Regulatory Preferences and Two-Part Tariffs: The Case of Electricity

Presented by: Fadhila

MICHAEL C. NAUGHTON

Purpose

Develop and demonstrate a method for deriving and testing regulatory preferences within and across customer classes

Assess the impact of these preferences on price structures and regulatory effectiveness in the electric utility industry

Methodology

In order to derive the regulatory weights:

A demand model is developed which extends the existing empirical literature on multipart tariff demand estimation to allow estimation of kWh output and customer connection demand elasticities with respect to both per-unit and fixed prices

The Regulator's Constituents I

(P1,L1) denoted for two-part tariff residential customers (class 1)

Where, P1 = per-unit price for kilowatt hour (kWh) output L1 = connection charge

Class 1 assumed to vary according to the index h1 Y(h1) = pre-purchase income of consumer type h1

An individual's demand is then defined as q1 = q1 (P1, L1, h1)

For an individual who decides to purchase q1 , surplus is defined as

s1(P1,L1, h1) = v1(P1,L1, h1) – v1 (0, h1) (1)

v1(P1,L1, h1) represents the level of utility from consuming q1 v1(0, h1) represents the level of utility assuming the individual is excluded from the market for q1

The Regulator's Constituents II

Assuming that income effects are equal across inframarginal households:

Where, and are partial derivatives of Q1 ( holding membership constant), is the consumption level of marginal consumers is the average consumption level = represents the inframarginal income effect

The Regulator's Constituents III

The first equality states that a small increase in P1 has the same effect in membership as an increase of in the connection charge. Because the effect on M1 due to a change in L1 or P1 depends

only on how the post-purchase surplus of the marginal consumer has changed.

Implies that a fall in kWh demand associated with an increase in the fixed charge is the effect on membership multiplied by the marginal consumption level (an exclusion effect) plus an inframarginal income effect

The Regulator's Constituents IV The producer surplus of the regulated firm is defined

as:

Where, w is a vector of input prices measures the marginal connection cost of an additional consumer in group i measures the marginal kWh output cost to group I

Costs are explicitly a function of M since the utility must not only produce electricity, but also deliver it to each member.

The Regulators' Optimal Prices I To maximize weighted social surplus (W) where the

surplus of each customer in class i is weighted by zi(hi) and the producer surplus of the regulated firm is weighted by zu.

If zi(hi) is increasing (decreasing) over qi, then regulators favor large (small) consumers within class i. If zi(hi) is constant over qi, then regulators favor all consumers within class i equally

The weighted social surplus for customer class i is:

Differentiating with respect to Pi and Li, it can be found that:

The Regulators' Optimal Prices II To maximize the sum of weighted consumer and

producer surplus

After taking the FOC, equations can be written as:

Ramsey Numbers and Price Structures I Rewriting equations (14) and (15), & giving that and then:

Results indicate: For class i the approximate deviation in Qi from first-best Qi is proportionate to and the

approximate deviation in Mi from first-best Mi is proportionate to Gi.

If regulations have constant preferences across and within customer classes then Gi = for all i and optimal pricing then requires that the proportionate change in kWh output and customer connection be equal across all customer classes. (preferences may not be constant)

Special cases, ○ If = zi = 0 for all i and zu > 0 then = Gi = 1 for all i and equations (14) and (15) are

monopoly pricing rules. ○ If = zi = zu for all i then = Gi = 0 for all i and equations (14) and (15) represent first-best

efficient price

Estimation of Demand Elasticities I Develop a demand model that is used to derive estimates of

kWh output and connection demand elasticities with respect to the per-unit and fixed prices for each customer class.

The logarithmic specification used:

Where ,

Xi and Wi are the additional exogenous variables, and i and vi are disturbances

Estimation of Demand Elasticities II

Logarithmic transformation is appropriate for the following reasons:

• It implies that changes in prices affect the relative quantity demanded. • This is useful, given that the purpose of this demand model is to

explain aggregate demand across utilities.

• Using absolute prices and income on the right-hand side results in elasticity estimates which can vary

Data The sample is restricted to those utilities whose

service areas are contained within one state

All variables are electric utility service area specific

Li and Pi are derived for each customer class by: The monthly fixed charge is defined as the difference between

the total expenditure in the second lowest usage bill and what total expenditure would have been if all kWh output had been sold at the marginal price in this bill

The annual fixed charge is then derived by multiplying by 12.

All the elasticity estimates are significant except for the residential class cross elasticities

is less elastic in the residential class as compared to the industrial and commercial class

The inframarginal income effect of LR on QR, as measured by , is significant, when the effect is combined with the exclusion effect of LR on QR to form they jointly become insignificant.

kWh output and customer connection demand are far less sensitive to the fixed charge than to the per-unit price

Regulatory Preferences and Price Structure I

Presents estimates of per-unit and connection price-marginal cost differentials along with output-weighted () and membership weighted (Gi) Ramsey numbers for each customer class

Regulatory Preferences and Price Structure II Findings:All Ramsey numbers are significantly different from zero at the 5 percent level, except Gi in the residential class:

○ Ramsey number greater than zero indicates that producer's surplus receives a higher weight than consumers' surplus and that first-best efficient pricing can be rejected

○ If the Ramsey numbers are equal to zero within a customer class (Gi = = 0) then prices for that class are set in a first-best level.

○ If the two Ramsey numbers are equal to one within a customer class then consumers' surplus receives a zero weight ( = zi = 0) and prices for that class are set at a monopoly level.

Regulatory Preferences and Price Structure IIITo test the possibility of second-best efficient pricing:

Calculate second-best Ramsey numbers through an iterative procedure using equations (14) and (15) and the estimated demand and cost function:

find that if regulators were attempting to maximize consumers' surplus subject to the constraint that the regulated firm earn a positive profit level they would set Gi = =0.71 for all i.

Intraclass preferences can be analyzed by comparing to Gi for each class i. In both the residential and commercial classes the hypothesis was rejected ( is significantly greater than Gi at the 1 percent level in both classes)

The hypothesis that regulators have constant intraclass preferences in the industrial class cannot be rejected at any reasonable level. The results indicate that regulators favor small consumers in the residential and commercial class.

Regulatory Preferences and Price Structure IV

Commercial class is the least favored since is 95 percent larger than the residential class and 82 percent larger than the industrial class

Under second-best pricing the price structures in the residential and commercial classes make a substantial shift towards increased fixed charges and lower per-unit prices, as the preference towards small consumers is eliminated.

Substantially less change occurs in the industrial price structure when moving from current to second-best environments.

In moving from actual to monopoly price structures, the fixed charges increase substantially in all classes. With regard to per-unit prices, they increase under monopoly pricing in the residential and industrial classes and fall in the commercial class

The average prices indicate that actual average prices in the residential and industrial classes are very close to their respective second-best average price

The actual average price in the commercial class is greater than the monopoly average price. Clearly price regulation is effective for non-commercial consumers, and goes a long way in reducing monopoly power in these classes

Conclusion The results from the above application indicate that

monopoly pricing, first-best efficient pricing and second-best efficient pricing can all be rejected

However, price structures tend to favor the residential and industrial classes over the commercial class and favor small users within the residential and commercial classes

  The preference towards small users in the non-

industrial classes may reflect a concern over equity, either derived from the regulators' own social welfare ideals or due to political pressures