Download Price Caps, Rate of Return Constraints and Universal

Price Caps, Rate of Return
Constraints and Universal
Service Obligations
Author: Pio Baake
Presented by: Jared Hayden
Price Cap Regulation (PCR)
 Created in Britain and has been heavily analyzed
since.
 Price Cap Regulation adjusts the:
 Operator’s prices according to a price cap index in a way
the reflect the overall rate of inflation in the economy.
 Ability of the operator to gain efficiencies relative to
other firms.
 Inflation in the operator’s input prices relative to the
average firm in the economy.
PCR Pros and Cons
 Proponent arguments
 Easy implementation
 Low informational requirements
 Implies cost minimization behavior
 Skeptical positions
 Strong incentives to reduce service quality
 Serve only classes with highest willingness to pay.
 Causes strategic price discrimination with potential
competitors
Augmented PCR
 This paper analyzes pricing distortion resulting from the
following three options in a profit-sharing scheme where firms
are allowed to use non-linear tariffs
 Assumes a stylized network industry.
 This paper aims to examine PCR in comparison to second best
pricing, as well as augmented forms of PCR.
 The first section aims to model a combination of price cap
regulation with a simple rate of return regulation, denoted as
PC/RORR.
 The latter section aims to model a combination of price cap
regulation with a universal service obligation, denoted as
PCR/USO.
PC/RORR Theory
 The PCR and RORR combination should have the result of
balancing opposing incentive effects.
 PCR gives the incentive to serve relatively few customers
 RORR gives the incentive to heavily invest in its network,
while not deviating from the optimal price.
 The combination should expand the network and lead to
near second best pricing.
 The downside is that the combination of PC/RORR gives a
strong incentive for overcapitalization, which may make an
augmentation with a universal service obligation more
efficient (assuming identical profits and customer base)
Research Building Blocks
 This paper adds to the comparison of PCR and PC/RORR
researched by Sappington and Sibley, Shmalensee, and Lyon.
 Similarly, the PC/RORR relates allowed revenue to firm’s cost,
capital used, and it reduces the pricing distortions by plain PCR.
 In contrast to prior research, analysis is based on optimal nonlinear tariffs where the network size is determined endogenously
 The model itself is an extension of Armstrong, Srinagesh, and
Sherman/Visscher.
 Armstrong focused on non-linear tariffs under PCR, while the
latter two focused on non-linear tariffs under RORR.
 This paper fuses both into one model and shows the comparison
to PCR/USO.
The Model
 Stylized network industry framework.
 Separate from perfect competition and assume there
is only one regulated firm operating a network,
producing one single commodity into the network.
 Using non-linear tariffs, the firm can implicitly choose
the number of customers and the aggregated
quantity purchased.
Utility Function
 (1) Utility Function
 Θ = preference
intensity of consumer
 T(x) = given tariff
 p(x, θ) = inverse
demand function
 Assume v(x, θ) = 0 and
(2)
Demand and Customer Base
 Individual demand
x(Θ,T) given that T(x) is
a monotone piecewise
differentiable function.
 Aggregated demand
X(T) and number of
customers N.
Technology and Indirect Utility
 Technology: quasiconvex function with
transformation where
I = (X,N)
 Implies no economies
of scope and constant
economies of scale
 Envelope theorem
yields indirect utility
function which is
transformed into a
revenue form
Profit Function
 Denote the factor prices
for K an L by r and w.
 Encompasses quantity
and customer base.
Second Best Solution
 Maximize unweighted sum of customers’ surplus and
firm’s profit subject to a minimum profit requirement.
 Resulting Lagrangian used to derive standard inverse
elasticity rule.
Modeling PCR, RORR, and PC/RORR
 Model PCR, RORR, and combination to examine
pricing distortions.
 Aim to analyze welfare under different methods.
 Under PCR the firm’s average tariff may not exceed
set price.
 Under RORR there is a regulatory bound on maximum
allowable rate of return on capital.
 PC/RORR uses a convex combination of both
constraints.
Price and Regulatory Constraint
 Shows price function
 If s=0 there is RORR, if s=1
there is PCR and if s€[0,1]
there is a combination
 So s represents type of
regulation
 The second equation
shows the regulatory
bound.
Lagrangian Profit and Effective Cost
Function
 Profit function derived
from constraint
lagrangian.
 Effective factor prices for
w and r which
correspond to L and K
 Effective Cost function
where L* and K* are
optimal input decisions
Optimal Tariff Rule
 Obtained by maximizing Lagrangian profit function
with respect to x(θ,s) and θ(s) (Reminder θ =
preference intensity of customer)
 Used to determine firm’s tariff under RORR, PCR and
PC/RORR
Proposition 1
 Based on tariff rule results, Baake concludes the
following:
 If the firm ears the same profit under PCR and RORR,
the number of customers is smaller under PCR, but
total quantity is higher.
Numerical Example
 Uses the following function forms for utility function
and production functions:
*Leontieff Production Functions (440!)
Results
 Superscripts W
= second best, P
= PCR and C =
PC/RORR,
respectively
 Cex = Marginal
cost of x
Results…
 PC/RORR induces firm to increase its network and
choose higher usage charges.
 Consumers with high willingness to pay are worse off
under PC/RORR.
 However, aggregate consumer’s surplus is increased
because more consumers are connected to the
network.
Universal Service Obligation
 Uses PCR, but forces a firm to serve a minimum
number of customers.
 PCR and universal service constraints put in place.
 Leading to a USO Profit Lagrangian
PCR/USO Tariff Rule
 The firm adapts its tariff so that is serves the
minimum service obligation while s=1 shows that the
formal structure is still PCR.
 This results in the firm deviating from optimal price
discrimination by providing large quantity discounts
while maintaining cost minimization.
Proposition 2
 After analyzing the tariff rule, Baake concluded:
 Suppose that the firm earns the same profits and has
to serve the same number of consumers under
PCR/USO and PC/RORR. Then, PCR/USO is welfare
superior to PC/RORR.
 PC/RORR induces higher capital investment and
subsequent higher revenue requirements, thus
PCR/USO is a more efficient way to reduce pricing
distortions implied by PCR.
Conclusion
 The paper focuses on pricing distortion implied by price
cap regulation, when using non-linear tariffs.
 Price cap regulation with a rate of return constraint leads
to less distortion and greater welfare when compared to
standard price cap regulation.
 Furthermore, price cap regulation with a universal service
requirement (assuming firm earns the same profits and has
to serve the same number of consumers) leads to less
distortion and greater welfare when compared to standard
price cap regulation with a rate of return constraint.