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http://clevelandfed.org/research/workpaper/index.cfm Best available copy Working Paper 8509 TOTAL FACTOR PRODUCTIVITY AND ELECTRIC UTILITIES REGULATION by Phi 1i p I s r a i l e v i c h Working papers o f t h e F e d e r a l Reserve Bank o f C l e v e l a n d are preliminary materials, circulated to stimulate d i s c u s s i o n and c r i t i c a l comment. The views expressed h e r e i n a r e t h o s e o f t h e a u t h o r and n o t n e c e s s a r i l y those o f t h e F e d e r a l Reserve Bank o f C l e v e l a n d or o f t h e Board o f Governors o f t h e Federal ReserveeSystem. The a u t h o r would l i k e t o t h a n k Amy D u r r e l l , who provided valuable research assistance. December 1985 Federal Reserve Bank o f C l e v e l a n d http://clevelandfed.org/research/workpaper/index.cfm Best available copy Introduction Regulators base electricity prices or rates on the average operating cost of producing electricity and on a "fair" rate of return on capital for a given year ' . There are two shortcomings with this procedure. First, it does not consider the dynamics of average total costs and its components. Regulations may influence the incentives of utilities to innovate and overcapitalize as well as the demand for electricity which, in turn, may influence utility operating costs. Second, regulators consider only tangible input factors (capital, labor, fuel, material) in the calculation of average costs. Intangible input factors (workers' discipline, managerial skills, returns to scale, for example) are not considered in the regulatory price mechanism because they have no explicit and measurable prices and their effect on utility output and costs is difficult to measure. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Nevertheless, t h e impact o f i n t a n g i b l e f a c t o r s on c o s t s and u t i l i t y p r o f i t s may be s u b s t a n t i a l . Moreover, t h e i n a b i l i t y t o b r i n g i n t a n g i b l e i n p u t f a c t o r s i n t o t h e r a t e - s e t t i n g process may c r e a t e t h e wrong i n c e n t i v e s f o r a u t i l i t y t o o p e r a t e i n t h e most s o c i a l l y e f f i c i e n t way. One s o l u t i o n t o these problems i s t o examine t h e components o f t o t a l f a c t o r p r o d u c t i v i t y (TFP). These components i n c l u d e t h e i n d i v i d u a l i n p u t p r o d u c t i v i t i e s , a r e t u r n s t o s c a l e e f f e c t , and an average c o s t (AC) s h i f t term. The i n d i v i d u a l i n p u t p r o d u c t i v i t i e s a r e t h e t a n g i b l e i n p u t c o n t r i b u t i o n s , t h e r e t u r n s t o s c a l e t e r m i d e n t i f i e s one o f t h e i n t a n g i b l e f a c t o r s , and t h e AC s h i f t t e r m i n c l u d e s t h e o t h e r i n t a n g i b l e e f f e c t s . Using t h i s decomposition, r e g u l a t o r s may o b t a i n a b e t t e r i d e a a b o u t t h e sources o f AC change. To measure TFP, economists t r a d i t i o n a l l y u t i l i z e t h e long- run p r i c e o f c a p i t a l services. T h i s paper argues t h a t f o r t h e purpose o f r e g u l a t i o n , t h e shadow r e n t on c a p i t a l , which i s t h e s h o r t - r u n measure o f t h e v a l u e o f c a p i t a l s e r v i c e s , i s more a p p r o p r i a t e . T h i s i s n o t a new concept -- r e g u l a t o r s have used t h e shadow c a p i t a l r e n t measure f o r decades, b u t i t s use w i t h t h e TFP c a l c u l a t i o n s , which have t r a d i t i o n a l l y employed a long- run c a p i t a l r e n t measure, i s new. An u n d e r s t a n d i n g o f t h e d i f f e r e n c e between t h e two n o t i o n s o f c a p i t a l r e n t h e l p s t o d i s t i n g u i s h a s h o r t - r u n s h i f t i n average c o s t s f r o m a long- run s h i f t . I n t h e second p a r t o f t h i s paper, t h e r e g u l a t o r y process i s b r i e f l y d e s c r i b e d and t h e u s e f u l n e s s o f TFP i n d i c a t o r s t o r e g u l a t o r s i s discussed. TFP and r e t u r n - t o - s c a l e e f f e c t s a r e e s t i m a t e d f o r seven m a j o r Ohio " u t i l i t i e s http://clevelandfed.org/research/workpaper/index.cfm Best available copy ( w h i c h produce about 90 p e r c e n t o f t h e e l e c t r i c i t y for t h e s t a t e ) o v e r t h e 1964-82 p e r i o d . The d a t a and t h e i r sources a r e d e s c r i b e d i n Appendix 111. The t h e o r e t i c a l d i s c u s s i o n of t h e s h o r t r u n average c o s t (AC) s h i f t ' i s I t i s argued i n t h e f o u r t h p r e s e n t e d i n t h e t h i r d s e c t i o n o f t h i s paper. s e c t i o n t h a t d u r i n g t i m e s when r a t e h e a r i n g s a r e h e l d f r e q u e n t l y , a u t i l i t y ' s i n c e n t i v e f o r p r o d u c t i v i t y i n c r e a s e s may d e c l i n e . The R e g u l a t o r y Process A u t i l i t y ' s a c c o u n t i n g p r o f i t , which i s t h e p r i m a r y concern o f t h e P u b l i c U t i l i t y Commission o f O h i o (PUCO), i s c a l c u l a t e d as: n=R-OC where R i s o p e r a t i n g revenue and OC i s t h e o p e r a t i n g c o s t . Whenever a r a t e change i s requested, PUCO c a l c u l a t e s t h e u t i l i t y ' s " f a i r " r e t u r n on c a p i t a l as: n , = B * r where r i s t h e " f a i r " r a t e of r e t u r n and B i s t h e r a t e base o r t h e book v a l u e o f net capital . The d i f f e r e n c e between t h e a c c o u n t i n g p r o f i t , n, and t h e f a i r p r o f i t , n,, i s t h e b a s i c reason f o r t h e r a t e change; e l e c t r i c i t y r a t e s a r e s e t by t h e r e g u l a t o r t o equate n w i t h n, on t h e d a t e t h e h e a r i n g i s h e l d . As t i m e passes, n may d e v i a t e f r o m n, i f i n p u t p r i c e s , e l e c t r i c i t y demand, and o t h e r f a c t o r s change, b u t a r a t e change t o re- equate n w i t h n, i s n o t made u n t i l t h e n e x t r a t e h e a r i n g . A u t i l i t y r e q u e s t s a p r i c e change h e a r i n g when i t i s convinced t h a t i t s p r o f i t , TI i s s m a l l e r t h a n n,. If PUCO e s t a b l i s h e s t h a t n exceeds a reasonable r e t u r n on c a p i t a l , say sB, t h e n PUCO.calls f o r a r a t e decrease h e a r i n g . Such h e a r i n g i s u s u a l l y prompted by consumer advocates, when n 2 sB i s observed. adjustment