Thirty Years with Spatial and Intertemporal Economics

  • Takashi Takayama
Part of the Advances in Spatial Science book series (ADVSPATIAL)


The decade of the 1950s could be called the most productive decade of applied economics. The nonlinear programming paper by Kuhn and Tucker (1951), announced the dawn of the decade, followed almost immediately by George Dantzig’s Maximisation of Linear Function of Variables subject to Linear Inequalities (1951). Within the decade a number of promising applications of especially ’linear programming (LP) methods’ appeared in the professional journals and bookstores all over the world. In the field of agriculture, the late Professor E. O. Heady, an outstanding educator and pioneer in applying neoclassical economic methods to economic problems (Economics of Agricultural Production and Resource Use, 1952), energetically applied linear programming methods to economic decision making problems which culminated in a seminar work (Linear Programming Methods, with W. Candler 1958). In the field of manufacturing industries, Alan S. Manne produced another seminar work (Scheduling of Petroleum Refinery Operations,) in 1956, which has since been used by most major oil companies in the world. A large number of transportation cost minimisation LP formulations and applications were published during this period (see Gass, Linear Programming: Methods and Applications, 1969).


Demand Function Price Equilibrium Storage Cost Energy Information Administration Linear Programming Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Aoki M (1967) Optimisation of Stochastic Systems. Academic Press, New YorkGoogle Scholar
  2. Aoki M (1976) A Stochastic Optimal Control Model of International Trade. Memoed, U.C.L.A.Google Scholar
  3. Athans M, Falb PL (1966) Optimal Control. McGraw-HillGoogle Scholar
  4. Batten D, Westin L (1990) Modelling Commodity Flows on Trade Networks, Retrospect and Prospect, New Frontiers in Regional Science. Chatterji et al. ( Eds) Macmillan, LondonGoogle Scholar
  5. Beckmann M, Marschak T (1956) An Activity Analysis Approach to Location Theory, Proceedings of the Second Symposium in Linear Programming, National Bureau of Standards and Directorate of Management Analyses, Washington, D.C.Google Scholar
  6. Charnes A, Cooper WW, Mellon B (1952) Blending Aviation Gasolines. Econometrica 20: 135–159CrossRefGoogle Scholar
  7. Cottle RW, Dantzig GB (1968) Complementary Pivot Theory of Mathematical Programming, Linear Algebra and Its Applicators pp 103–25Google Scholar
  8. Dantzig GB (1951) Maximization of Linear Function of Variables Subject to Linear Inequalities. In: Koopmaris TC (Ed) Activity Analysis of Production and Allocation. Cowles Commission Monograph 13: 339–347Google Scholar
  9. Dreyfus SE (1954) Some Types of Optimal Control of Stochastic Systems. Journal of Society of Industrial and Applied MathematicsGoogle Scholar
  10. Driskill RA, McCafferty S (1989) Dynamic Duopoly with Adjustment Costs. A Differential Game Approach. J Econ Theory 49: 324–338Google Scholar
  11. Elbers CIM (1992) Spatial Disaggregation in General Equilibrium Models, with an application to the Nepalese Economy, VU Press, AmsterdamGoogle Scholar
  12. Enke S (1951) Equilibrium among Spatially Separated Markets Solution by Electric Analogue. Econometrica 19: 40–48CrossRefGoogle Scholar
  13. Fershtman C, Kamien MI (1987) Dynamic Duopolistic Competition with Sticky Prices. Econometrica 55: 1151–1164CrossRefGoogle Scholar
  14. Fox KA (1953) A Spatial Equilibrium Model of the Livestock Feed Economy. Econometrica 21: 547–566CrossRefGoogle Scholar
  15. Gass SI (1969) Linear Programming. Methods and Applications, 3rd edition. McGraw-Hill, New YorkGoogle Scholar
  16. Guise JWB, Aggrey-Mensah W (1973) An Evaluation of Policy Alternatives facing Australian Banana Producers. Studies in Economic Planning over Space and Time. Judge GG, Takayama T (Eds) North-HollandGoogle Scholar
  17. Guvenen O, Labys WC, Lesourd JB (Eds) (1991) International Commodity Market Models. Chapman and Hall, New YorkGoogle Scholar
  18. Hall HH, Heady EO, Plessner Y (1968) Quadratic Programming Solution of Competitive Equilibrium for US Agriculture, Am J Agricult Econ 50: 536–555CrossRefGoogle Scholar
