The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Calculus of Variations

  • Morton I. Kamien
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_132

Abstract

The development of the calculus of variations is attributed to Euler and Lagrange, although some of it can be traced back to the Bernoullis. A history of the calculus of variations is provided by Goldstine (1980). The calculus of variations deals with the problem of determining a function that optimizes some criterion that is usually expressed as an integral. This problem is analogous to the differential calculus problem of finding a point at which a function is optimized, except that the point in the calculus of variations is a function rather than a number. The function over which the optimum is sought is usually restricted to the class of continuous and at least piecewise differentiable functions.

JEL Classifications

C61 
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Bibliography

  1. Edgeworth, F.Y. 1881. Mathematical psychics. Reprinted, New York: Augustus M. Kelley, 1967.Google Scholar
  2. Evans, G.C. 1924. The dynamics of monopoly. American Mathematical Monthly 31: 75–83.CrossRefGoogle Scholar
  3. Fershtman, C., and M. Kamien. 1987. Dynamic duopolistic competition with sticky prices. Econometrica 55: 1151–1164.CrossRefGoogle Scholar
  4. Goldstine, H.H. 1980. A history of the calculus of variations. New York: Springer.Google Scholar
  5. Hotelling, H. 1931. The economics of exhaustible resources. Journal of Political Economy 39: 137–175.CrossRefGoogle Scholar
  6. Kamien, M.I., and N.L. Schwartz. 1981. Dynamic optimization. New York: North-Holland.Google Scholar
  7. Ramsey, F.P. 1928. A mathematical theory of saving. Economic Journal 38: 543–559.CrossRefGoogle Scholar
  8. Roos, C.F. 1925. A mathematical theory of competition. American Journal of Mathematics 47: 163–175.CrossRefGoogle Scholar
  9. Strotz, R.H. 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies 23: 165–180.CrossRefGoogle Scholar
  10. Yaari, M.E. 1965. Uncertain lifetime, life insurance and the theory of the consumer. Review of Economic Studies 32: 137–150.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Morton I. Kamien
    • 1
  1. 1.