mechanism can be d e s c r i b e d as This r e g u l a t o r y p r i c e http://clevelandfed.org/research/workpaper/index.cfm Best available copy P < <sB (no rate change) if n, P o < P l5 P,*1.2 if n < P, < Po if n > sB (rate decrease hearing). n n, (rate increase hearing)' Due to the passive nature of the regulatory process, the last constraint is observed very rarely. This issue is addressed later in the text. The rate increase hearing is the most common one. In this case, electricity price increases from Po to P I . At first blush, this rate-setting scheme appears sensible. It seems ,reasonably efficient to allow utilities to pass along operating costs. However, there are potentially serious problems related to consumer reactions to rate increases and to the types of incentives given to utilities. First, rate increases may lower the consumption of electricity, which may reduce n below n, and trigger a rate increase, which in turn may lower consumption and trigger another rate increase and so on. That is, the proper response to falling utility profits because of lower demand may not be to raise rates. Second, utilities may be able to effect rate increases by overcapitalizing, which affects their rate base B. Indeed, rate increases lower the risk of capital investment below the risk level of nonregulated industries, clearly giving utilities the incentive to overcapitalize. Finally, the ability to obtain rate increases because of operating cost increases originating from productivity declines suggests that utilities may not have the incentive to raise productivity. Thus, not all AC increases should be treated equally. Increases in AC due to input price increases and to environmental regulation, for example, http://clevelandfed.org/research/workpaper/index.cfm Best available copy s h o u l d be passed on, w h i l e i n c r e a s e s due t o i n e f f i c i e n t c a p i t a l investment d e c i s i o n s and i n c r e a s e s t h a t may l e a d t o a long- run d e c l i n e i n u t i l i t y revenues s h o u l d n o t be passed on t o consumers. I t should be c l e a r t h a t i t i s i m p o r t a n t t o be a b l e t o d i s t i n g u i s h among t h e causes of AC change. In t h e f o l l o w i n g two p a r t s o f t h e paper, a s e t o f measures t h a t e x p l a i n s t h e c o s t change as a weighted sum o f d i f f e r e n t economic f a c t o r s , based on a TFP approach, i s p r o v i d e d . A Simple T o t a l F a c t o r P r o d u c t i v i t y Measure f o r Ohio E l e c t r i c U t i l i t i e s We b e g i n t h e d i s c u s s i o n b y r e l a t i n g AC t o o p e r a t i n g revenue. Operating revenue i n c l u d e s n e t income and o p e r a t i n g c o s t s : (1) R = B*~K + LorL + F * ~ E+ M * ~ M , where r K i s t h e r a t e o f r e t u r n on c a p i t a l , computed as r K= w/B w i t h IT c a l c u l a t e d as a r e s i d u a l between OC, and R L, E, and M a r e t h e number o f employees, f u e l (energy) consumption i n p h y s i c a l u n i t s , and m a t e r i a l , computed as M = ( m a t e r i a l expense)/r , r e s p e f i t i v e l y used i n t h e p r o d u c t i o n o f e l e c t r i c i t y . r L , r E , and r~ a r e t h e average p r i c e s o r wage r a t e s f o r t h e corresponding inputs. When r, i n ( 1 ) i s equal t o t h e f a i r r a t e o f r e t u r n on c a p i t a l , revenue i s equal t o c o s t and n equals w, from t h e r e g u l a t o r ' s p o i n t o f view. I n a d d i t i o n , t h e p r i c e o f e l e c t r i c i t y i s equal t o t o t a l average c d s t , a c o n d i t i o n we w i l l m a i n t a i n i n t h i s p a r t o f t h e paper. Later, t h i s assumption i s r e l a x e d by t a k i n g i n t o account the d e v i a t i o n o f r k from t h e http://clevelandfed.org/research/workpaper/index.cfm Best available copy f a i r r e t u r n and t h e d e v i a t i o n o f t h e f a i r r e t u r n f r o m t h e long - run c o s t o f capital. Changes i n average c o s t s can be decomposed i n t o changes i n i n p u t f a c t o r c o s t s and changes i n TFP. A c c o r d i n g t o K e n d r i c k (19731, p. 32, "The TFP r a t i o i n d i c a t e s t h e r e l a t i o n s h i p between r e a l p r o d u c t i n a g i v e n year t o t h e r e a l p r o d u c t t h a t would have been produced ( r e a l f a c t o r c o s t ) i f t h e p r o d u c t i v e e f f i c i e n c y o f t h e f a c t o r s had been t h e same i n t h e g i v e n year as i n t h e base y e a r . " Qc The TFP r a t i o i s : A=Q/Qc, i s r e a l f a c t o r c o s t i n t h e base y e a r . where Q i s r e a l o u t p u t and Taking t h e t i m e d e r i v a t i v e o f t h e above e q u a t i o n and d i v i d i n g i t by A, one d e r i v e s : ( * " ) i n d i c a t e s p r o p o r t i o n a l r a t e o f change. AO=QO-QC0 . Where The d i s c r e t e f o r m o f O Q c is measured by t h e Tornqui s t a p p r o x i mation: QcO=Cs, iO (2) where s , i s t h e c o s t share i n t h e base year o f t h e i - t h i n p u t and i i s t h e amount o f t h e t a n g i b l e i n p u t f a c t o r employed, such as c a p i t a l (K), l a b o r ( L ) , energy (E) and m a t e r i a l ( M ) . S u b s t i t u t i n g ( 2 ) i n t o ( I ) ,t h e TFP r a t e of change i s measured as a r e s i d u a l growth o f o u t p u t t h a t cannot be e x p l a i n e d by t h e growth o f t a n g i b l e i n p u t s : (3) A" = Q O - I s ,i O T h i s TFP measure i g n o r e s t h e impact o f t h e i n t a n g i b l e i n p u t f a c t o r s . A b e t t e r TFP measure can be d e r i v e d by e l i m i n a t i n g one o f these i n t a n g i b l e factors, O t h e r e t u r n s - t o - s c a l e e f f e c t f r o m A i n ( 3 ) , l e a v i n g a new r e s i d u a l denoted as Do as t h e new TFP measure. This decomposition o f TFP can b e s t be demonstrated w i t h t h e use o f a c o s t f u n c t i o n f o l l o w i n g G o l l o p and Roberts (1981). (4) L e t t h e c o s t f u n c t i o n be: C = G ( r L , r ~ r, ~ r , ~ Q,, T) http://clevelandfed.org/research/workpaper/index.cfm Best available copy where G i s t h e minimal c o s t f u n c t i o n f o r each e l e c t r i c u t i l i t y . maximizes p r o f i t by o p t i m i z i n g t h e c h o i c e o f i n p u t f a c t o r s . A utility Differentiating ( 4 ) i n r e s p e c t t o t i m e one d e r i v e s : where i = K, L, E and M. A c c o r d i n g t o Sheppard's lemma f o r a c o s t m i n i m i z i n g f i r