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Further results on a discriminating monopolist model
Applied Energy 13 (1983) 317-322
Technical Note Further Results on a Discriminating Monopolist Model
SUMMARY This note represents an extension o f a paper which appeared in this Journal in 1981~'A Discriminating Monopolist Model o f Natural Gas Markets in the US'. One o f the conclusions o f the previouspaper was that the supply side of the market needed to be examined. Here we make some additional inferences about whether the companies are in fact monopolists, by looking at optimal marginal revenues and average costs.
INTRODUCTION Previously I I investigated the optimality of the quantity split between inter- and intrastate natural gas markets in the US. Model consistency with historical supply was assumed for the purposes of that paper. 1 This was a fair test of the monopoly power of the pipeline transmission companies. However, there was a test of the hypothesis within the framework of the same model which I did not perform. By assuming revenue maximising behaviour, I tied the model to the monopoly hypothesis. With costs given through the assumption of a fixed supply, even a perfectly competitive firm will maximise revenues in the process of maximising profits. So there should not have been a claim that those profits were not normal profits. In this communication I re-estimate the model over a larger time frame (1960-1978 instead of 1960-1966) and compute the implied marginal revenue from the estimated coefficients. Actual inter- and intrastate gas prices used here differ slightly from those used previously due to the 317 Applied Energy 0306-2619/83/0013-0317/$03-00
© Applied Science Publishers Ltd,
318
S. Borg
update of the database. These 'implied' marginal revenues (MRs) are then compared with the average well-head cost of gas in order to see whether the firms might qualify for the M R equal to the marginal cost ( M C ) m o n o p o l y condition. It can be concluded that the transmission companies supply more gas than a m o n o p o l y would, and it is even possible that the transmission companies satisfy the condition that the price P = M C , and hence are perfect competitors.
THE MODEL Transmission companies are assumed to maximise revenues from the sale of gas to inter- and intrastate customers subject to the condition that they sell the actual marketed supply in each year in question. The Lagrangean becomes L ( p o , p l , w) =Po(Ao - B o p o + Gopopo ) + p~(A 1 - B l P x + G l P O P l ) + w ( S - A o + BoP o - GoPOpo - A 1 + B l p I -- G l p o p l )
(1) Where:
Po = Intrastate price of natural gas. p~ = Inter-state price of natural gas. popi = Regional population. S = Actual historical marketed supply. w = Lagrange multiplier. A o - BoP o + Gopopo = Intrastate demand. A 1 - B l P 1 + GlPOpl = Inter-state demand.
Solving the first-order conditions, one obtains the implied optimal prices in the inter- and intrastate markets, namely /lax
(Bo + B 1 ) ( A o + GoPOPo) - Bo[2S - (A o + A1) - (GoPOPo + G l p o p l ) ]
2(Bo + B1)B o
(2) When d e m a n d curves are estimated, the p r e d i c t e d optimal prices can be computed and compared with actual prices. Table 1 shows one set of estimated coefficients which predict well when the regressions are run over the period 1960-1978.
319
Further results on a discriminating monopolist m o d e l
TABLE 1 Estimated Coefficients Intrastate D e m a n d : D o = A o - B o P o + GoPOPo
Ao Bo GO
Coefficient
t-Statistic
- 2 1 095.7 7 559-5 1.427 64
-4.5 4.4 5-1
Inter-state D e m a n d . D 1 = A 1 - Blp I + Glpopl
A1 B1 G1
- 35 848"5 11 182-0 0"315 687
10.0 7.8 13.5
TABLE 2 Actual a n d Predicted Prices (75 c e n t s / M M B t u )
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978
Po
p~.X
Pl
p~X
51 47 49 52 51 46 48 48 47 47 47 49 52 51 64 85 103 119 113
38 49 50 50 51 49 50 51 49 51 54 57 62 67 75 87 92 101 106
106 111 108 105 101 98 94 94 88 83 82 83 86 82 85 99 111 125 129
76 81 85 90 92 94 94 95 96 96 99 103 107 110 116 127 130 138 141
320
S. Borg TABLE 3
Implied Marginal Revenues and the Actual Well-Head Cost of Natural Gas (75 cents/MMBtu) Year
w = MR
AC
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974
14 19 20 21 19 18 11 8 6 1 2 2 5 10 15
25 26 27 27 26 25 25 25 24 23 23 23 23 25 32
1975 1976 1977 1978
36 39 48 60
42 53 68 72
Prices p r e d i c t e d f r o m eqn. (2) are given in T a b l e 2. M a r g i n a l r e v e n u e s i m p l i e d b y this specification c a n be c o m p u t e d as: w = MR
= 2p'on'~x- ( A o / B o )
- (Go/Bo)pOPo
(3)
T a b l e 3 is a t a b u l a t i o n o f this c o m p u t a t i o n t o g e t h e r with the a v e r a g e wellh e a d price o f gas for the y e a r in q u e s t i o n . I f the M R s were a b o v e the a v e r a g e w e l l - h e a d cost o f n a t u r a l gas, the difference m i g h t be a t t r i b u t e d to user costs. T h e fact t h a t t h e y are b e l o w the a v e r a g e w e l l - h e a d cost, h o w e v e r , i n d i c a t e s t h a t m a r g i n a l c o s t is p r o b a b l y g r e a t e r t h a n the M R .
