Abstract
Samuelson (1947, p. 3) argued that seemingly diverse fields in economics possessed formal similarities and that the same inequalities and theorems appeared again and again in these theories. He recognized that each field involved interdependent unknowns determined by presumably efficacious equilibrium conditions but argued that there exists identically meaningful theorems in other fields, each derived by essentially analogous methods. Consider microeconomic theory. The interaction between consumers and firms is studied using two major analytical techniques—optimization and equilibrium (Varian 1984, pp. 1–3). The characterization of the optimum behavior requires specification of the actions that the unit can take, the constraints to such actions and the objective function that the unit has. In examining the equilibrium of the model, we are considering whether the actions of all units are compatible. Equilibrium is modeled as the solution of a set of equations.
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Notes
- 1.
In the case of the two examples discussed in the text, the orbits are straight lines and so the tangent vectors are collinear with them.
References
Arnord, K.J. (1973). Rawls’ principle of just saving. Swedish Journal of Economics, 75, 323–335.
Afriat, S.N. (1984). The true index. In A. Ingham, & A.M. Ulph (Eds.), Demand, equilibrium and trade: essays in honor of Ivor Pearce. London: McMillian.
Allen, R.G.D. (1975). Index numbers in theory and practice. London: Macmillian.
Arnold, V.I. (1973). Ordinary differential equations. Cambridge, MA: MIT Press.
Arnold, V.I. (1989). Mathematical methods of classical mechanics. New York: Springer.
Banerjee, K.S. (1975). Cost of living index numbers. New York: Marcel Dekker.
Bowley, A.L. (1928). Notes on index numbers. Economic Journal, 38, 216–237.
Carlson, S. (1939). A study on the pure theory of production, Stockholm economic studies, no. 9. London: P.S. King & Sons.
Clapham, J.H. (1922a). Of empty economic boxes. Economic Journal, 32, 305–314.
Clapham, J.H. (1922b). The economic boxes: a rejoinder. Economic Journal, 32, 560–563.
Cohen, A. (1931). An introduction to the Lie theory of one-parameter groups. Boston, MA: Heath.
Cornes, R. (1992). Duality and modern economics. Cambridge: Cambridge University Press.
Darrough, M.N., & Southey, C. (1977). Duality in consumer theory made simple: the revealing of Roy’s identity. Canadian Journal of Economics, 10, 307–317.
Deaton, A., & Muelbauer, J. (1980). Economics and consumer behavior. Cambridge: Cambridge University Press.
Diewert, W.E. (1981). The economic theory of index numbers: a survey. In A. Deaton (Ed.), Essays in the theory and measurement of consumer behaviour in honour of Sir Richard Stone. London: Cambridge University Press.
Diewert, W.E. (1982). Duality approaches to microeconomic theory. In K.J. Arrow, & M.D. Intriligator (Eds.), Handbook of mathematical economics, vol. II (pp. 535–599). Amsterdam: North Holland.
Diewert, W.E. (1987). Index numbers. In J. Eatwell, M. Milgate, & P. Newman (Eds.), The new palgrave: a dictionary of economics. London: Macmillian.
Dirac, P.A.M. (1958). The priniciples of quantum mechanics. Oxford: Clarendon Press.
Dixit, A.K. (1976). The theory of equilibrium growth. London: Oxford University Press.
Dorfman, R., Samuelson, P.A., & Solow, R.M. (1958). Linear programming and economic analysis. New York: McGraw Hill.
Edwards, H.M. (1994). Advanced calculus: a differential forms approach. Boston: Birkhauser.
Evans, G.C. (1930). Mathematical introduction to economics. New York: McGraw-Hill.
Feynman, R.P., Leighton, R.B., & Sands, M. (1964). Feynman lectures in physics. Massachusetts: Addison-Wesley.
Fisher, I. (1922). The making of index numbers. Boston: Houghton.
Friedman, M. (1983). Foundations of space-time theories: relativity physics and philosophy of science. NJ: Princeton University Press.
Frisch, R. (1936). Annual surveys of general economic theory: the problem of index numbers. Econometrica, 4, 1–38.
