Normative Aspects of Natural
Monopoly Pricing - I
March, 2008
Marginal Cost Pricing
ADEF: Consumer Gross surplus
ACEF: Income spent on the good
CDE: Consumer net surplus
BCE: Firm’s profit
D
Consumer net surplus
MC
E
P*
C
Q=D (P)
B
A
When price does not reflect
marginal cost, consumers
receive deceptive information
about the societal cost of a
marginal increase in demand;
however if the firm operates
under increasing returns to
scale (as a natural monopoly),
marginal cost pricing creates a
deficit driving the firm out of
business.
F
Q*
Q
When demand is perfectly inelastic
the amount of consumer surplus is infinite.
When demand is perfectly elastic consumer surplus is zero; consumers
Have their needs met by the ability to find substitutes products at lower prices
Consumer surplus is the amount that
consumers benefit by being able to
purchase a product for a price that is
less than they would be willing to pay.
Natural Monopoly Model
P
Above Normal Profit
Dead Weight Loss
under Monopoly
In most cases that will manifest itself as shown
in the graph, with a standard average cost, and demand, but a
very low marginal cost, under the average cost curve. Based on
the assumptions of a natural monopoly, the slope of the marginal
cost curve will always be close to 0.
A
Pm
B
AC
E
C
MR
Natural Monopolies occur in markets where the standard
monopoly market factors apply; often there are high fixed costs,
and low marginal costs. This occurs most often in the utilities
markets where the infrastructure for distribution represents a
high fixed cost, however, for every extra unit of distribution after
that, there is a low marginal cost.
MC
D
Qm
Q
As shown in the graph, profit is defined as the area left of the
difference between price on the demand curve and the average
cost curves (the grey area on the graph).
The graph also denotes 3 points on the demand curve:
•A – The profit maximization point for the firm (above normal profits, here)
•B – The point where the firm breaks even (with an average rate of return)
•E – The efficient point (price or marginal valuation equals MC)
The profit maximization point is found where the quantity produced is at the point where marginal revenue meets marginal cost (C ).
From this, point A may be found . In this instance, there usually is a very large dead weight loss (pink area on graph).
The breakeven point is where average cost meets demand, in this instance the firm will make no (above-normal) profit, but the average cost
already takes into account an average rate of return required by investors for firms in this risk class.
Dead weight loss is significantly decreased (not shown in graph).
The efficient point is found where marginal cost meets the demand curve . Since this point is below the average cost curve, there will be
a financial loss incurred by the firm. The challenge of any regulatory regime is to address the problem of firm’s financial sustainability
while being “fair” to customers.
Uniform Pricing
The regulator faces pricing challenges
when the monopoly firm delivers multiproduct or multi-service.
The goal for regulators is not to equalize the
deadweight loss in each market but to
maximize overall surplus (so income
distributional concerns are ignored).
The most basic pricing scheme is to set
a uniform price scheme as shown on
graph below. The dead-weight losses are
shown as colored triangles.
This may be done by departing from
uniform pricing and introducing other pricing
techniques and tariff structures depending
on products’ demand, so the monopoly firm
may charge above MC but below the high
monopolist price.
It can be noticed that each service, when
having different demand elasticities,
generates different DWL.
DD1
1
2
D2
u
Pu
P1
u
P1
Pu
m
m
u
YQ1
1
Y1
Q
u
Y
Q2
2
YQ
2
Ramsey Pricing
Consist of constrained profit maximization with a balanced budget – It balances customers
and firm benefits and minimizes the monopoly inefficiency which arises from pricing above MC.
Price is adjusted differentially in each market by adjusting quantities by same amount. In this sense,
this pricing technique is viewed as price discriminatory.
The figure below shows price reduction from initial monopolist price.
Pm
DD1
1
D2
D2
DWL
Pm
DWL
R
P2
P1
R
mc
mc
Qm Qr
Y1
Q1
Qm
Qr
Q2
2
Ramsey Pricing
Ramsey pricing is a linear pricing scheme designed for the multiproduct natural
monopolist [see Frank Ramsey. "A Contribution to the Theory of Taxation," Economic Journal, March 1927].
Basic idea: Set prices (or rates) on the various services provided by the regulated firm
such as to maximize social welfare subject to a profit constraint:
Max CS(p) +π(p)
P
s.t.
π(p)≥0 ;
(TR - TC = M)
Where M is some fixed amount, which can be 0.
Assumption: Constant marginal cost (MC) so that producer surplus is equal to zero.
We use calculus (specifically, the Lagrangean methodology -but you do not need to
know this)
to derive the Ramsey Pricing Rule, which can be stated as follows:
Pi − mci  λ  1
=

Pi
 1+ λ  | εi |
The price that maximizes social welfare subject to a
profit constraint will exceed marginal cost by an amount
that is inversely proportional to elasticity of demand.
where:
Pi is the price of service i;
mci is the marginal cost of service i;
is a constant; and
εi is elasticity of demand for service i;
Peak Load Pricing
It consists of pricing a product (service) at higher levels during periods of highest demand.