m ( a G / a r i > = i, where i i s i n p u t f a c t o r . Applying Sheppard l s lemma t o ( 5 > , one d e r i v e s : 1 dC= C r i + I - ' Cdt c ri dri dt +aGQ@aQcQdt aG 1 atc then: C0 (6) = C sir 0 i + Ec,QO + Do I where Ec, = aG Q i s t h e e l a s t i c i t y o f c o s t w i t h r e s p e c t t o o u t p u t , and aQ c Do = -aG 1 i s the p r o p o r t i o n a t e s h i f t o f the cost f u n c t i o n over time. at c U s i n g t h e e x p r e s s i o n f o r t o t a l c o s t , we can d e f i n e t h e dynamic r e 1 a t i o n s h i p between average c o s t and i t s components. O O Si nce AC=C/Q, O AC =C -Q , then a c c o r d i n g t o ( 6 ) : The change i n average c o s t , h o l d i n g i n p u t f a c t o r p r i c e s f i x e d , i s due t o two f a c t o r s : E - 1 If Ec, Ec, Do, which i s a dynami-c source o f economic g r o w t h and , which i s a s t a t i c source o f economic g.rowth o r s c a l e e f f e c t . < 1, t h e n average c o s t w i l l d e c l i n e w i t h t h e r i s e o f o u t p u t . If > 1 , average c o s t w i l l i n c r e a s e . I n t h e case o f c o n s t a n t r e t u r n s t o http://clevelandfed.org/research/workpaper/index.cfm Best available copy scale, EcQ = 1 , average c o s t i s n o t a f f e c t e d by t h e change i n o u t p u t . E q u a t i o n ( 7 ) can be d i r e c t l y r e l a t e d t o TFP, d e r i v e d f r o m e q u a t i o n ( 3 ) . To i l l u s t r a t e t h e r e l a t i o n s h i p between t h e change i n c o s t and t h e change i n t h e p r o d u c t i o n f u n c t i o n , we proceed as f o l l o w s . Totally differentiating t h e c o s t a c c o u n t i n g i d e n t i t y w i t h r e s p e c t t o t i m e , one d e r i v e s : Then t h e p r o p o r t i o n a l change i n average c o s t i s : The change i n TFP i s a d i f f e r e n c e between o u t p u t g r o w t h and a d i v i s i a i n d e x o f i n p u t g r o w t h (see e q u a t i o n ( 3 ) ) , t h e r e f o r e : ( 8 ) -A0 = AC - C s i r , O O s u b s t i t u t i n g ( 7 ) i n t o ( 8 ) and changing s i g n (9) A " = ( 1 - EcQ>QO- Do E q u a t i o n 9 shows t h a t t h e TFP measure i n ( 2 ) has a r e t u r n s - t o - s c a l e b i a s . The sources o f economic g r o w t h o f t h e seven m a j o r O h i o u t i l i t i e s a r e q u a n t i f i e d i n t h e dual ( c o s t ) form." u s i n g an e s t i m a t e o f Ec, An e s t i m a t e o f D can be made by c a l c u l a t e d b y G o l l o p and R o b e r t s (1981). They found t h a t Ec, v a r i e d between 0.7 and 0 . 9 i n t h e i r sample o f e l e c t r i c u t i l i t i e s which i n c l u d e d f o u r o f t h e seven m a j o r O h i o u t i l i t i e s . f o l l o w i n g c a l c u l a t i o n s , we use a v a l u e o f 0 . 8 f o r EcQ. For t h e We f i r s t d i s c u s s http://clevelandfed.org/research/workpaper/index.cfm Best available copy t h e components o f t h e change i n AC o v e r t i m e . Four d i s t i n c t p e r i o d s o f e l e c t r i c i t y p r i c e and consumption b e h a v i o r o v e r t h e 1964-1982 i n t e r v a l were observed. W i t h i n each p e r i o d , t h e d i r e c t i o n o f p r i c e s (AC) and s a l e s o f e l e c t r i c i t y changes were t h e same f o r each u t i l i t y i n t h e sample. f o u r s u b p e r i o d s a r e 1964-1968, 1969-1973, 1974- 1979 and 1980- 1982. These Price and t o t a l s a l e s f i g u r e s f o r a l l seven u t i l i t i e s a r e p l o t t e d i n c h a r t 1. I n t h e f i r s t p e r i o d , 1964-1968, t h e average p r i c e o f e l e c t r i c i t y was f a 1 1i n g and s a l e s were r i s i n g . I n t h e second and t h i r d p e r i o d s , 1969-1973 and 1974-1979, e l e c t r i c i t y consumption i n c r e a s e d b u t p r i c e s a l s o i n c r e a s e d . I n 1969-1973 p e r i o d , t h e i n c r e a s e i n s a l e s was g r e a t e r t h a n i n t h e p r e v i o u s p e r i o d , b u t i n 1974-1979 p e r i o d e l e c t r i c i t y consumption f e l l c o n s i d e r a b l y . F i n a l l y , i n t h e t h i r d p e r i o d , 1980- 1982, e l e c t r i c i t y consumption d e c l i n e d f o r t h e f i r s t t i m e i n O h i o ' s h i s t o r y and p r i c e s i n c r e a s e d a t t h e f a s t e r r a t e than i n t h e previous periods. The sources o f t h i s b e h a v i o r can be i d e n t i f i e d b y decomposing AC i n t o t h e c o n t r i b u t i o n s made b y p r i c e changes of t a n g i b l e i n p u t s , b y t h e r e t u r n s - t o - s c a l e e f f e c t , and by t h e s h i f t o f t h e c o s t c u r v e o v e r t i m e u s i n g (7). T h i s i s shown i n t a b l e 1. I n t h e 1964-1968 p e r i o d , t h e s c a l e e f f e c t and Do i n d i c a t o r o f TFP were t h e m a j o r c o n t r i b u t o r s t o t h e d e c l i n e o f AC. W i t h o u t these e f f e c t s , t h e t a n g i b l e i n p u t p r i c e changes would have r a i s e d AC by 1.5 p e r c e n t , i n s t e a d o f t h e observed d e c l i n e of 1.5 p e r c e n t . I n the 1969- 1973 p e r i o d , t h e c o n t i n u i n g i n c r e a s e o f s a l e s o f e l e c t r i c i t y l o w e r e d AC by 1.2 p e r c e n t f r o m t h e r e t u r n s - t o - s c a l e e f f e c t . Do a l s o r e v e r s e d i t s e f f e c t f r o m t h e p r e v i o u s p e r i o d , r a i s i n g AC b y 1.2 p e r c e n t . I n the 1974- 1979 p e r i o d , t h e s c a l e e f f e c t on AC was l e s s t h a n a p e r c e n t a g e p o i n t http://clevelandfed.org/research/workpaper/index.cfm Best available copy http://clevelandfed.org/research/workpaper/index.cfm Best available copy ' Table 1 Sources o f Change o f AC f o r O h i o U t i l i t i e s Average Annual Rates f o r t h e P e r i o d 1964-68 O 1969-73 1974-79 1980-82 Change i n average c o s t AC - 0.015 0.057 0.130 0.120 AC c u r v e s h i f t Do - 0.012 0.012 0.029 0.036 Return to scale e f f e c t (EcQ-l)QO - 0.018 - 0.028 - 0.007 0.007 Input price effect o f capital sK.r; -0.002 -0.005 - 0.000 0.004 Input price effect o f 1a b o r sL.r; 0.005 0.010 0.008 0.010 Input price effect o f energy sE.r: 0.000 0.034 0.076 0.041 Input price effect o f m a t e r i a1 sM.rl 0.01 1 0.018 0.025 0.022 and Do r a i s e d AC by 2.9 p e r c e n t . F i n a l l y , i n t h e 1980-1982 p e r i o d , consumption o f e l e c t r i c i t y d e c l i n e d , f o r c i n g u t i l i t i e s away f r o m t h e o p t i m a l s c a l e o f p r o d u c t i o n and i n c r e a s i n g AC