2 2 1 TAKEUCHI, Kenzo 1 Ramsey 1 Boiteux 2 19701980 ICC Baumol and Bradford 3 Braeutigam 4 Winston 5 Damus 6 1 Damus 7 McFarland 8 9 Damus 7 Two- Way Access Armstrong 10 2 Vol.13 No.3 2010 Autumn 015
3 43 5 2 1 AB ABCDEF ABA EFBBDC Aab AB DGEHD E CF 2 q a q b ABab p a p b AB abq 0 p C 0 p 0A p 0B p H 0 p H 0 p 0A p 0B q 0A q 0B AB q 0A q 0 q 0B 1q 0 TB q 0 abq a q b 3TC 1 TC A TC B AB MC 0A MC 0B AB 1 2 MC a MC b AB ab 3 G A a D B E b F 4 MC 0 1 5 1 C CDEFAB DGAa EHBb H 3 2 4 A1000 1B10014 0.5 3 3.1 ab2 2 016 Vol.13 No.3 2010 Autumn
6 7 q 0A q 0 q 0B 1q 0 8 9 10 TB/q 0 p C 0 4 11 e 0 e 0 q 0 /p C 0 p C 0 /q 0 12 ab 13 14 e a e b ab 3.2 3.1 k0k1 17 18 19 18 197 3.1 k Damus 7 k 1Damus 2 p.57 k 1 Damus k k 1 Damus 7 p.57 k k McFarland 8 Damus 7 15 16 3.3 5 Vol.13 No.3 2010 Autumn 017
20 21 22 q 0A q 0 q 0B 1q 0 23 24 25 /10 7 30 26 31 2 32 33 27 2 p H 0 28 3.4 1 AB1 1 p 0 34 35 1 36 /10q 0 6 37 38 29 1 21 018 Vol.13 No.3 2010 Autumn
8 ab 1 4 1 /101 TB 40 41 1 42 43 39 44 9 AB 45 1 Vol.13 No.3 2010 Autumn 019
10 0.5AB 2 2 1 1 2 k 3/1 0 1 1 2 1 2 3 3 5 2 1 1 0.5 1 1 1 0 a b q 0 e 0 p a q a e a p b q b e b 191.49 1,808.51 326.53 918.37 0.09 326.53 918.37 0.09 p 0 222.73 1,777.27 0.13 0.13 387.44 903.14 0.15 387.44 903.14 0.15 p 0C 268.07 1,731.93 0.15 0.17 369.37 907.66 0.10 369.37 907.66 0.10 p 0H 294.07 1,705.93 0.17 0.15 488.65 877.84 0.14 0.33 488.65 877.84 0.14 0.33 1,123.71 876.29 1.28 0.78 2,181.82 454.55 1.20 0.83 2,181.82 454.55 1.20 0.83 k 0.50 165,591.67 4,843,356.49 0.02 4,841,988.79 0.01 4,795,156.75 0.05 0.02 4,788,318.27 1.00 2,381,209.00 3,591,596.12 020 Vol.13 No.3 2010 Autumn
0 a b 0.5 q 0 e 0 p a q a e a p b q b e b k 1 207.74 1,792.26 0.12 0.27 360.75 909.81 0.10 0.32 360.75 909.81 0.10 0.32 2 3 2 0.03 4,917,123.12 1 2 OD 3 Vol.13 No.3 2010 Autumn 021
q 0 q a q b p 0 p 0 C p 0 H p 0A p 0B p a p b q 0A q 0B k TB TC TC A TC B MC 0 MC 0A MC 0B MC a MC b e 0 e a e b Aa Bb 1 p 0H p 0A p 0B A B Aa Bb Aq 0A q 0 Bq 0B 1q 0 1 A B 1 A B Aa Bb Aa Bb A4 p 0B p H 0 p 0A p 0B A5 2 27 26p 0A p H 0 p 0A p 0B A4A5 A6 q 0 0 A7 A4p H 0 =p 0A p 0B A1 A8 3MC 0A MC 0A 1 MC 0A MC 0B MC 0B 1MC 0B Damus1984p. 534 A9 A2 p 0 H =p 0A p 0B A3 A10 022 Vol.13 No.3 2010 Autumn
A11 Laffont and Tirole 14 pp. 185-186 8 9 10EXCEL A12 1Arnott and Kraus 11 2Damus 7 AB AB 30.5 4TB/q 0 p C 0 12 pp. 239-240 46 qidamus 7 p. 53 5 6Train 13 2 1 Train 13 p. 185 7double-marginalization double-marginalization double-marginalization 1Ramsey, F.1927A Contribution to the Theory of TaxationEconomic JournalVol. 37pp. 47-61 2Boiteux, M.1956Sur la Gestion des Monopoles Publics Astreints á lequilibre BudgetaireEconometricaVol. 24pp. 22-40 3Baumol, W. J. and Bradford, F.1970Optimal Departures from Marginal Cost PricingAmerican Economic ReviewVol. 67No. 3pp. 350-365 4Braeutigam, R. B.1979Optimal Pricing with Intermodal Competition American Economic ReviewVol. 69No. 1pp. 38-49 5Winston, C.1981The Welfare Effects of ICC Rate Regulation RevisitedBell Journal of EconomicsVol. 12No. 1pp. 233-244 6Damus, S.1981Two-Part Tariffs and Optimum Taxation: the Case of Railway RatesAmerican Economic ReviewVol. 71No. 1pp. 65-79 7Damus, S.1984Ramsey Pricing by U. S. RailroadsJournal of Transport Economics and PolicyVol. 18No. 1pp. 51-61 8McFarland, H.1986Ramsey Pricing of Inputs with Downstream Monopoly Power and RegulationJournal of Transport Economics and PolicyVol. 20No. 1pp. 81-90 91987 309pp. 24-32 10Armstrong, M.1998Network Interconnection in Telecommunications Economic JournalVol. 108No. 448pp. 545-564 11Arnott, R. and Kraus, M.1993The Ramsey Problem for Congestible FacilitiesJournal of Public EconomicsVol. 50pp. 371-396 122002 13Train, K.1977Optimal Transit Prices under Increasing Returns to Scale and a Loss ConstraintsJournal of Transport Economics and PolicyVol. 11No. 2pp. 185-194 14Laffont, J-J. and Tirole, J.2000Competition in TelecommunicationMIT Press An Economic Analysis of Ramsey Pricing in Pool Train Fares By Kenzo TAKEUCHI Given the case that trains are operated over a track owned by two railway companies, the common fare in which they share a single break-even constraint, the common fare in which they have its own break-even constraint, an added-up fare, and a fare by the merged company are considered from the view point of Ramsey pricing. It is shown in qualitative analyses and numerical examples that the common fare is likely to be superior to the adding-up fare in terms of social net benefits. It is also shown that Ramsey rules are applicable in branch lines operated by each company. Key Words : Ramsey pricing, Ramsey rule, pool train, economy of scale, economy of scope Vol.13 No.3 2010 Autumn 023