Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T16:11:57.892Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMUM SAVINGS AND OPTIMAL GROWTH: THE CASS–MALINVAUD–KOOPMANS NEXUS

Published online by Cambridge University Press:  25 July 2013

Stephen E. Spear  and
Warren Young
Stephen E. Spear*
Affiliation:
Carnegie–Mellon University
Warren Young
Affiliation:
Bar Ilan University
*
Address correpondence to: Stephen E. Spear, Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA; e-mail: ss1f@andrew.cmu.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper surveys the contributions of David Cass, Tjalling Koopmans, and Edmond Malinvaud over the decades during which modern optimal growth theory was developed. By utilizing material ranging from dissertations, drafts, and working papers through conference presentations, discussions, and published papers, we show that both Malinvaud and Cass had significant impacts on the evolution of Koopman's thought, and the development of his part of what is known as “the Cass–Koopmans model.” Based on our findings, we conclude that the modern optimal growth model should include the contributions of Malinvaud, and be retitled “the Cass–Malinvaud–Koopmans” model accordingly.

Keywords

Optimal GrowthEconomic HistoryNeoclassical Growth Model
Type
MD Survey
Information
Macroeconomic Dynamics , Volume 18 , Issue 1 , January 2014 , pp. 215 - 243
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Allais, M. (1947) Economie et intérét. Paris: Imprimerie Nationale.Google Scholar
Allais, M. (1959) Influence of the Capital–Output Ratio on Real National Income. Paper presented at Cowles Foundation Seminar, 25 May 1959.Google Scholar
Allais, M. (1962) The influence of the capital–output ratio on real national income. Econometrica 30, 700–728.CrossRefGoogle Scholar
Allais, M. (1965) Comments on Malinvaud's “Croissances optimales dans un modele macroeconomique.” In Study Week on the Econometric Approach to Development Planning, 7–13 October 1963, pp. 379–384. Rome: Pontifical Academy of Sciences.Google Scholar
Allais, M. (1967) Some analytical and practical aspects on the theory of capital. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning. Proceedings of a Conference held by the International Economic Association, pp. 64–110. New York: St. Martin's Press.CrossRefGoogle Scholar
Arrow, K. (2009) Some developments in economic theory since 1940: An eyewitness account. Annual Review of Economics 1, 1–16.CrossRefGoogle Scholar
Barro, R. (2008) Macroeconomics: A Modern Approach. Mason, OH: Thomson South-Western.Google Scholar
Cass, D. (1963) Optimum Savings in an Aggregative Model of Capital Accumulation. Technical Report 5, Institute for Mathematical Studies in the Social Sciences, Stanford University, 27 November [draft of Chapter 1 of Cass (1965a), as cited by Koopmans (1965: 286)].Google Scholar
Cass, D. (1964a) Studies in the Theory of Optimum Economic Growth. Technical report 6, University of Chicago, Department of Economics Summer [draft of Chapters 1 and 3 of Cass (1965a)].Google Scholar
Cass, D. (1964b) Optimum Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem. Discussion paper 178, Cowles Foundation, New Haven, CT.Google Scholar
Cass, D. (1965a) Studies in the Theory of Optimum Economic Growth. Unpublished Ph.D dissertation, Stanford University.Google Scholar
Cass, D. (1965b) Optimum growth in an aggregative model of capital accumulation. Review of Economic Studies 37, 233–240.CrossRefGoogle Scholar
Cass, D. (1966) Optimum growth in an aggregative model of capital accumulation: A turnpike theorem. Econometrica 34, 838–850.CrossRefGoogle Scholar
Chakravarty, S. (1967) Alternative preference functions in problems of investment planning on the national level. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning, Proceedings of a Conference held by the International Economic Association. New York: St. Martin's Press.Google Scholar
Darity, W. and Young, W. (2001) The early history of rational and implicit expectations. History of Political Economy 33, 773–814.Google Scholar
Desrousseaux, J. (1959) Variations sur la croissance économique. Unpublished manuscript [cited by Allais (1962, 726)].Google Scholar
Desrousseaux, J. (1961a) Expansion stable et taux d'intérêt optimal. Annales des Mines, 31–46, Novembre [cited by Allais (1962, 726) and Koopmans (1965, 286)].Google Scholar