  19. Hashimoto H (1976) World Food Projection Models, Projections, and Policy Evaluation. PhD Thesis. Department of Economics, University of Illinois (unpublished)Google Scholar
  20. Heady EO (1952) Economies of Agricultural Production and Resource Use. Prentice Hall, New YorkGoogle Scholar
  21. Heady EO, Candler W (1958) Linear Programming Methods, Iowa State University PressGoogle Scholar
  22. Intrilligator MD (1971) Mathematical Optimisation and Economic Theory. Prentice-Hall. Inc. Englewood Cliffs. N.J.Google Scholar
  23. Judge GG (1956) Spatial Equilibrium Model for Eggs, Bulletin 318. Storrs, Connecticut Agricultural Experiment StationGoogle Scholar
  24. Judge GG, Takayama T (Eds) (1973) Studies in Economic Planning over Space and Time. North-Holland, AmsterdamGoogle Scholar
  25. Judge GG, Wallace TD (1959) Spatial Equilibrium Analysis of the Livestock Economy, Technical Bulletin TB-78, Department of Agricultural Economics, Oklahoma State UniversityGoogle Scholar
  26. Kennedy M (1974) Optimum Utilization of Transportation System. In Proceedings of the International Statistics Conferences, Washington, DC, 5Google Scholar
  27. Kuhn HW, Tucker AW (1951) Nonlinear Programming. In: Neyman J (Ed) Proceedings of the Second Berkely Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, pp 481–492Google Scholar
  28. Labys WC, Polak PK (1984) Commodity Models for Forecasting and Policy Analysis. Croom Helm, LondonGoogle Scholar
  29. Labys WC, Wood DO (1985) Energy Modelling. Economics of Mineral Industry. In: Vogel W (Ed) American Institute of Mining Engineers, New YorkGoogle Scholar
  30. Labys WC (1987) Commodity Markets and Models. An International Bibliography, Gower Publishing CoGoogle Scholar
  31. Labys WC, Takayama T, Uri N (1989) Quantitative Methods for Market-Oriented Economic Analysis over Space and Time, Gower, LondonGoogle Scholar
  32. Labys WC, Yang CW (1991) Advances in Spatial Equilibrium Modelling of Mineral and Energy. International Regional Science Review 14: 61–94 (A most recent review of works in this subject)Google Scholar
  33. Lefeber L (1958) Allocation in Space, North-Holland, AmsterdamGoogle Scholar
  34. Mann AS (1956) Scheduling of Petroleum Refinery Operations, Harvard University Press, CambridgeGoogle Scholar
  35. Modigliani F, Hohn F (1955) Production Planning over Time and the Nature of the Expectation and Planning Horizon. Econometrica 23Google Scholar
  36. Nagurney A (1993) Network Economics, Kluwer, DordrechtGoogle Scholar
  37. Plessner Y, Heady EO (1965) Competitive Equilibrium Solutions with Quadratic Programming. Metroeconomica 17: 117–130CrossRefGoogle Scholar
  38. Popovic B (1972) Analytic Solutions to Some Stochastic, Adaptive, and Dual Optimal Control Problems for Economic Decision Making. PhD Thesis (unpublished). Department of Economics. University of Illinois. Also available in the form of Report T-4 (September 1972) UILU-ENG 72–2245. Coordinated Science laboratory, University of Illinois, Urbana, IllioisGoogle Scholar
  39. Prescott EC (1967) Adaptive Decision Rules for Macro Economic Planning PhD Thesis (unpublished) Graduate School of Industrial Administration. Carnegie-Mellon UniversityGoogle Scholar
  40. Robinson J (1933) Tlie Economics of Imperfect Competition, MacMillan, LondonGoogle Scholar
  41. Rojko AS, Urban FS, Naive JJ (1971) World Demand Prospects for Grains in 1980 with Emphasis on Less Development Countries, FAER-75, Economic Research Service, USDA, Washington, DCGoogle Scholar
  42. Samuelson PA (1952) Spatial Price Equilibrium and Linear Programming. Am Econ Rev 42: 283–303Google Scholar
  43. Samuelson PA (1957) Intertemporal Price Equilibrium. A Prologue to the Theory of Speculation. Weltwirtschaftliches Archiv. 79: 181–221Google Scholar
  44. Samuleson PA (1959) Using Full Duality to Show that Simultaneously Additive Direct and Indirect Utilities Implies Unitary Price Elasticities of Demand. Econometrica. 33: 731–796Google Scholar
  45. Sasaki K (1969) Spatial Equilibrium in Eastern Japan’s Milk Market (in Japanese), J Rural Econ 41Google Scholar