Frisch, R. (1965). Theory of production. Chicago: Rand-McNally.
Gelfand, I.M., & Fomin, S.V. (1963). Calculus of variations. Englewood Cliffs, NJ: Prentice-Hall.
Goldman, S.M., & Uzawa, H. (1964). A note on seperability in demand analysis. Econometrica, 32, 387–398.
Hanoch, G. (1975). Production or demand models with direct or indirect implicit addictivity. Econometrica, 43, 395–420.
Hicks, J.R. (1946). Value and capital, 2nd edn. Oxford: Clarendon Press.
Hicks, J.R. (1969). Direct and indirect addictivity. Econometrica, 37, 353–354.
Houthakker, H.S. (1960). Addicitive preferences. Econometrica, 28, 244–257.
Houthakker, H.S. (1965). A note on self-dual preferences. Econometrica, 33, 797–801.
Johnson, W.E. (1913). The pure theory of utility curves. Economic Journal, 23, 483–513.
Katzner, D.W. (1970). Static demand theory. New York: McMillian.
Kemp, M.C., & Long, N.V. (1982). On evaluation of social income in a dynamic economy: variations on the Samuelsonian theme. In G.R. Feiwel (Ed.), Samuelson and neoclassical economics. Boston: Kluwer-Nijhoff.
Keynes, J.M. (1930). A treatise on money. London: McMillian.
Klein, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.
Konus, A.A. (1939). The problem of the true index of the cost of living (English translation of 1924 article). Econometrica, 7, 10–29.
Koopmans, T.C. (1967). Intertemporal distribution and ‘optimal’ aggregate economic growth. In Ten economic studies in the tradition of Irving Fisher. New York: Wiley.
Lau, L.J. (1969). Duality and the structure of utility preferences. Journal of Economic Theory, 1, 374–396.
Lau, L.J. (1978). Applications of profit functions. In M. Fuss, & D. Mc-Fadden (Eds.), Production economics: a dual approach to theory and applications, vol. 1. Amsterdam: North-Holand.
Marshall, A. (1920). Principles of economics: an introductory volume. London: McMillian.
Minhas, B.S. (1963). An international comparison of factor costs and factor use. Amsterdam: North-Holland.
Olver, P.J. (1986). Applications of Lie groups to differential equations. New York: Springer.
Olver, P.J. (1995). Equivalence, invariants, and symmetry. Cambridge: Cambridge University Press.
Pearce, I.F. (1962). The end of the golden age in Solovia. American Economic Review, 52, 1088–1097.
Phelps, E.S. (1987). Golden rule. In J. Eatwell, M. Milgate, & P. Neuman (Eds.), New pelgrave: a dictionary of economics. London: McMillian.
Pigou, A.C. (1922). Empty economic boxes: a reply. Economic Journal, 32, 16–30.
Pollak, R.A. (1971). Additive utility functions and linear engel curves. The Review of Economic Studies, 37, 401–413.
Ramsey, F. (1928). A mathematical theory of saving. Economic Journal, 38, 543–559.
Richter, M.K. (1966). Invariance axioms and economic indexes. Econometrica, 34, 739–755.
Robertson, D.H. (1924). Those empty economic boxes. Economic Journal, 34, 16–30.
Russell, R.R. (1964). The empirical evaluation of theoretically plausible demand functions, Ph.D. Dissertation. Harvard University, Cambridge, MA.
Samuelson, P.A. (1938). A note on the pure theory of consumer’s behavior. Economical, 5, 62–71.
Samuelson, P.A. (1947). Foundations of economic analysis. Cambridge, MA: Harvard University Press.
Samuelson, P.A. (1950). The problem of integrability in utility theory. Economica, 17, 355–385.
Samueslon, P.A. (1961). The evaluation of social income: capital formation and wealth. In F.A. Lutz, & D.C. Hague (Eds.), Theory of capital. London: McMillian.
Samuelson, P.A. (1965). A catenary turnpike theorem involving consumption and the golden rule. American Economic Review, 55, 486–496.
Samuelson, P.A. (1967). Turnpike refutation of the golden rule in the welfare-maximizing many year plan. In K. Shell (Ed.), Essays in the theory of optimal economic growth. Cambridge: MIT Press.