b y .07 p e r c e n t and Do i n c r e a s e d i t s c o n t r i b u t i o n t o t h e AC i n c r e a s e by 3.6 p e r c e n t . The i m p a c t o f o t h e r i n t a n g i b l e f a c t o r s on AC was n e g a t i v e i n t h e f i r s t p e r i o d (DO<O). T h i s was p o s s i b l y due t o improvements i n e a r l i e r - i n s t a l l e d t e c h n o l o g i e s and t o t h e i n t r o d u c t i o n o f more e f f i c i e n t generators.. In later p e r i o d s , f e w e r new g e n e r a t o r s were i n s t a l l e d , c a u s i n g a slowdown i n t h e d e c l i n e o f AC. I n t h e 1970s, most O h i o u t i l i t i e s were b u i l d i n g n u c l e a r p l a n t s , which p o s s i b l y l i m i t e d r e s o u r c e s f o r t h e improvement o f u t i l i z e d facilities. T h i s p o s s i b i l i t y , p l u s t i g h t e r r e g u l a t i o n s on a i r qua1 it y may have caused e i t h e r t h e d e c l i n e o f TFP (DO>O) or t h e i n c r e a s e i n AC. http://clevelandfed.org/research/workpaper/index.cfm Best available copy C a p a c i t y U t i l i z a t i o n , R e g u l a t o r y Lag, and a SRAC s h i f t . I n t h i s s e c t i o n Do i s decomposed f u r t h e r i n t o a c a p a c i t y u t i l i z a t i o n e f f e c t and a r e g u l a t o r y l a g e f f e c t . The r e g u l a t o r y l a g a r i s e s because r a t e r e q u e s t s a r e made o n l y a f t e r c o s t s have changed enough t o w a r r a n t a r a t e increase. Thus, r e g u l a t o r y l a g , t h r o u g h c a p i t a l r e n t s and revenues, a f f e c t s b o t h AC and TFP e s t i m a t e s . I n t h e p r e v i o u s s e c t i o n , TFP was c a l c u l a t e d u s i n g t h e l o n g - r u n assumption o f c o s t and revenue e q u a l i t y . i f t h e u t i l i t y pays t h e long- run p r i c e , p k , o f c a p i t a l . T h i s assumption h o l d s I t can be measured u s i n g t h e Christensen- Jorgenson (1969) r e n t a l p r i c e index, b u t because t h e p r i c e o f c a p i t a l i s s e t by t h e r e g u l a t o r as t h e f a i r r a t e of r e t u r n on c a p i t a l , i t may n o t be equal t o t h e long- run p r i c e o f c a p i t a l P k . Thus, o u r e s t i m a t e s o f AC and TFP w i l l be i n c o r r e c t i f P k does n o t equal t h e f a i r r a t e o f return. I n t e r e s t i n g l y , i t t u r n s o u t t h a t these c a p i t a l p r i c e d i s c r e p a n c i e s r e f l e c t economic measures o f c a p a c i t y u t i l i z a t i o n . A detailed explanation o f t h i s phenomenon, p r o v i d e d by Berndt and Fuss(1982>, i s presented below. The k e y n o t i o n i n t h e Berndt- Fuss approach i s t h e f i r m ' s c a p a c i t y l e v e l o f output. The c a p a c i t y l e v e l o f o u t p u t Q* i s c h a r a c t e r i z e d by t h e t a n g e n t i a l p o i n t o f t h e long- run average c o s t (LRAC) curve and t h e s h o r t - r u n average c o s t (SRAC) c u r v e . If t h e o u t p u t p r i c e i s h i g h e r than t h e LRAC a t p o i n t Q*, f i r m w i l l o p e r a t e i n t h e r e g i o n Q*<Q i n o r d e r t o maximize p r o f i t s . case, t h e company o v e r u t i l i z e s i t s q u a s i - f i x e d c a p i t a l . the I n this If t h e p r i c e o f t h e o u t p u t i s lower than t h e LRAC a t p o i n t Q*, then t h e f i r m w i l l o p e r a t e a t t h e l e v e l Q<Q* i n o r d e r t o m i n i m i z e l o s s e s . u n d e r u t i l i z a t i o n o f quasi- fixed capital. This w i l l l e a d t o t h e Capacity u t i l i z a t i o n , according t o http://clevelandfed.org/research/workpaper/index.cfm Best available copy B e r n d t and Fuss, can then be measured by q = ( Z k 1 P k ) , where Z k i s t h e expected shadow r e n t a l p r i c e o f c a p i t a l . Thus t h e problem o f measuring c a p a c i t y u t i l i z a t i o n becomes one o f measuring t h e shadow p r i c e o f c a p i t a l . B e r n d t and Fuss(1982,p. 28) argue " . . . t h e As v a l u e o f s e r v i c e s f r o m stocks o f t h e q u a s i - f i x e d i n p u t s should be a l t e r e d r a t h e r than t h e i r q u a n t i t y . " A t the o u t p u t l e v e l Q*, t h e shadow p r i c e o f c a p i t a l i s equal t o t h e long- run p r i c e o f c a p i t a l , Z k =P k , and t h e r e f o r e , q = l . Nevertheless, i f the f i r m increases i t s o u t p u t above Q*, a d d i t i o n a l u n i t s of c a p i t a l would i n c r e a s e SRAC, meaning t h a t t h e f i r m o v e r u t i l i z e s i t s c a p i t a l and t h e r e f o r e i s w i l l i n g t o pay more f o r i t s q u a s i - f i x e d c a p i t a l t h a n t h e market p r i c e , Z k > P k , and q > l . To make t h i s t h e o r y o p e r a t i o n a l , o p e r a t i o n a l i z e t h i s t h e o r y , one needs a measure f o r t h e c a p i t a l r e n t , Z k . Hul t e n (1983) argues t h a t t h e r e s i d u a l income accounted as a d i f f e r e n c e between revenue and v a r i a b l e c o s t p e r u n i t o f c a p i t a l i s an e s t i m a t e o f Z k , which i s t h e payment f o r a u n i t o f c a p i t a l a t time t. Zk't' -. = P ( t > *Q(t> - C r i ( t > * i ( t ) , K( t ) where i = L,E,M I n t h e s h o r t r u n , the f i r m minimizes r e s t r i c t e d v a r i a b l e c o s t s c o n d i t i o n a l on v a r i a b l e f a c t o r s p r i c e s , t h e amount o f q u a s i - f i x e d c a p i t a l , and o u t p u t : where i = L, E, M, and P k ( t > i s a " long - run " r e n t per u n i t o f c a p i t a l s t o c k ( t h e t parameter i s o m i t t e d i n t h e f o l l o w i n g f o r convenience). P k , as opposed t o Z k , i s t h e o p p o r t u n i t y r e n t f o r t h e a1 t e r n a t i v e use o f t h e c a p i t a l stock. I n t h e case o f nonconstant r e t u r n s , t h e e q u a l i t y P k = Zk http://clevelandfed.org/research/workpaper/index.cfm Best available copy would be a t t a i n e d a t t h e l e v e l o f o u t p u t where t h e LR c o s t i s t a n g e n t i a l t o t h e SR c o s t , which i s n o t n e c e s s a r i l y t h e minimum p o i n t o f s h o r t - r u n c o s t s (see M o r r i s o n and B e r n d t ) . The d i f f e r e n c e between P k and Z k h e l p s t o f o r m u l a t e t h e r e l a t i o n s h i p between s h o r t - and long- run average c o s t . To r e p r e s e n t t h i s r e l a t i o n s h i p , we f o l l o w t h e H u l t e n approach w i t h some modification. F i r s t , we