Pricing Efficiency Under Rate-of-Return Regulation: Some Empirical Evidence from the Electric Utility Industry

1. Pricing Efficiency Under Rate-of-Return Regulation: Some Empirical Evidence from the Electric Utility Industry Article by Paul M. Hayashi, Melanie Sevier, and John M. Trapani

2. Introduction • Purpose: to develop a method for testing the rate-of-return formulation of the quasi-optimal pricing rule and apply the methodology to a sample of electric utility firms. • Approach: specify a regulated cost function for the production of electric power which reflects the cost of production under rate-of-return regulation and the role of above normal profits the firm is permitted to earn on its capital stock. • Data: cross-sectional sample of 32 privately-owned electric utility firms- the firms selected employ only conventional fossil fuel methods of production and have an insignificant amount of purchase power. Data is from 1965 and 1970.

3. Rate of Return Regulation and Welfare Maximization • Goal: identify the welfare-maximizing criterion for pricing various outputs of a multiproduct firm facing a rate-of-return to capital constraint. • Assumption:The regulatory body determines the “fair rate-of-return to capital”, s, which is generally assumed to fall between the market cost of capital, r, and the rate achievable at the monopoly profit maximization solution, rπ. That is,rπ > s > r.

4. Rate of Return Regulation and Welfare Maximization • Once s has been determined, the next step is to find quasi-optimal prices by solving the optimization problem of maximizing consumer plus producer surplus subject to the constraint that the firm will earn the maximum allowable profit. • FOC’s produce the quasi-optimal pricing rule for welfare-maximization in the presence of a rate-of-return regulatory constraint: R= total revenue S= consumer surplus Cr= regulated cost C*= total production cost K*= firm’s capital choice under ROR regulation Pi= price of the ith output εi= absolute value of the price elasticity of demand for the ith output MCir= regulated marginal cost

5. Rate of Return Regulation and Welfare Maximization • Note the relation between regulated marginal cost and marginal cost to the producing unit: • Regulated marginal cost is the marginal cost to society involving MCi*, the production cost incurred under ROR regulation, plus the excess valuation of additional capital employed. • Variant of the quasi-optimal pricing rule: • The new term on the end reflects the excess capital valuation under ROR regulation. • If s=rthen this term disappears. • If s>r and K is a normal input then the presence of ROR constraint will require a greater different between price and marginal cost at the optimal solution.

6. Empirical Model • Multiproduct cost function for the typical privately-owned electric utility firm regulated on the basis of a fair rate-of-return to capital: • The regulated cost function is not homogeneous of degree one in actual factor prices so Shephard’s lemma must be modified in order to identify the minimum cost input levels f= index of fuel cost qi= various outputs by class of customer δ= Lagrangian multiplier of the ROR constraint K, L, F= cost minimizing input levels

7. Empirical Model • Regulated cost function: • Regulated cost function can be expressed as: • When regulation is effective, Cr will be greater than C, the frontier minimum cost of production, due to the input distortions from the binding ROR constraint and the valuation of capital at s, the allowable ROR to capital. K*= constrained profit maximizing level of capital input

8. Empirical Model • We can specify the multi-product firm cost by a translogfunction:

9. Empirical Model • Factor cost share equations for labor and fuel: • Regulated marginal cost: • Regulated marginal cost curve:

10. Empirical Model Residential Commercial Industrial

11. Cost Equation Results • Note: residential and commercial output were combined into the single output variable q1. This assumes the costs of production is the same for both. • Note: the interaction term is not significant in 1965, but is significant in 1970. This may suggest that economies of scope were not present in this industry until output reached a certain level after 1965. However, tests for economies of scope failed for both years.

12. Cost Equation Results • The estimates of MCrreflect higher MC of producing power for residential/commercial customers than for industrial. • Regulated MC is higher than measured MC in each year for each customer class. This suggests there are regulatory effects present in MC which should not be ignored. This combined with the significance of the regulatory variables in the estimated cost equation give strong support to the appropriateness of ROR for this industry.

13. Demand Equation Results: Residential Customers • The price elasticity of demand (lnPIR) estimates are consistent with other studies of residential demand for electricity. • The price of gas (lnPGR) and per capita income (lnYP) do not appear to be significant determinants of residential electric power consumption. This may be because income was measured in a state wide basis rather than the service area. • All other variables are significant with the appropriate sign.

14. Demand Equation Results:Commercial Customers • The price of gas was again found to be insignificant for commercial customers. • Weather (lnCDD) plays less of a role in determining demand for commercial customers than for residential.

15. Demand Equation Results:Industrial Customers • For industrial customers, the price of gas was found to be significant, unlike in the cases for residential and commercial customers. • The explanatory power for this model was the lowest of the 3, however it still explains 60% of the variation in sales.

16. Tests for Pricing Efficiency • The percentage markup for residential and commercial customers is similar at about 38-43%, but lower for industrial customers at 25-32%. • If the weighted markup (seen in last column) is the same for each customer class, then the price structure is quasi-optimal. The bottom table gives the results of F-Tests for pricing efficiency. In all cases but one, the null hypothesis of equal weighted markups is rejected so we conclude that pricing is not quasi-optimal. • Result: welfare improvements might be possible under an alternative price structure by class of customer.

17. Tests for Pricing Efficiency • In order to determine optimal prices once the allowable ROR was established estimates of regulated MC and the price elasticity of demand by customer class would be necessary. Then one must solve for prices which satisfy the following conditions: • Using the sample data the authors search for optimal prices. All variables were set to their mean values and prices were started at their mean levels and restricted to a range to include only those prices which were reasonable in light of production costs. The results are shown on the following table.

18. Tests for Pricing Efficiency • The results show that commercial rates appear to have been set too high relative to residential rates for both years. • Commercial rates should be lowered by 20% and 32% in 1965 and 1970 respectively. This would produce a significant increase in sales given the elastic demand of the this customer class. • Residential rates should be raised 8.5% (‘65) and 21% (‘70). This would reduce residential sales by 9.8% (‘65) and 24% (‘70). • Industrial rates should be increased 8% (‘65) and 4.7% (‘70) which would reduce industrial sales by 19% (‘65) and 17% (‘70). • The overall effect on total output would be insignificant in 1965 and would slightly increase in 1970. The results suggest that regulators have permitted rate structures to favor the interests of residential consumers primarily at the expense of commercial users. This is consistent with the fact that residential users are normally well organized politically and are thus effective at holding their rates below optimum. Industrial users see favorable treatment partly because of lower costs and higher demand elasticity and also because of political organization as well as spillover effects of expanded industrial growth.

19. Conclusions • The price structure of electricity by class of customer for the firm in the same is not quasi-optimal and welfare improvements might be possible under alternative prices for the customer classes. • Commercial user rates have been too high relative to residential, and to a lesser extent, industrial rates. Adjustment to the optimal solution requires a lowering of commercial rates and increases in residential and industrial rates. • The outcome is fairly consistent with the general theory of regulationin that residential and industrial customers are better organized politically and effective in holding their rates below the social optimum levels. Commercial users, on the other hand, tend to be less organized and more poorly represented in the rate-making process.