Sustainable Energy Systems
Theory of Regulation
PhD, DFA
M. Victor M. Martins
Semester 2
2008/2009
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation
2. 1 Natural monopoly regulation: efficient pricing,
linear, non linear pricing and Ramsey pricing.
Bibliography:
{ ( VVH) Chap 11
{ Baumol 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.
Slide 2
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
The natural monopoly problem
{
An industry is a natural monopoly if the production
of a particular good or service ( or all combinations
of outputs in the multiple output case ) by a single
firm minimizes cost
z
z
It used to be that natural monopoly was simply defined as
existing when the AC curve is everywhere downwardsloping relative to market demand ( economies of scale )
( Baumol et al., 1970 ) introduced formally the notion of
subadditive costs as a characteristic of natural monopoly
Slide 3
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation
{
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:
z
z
z
The existence of substantial fixed costs;
Opportunities for specialization in the deployment of
resources and
A strong market position of factor inputs
Slide 4
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
{
{
{
Subadditivity: definition
Consider a market for a homogeneous product where each of k
firms produces output qi and total output is given by Q = ∑ qi
k
Each firm has an identical cost function C(qi)
Acording to technological or cost based definition, a natural
monopoly will exist when:
C(Q) < C(q1 ) + C(q2 ) + ... + C(qk )
{
{
Since it is less costly to supply output with a single firm. Firm cost
functions that have this attribute are said to be subadditive at
output level Q
When firm cost functions for all values of Q, consistent with
demand Q=D(q), then the cost function is said to be globally
subadditive
Slide 5
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
{
According to this definition assume that firms i´s cost function is
defined as Ci=F+cqi
Than the firm´s average cost of production ACi= (F/ qi )+c
declines continuosly as its output expands.
Price
Cost
P=D(Q)
Q=q1+...+qn
ACi=(F/ qi )+c
c
Quantity
Slide 6
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
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 subadditivity
over 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
Slide 7
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
Subadditivity and economies of scale
One firm
Two firms
Price
Cost
P=D(Q)
AC
Fig. 11.4 VVH
Price
Cost
€
AC1
AC2
MC
q1
q2
Quantity
Q1
Q*
Q2
Q
Slide 8
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: definitions
{
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
Slide 9
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Definitions
Economies of scope and subadditivity
As 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 upwardsloping portion of the individual-firm AC curve). Thus the
presence of economies of scale is sufficient (in the singleproduct 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).
Slide 10
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Definitions
Multiproduct natural monopoly
z
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.
Slide 11
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Definitions
{
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 scope
z shared inputs
z shared advertising creating a brand name
z cost complementarities (producing one good reduces the cost
of producing another)
Slide 12
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Definitions
Economies of scope and subadditivity
z
In the multiproduct case, product-specific scale economies is
not a sufficient condition.
z
Economies of scope is a necessary but not sufficient condition
for subadditivity.
z
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 13
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation:
{
Natural monopoly: Fundamental conflict
between productive and allocative efficiency
z
Is natural monopoly productive efficient?
{
z
Yes: Productive efficiency requires cost to be
minimized
Is natural monopoly allocative efficient
{
No: A monopolist generates a deadweight loss by
restricting output below the competitive level, since
PM>MC
Slide 14
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation
{
{
The natural monopoly regulation
Solutions:
z
z
Doing nothing
Pricing solutions
{
Linear pricing
z
z
Marginal cost pricing
Average cost pricing
Non linear pricing or multipart tariff
{ Ramsey pricing
{
Slide 15
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation : Pricing solutions with symmetric information
{
Marginal cost pricing
{
Efficient Marginal Cost Pricing: P0=C´( Q(P0))
Price
Cost
€
D
AC
P0
Losses
MC
Q0
{
Firm ( NM ) is not able to break-even under the presence of fixed
costs or economies of scale
Slide 16
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
{
Problems with linear pricing
Marginal cost pricing
z
z
z
Outcome has allocative efficiency
Weak incentive to reduce costs
Firm does not cover costs and makes losses
Use tax revenues or direct subsidy to firm to cover
revenue shortfall?
{
{
Govt need to raise new taxes to fund the subsidy
The producer knows that revenue gap would always be
funded
Slide 17
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
Average cost pricing
{
Efficient Average Cost Pricing: P0=C( Q(P0))/Q(P0)
Price
Cost
€
D
AC
P0
MC
Q0
{
The rule maximizes total welfare subject to the break-even
constraint.
Slide 18
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
{
Problems with linear pricing
Average cost pricing
z
z
z
z
Firm covers costs and earns economic profits
Failure 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 costs
Deadweight loss
Slide 19
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
{
Non linear pricing
Two-Part Tariff (1)
z
z
A fixed fee, regardless of consumption, plus a marginal
cost price per unit
z T(q)= A+Pq
Non 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 and
consumers are homogeneous, then it would be optimal to set
the two-part tariff with A*=K/N and P*=c
Slide 20
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
Non linear pricing
{
Two-Part Tariff :T(q)= A+Pq
€
T(q)
P
A
0
q
Slide 21
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
Two-Part Tariff (2)
z
z
z
This argument breaks down when consumers are
heterogeneous
Consumers with low willingness to pay drop out of the
market if K/N>CS(c´)
When consumers are hetereogeneous, welfare
maximizing nonlinear tariffs will most likely involving the
firm offering consumers discriminatory two-part tariffs:
{ Quantity discounts
Multipart tariffs
{ Self selecting tariffs
{
Slide 22
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
Increasing and declining block tariffs
€
€
0.50
0.50
0.40
0.40
0.30
0.30
0.20
0.20
100
200
300
100
200
300
kWh
Increasing block rate
Decreasing block rate
Slide 23
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation
{
Multi-part tariff or self-selecting two part tariffs
Total
Expenditure
€
20
C
D
B
10
5
A
100
200
Calls/month
Slide 24
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
{
{
Two-part tariff (3)
What is the optimal two-part tariff?
Trade-off:
Efficiency losses because of exclusion of additional
consumers when A raises
z Consumption losses as P increases marginal cost
z Optimal two-part tariffs generally involve a P that exceeds
marginal cost and a fixed fee that excludes some consumers
from the market
The socially optimal (and discriminatory) two-part tariff will
usually have an “A" that excludes some consumers (failure
of universal service) and a “P" > MC (failure of allocative
efficiency).
z
Slide 25
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
{
Pricing the multiproduct NM
z
For multiproduct natural monopolist, MC pricing leads to
negative profits.
z
But if price for each product exceeds MC it can cover this
shortfall,
z
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.
Slide 26
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
The Ramsey rule
z
z
z
z
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.
Slide 27
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
€
€
X
Y
Y
P1
A
P0
C
D
Qy
Qx Q0
0
X
B
F
Proportionate price increase
Q
Px
G
Py
H
P0
I
0
Q1Q0
J
Q
Ramsey prices
Slide 28
Theory of Regulation
Sustainable
Energy
Systems
2. 1 Natural monopoly regulation: Pricing solutions with symmetric information
{
Ramsey Pricing
z Linear prices that satisfy the total revenues
z Equal total cost constraint and minimize the deadweight
welfare losses
P − M C
i
i = λ
ε
P
i
i
{
Factors limiting the use of Ramsey Pricing
z Redistributive concerns
z Regulatory capture
z Utility opportunism and non discriminatory rules
z Single cost recovery problem
Slide 29