d e r i v e a s h i f t i n t h e SRAC curve. For t h a t purpose, we need t o define the p a r t i a l d e r i v a t i v e o f the r e s t r i c t e d variable cost w i t h respect t o capital: The d e r i v a t i o n o f e q u a t i o n (11) i s p r e s e n t e d i n Appendix I. A s i m i l a r e q u a t i o n was d e r i v e d by H u l t e n f o r o n l y one v a r i a b l e component. short- run e q u i l i b r i u m , marginal cost equals p r i c e : logarithmically differentiating (lo), (aS/aQ> = In a P, and we f i n d ( t h e d e r i v a t i o n i s s i m i l a r t o t h a t o f (6) and presented i n Appendix 11): The o n l y t e r m l e f t undefined i n (12) i s a s l a t . S I t can be expressed as a f u n c t i o n o f t h e TFP change A", h a v i n g a l l i n p u t f a c t o r s f i x e d Denote SRAC as a = SIQ. (1): Then a =S - Q . O O O To d e r i v e t h e s h i f t o f theaSRAC, we assume i n p u t p r i c e s a r e c o n s t a n t i n ( 1 2 ) , ( t h i s d e f i n e s s h i f t o f t h e r e a l http://clevelandfed.org/research/workpaper/index.cfm Best available copy SRAC), t h e n where = S-PQ, and by r e a r r a n g i n g terms, (13) oO=-A" + PQ-S- (QO-A"-KO) . The second t e r m i n e q u a t i o n (13) i s a c a p a c i t y u t i l i z a t i o n measure. If the u t i l i t y o p e r a t e s a t t h e c a p a c i t y l e v e l , revenue equals c o s t (PQ=S>, and t h e shadow p r i c e o f c a p i t a l i s equal t o long- run p r i c e o f c a p i t a l ( P k = Z k ) . Therefore, a t c a p a c i t y , t h e SRAC change 0 o f LRAC ( - A ) . (0") i s d e f i n e d s o l e l y by t h e s h i f t Otherwise, t h e s h i f t i n t h e SRAC ( b e s i d e s , t h e LRAC s h i f t ) i s d e f i n e d by t h e change i n t h e o u t p u t - t o - c a p i t a l r a t i o e x c l u d i n g t e c h n o l o g i c a l change A", a d j u s t e d by t h e r a t i o o f p r o f i t t o c o s t . The sense o f t h e second term o f e q u a t i o n (13) i s i l l u s t r a t e d on F i g . 2, O assuming A =O. Q,, Say a u t i l i t y w i t h t h e SRAC curve which i n d i c a t e s an o v e r u t i l i z a t i o n of c a p i t a l . (KO, P k ) produces o u t p u t I n o r d e r t o increase p r o f i t s , t h e u t i l i t y should i n c r e a s e i t s c a p i t a l s t o c k , which would s h i f t t h e SRAC curve t o t h e r i g h t . http://clevelandfed.org/research/workpaper/index.cfm Best available copy F i g . 2. $ S h o r t - r u n C o s t s , Long- run C o s t s , and C a p a c i t y U t i l i z a t i o n I O I n t h i s case, KO>O, Q =O, and (PQ-S>>O i m p l y t h a t t h e r i g h t w a r d s h i f t o f t h e SRAC c u r v e w i l l l o w e r average c o s t s ( o O < O assuming A O = O ) . S i n c e P and Q a r e f i x e d , t h e d e c l i n e i n average c o s t s w i l l r a i s e t h e p r o f i t - t o - c o s t r a t i o (PQ-S)/S. T h i s i s d i f f e r e n t f r o m e q u a t i o n ( 1 3 ) where t h i s r a t i o i s assumed f i x e d a t p o i n t Z,. Thus e q u a t i o n ( 1 3 ) u n d e r e s t i m a t e s t h e average c o s t d e c l i n e i n t h i s case. On t h e o t h e r hand, t h i s r a t i o measured a t p o i n t Z 1 would o v e r e s t i m a t e t h e change i n o . " S i m i l a r l y , i n t h e case o f n e g a t i v e p r o f i t s , t h e decrease i n c a p i t a l would l o w e r a v e r a g e c o s t s and a f i x e d p r o f i t - t o - c o s t r a t i o ( a t t h e b e g i n n i n g o f t h e p e r i o d ) would o v e r e s t i m a t e t h e cost decline. B e s i d e s t h e s h i f t f r o m So t o S 1 , t h e r e i s a s h i f t i n t h e LRAC, w h i c h i s measured by A", ( i . e . t h e v e r t i c a l s h i f t i n SRAC as opposed t o t h e h o r i z o n t a l one d i s c u s s e d above). T h i s i s i l l u s t r a t e d on F i g . 3 . http://clevelandfed.org/research/workpaper/index.cfm Best available copy F i g . 3. Ib - Average Cost Change Due t o V e r t i c a l and H o r i z o n t a l S h i f t s i n SRAC. Lf?AC0 L RAC I I I I I Output Costs i n F i g . 3 have i n c r e a s e d f r o m So t o S, due t o t h e change i n capaci t y u t i 1i z a t i o n and capi t a l - o u t p u t r a t i o . But, due t o t h e advancement i n t e c h n o l o g y (AO>O), c o s t s have d e c l i n e d from S , t o S2. The second t e r m i n e q u a t i o n (13) v a r i e s o v e r t h e business c y c l e f o r unregulated industries. I n a p e r i o d of economic expansion, t h e c o m p e t i t i v e f i r m o v e r u t i l i z e s i t s c a p i t a l because of an i n c r e a s i n g p r o f i t - t o - c o s t r a t i o making o0 p o s i t i v e ( c o n s i d e r i n g AO=O>. I n t h i s case, t h e p r o f i t - t o - c o s t r a t i o i n c r e a s e s and more o u t p u t i s produced p e r u n i t of c a p i t a l (QO-KO). In a p e r i o d o f economic downturn, o u t p u t w i 11 d e c l i n e toward Q* ( Q O < O > w i t h a d e c r e a s i n g o u t p u t - t o - c a p i t a l r a t i o (QO-KO)<O, making o 0 n e g a t i v e . Finally, a t t h e t r o u g h , Q m i g h t be below t h e o p t i m a l l e v e l w i t h n e g a t i v e p r o f i t and AC w i l l i n c r e a s e (oO>O) i f o u t p u t c o n t i n u e s t o d e c l i n e . When economic r e c o v e r y r e t u r n s , o u t p u t i n c r e a s e s and (QO-KO>>Oand AC w i l l s t a r t t o d e c l i n e . I n most o f t h e e x i s t i n g TFP s t u d i e s , t h e c a p a c i t y u t i l i z a t i o n e f f e c t i s n o t considered ( i . e . o i s equated t o TFP). I n such a case, TFP has a http://clevelandfed.org/research/workpaper/index.cfm Best available copy capacity u t i l i z a t i o n bias. The d i r e c t i o n o f t h e b i a s f o r u n r e g u l a t e d i n d u s t r i e s most l i k e l y c o i n c i d e s w i t h t h e business c y c l e . For t h i s reason, comparison o f o 0 across u n r e g u l a t e d companies m i g h t be s a t i s f a c t o r y . N e v e r t h e l e s s , comparing TFPs ( u n a d j u s t e d f o r c a p a c i t y b i a s ) o f r e g u l a t e d and u n r e g u l a t e d i n d u s t r i e s has a s e r i o u s problem (such comparison was done, f o r example, b y G o l l o p & Jorgenson [19801>. The d e v i a t i o n o f revenue f r o m c o s t i n r e g u l a t e d i n d u s t r i e s i s a f f e c t e d more by t h e frequency o f hearings t h a n t h e business c y c l e ; i t was observed i n Ohio t h a t t h e d i s t r i b u t i o n