Samuelson, P.A. (1969). Corrected formulation of direct and indirect additivity. Econometrica, 37, 355–359.
Samuelson, P.A. (1970). Law of conservation of capital-output ratio in closed von Neumann systems. Proceedings of the National Academy of Science, Applied Mathematical Science, 67, 1477–1479.
Samuelson, P.A., & Solow, R.M. (1956). A complete capital model involving heterogeneous captial goods. Quarterly Journal of Economics, 70, 537–567.
Samuelson, P.A., & Swamy, S. (1974). Invariant economic index numbers and canaoncial duality: survey and synthesis. American Economic Review, 64, 566–593.
Sato, R. (1974). On the separable class of non-homothetic CES functions. Economic Studies Quarterly, 25, 42–55.
Sato, R. (1976). Self-dual preferences. Econometrica, 44, 1017–1032.
Sato, R. (1977a). Homothetic and non-homothetic CES functions. American Economic Review, 67, 559–569.
Sato, R. (1977b). The implicit formulation and non-homothetic structure of utility functions. In H. Albach, E. Helmstadter, & R. Henn (Eds.), Qualitative wirtshcaftsfors chung: W. Krelle zum 60. Geburstag. Tubingen: Mohr.
Sato, R. (1981). Theory of technical change and economic invariance: application of Lie groups. New York: Academic Press.
Sato, R. (1985). The invariance principle and income-wealth conservation laws. Journal of Econometrics, 30, 365–389. Reprint (1990) In R. Sato, & R. Ramchandran (Eds.), Conservation laws and symmetry: applications to economics and finance (pp.71–106). Norwell, MA: Kluwer.
Sato, R. (1990). The invariance principle and income-wealth conservation laws. In R. Sato, & R. Ramachandran, Conservation laws and symmetry. Boston:Kluwer
Sato, R., & Matsushita, M. (1989). Estimation of self-dual demand functions: an international comaprison. In R. Sato, & T. Negishi (Eds.), Developments in Japanese economics. Tokyo: Academic Press.
Sato, R., & Ramachandran, R. (1974). Models of optimal endogenous technical progress, scale effect, and duality of production functions, Discussion Paper, Department of Economics, Brown University, Providence, RI
Schneider, E. (1934). Theorie der production. Vienna: J. Springer.
Shepherd, R.W. (1953). Cost and production fucntions. Princeton, NJ: Princeton University Press.
Solow, R.M. (1957). Technical change and the aggregte production function. Review of Economic Statistics, 39, 312–320.
Silberberg, E. (1990). The structure of economics: a mathematical analysis. New York: McGraw Hill.
Sraffa, P. (1926). The laws of return under competitive conditions. Economic Journal, 36, 535–550.
Stephani, H, & MacCullum, M. (1989). Differential equations: their solution using symmetries. Cambridge: Cambridge Unviversity Press.
Stigler, G.J. (1961). Economic problems in measuring changes in productivity. Output, input, and productivity, measurement, conference on research in income and wealth (pp. 47–63). Princeton, NJ: Princeton University Press.
Vanek, J. (1968). Maximal economic growth. Ithaca, NY: Cornell University Press.
Varian, H.R. (1984). Microeconomic analysis. New York: W.W. Norton & Co.
Weitzman, M.L. (1976). On the welfare significance of national product in a dynamic economy. Quarterly Journal of Economics, 90, 156–162.
Whitaker, J.K. (1990). Marshall’s theories of competitive price. In R.M. Tullberg (Ed.), Alfred Marshall in retrospect (pp. 29–48). Vermont: Edward Elgar.
Yoglam, I. (1988). Felix Klein and Sophus Lie: evolution of the idea of symmetry in the nineteenth century. Boston: Birkhauser.
Zellner, A., & Revanker, N.S. (1969). Generalized production functions. Review of Economic Studies, 36, 241–250.
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Sato, R., Ramachandran, R.V. (2014). Introduction. In: Symmetry and Economic Invariance. Advances in Japanese Business and Economics, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54430-2_1
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