scale and subadditivity

There is a range of output ( Q<q1) where there are economies of sale.

After Q>q1 the function flattens out and then enters a range of decreasing returns to scale

However this cost function is still subadditive for some values of Q>q1, despite there is decreasing returns to scale.

This is the case because the market demand P=D(Q) is not large enough to support efficient production by two firms

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2. 1 Natural monopoly regulation: Definitions

Economies of scope and subadditivityAs figure 11.4 in the Viscusi et al. text illustrates, natural monopoly based on the subadditivity definition can occur even in a range of outputs for which there are diseconomies of scale in production (i.e., on the upward-sloping portion of the individual-firm AC curve). Thus the presence of economies of scale is sufficient (in the single-product case) but not necessary for the existence of natural monopoly. In the case of multiple products, the existence of economies of scale in the production of any one product is neither necessary nor sufficient (because of economies of scope in the production of multiple products).

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Multiproduct natural monopoly

Most NM ( public utilities) produce more than one product and the interdependence among outputs becomes very important

Economies of scope: definition• Economies of scope are comparable to economies of scale but

imply efficiency gains resulting from expansion of scope, or number of different output types, rather than from an increase in the volume of total output.

• Economies of scope exist when it is cheaper to produce two products together (joint production) than to produce them separately.

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Economies of scope

When a firm produces two outputs, Q1 and Q2 , economies of scope exist if the total cost function has the following structure

C(Q1,0)+C(Q2,0)>C(Q1,Q2)

Sources of economies of scopeshared inputsshared advertising creating a brand namecost complementarities (producing one good reduces the cost of producing another)


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Economies of scope and subadditivity

In the multiproduct case, product-specific scale economies is not a sufficient condition.

Economies of scope is a necessary but not sufficient condition for subadditivity.

One set of sufficient conditions for subadditivity of a multiproduct cost functions that it exhibit both economies of scope and declining average incremental cost for all products..

Slide 14



2. 1 Natural monopoly regulation:

Natural monopoly: Fundamental conflict between productive and allocative efficiency

Is natural monopoly productive efficient?Yes: Productive efficiency requires cost to be minimized

Is natural monopoly allocative efficientNo: A monopolist generates a deadweight loss by restricting output below the competitive level, since PM>MC

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The natural monopoly regulationSolutions:

Doing nothingPricing solutions

Linear pricingMarginal cost pricingAverage cost pricing

Non linear pricing or multipart tariffRamsey pricing

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2. 1 Natural monopoly regulation : Pricing solutions with symmetric information

Marginal cost pricingEfficient Marginal Cost Pricing: P0=C´( Q(P0))

Firm ( NM ) is not able to break-even under the presence of fixedcosts or economies of scale

PriceCost

€

P0

Q0

Losses

D

AC

MC

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2. 1 Natural monopoly regulation: Pricing solutions with symmetric information

Problems with linear pricingMarginal cost pricing

Outcome has allocative efficiencyWeak incentive to reduce costsFirm does not cover costs and makes lossesUse tax revenues or direct subsidy to firm to cover revenue shortfall?

Govt need to raise new taxes to fund the subsidyThe producer knows that revenue gap would always be funded

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Average cost pricingEfficient Average Cost Pricing: P0=C( Q(P0))/Q(P0)

The rule maximizes total welfare subject to the break-evenconstraint.

PriceCost

€

P0

Q0

D

AC

MC

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Problems with linear pricingAverage cost pricing

Firm covers costs and earns economic profitsFailure of allocative efficiency: less quantity and higher price than in MC pricing case ( but lower P and high quantity than profit maximization by NM)Weak incentives to reduce costsDeadweight loss

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Non linear pricingTwo-Part Tariff (1)

A fixed fee, regardless of consumption, plus a marginal cost price per unit

T(q)= A+PqNon linear pricing than linear tariffs are more efficient

Often used in the utility industries ( Telecom., Gas, Water, Electricity ) If the firm cost function is of the form: C(q)= K+cQ andconsumers are homogeneous, then it would be optimal to setthe two-part tariff with A*=K/N and P*=c

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Non linear pricing

Two-Part Tariff :T(q)= A+Pq

T(q)

€

A

P

q0

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Two-Part Tariff (2)This argument breaks down when consumers are heterogeneousConsumers with low willingness to pay drop out of themarket if K/N>CS(c´)When consumers are hetereogeneous, welfaremaximizing nonlinear tariffs will most likely involving thefirm offering consumers discriminatory two-part tariffs:

Quantity discountsMultipart tariffsSelf selecting tariffs

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Increasing and declining block tariffs

Increasing block rate Decreasing block rate

100 200 100 200 300

kWh

300

0.20

0.30

0.40

0.50

€ €

0.50

0.40

0.30

0.20

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Multi-part tariff or self-selecting two part tariffs

Calls/month

A

B

C D

100 200

TotalExpenditure

€20

10

5

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Two-part tariff (3)What is the optimal two-part tariff?Trade-off:

Efficiency losses because of exclusion of additionalconsumers when A raisesConsumption losses as P increases marginal costOptimal two-part tariffs generally involve a P that exceedsmarginal cost and a fixed fee that excludes some consumersfrom the market

The socially optimal (and discriminatory) two-part tariff willusually have an “A" that excludes some consumers (failure of universal service) and a “P" > MC (failure of allocativeefficiency).

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Pricing the multiproduct NM

For multiproduct natural monopolist, MC pricing leads to negative profits.

But if price for each product exceeds MC it can cover this shortfall,

By how much?

In the context of a multi-product monopolist, each product would have a linear price, and the set of prices would minimize deadweight social losses subject to the zero profit constraint.

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The Ramsey rule

The Ramsey problem or Ramsey- Boiteux pricing is a policy rule concerning what price a monopolist should set in order to maximize social welfare subject to a constraint on profit.Ramsey found the result before ( 1927) in the context of the theory of taxation. The rule was later applied by M. Boiteux( 1956 ) to natural monopolies.Hence the Ramsey-Boiteux pricing consists into maximizing the total welfare under the condition of non-negative profit, that is, zero profit.In the Ramsey-Boiteux pricing, the markup of each commodity is also inversely proportional to the elasticities of demand but it is smaller as the inverse elasticity of demand is multiplied by a constant lower than 1.

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€

0 Q

Y

X

P0

P1

Px

Py

P0

€

Q0

Y

X

Q0Qy Qx Q0Q1

A B

C D F

G

HI J

Proportionate price increase Ramsey prices

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Ramsey PricingLinear prices that satisfy the total revenuesEqual total cost constraint and minimize the deadweightwelfare losses

Factors limiting the use of Ramsey PricingRedistributive concernsRegulatory captureUtility opportunism and non discriminatory rulesSingle cost recovery problem

P M Ci iPi i

λε

−=

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