Price Caps, Rate of Return Constraints and Universal Service

Obligations

Author: Pio Baake

Presented by: Jared Hayden

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.

Price Cap Regulation (PCR)

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

PCR Pros and Cons

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.

Augmented PCR

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)

PC/RORR Theory

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 non-

linear 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.

Research Building Blocks

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.

The Model

(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)

Utility Function

Individual demand x(Θ,T) given that T(x) is a monotone piecewise differentiable function.

Aggregated demand X(T) and number of customers N.

Demand and Customer Base

Technology: quasi-convex 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

Technology and Indirect Utility

Denote the factor prices for K an L by r and w.

Encompasses quantity and customer base.

Profit Function

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.

Second Best Solution

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.

Modeling PCR, RORR, and PC/RORR

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.

Price and Regulatory Constraint

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

Lagrangian Profit and Effective Cost Function

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

Optimal Tariff Rule

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.

Proposition 1

Uses the following function forms for utility function and production functions:

Numerical Example

*Leontieff Production Functions (440!)

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.

Results…

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

Universal Service Obligation

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.

PCR/USO Tariff Rule

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.

Proposition 2

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.

Conclusion