CONCLUSIONS (1)
T h e t r a n s m i s s i o n c o m p a n i e s h a v e n o t realised m o n o p o l y profits ( p e r h a p s d u e to r e g u l a t i o n ) .
Further results on a discriminating monopolist model
(2)
321
The transmission companies may satisfy the condition that p = M C and hence are perfect competitors.
The analysis cannot be carried further than this without stretching the boundaries of the model beyond realism.
REFERENCES I. S. Borg, A discriminating monopolist model of natural gas markets over the period 1960-1966, Applied Energy, 9 (1981), pp. 153-8. S. Borg, 101 Winants Hall, Rutger's University, New Brunswick, N J 08903 (USA)
APPENDIX In this Appendix we define MR, AC and M C - - o r marginal revenue, average cost, and marginal cost, respectively. Marginal revenue ( M R ) is the addition to total receipts that follows from sale of an additional unit of product in this case, an additional M c f of gas--after taking into account the fact that price falls in the market as the a m o u n t sold is increased.
M R = d(pq)/dq where q = q(p) is the demand curve. Average cost (AC) is equal to total costs divided by output. A C = Total c o s t / O u t p u t = C(q)/q Marginal cost (MC) is equal to the derivative of total cost with respect to output, and is the part of total costs attributable to the last unit produced.
M C = dC(q)/dq A standard result of economic theory is that the monopolist will equate M R with MC. As long as M R is greater than the cost of producing that
322
S. Borg
unit (i.e. MC), the monopolist will expand output. When marginal cost exceeds the change in proceeds, the monopolist will be making losses on that unit and will decrease output. For the discriminating monopolist, M R is the same in both parts of the market he has successfully segmented. If this were not true he could expand proceeds by reallocating sales with no change in costs.
Technical Note Further Results on a Discriminating Monopolist Model
SUMMARY This note represents an extension o f a paper which appeared in this Journal in 1981~'A Discriminating Monopolist Model o f Natural Gas Markets in the US'. One o f the conclusions o f the previouspaper was that the supply side of the market needed to be examined. Here we make some additional inferences about whether the companies are in fact monopolists, by looking at optimal marginal revenues and average costs.
INTRODUCTION Previously I I investigated the optimality of the quantity split between inter- and intrastate natural gas markets in the US. Model consistency with historical supply was assumed for the purposes of that paper. 1 This was a fair test of the monopoly power of the pipeline transmission companies. However, there was a test of the hypothesis within the framework of the same model which I did not perform. By assuming revenue maximising behaviour, I tied the model to the monopoly hypothesis. With costs given through the assumption of a fixed supply, even a perfectly competitive firm will maximise revenues in the process of maximising profits. So there should not have been a claim that those profits were not normal profits. In this communication I re-estimate the model over a larger time frame (1960-1978 instead of 1960-1966) and compute the implied marginal revenue from the estimated coefficients. Actual inter- and intrastate gas prices used here differ slightly from those used previously due to the 317 Applied Energy 0306-2619/83/0013-0317/$03-00
© Applied Science Publishers Ltd,
318
S. Borg
update of the database. These 'implied' marginal revenues (MRs) are then compared with the average well-head cost of gas in order to see whether the firms might qualify for the M R equal to the marginal cost ( M C ) m o n o p o l y condition. It can be concluded that the transmission companies supply more gas than a m o n o p o l y would, and it is even possible that the transmission companies satisfy the condition that the price P = M C , and hence are perfect competitors.
THE MODEL Transmission companies are assumed to maximise revenues from the sale of gas to inter- and intrastate customers subject to the condition that they sell the actual marketed supply in each year in question. The Lagrangean becomes L ( p o , p l , w) =Po(Ao - B o p o + Gopopo ) + p~(A 1 - B l P x + G l P O P l ) + w ( S - A o + BoP o - GoPOpo - A 1 + B l p I -- G l p o p l )
(1) Where:
Po = Intrastate price of natural gas. p~ = Inter-state price of natural gas. popi = Regional population. S = Actual historical marketed supply. w = Lagrange multiplier. A o - BoP o + Gopopo = Intrastate demand. A 1 - B l P 1 + GlPOpl = Inter-state demand.