o f h e a r i n g s does n o t f o l l o w t h e business c y c l e ; s i m i l a r o b s e r v a t i o n s were made on t h e U.S. l e v e l (see Braeutigam and Q u i r k l19841). Thus TFP e s t i m a t e s should be d i f f e r e n t b e f o r e and a f t e r r a t e h e a r i n g s even when t h e t r u e TFP does n o t change because Z k v a r i e s around r a t e h e a r i n g s . For t h e same reason, TFP comparisons across u t i l i t i e s i n d i f f e r e n t s t a t e s can be m i s l e a d i n g because o f the differences i n the regulatory lags. Therefore, f o r t h e proper TFP measure, t h e r e g u l a t o r y l a g should be t a k e n i n t o account. Besides measuring t h e c a p a c i t y u t i l i z a t i o n e f f e c t , e q u a t i o n (13) can be used t o measure t h e r e g u l a t o r y l a g e f f e c t on TFP. For t h i s purpose, a shadow p r i c e o f c a p i t a l Z k should be compared w i t h t h e f a i r - return - on - capi t a l i n d e x d e f i n e d by PUCO. I f t h e shadow p r i c e o f c a p i t a l i s n o t equal t o t h e f a i r r e t u r n , t h e n two parameters would be changed by r e g u l a t o r s : t h e shadow p r i c e o f c a p i t a l and revenues. These changes can be d e s c r i b e d as f o l l o w s . Let the f a i r r e t u r n on c a p i t a l be ( Z k + G k ) , where Gk i s s i m p l y t h e d i f f e r e n c e between Z k and t h e f a i r r e t u r n . Then, a c c o r d i n g t o e q u a t i o n (1 ) , t h e c o r r e s p o n d i n g revenue i s (PQ + GkK). S u b s t i t u t i n g t h e new p r i c e of c a p i t a l and revenue f i g u r e s i n t o e q u a t i o n ( 1 I ) , one de;ives: ( a s / a ~ ) =p k - ( z ~ + G ~and ) P~K-Z,K-G~K=S-PQ-G~K. http://clevelandfed.org/research/workpaper/index.cfm Best available copy C o r r e s p o n d i n g l y , under t h e new c o n d i t i o n s : a s l a t = PQ+GkK A" and t h e t e r m PQ Q i n e q u a t i o n (12) i s s u b s t i t u t e d b y S S S (PQ+GkK>QO. T h e r e f o r e , e q u a t i o n (1 3) can be r e w r i t t e n as O The l a s t t e r m on t h e r i g h t i n t h e above e x p r e s s i o n i s a r e g u l a t o r y l a g e f f e c t on t h e change i n TFP. Note t h a t i t e q u a l s z e r o when G k i s equal t o z e r o , t h a t i s , when t h e shadow p r i c e o f c a p i t a l i s equal t o t h e f a i r r e t u r n on capital. F i n a l l y , n o t i n g Q O - K O - A O = C ~ i i O - ( C ~ i > Kwhere ", i=L,E,M, and r e w r i t i n g A" i n i t s s t a t i c and dynamic components (see e q u a t i o n [ 9 1 > , e q u a t i o n (14) can be r e w r i t t e n a s 7 : (15) o0 = (Ec,-1 )QO+DO+ (CS, i "-(Cs, )KO).PQ-S+GkK , where i=L,E,M. S Since a l l t h e parameters i n e q u a t i o n (15) can be c a l c u l a t e d , computed as a r e s i d u a l . Do can be I n t h i s s t u d y , P k and G k f o r u t i l i t i e s were n o t e s t i m a t e d and thus t h e D values d e r i v e d f r o m e q u a t i o n (14) (which would be d i f f e r e n t f r o m D values d e r i v e d i n e q u a t i o n ( 7 ) ) a r e n o t a v a i l a b l e . How F a i r i s t h e F a i r Rate o f Return R e g u l a t i o n ? I n t h e f i r s t p e r i o d , 1963-1969, u t i l i t i e s r a r e l y r e q u e s t e d r a t e h e a r i n g s (see t a b l e 3 ) , which suggests t h a t t h e i r r e t u r n on c a p i t a l was g r e a t e r o r equal t o t h e f a i r r e t u r n (as d e f i n e d by PUCO), t h a t i s , Gk<O The AC d e c l i n e d u r i n g t h i s p e r i o d c o n t r i b u t e d t o u t i l i t y p r o f i t s w i t h o u t t h e need f o r mandatory e l e c t r i c i t y p r i c e i n c r e a s e s (see t a b l e 1 ) . Thus, d u r i n g t h e f i r s t p e r i o d , u t i l i t i e s were i n t e r e s t e d i n maximizing TFP growth because i t was translated into profit. http://clevelandfed.org/research/workpaper/index.cfm Best available copy According to a popular view developed by Joskow (1974), an electricity regulator is an extremely passive agent. Price changes should be triggered by a request from utilities or consumer advocates. Utilities, however, have a much better knowledge of their present and expected profit than consumer advocates. Consumer advocates are more concerned with price increases than with utility profits. In the first period, electricity prices were declining, which would make consumer advocates hesitant to request an even lower price decreases. Thus, utilities were in a position to gain extra profit given the passivity of the reguEtor-. As a result, during the first period, an extremely long regulatory lag occurred. In the second period, 1969-1973, A C increased slightly, which triggered a modest increase in the frequency of heari ngs . In the third and fourth periods, the situation was very different. Fuel prices started to increase very quickly, due to the Arab oil embargo 8 , as we1 1 as to other input Tactors, such as inflation. utility operating costs. These were shocks to For a given electricity price, such operating-cost increases drove utility profits below the fair return. Utilities promptly .responded to this shock by requesting electricity price increases that, in most cases, were granted. The frequency of hearings increased sharply as utilities had trouble keeping up with the effects of these shocks. Moreover, a decline in productivity ( D O > O > contributed to the rise in AC. The productivity decline could have been due to a number of intangible factors, some of which are under a utility's control. Therefore, the decline in TFP might have been due to a lack of incentives provided by the regulatory process during the last two periods. is illustrated below. The hypothetical argument for such a possibility http://clevelandfed.org/research/workpaper/index.cfm Best available copy Assume t h a t p r i c e Po ( i n f i g u r e 4) i s t h e e q u i l i b r i u m . i n p u t - p r i c e i n c r e a s e , LRAC moves up t o p o i n t PI. loss per u n i t o f output. i n c r e a s e o f (PI--Po). Due t o a s h a r p A r e a PoABPl i s t h e I n t h i s case, u t i l i t i e s w i l l be g r a n t e d a p r i c e Such a p r i c e s e t t i n g p r o c e s s i n g e n e r a l t a k e s a year, f o l l o w i n g a u t i l i t y ' s request. Now, c o n s i d e r t h a t t h e u t i l i t y c o u l d have i n c r e a s e d i t s TFP t o p a r t l y o f f s e t t h e i m p a c t of t h e p r i c e h i k e , so t h a t i n s t e a d o f