Testing for subadditivity of vertically integrated electric utilities.

• Author: Gilsdorf, Keith

1. Introduction

   The public policy debate over electric utility deregulation has a long history and generated a considerable amount of research. Much of this research focused on estimating the degree of scale economies in generation with little attention given to the effect vertical integration may have on cost structure. The vertical integration issue is important because most observers consider the transmission and distribution stages to be natural monopolies. According to Joskow and Schmalensee, economies of integration, if any, would link the production stages together, possibly extending natural monopoly conditions from transmission/distribution to generation even if the latter exhibited no economies of scale [11, 30].

   Thus, the deregulation issue raises an important cost structure question: what impact does vertical integration have on cost structure?(1) That is, do integration economies make the cost function subadditive? Subadditivity would imply that electric firms are multistage natural monopolies and, as a result, deregulated generation markets would not exhibit effective competition. This paper investigates the subadditivity question utilizing a multiproduct cost framework where an integrated firm is, in effect, a multiproduct firm producing an output from each production stage. To capture the effect of vertical integration on cost structure, a multistage cost function is estimated because it provides information about conditions necessary for multistage natural monopoly.

   The study also examines two other important cost structure questions. First, what impact does capacity utilization have on production costs? If deregulation proposals expand generation market areas, utilities may be better able to increase customer diversity and operate at a higher load factor. Higher load factors would allow firms to use base load plants more extensively and reduce reliance on peak load capacity. Second, what effect does the utility's sales-output mix have on production costs? Specifically, will greater specialization in retail sales rather than sales for resale result in higher or lower production costs? The paper begins with a review of the study's methodology, including the test for subadditivity, followed by a presentation of the empirical results.

2. Methodology

   In order to investigate the cost effect of vertical integration, the study utilizes a multiproduct perspective. Specifically, the analysis tests for subadditivity using a procedure developed by Evans and Heckman [8]. Suppose a utility produces two outputs: generation (G) and transmission-distribution services (T). The utility's cost function is globally subadditive at output vector [u.sub.0] = ([G.sub.0], [T.sub.0]) if:

   C([u.sub.0]) [less than] C([u.sup.*]) + C([u.sub.0] - [u.sup.*]), (1)

   for all [u.sup.*] [less than or equal to] [u.sub.0]. A cost function is additive at [u.sub.0] if C([u.sub.0]) = C([u.sup.*]) + C([u.sub.0] - [u.sup.*]) and is super-additive if "[greater than]" is inserted into the equation. Superadditivity would indicate some degree of cost diseconomies exists between outputs and entail lower production costs with further divestiture. If the cost function is additive, Evans and Heckman (E&H) state this may imply that the utility is optimally decentralized [8, 616-17].

   From a practical perspective, it is often impossible to have cost information at all output levels of [u.sup.*] [less than or equal to] [u.sup.0]. Thus, E&H suggest a local test for subadditivity. A cost function is globally subadditive if and only if it is subadditive over the observed output levels. If costs are not subadditive over this relevant range, global subadditivity can be rejected. The advantage of the E&H test is that it avoids extrapolating costs beyond the observed industry data. The limitation, however, is that local subadditivity does not ensure global subadditivity.

   To operationalize the subadditivity test, the analysis follows the procedures adopted by E&H in their study of the Bell system. A hypothetical two-firm industry configuration is set up and its total cost is compared to the single firm's total costs.

   Let the two hypothetical firms be called A and B where [u.sup.A] and [u.sup.B] represent their respective output levels. In addition, let [u.sup.A] + [u.sup.B] = [u.sub.0] and C([u.sup.A]), C([u.sup.B]), and C([u.sub.0]) represent total production cost for firms A, B, and the single firm, respectively. If C([u.sup.A]) + C([u.sup.B]) [less than] C([u.sub.0]), the cost function is superadditive at output level [u.sub.0] for the two-firm configuration. If C([u.sup.A]) + C([u.sup.B]) [greater than] C([u.sub.0]) at all other combinations of [u.sup.A] and [u.sup.B], subject to [u.sup.A] + [u.sup.B] = [u.sub.0], the cost function is subadditive at [u.sup.0] over the admissible region.

   The next step is to define the admissible region. Following E&H, the admissible region meets two constraints. First, the smallest output level per hypothetical firm for generation (G) and transmission/distribution (T) must be at least as large as the minimum observed output level for each stage, respectively ([G.sub.m], [T.sub.m]). This constraint is developed as follows. Suppose the single firm has an output level [u.sub.0] = ([G.sub.0], [T.sub.0]). To obtain output levels for hypothetical firms A and B, fractions of [G.sub.0) and [T.sub.0] will be assigned to each firm such that their sum equals the single firm's total output. That is, firm A and firm B must each produce at least [G.sub.m] and [T.sub.m] levels of output. In addition, the single firm's generation and transmission-distribution output levels in excess of twice their respective minimums, defined as [G.sup.*] and [T.sup.*], will be apportioned between firms A and B. Let [Phi] and w represent the proportion of [G.sup.*] and [T.sup.*] assigned to firm A. Thus, firm A's output vector is [u.sup.A] = ([Phi][G.sup.* ] + [G.sub.m], w[T.sup.*] + [T.sub.m]) and firm B's output vector is [u.sup.B] = ((1 - [Phi])[G.sup.*] + [G.sub.m], (1 -w)[T.sup.*] + [T.sub.m]), where [u.sup.A] + [u.sup.B] = [u.sup.0], 0 [less than or equal to] [Phi] [less than or equal to] 1, 0 [less than or equal to] w [less than or equal to] 1, and [G.sub.m] and [T.sub.m] measure the minimum observed sampe output...