Testing for Subadditivity of Vertically Integrated Electric Utilities Keith Gilsdorf

Research Questions Do integration economies make the cost function subadditive? What impact does capacity utilization have on production costs? What effect does the utility’s sales output mix have on production costs?

Methodology Gilsdorf uses a multiproduct cost framework where an integrated firm is a multiproduct firm producing an output from each production stage. In this case, the outputs are generation (G) and transmission/distribution (T) of electricity. To test for subadditivity compares estimated cost functions of firms in his sample to two hypothetical firms

Subadditivity Condition The utility’s cost function is globally subadditive at output vector u 0 = ( G 0, T 0 ) if C ( u 0 ) < C ( u* ) + C (u 0 - u* ) for all u* ≤ u 0.

Hypothetical Firms Hypothetical firm A’s and B’s output denoted by u A and u B C(u A ), C(u B ), and C(u 0 ) represent total production cost for firms A, B, and the observed single firm, respectively. If C(u A ) + C(u B ) > C(u 0 ) subject to u A + u B = u 0, then the cost function is subadditive at output level u 0 over the admissible region.

Defining the Admissible Region For the hypothetical firms Constraint One u 0 = G 0 + T 0 G 0 = (φG* + G m ) + [(1 – φ) G* + G m ] T 0 = (wT* + T m ) + [(1 – w) T* + T m ] where 0≤ φ ≤1 and 0≤w≤1 and G m and T m are the minimum observed output levels for goods G and T.

Defining the Admissible Region For the hypothetical firms Constraint Two R L < (φG* + G m ) / (wT* + T m ) < R u R L < [(1-φ) G* + G m ] / [(1-w) T* + T m ] < R u where R L and R u are the smallest and largest observed output ratios in the sample. This constraint keeps the degree of specialization for the hypothetical firms within the range of specialization observed in the sample.

Given these constraints, C(u A ) = C(φG* + G m, wT* + T m ) C(u B ) = C[(1 – φ) G* + G m,(1 – w) T* + T m ] and C(u 0 ) = C(u A +u B ) The measure of subadditivity is calculated as Sub (φ,w) = [C(u 0 ) – C(u A ) – C(u B )] / C(u 0 ) If Sub(φ,w)<0, the cost function is subadditive at u 0 for the particular φ and w combination.

Variable Description The multistage cost function contains two outputs (G and T), three input prices (wages, fuel, and capital services), and three hedonic variables (customer density, capacity utilization, and percentage of sales to ultimate customers). See pages for a more in depth discussion of variables. Note: Analysis concentrates on fossil fuel steam plants because other production technologies, like nuclear and hydroelectric, differ substantially.

Cost Function lnC = β 0 + Σ β i lnY i + Σ γ j lnP j + Σ α i lnZ i + ½ ΣΣ β ij lnY i lnY j + ½ ΣΣ γ ij lnP i lnP j + ½ ΣΣ α ij lnZ i lnZ j + ΣΣ δ ij lnY i lnP j + ΣΣ σ ij lnZ i lnP j + ΣΣ λ ij lnY i lnZ j where Y i = outputs P j = input prices Z i = hedonic variables

Results Subadditivity Test – Sixteen companies returned estimates that suggest subadditivity, but none are statistically significant. Implying integration economies do not make the multistage cost function subadditive. Capacity Utilization – Increased utilization reduces production costs in all but sixteen cases (although only ten are statistically significant). Sales-Output Mix – Sales-ouput mix estimates are negative in sixty cases (nine statistically significant). Implying production costs may fall with increased, but not complete, specialization in retail sales.

Conclusion Results imply vertically integrated utilities are not multistage natural monopolies. However, the results do not necessarily support complete industry divestiture since economies of scope between stages may exist in the absence of subadditivity. The evidence provides some support for the hypothesis that scope economies exist between retail sales and wholesale activities. A complete separation of the activities would entail a loss of efficiency. Analysis offers support for regulatory policies which encourage higher annual utilization rates, including ensuring non-discriminatory access to transmission service.