Usually, the higher prices are in effect during a specific set of hours.
A uniform price scheme may cause over consumption by the peak demanders
and under consumption by off peak demanders (see top left graph next slide)
Such an approach signals users that continuing high levels of usage are
imposing high costs on the system (the system capacity must be expanded
sooner than otherwise would be the case).
The objective of using peak-load-pricing scheme is that while covering costs, the firm will
give peak demanders an incentive to reduce consumption.
Dynamics:
Step 1
In the next graph, Ck is the cost incurred by firm to install capacity K; MC is the marginal cost
of producing additional service to satisfy peak demand. The firm is pricing to recover
capacity costs Pu = Ck
MC increases above installed capacity K at an increasing rate determined
by additional production (positive and steep slope).
Qp is the quantity consumed by peak demanders.
Step 2
The firm increases price from Pu to P’
Both type of consumers reduce their consumption and the company is making profits
Step 3
The firm reduces price for off peak from P’ to P” ; then customers increase consumption to K’’’
Firm profits are reduced and compensate losses from lower price to off peak demanders
A
Uniform &Peak Load Pricing
Peak-Demand
Uniform Price Scheme – step 1
MC
Offpeak quantity=K ; Peak quant ity= Qp
F
G
Off-Demand
APuC = gross CS for peak demand
GPuE= gross CS for off peak demand
DWL
From firm over production
B
E
C
Pu
PuOKE =firm revenue from off peak D
PuOQpC = firm revenue from peak D
Ck
EFC = firm loss from peak demand
BFC=DWL from overproduction
O
K
Qp
A
Peak-D
MC
Peak Load Scheme – step 2
D
Off-D
Off peak quantity = K” ; Peak quantity = K’
B
H
AP’B = gross CS for peak customers
DP’H = gross CS for off peak customers
DWL
For off-peak customers
P’
E
Pu
I
G
C
P’PuEB = firm profits from peak and off peak D
PuOK’B = firm revenues from peak and off peak D
IBC= DWL for society due to off peak reduced
consumption
O
K”
K
K’
Qp
Ck
Uniform &Peak Load Pricing
The regulatory Challenge
The challenge for the regulator is to
allow a price increase for peak
demanders and a price decrease for
off peak demanders such that firm loss
from off peak consumption
compensates firm’s gain from peak
consumption while balancing out DWL
for society.
The goal is to incentive less
consumption from peak consumers
while increasing off peak consumers.
Peak Load Scheme – step 3
Calculations are not shown;
It may get messy using just labels
Instead of numbers;
A
Peak-D
MC
D
Off-D
P’
Ck
Pu
P”
O
K”
K
K”’
General view: Cross-Subsidies
Basis:
1)Two demands with different elasticities; Do less elastic than D1
2)Average costs are different: for supplying Urban market AC=$1; Rural AC=$3
3)Max amount consumed in urban market equals 150 units of service; In Rural market equals 250 units of service
4)Max price $5
Dynamics : Assume Uniform pricing the firm is required to charge same tariff to both type of customers even with diff AC
1)In Urban market the firm is charging P”=2, above AC with excess profits = (100)(1)=100; net CS=(1/2)(100)(5-2)=150
The gains for the firm from selling at higher price is netted out by the loss of consumer surplus producing DWL
2)In Rural market the firm is charging P” =2 , below AC with a loss = (150)(1) =150 ; net CS= (1/2)(100)(5-3) = 100
The gains for society from paying lower a price is offset by firm’s loss, producing DWL
Price $
Urban D0
Price $
5
4
AC
3
P’ =
DWL->loss from firm
5
4
P” =
Rural D1
P’ = 3
2
P” = 2
AC
1
50
100
150
200
250
1
Q
50
100
150
200
250
Q
DWL->loss from customers
Result: the firm is partially subsidizing the larger rural demand with revenue from urban customers;
(it is based on the inelastic Urban demand and based on the assumption that there is no competition to come in and supply
the urban demand at AC)
Cross -Subsidies
Formal (Faulhaber 1975) :
Let Q denote the vector of outputs (q1…qn) where qj denotes a sub-vector of k outputs, with k ε J
Let C(Q) and C(qj) denote respectively the cost of producing the whole set of products and the
subset of j products.
A firm does not cross-subsidize if for all j, pjqj <=C(qj)
Meaning-no subset of goods yields a net profit by itself to the firm. Entry by a firm with identical
technology on market j alone is not profitable.
Thus the revenue from the product or set of products must be at least as high as its incremental
Cost (basic to keep producing it), and at most equal to its stand alone cost.
Implicit assumption in a regulated industry TR=TC