Desrousseaux, J. (1961b) Caractéristiques globales des economies quelconques et taux d'intérêt dans les mondes évolutifs. Unpublished manuscript [cited by Allais (1962, 727)].Google Scholar
Drèze, J. (1964) Some postwar contributions of French economists to theory and public policy: With special emphasis on problems of resource allocation. American Economic Review 54, Supplement: 2–64.Google Scholar
Durlauf, S. and Quah, D. (1999) The new empirics of economic growth. In Taylor, J. and Woodford, M. (eds.), Handbook of Macroeconomics, vol. 1, pp. 235–308. New York: Elsevier.CrossRefGoogle Scholar
Hood, W. and Koopmans, T. (eds.) (1953) Studies in Econometric Method. New York: Wiley.Google Scholar
Hurwicz, L. (1967) Programming involving infinitely many variables and constraints. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning, Proceedings of a Conference held by the International Economic Association. New York: St. Martin's Press.Google Scholar
Koopmans, T. (1951) Letter to Herbert Simon, 29 June [in Simon Papers at Carnegie-Mellon Uni-break versity].Google Scholar
Koopmans, T. (1957) Three Essays on the State of Economic Science. New York: McGraw-Hill.Google Scholar
Koopmans, T. (1962) On Flexibility of Future Preference. Discussion paper 150, 13 December, Cowles Foundation, New Haven, CT.Google Scholar
Koopmans, T. (1963a) Proportional Growth and Turnpike Theorems. Discussion paper 152, 24 January, Cowles Foundation, New Haven, CT.Google Scholar
Koopmans, T. (1963b) Economic Growth at a Maximal Rate. Paper presented at July 1963 meeting of Econometric Society, Copenhagen.Google Scholar
Koopmans, T. (1963c) On the Concept of Optimal Economic Growth. Paper presented at the Vatican Study Week on the Econometric Approach to Development Planning, Rome, Pontifical Academy of Science, 7–13 October.Google Scholar
Koopmans, T. (1963d) On the Concept of Optimal Economic Growth. Discussion paper 163, Cowles Foundation, New Haven, CT.Google Scholar
Koopmans, T. (1963e) Appendix—On the Concept of Optimal Economic Growth. Discussion paper 163-A, Cowles Foundation, New Haven, CT.Google Scholar
Koopmans, T. (1964a) On flexibility of future preference. In Bryan, G. and Shelly, M. (eds.), Human Judgments and Optimality, pp. 243–254. New York: Wiley.Google Scholar
Koopmans, T. (1964b) Economic growth at a maximal rate. Quarterly Journal of Economics 78, 355–394.CrossRefGoogle Scholar
Koopmans, T. (1965) On the Concept of Optimal Economic Growth. Paper presented at the Vatican Study Week on the Econometric Approach to Development Planning, Rome, Pontifical Academy of Science, 7–13 October, pp. 225–300.Google Scholar
Koopmans, T. (1966a) On the concept of optimal economic growth. In The Econometric Approach to Development Planning. New York: North-Holland and Rand-McNally.Google Scholar
Koopmans, T. (1966b) Objectives, Constraints, and Outcomes in Optimal Growth Models. Discussion paper 212, Cowles Foundation, New Haven, CT.Google Scholar
Koopmans, T. (1967) Objectives, constraints, and outcomes in optimal growth models. Econometrica 35, 1–15.CrossRefGoogle Scholar
Koopmans, T. (1970) Scientific Papers, edited by Beckmann, M., Christ, C., and Nerlove, M.. Berlin: Springer.Google Scholar
Koopmans, T. and Bausch, A. (1959) Selected topics in economics involving mathematical reasoning. SIAM Review 1, 79–148.CrossRefGoogle Scholar
Krueger, Alan B. (2003) An interview with Edmond Malinvaud. Journal of Economic Perspectives 17, 181–198.CrossRefGoogle Scholar
Kurz, M (1965) Optimal paths of capital accumulation under the minimum time objective. Econometrica 33, 42–66.CrossRefGoogle Scholar
Lucas, R., Stokey, N., and Prescott, E. (1989) Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press.Google Scholar
Malinvaud, E. (1951a) Optimum Amount of Capital in a Stationary Economy. Discussion paper 2007, Cowles Commission, New Haven, CT.Google Scholar
Malinvaud, E. (1951b) Efficient Allocation of Resources and Capital Accumulation. Discussion paper 2014, Cowles Commission, New Haven, CT.Google Scholar
Malinvaud, E. (1951c) Efficent Accumulation of Capital. Paper presented at the Minneapolis meeting of the Econometric Society, 4–7 September.Google Scholar
Malinvaud, E. (1951d) Capital Accumulation and Efficient Allocation of Resources. Discussion paper 2026, Cowles Commission, New Haven, CT.Google Scholar
Malinvaud, E. (1953) Capital accumulation and efficient allocation of resources. Econometrica 21, 233–268.CrossRefGoogle Scholar