Solving the first-order conditions, one obtains the implied optimal prices in the inter- and intrastate markets, namely /lax
(Bo + B 1 ) ( A o + GoPOPo) - Bo[2S - (A o + A1) - (GoPOPo + G l p o p l ) ]
2(Bo + B1)B o
(2) When d e m a n d curves are estimated, the p r e d i c t e d optimal prices can be computed and compared with actual prices. Table 1 shows one set of estimated coefficients which predict well when the regressions are run over the period 1960-1978.
319
Further results on a discriminating monopolist m o d e l
TABLE 1 Estimated Coefficients Intrastate D e m a n d : D o = A o - B o P o + GoPOPo
Ao Bo GO
Coefficient
t-Statistic
- 2 1 095.7 7 559-5 1.427 64
-4.5 4.4 5-1
Inter-state D e m a n d . D 1 = A 1 - Blp I + Glpopl
A1 B1 G1
- 35 848"5 11 182-0 0"315 687
10.0 7.8 13.5
TABLE 2 Actual a n d Predicted Prices (75 c e n t s / M M B t u )
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978
Po
p~.X
Pl
p~X
51 47 49 52 51 46 48 48 47 47 47 49 52 51 64 85 103 119 113
38 49 50 50 51 49 50 51 49 51 54 57 62 67 75 87 92 101 106
106 111 108 105 101 98 94 94 88 83 82 83 86 82 85 99 111 125 129
76 81 85 90 92 94 94 95 96 96 99 103 107 110 116 127 130 138 141
320
S. Borg TABLE 3
Implied Marginal Revenues and the Actual Well-Head Cost of Natural Gas (75 cents/MMBtu) Year
w = MR
AC
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974
14 19 20 21 19 18 11 8 6 1 2 2 5 10 15
25 26 27 27 26 25 25 25 24 23 23 23 23 25 32
1975 1976 1977 1978
36 39 48 60
42 53 68 72
Prices p r e d i c t e d f r o m eqn. (2) are given in T a b l e 2. M a r g i n a l r e v e n u e s i m p l i e d b y this specification c a n be c o m p u t e d as: w = MR
= 2p'on'~x- ( A o / B o )
- (Go/Bo)pOPo
(3)
T a b l e 3 is a t a b u l a t i o n o f this c o m p u t a t i o n t o g e t h e r with the a v e r a g e wellh e a d price o f gas for the y e a r in q u e s t i o n . I f the M R s were a b o v e the a v e r a g e w e l l - h e a d cost o f n a t u r a l gas, the difference m i g h t be a t t r i b u t e d to user costs. T h e fact t h a t t h e y are b e l o w the a v e r a g e w e l l - h e a d cost, h o w e v e r , i n d i c a t e s t h a t m a r g i n a l c o s t is p r o b a b l y g r e a t e r t h a n the M R .
CONCLUSIONS (1)
T h e t r a n s m i s s i o n c o m p a n i e s h a v e n o t realised m o n o p o l y profits ( p e r h a p s d u e to r e g u l a t i o n ) .
Further results on a discriminating monopolist model
(2)
321
The transmission companies may satisfy the condition that p = M C and hence are perfect competitors.
The analysis cannot be carried further than this without stretching the boundaries of the model beyond realism.
REFERENCES I. S. Borg, A discriminating monopolist model of natural gas markets over the period 1960-1966, Applied Energy, 9 (1981), pp. 153-8. S. Borg, 101 Winants Hall, Rutger's University, New Brunswick, N J 08903 (USA)
APPENDIX In this Appendix we define MR, AC and M C - - o r marginal revenue, average cost, and marginal cost, respectively. Marginal revenue ( M R ) is the addition to total receipts that follows from sale of an additional unit of product in this case, an additional M c f of gas--after taking into account the fact that price falls in the market as the a m o u n t sold is increased.
M R = d(pq)/dq where q = q(p) is the demand curve. Average cost (AC) is equal to total costs divided by output. A C = Total c o s t / O u t p u t = C(q)/q Marginal cost (MC) is equal to the derivative of total cost with respect to output, and is the part of total costs attributable to the last unit produced.
M C = dC(q)/dq A standard result of economic theory is that the monopolist will equate M R with MC. As long as M R is greater than the cost of producing that
322
S. Borg
unit (i.e. MC), the monopolist will expand output. When marginal cost exceeds the change in proceeds, the monopolist will be making losses on that unit and will decrease output. For the discriminating monopolist, M R is the same in both parts of the market he has successfully segmented. If this were not true he could expand proceeds by reallocating sales with no change in costs.