i n c r e a s i n g c o s t t o t h e P, l e v e l , i t w o u l d have i n c r e a s e d c o s t s o n l y t o t h e P2 l e v e l (and c o r r e s p o n d i n g l y r e q u e s t p r i c e Pr i n s t e a d o f PI>. I f s t a b l e i n p u t p r i c e s a r e e x p e c t e d i n t h e n e x t y e a r , t h e u t i l i t y may n o t be w i l l i n g t o i n c r e a s e i t s TFP. I n s t e a d , t h e u t i l i t y would r a i s e t h e p r i c e t o P I , and i n t h e n e x t y e a r , i t would l o w e r t h e c o s t p e r u n i t o f o u t p u t b y A". I f o u t p u t r e m a i n s t h e same, i n t h e second y e a r t h e u t i l i t y O would r e g a i n t h e l o s s o f t h e p r e v i o u s y e a r , w h i c h was due t o h a v i n g A =O. N e v e r t h e l e s s , i f o u t p u t i n c r e a s e s , t h e g a i n i n t h e second y e a r ( f r o m O s u p p r e s s i n g A =O i n t h e f i r s t y e a r ) w i l l exceed t h e l o s s e s . This s i m p l i s t i c example i l l u s t r a t e s t h e l a c k o f i n c e n t i v e s f o r u t i l i t i e s t o i n c r e a s e t h e i r TFP under t h e s e c o n d i t i o n s . http://clevelandfed.org/research/workpaper/index.cfm Best available copy TABLE 2 : YEAR: FREQUENCY OF PUCO RATE HEARINGS % OF U T I L I T I E S REQUESTED RATE INCREASE R a t e c a s e s f i l e d ; m a t e r i a l p r o v i d e d by PUCO. Source: FIGURE 4. 1 Two- Year P l a n I I Quantity http://clevelandfed.org/research/workpaper/index.cfm Best available copy Conclusion Input prices and productivity changes are two major sets of factors affecting utility operating costs. While input prices are little affected by a utility, its productivity changes are mostly the result of its long- and short-term planning. Yet PUCO grants equal significance to both sets of factors in their process of electricity price determination. As a result, the present regulation may not provide an adequate incentive for a utility to lower its cost by means of raising its TFP level. In this paper, three types of factors determining shifts in the SRAC curve were considered. Each of these factors (technological change--D, return to O scale effect--E c Q , and capacity utilization effect--equation C141) is a Q result of different activities and should be weighted differently in the price determination process. It was indicated that, contrary to common practice, TFP measurement without consideration of the capacity utilization and regulatory lag effects, is inadequate for comparing regulated and unregulated sectors. The most controversial of these three factors is technological change (D) because the determinants of D are poorly understood. Nevertheless, economists are making initial strides in understanding this factor. For example, Gollop and Roberts (1983) developed a method to consider pollution control bias in the determination of technological change. Obviously, more work is needed in this direction to give regulators valuable tools for measuring different economic and managerial activities. http://clevelandfed.org/research/workpaper/index.cfm Best available copy - 23 - FOOTNOTES 1. For t h e d i s c r i p t i o n o f t h e " F a i r " r a t e o f r e t u r n , t h e Hope case i s o f t e n c i t e d i n t h e l i t e r a t u r e : " Rates, w h i c h e n a b l e s t h e company t o o p e r a t e s u c c e s s f u l l y , t o m a i n t a i n i t s f i n a n c i a l i n t e g r i t y , t o a t t r a c t c a p i t a l , and t o compensate i t s i n v e s t o r s f o r t h e r i s k assumed Hope N a t u r a l Gas Co., 2. 320 U.S. ...". Fed. Power Comm'n v . 591 (1944): 20 p e r c e n t i s an upper boundary f o r an anual p r i c e i n c r e a s e e s t a b l i s h e d by PUCO. 3. F o r d e t a i l s on t h e T o r n q u i s t a p p r o x i m a t i o n , see Cowing, e t . a l . (1981) 4. These u t i l i t i e s a r e : O h i o Power, C i n c i n n a t i Gas and E l e c t r i c , C l e v e l a n d E l e c t r i c I l l u m i n a t i n g , Columbus and S o u t h e r n O h i o E l e c t r i c , D a y t o n Power and L i g h t , O h i o Edison, and T o l e d o E d i s o n . 5. I n case o f constant r e t u r n s t o scale, t h i s p o i n t i s always a t t h e m i n imum o f SRAC. 6. T h i s p r o b l e m i s s i m i l a r t o t h e q u e s t i o n o f whether t o measure s h a r e s for D i v i s i a i n d e x a t t o r t+l p e r i o d . The T o r n q u i s t a p p r o x i m a t i o n s u g g e s t s an a v e r a g e s h a r e o f t w o p e r i o d s . 7. The e x p r e s s i o n f o r Q0-K0-A" can be d e r i v e d as f o l l o w s A 0 = Q 0 - C s , i O for i = K,L,E,M Q0-K0-A" = C s , i o r -Q + C s , i 0 - (1-s,)K0=-K0-A" O O - (Cs,)KO f o r i = L,E,M f o r i = L,E,M, then http://clevelandfed.org/research/workpaper/index.cfm Best available copy 8. O h i o utilities consume coal, which had a much less severe price increase than oi 1 fuel. http://clevelandfed.org/research/workpaper/index.cfm Best available copy BIBLIOGRAPHY B e r n d t , E r n s t R. and M e l v y n A. Fuss. " P r o d u c t i v i t y Measurement U s i n g C a p i t a l Asset V a l u a t i o n to A d j u s t f o r V a r i a t i o n s i n U t i l i z a t i o n , " Working Paper No. 895 (May, 19821, N a t i o n a l Bureau of Economic Research, Inc. B r a e u t i g a m , R. R. and J . P. Q u i r k . "Demand U n c e r t a i n t y and t h e R e g u l a t e d F i r m , " I n t e r n a t i o n a l Economic Review, V o l . 25, No. 1 ( F e b r u a r y , 1 9 5 4 ) . C h r i s t e n s e n , L. R. and W . H . Greene. "Economics o f S c a l e i n U.S. E l e c t r i c Power G e n e r a t i o n , " J o u r n a l o f P o l i t i c a l Economy, v o l . 