  46. Sasaki K (1970) Spatial Equilibrium in Eastern Japan’s Port Industry (in Japanese), J Rural Econ 42Google Scholar
  47. Simaan M, Takayama T (1976) Optimal Monopolist Control in a Dynamic Market. IEEE Trans Syst Mon and Cybern 6: 799–807CrossRefGoogle Scholar
  48. Simaan M, Takayama T (1978) Game Theory Applied to Dynamic Duopoly Problems with Production Constraints. Automatica 14: 161–166CrossRefGoogle Scholar
  49. Simaan M, Takayama T (1980) Optimal Harvesting Policies and Regulations for Renewable Resources, Int J Syst Sci 11: 281–290CrossRefGoogle Scholar
  50. Simon HA (1956). Dynamic Programming under Uncertainty with a Quadratic Criterion Function. Econometrica 24Google Scholar
  51. Stevens BH (1959) An Interregional Linear Programming Model, J Reg Sci 1: 60–98CrossRefGoogle Scholar
  52. Takayama T (1959) Production Economics for Agriculture ( Nogyo no Seisan Keizaigaku) Tenshi-in Press, SapporoGoogle Scholar
  53. Takayama T, Judge GG (1964a) Spatial Equilibrium and Quadratic Programming. Journal of Farm Economic (JFE) 44: 67–93CrossRefGoogle Scholar
  54. Takayama T, Judge GG (1964b) Equilibrium among Separated Markets; A Reformulation. Econometrica 32: 510–524CrossRefGoogle Scholar
  55. Takayama T, Judge GG (1964c) An Interregional Activity Analysis Model of the Agricultural Sector. JFE 46: 349–365Google Scholar
  56. Takayama T, Judge GG (1964d) Intertemporal Price Equilibrium Model. JFE 46: 477–484Google Scholar
  57. Takayama T, Judge GG (1966) Spatial Economic Analysis. Inaugural Lecture Publication. University of New England, Armidale, NSW, AustraliaGoogle Scholar
  58. Takayama T (1967) International Trade and Mathematical Programming. Australian J Agricult Econ 11: 36–48Google Scholar
  59. Takayama T, Judge GG (1971) Spatial and Temporal Price and Allocation Models. North-HollandGoogle Scholar
  60. Takayama T, Hashimoto H (1976) World Food Projection Models. 1972 and 1974, Illinois Agricultural Economics. 16Google Scholar
  61. Takayama T, Woodland A (1970) Equivalence of Price and Quantity Formulations of Spatial Equilibrium. Purified Duality in Quadratic and Concave Programming. Econometrica 38: 889–906CrossRefGoogle Scholar
  62. Takayama T, Simaan M (1984) Differential Game Theoretic Policies for Consumption Regulations of Renewable Resources, IEEE Trans Syst Man Cybern. pp 764–766Google Scholar
  63. Theil H (1964) Optimal Decision Rules for Government and Industry. North-HollandGoogle Scholar
  64. Thompson R (1989) Spatial and Temporal Price Equilibrium Models. Quantitative Methods for Market-Oriented Economic Analysts over Space and Time. Labys Takayama Uri ( Eds ). Avebury pp 49–65Google Scholar
  65. Tse E, Athans M (1970) Optimal Minimal-Order Observer-Estimators for Discrete Linear Time-Varying Systems. I.E.E.E. Trans, on Automatic Control. AC 15: 416–426Google Scholar
  66. Tsukui S, Mino K (1990) Nonlinear Strategies in Dynamic Duopolistic Competition with Sticky Prices. J Econ Theory 52: 136–161CrossRefGoogle Scholar
  67. Uri N (1975) Toward an Efficient Allocation of Electric Energy, Health Lexington Books. Lexington, MAGoogle Scholar
  68. West DA, Brandow GE (1964) Space-product Equilibrium in the Dairy Industry in the North Eastern and North Central Regions, J Farm Econ 46: 719–731CrossRefGoogle Scholar
  69. Westin L (1990) Vintage Models of Spatial Structural Change, Umea Economic Studies 227. University of Umea, SwedenGoogle Scholar
  70. Wolfe PM (1959) The Simplex Method for Quadratic Programming. Econometrica 27: 382–398CrossRefGoogle Scholar
  71. Woodland A (1969) Competitive Equilibrium in International Trade, unpublished PhD thesis. University of New England, Armidale, NSW, AustraliaGoogle Scholar
  72. Zellner A (1971) An Introduction to Bayesian Inference in Econometrics. Wiley, New YorkGoogle Scholar
  73. Zusman P, Melamed A, Katzin I (1969) Possible Trade and Welfare Effects of EEC Tariff and Reference Price Policy on the European-Mediterranean Market for Winter Oranges. Monograph 24, Gianini Foundation, UC BerkeleyGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • Takashi Takayama
    • 1
  1. 1.University of Western AustraliaAustralia

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