1. Testing for subadditivity of Vertically Integrated Electric Utilities

2. The paper by Gilsdorf examines the subadditivity question using a multi-product cost framework, where the vertically integrated firm is in effect a multi-product firm producing an output from each production stage.

3. Two other questions: – 1. What impacts does capacity utilization have on production costs? – 2. What effect does the utility’s sales- output mix have on production costs?

4. Suppose a utility has two outputs, generation (G) and transmission-distribution (T) The cost function is subadditive for output vector if: C(u o ) < C(u 0 ) + C(u 0 -u * ) for all u * ≤ u 0

5. Evans and Heckman suggest is sufficient to a local test for subadditivity is all that is required. – A cost function is globally subadditive if and only if it is subadditive over observed output levels. – This means no extrapolating costs.

6. Given all constraints Sub (φ, w) = (C(u 0 ) – C(u A ) – C(u B ))/C(u 0 ) Sub (φ, w) = 0 Additive Sub (φ, w) > 0 Supperadditive Therefore Sub (φ, w) ≥ 0 we will reject the subadditivity hypothesis

7. Multi-stage cost function – Two outputs – Generation and transmission – Three inputs – Wages, fuel, and capital services – Three hedonic variables – Customer Density (DN), capacity utilization (CU), and percentage of total sales to ultimate consumers (PULT)

8. This yields the following equation (3)

9. Shepherd's Lemma provides the basis for the cost share equations. (4)

10. Combining (3) and (4) we get

11. Impact of capacity utilization and sales mix on cost structure we use Since they are both negative increases in capacity utilization and specialization in retail sales reduces production costs.

12. Conclusions Study found that vertically integrated electric utilities are not subadditive implying they are not multistage natural monopolies. The study also offers support for regulatory policies which encourage higher annual utilization rates, including ensuring non- discriminatory access to transmission service.