84, no. 4, P a r t 1 ( A u g u s t , 1976), 655- 676. The U n i v e r s i t y o f Chicago. C h r i s t e n s e n , L.R. and D a l e W. Jorgenson. "U.S. Real P r o d u c t and Real F a c t o r I n p u t , 1929- 1967," The Review o f Income and Wealth, S e r i e s 16, Number 1 , (March, 1970). Cowing, Thomas G . , J e f f r e y S m a l l , Rodney E. Stevenson. " C o m p a r a t i v e Measures o f T o t a l F a c t o r P r o d u c t i v i t y i n t h e R e g u l a t e d S e c t o r : The E l e c t r i c U t i l i t y I n d u s t r y " i n T.C. Cowing and R . E . Stevenson, Ed., P r o d u c t i v i t y Measurement i n R e g u l a t e d I n d u s t r i e s , Academic P r e s s , 1981. Denny, M i c h a e l , M e l v y n Fuss, Leonard Waverman. "The Measurement and I n t e r p r e t a t i o n o f T o t a l F a c t o r P r o d u c t i v i t y i n Regulated I n d u s t r i e s , w i t h an A p p l i c a t i o n t o Canadian T e l e c o m m u n i c a t i o n " i n T.C. Cowing and R . E . Stevenson, Ed., P r o d u c t i v i t y Measurement i n R e g u l a t e d I n d u s t r i e s , Academic P r e s s , 1981. G o l l o p , F.M., and D.W. Jorgenson. "U.S. P r o d u c t i v i t y Growth b y I n d u s t r y , 1947-1 973, i n New ~ e v e r o p m e n t s i n P r o d u c t i v i t y ~ e a s u r e m e n t and ~ n a l y ss,i ( W . K e n d r i c k and B.N. Vaccara, e d s ) , N B E R , ' U n i v e r s i t y o f C h i c a g o P r e s s , C h i c a g o , I l l i n o i s (1980) G o l l o p , Frank M . , and Mark J . R o b e r t s . "The Sources o f Economic Growth i n t h e U.S. E l e c t r i c Power I n d u s t r y , " i n T.C. Cowing and R.E. Stevenson, Ed., P r o d u c t i v i t y Measurement i n R e g u l a t e d I n d u s t r i e s , Academic P r e s s , 1981, p p . 107-143. . " E n v i r o n m e n t a l R e g u l a t i o n s and P r o d u c t i v i t y Growth: The Case o f F o s s i l - F u e l e d E l e c t r i c Power G e n e r a t i o n . " J o u r n a l o f P o l i t i c a l Economy, v o l . 91, no. 4 ( A u g u s t , 1983), pp. 654- 674. H u l t e n , C h a r l e s R. " P r o d u c t i v i t y Change, C a p a c i t y U t i l i z a t i o n , and t h e S o u r c e s o f E f f i c i e n c y Growth," Working Paper 137, (June, 1983), t h e B u r e a u o f Labor S t a t i s t i c s . Joskow, Paul L. " I n f l a t i o n and E n v i r o n m e n t a l Concern: S t r u c t u r a l Change i n t h e Process o f P u b l i c U t i l i t y P r i c e R e g u l a t i o n , " The J o u r n a l o f Law and Economics, v o l . 17 ( O c t o b e r , 1974), pp. 291- 328. K e n d r i c k ; J . W. " Postwar P r o d u c t i v i t y Trends i n t h e U n i t e d S t a t e s , 1948- 1969," NBER General S e r i e s 98 ( 1 9 7 3 ) . http://clevelandfed.org/research/workpaper/index.cfm Best available copy M o r r i s o n , C. J . and E. R. B e r n d t . "Short- Run Labor P r o d u c t i v i t y i n a Dynamic Model," J o u r n a l o f Econometrics, 16, (1981), pp. 339-365. N o r t h H o l l a n d P u b l i s h i n g Company. Solow, R o b e r t M. " T e c h n i c a l Change and t h e Aggregate P r o d u c t i o n F u n c t i o n , " The Review o f Economics and S t a t i s t i c s , V o l . 39, (August, 1957) pp. 31 2-320 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Appendix I - 27 - The D e r i v a t i o n o f E q u a t i o n (11) We p r o v e t h a t = Pk - Zk aK From e q u a t i o n (lo), we d e r i v e i s t h e marginal r a t e o f t e c h n i c a l s u b s t i t u t i o n (MRTS) . I n t h e SR, aK o u t p u t i s a f u n c t i o n o f q u a s i - f i x e d c a p i t a l and o f v a r i a b l e i n p u t s , which where depend on g i v e n c a p i t a l : Q =fCK, L(K>, E(K), M ( K ) l f f ( X ) Rates o f t e c h n i c a l s u b s t i t u t i o n can be d e r i v e d h o l d i n g o u t p u t f i x e d , w i t h corresponding inputs combination X*: where i = variable. L, E, M. \ single For t h e p r o o f , we have t o d e r i v e MRTS f o r any Consider l a b o r t o c a p i t a l MRTS t h e n from t h e above e q u a t i o n f o r i = I n t h e SR: a f ( X * > = ZK and a f ( X * ) aK ai = ri. Then s u b s t i t u t i n g ( 1 . 2 ) i n t o ( 1 . I > , Q.E.D. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Appendix 11. D e r i v a t i o n o f equation (12). Based on t h e s h o r t - r u n c o s t f u n c t i o n (10) we d e r i v e e q u a t i o n ( 1 2 > , as f o l l o w s : ds = as d ~ + dt aK d t = (Pk-Zk)K*KO c % dri ar, dt - % + as d ~ at a~ dt + C i * r * r O - & + PQ*QO t h e n , d i v i d i n g at both sides by S http://clevelandfed.org/research/workpaper/index.cfm Best available copy Appendix 111 Revenue ( E l e c t r i c o p e r a t i n g revenue) r e p r e s e n t s t o t a l o p e r a t i n g revenues f r o m the sale o f e l e c t r i c i t y . Output ( E l e c t r i c s a l e s ) r e p r e s e n t s t h e t o t a l k i l o w a t t hours o f e l e c t r i c i t y s o l d t o a l l r e s i d e n t i a l , commercial and i n d u s t r i a l customers i n c l u d i n g s a l e s f o r r e s a l e. Fuel O p e r a t i o n Expense r e p r e s e n t s t h e t o t a l c o s t o f f u e l used e x c l u s i v e l y f o r p r o d u c t i o n o f e l e c t r i c energy. Average Cost of f u e l per m i l l i o n Btu, r e p r e s e n t s t h e t o t a l c o s t o f f u e l consumed f o r e l e c t r i c g e n e r a t i o n d i v i d e d by i t s t o t a l B t u c o n t e n t . M a t e r i a l Expense was d e r i v e d f r o m E l e c t r i c O p e r a t i n g Expenses minus t a x e s , l a b o r and f u e l expense. M a t e r i a l P r i c e Index. Handy-Whitman c o s t ( i n d e x of U t i l i t y P l a n t M a t e r i a l s . Rate Base i s computed as a sum o f Net U t i l i t y P l a n t and t h e Change i n Working C a p i t a l . T h i s computation i s c o n s i s t e n t w i t h a r e g u l a t o r y d e f i n i t i o n o f t h e r a t e base. Return on c a p i t a l i s computed as a r a t i o between O p e r a t i n g Income and t h e r a t e Base. Net U t i l i t y P l a n t r e p r e s e n t s t h e h i s t o r i c a l c o s t , l e s s accumulated d e p r e c i a t i o n o f t h e t o t a l f i x e d u t i l i t y p l a n t and equipment. Change i n Working C a p i t a l r e p r e s e n t s t h e amount o f cach o r l i q u i d a s s e t s a company must have t o meet c u r r e n t c o s t s u n t i l . r e i m b u r s e d by i t s customers. O p e r a t i n g Income r e p r e s e n t s t o t a l o p e r a t i o n revenues earned f r o m e l e c t r i c s e r v i c e s minus t o t a l o p e r a t i n g expenses. Number o f Employees i s e l e c t r i c department employees where each p a r t - t i m e worker i s counted as o n e - h a l f o f a f u l l - t i m e employee. Labor Expenses i s d e f i n e d as t o t a l s a l a r i e s and wages charged t o e l e c t r i c o p e r a t i o n and maintenance p r o d u c t i o n . Wage Rate i s measured as l a b o r expenses d i v i d e d by t h e number o f employees. Number o f employees and l a b o r expenses were d e r i v e d f r o m " F i n a n c i a l S t a t i s t i c s o f S e l e c t e d E l e c t r i c U t i l i t i e s . " The r e s t o f d a t a were d e r i v e d f r o m Cornpustat Co .
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