Malinvaud, E. (1959) Programmes d'expansion et taux d'interet. Econometrica 27, 215–227.CrossRefGoogle Scholar
Malinvaud, E. (1961) On the Rate of Onterest of Efficient Proportional Growth Programs. Paper presented at the Stillwater meeting of the Econometric Society, 30 August–1 September.Google Scholar
Malinvaud, E. (1963) Croissances optimales dans un modele macroecononomique. Paper presented at the Vatican Study Week on the Econometric Approach to Development Planning, Rome, Pontifical Academy of Science, 7–13 October.Google Scholar
Malinvaud, E. (1965a) Croissances optimales dans un modele macroecononomique. In Study Week on the Econometric Approach to Development Planning, 7–13 October, pp. 301–384. Rome: Pontifical Academy of Science.Google Scholar
Malinvaud, E. (1965b) Les croissance optimales. Cahiers du Séminaire d'Économétrie 8, 71–100.CrossRefGoogle Scholar
Malinvaud, E. (1967) Decentralized procedures for planning. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning, Proceedings of a Conference Held by the International Economic Association, pp. 170–208. New York: St. Martin's Press.CrossRefGoogle Scholar
Malinvaud, E. (1972) The scientific papers of Tjalling C. Koopmans: A review article. Journal of Economic Literature 10, 798–802.Google Scholar
McKenzie, L. (1967) Maximal paths in the Von Neumann model. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning, Proceedings of a Conference Held by the International Economic Association, pp. 43–63. New York: St. Martin's Press.CrossRefGoogle Scholar
McKenzie, L. (1999) The First Conferences on the Theory of Economic Growth. Working paper 459, University of Rochester: Center for Economic Research.Google Scholar
Pontryagin, L., Bolyyanskii, V., Gamkriledze, R., and Mischenko, E. (1962a) The Mathematical Theory of Optimal Processes. New York: Interscience.Google Scholar
Pontryagin, L., Bolyyanskii, V., Gamkriledze, R., and Mischenko, E. (1962b) Ordinary Differential Equations. Reading, MA: Addison–Wesley.Google Scholar
Radner, R. (1967) Dynamic programming of economic growth. In Malinvaud, E. and Bacharach, M. (eds.), Activity Analysis in the Theory of Growth and Planning, Proceedings of a Conference Held by the International Economic Association, pp. 111–141. New York: St. Martin's Press.CrossRefGoogle Scholar
Ramsey, F. (1928) A mathematical theory of saving. Economic Journal 38, 543–559.CrossRefGoogle Scholar
Report of the Boston Meeting, December 27–29, 1963. Econometrica 32 (October 1964), 688–707.Google Scholar
Report of the Boulder Meeting, August 29–September 2, 1949. Econometrica 18 (April 1950), 173–192.Google Scholar
Report of the Minneapolis Meeting, September 4–7, 1951. Econometrica, 20 (January 1952), 88–103.Google Scholar
Report of the Stillwater Meeting, August 30–September 1, 1961. Econometrica 30 (April 1962), 351–377.Google Scholar
Report of the Warsaw Meeting, September 1966 (1967) In Supplementary Issue, Econometrica 35, 14–18.Google Scholar
Samuelson, p. (1965) A catenary turnpike theorem involving consumption and the golden rule. American Economic Review 55, 486–496.Google Scholar
Scarf, H. and Koopmans, T. (1965) Some Suggestions for Computing the Von Neumann Path of Maximal Proportional Growth. Preliminary discussion paper, Cowles Foundation, New Haven, CT.Google Scholar
Solow, R. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics 32, 65–94.CrossRefGoogle Scholar
Spear, S. and Wright, R. (1998) Interview with David Cass. Macroeconomic Dynamics 2, 533–558.CrossRefGoogle Scholar
Srinivasan, T. (1962) On a Two-Sector Model of Growth. Discussion paper 139 (Revised), Cowles Foundation, New Haven, CT.Google Scholar
Srinivasan, T. (1964) Optimal savings in a two-sector model of growth. Econometrica 32, 358–373.CrossRefGoogle Scholar
Stoleru, L. (1965) An optimal policy for economic growth. Econometrica 33, 321–347.CrossRefGoogle Scholar
Swan, T. (1956) Economic growth and capital accumulation. Economic Record 66, 334–361.CrossRefGoogle Scholar
Uzawa, H. (1963) Optimal Growth in a Two-Sector Model of Capital Accumulation. Technical report 121, Institute for Mathematical Studies in Social Sciences, Stanford University.Google Scholar
Uzawa, H. (1964) Optimal growth in a two-sector model of capital accumulation. Review of Economic Studies 31, 1–24.CrossRefGoogle Scholar
Young, W. (1987) Interpreting Mr Keynes: The IS–LM Enigma. Oxford, UK: Polity–Blackwell.Google Scholar