Optimal programs and their price characterization in a multisector growth model with uncertainty
HTML articles powered by AMS MathViewer
- by Nikolaos S. Papageorgiou PDF
- Proc. Amer. Math. Soc. 122 (1994), 227-240 Request permission
Abstract:
In this paper we examine a nonstationary multisector growth model with uncertainty in which future utilities are discounted. First we establish the existence of strongly optimal programs emanating from a given initial capital stock. Then we show that this optimal program $\hat x$ is sustained by a system of prices $\hat p$ so that the pair $[\hat x,\hat p]$ is competitive and a strong transversality condition holds. We also show that competitiveness and transversality imply optimality.References
- Charalambos D. Aliprantis, Donald J. Brown, and Owen Burkinshaw, Existence and optimality of competitive equilibria, Springer-Verlag, Berlin, 1990. MR 1075992, DOI 10.1007/978-3-642-61521-4 K. Arrow and M. Kurz, Public investment, the rate of return and optimal fiscal policy, Johns Hopkins Press, Baltimore, 1970.
- H. Attouch, Variational convergence for functions and operators, Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, MA, 1984. MR 773850
- Giuseppe Buttazzo, Semicontinuity, relaxation and integral representation in the calculus of variations, Pitman Research Notes in Mathematics Series, vol. 207, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 1020296
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
- Mario Dolcher, Topologie e strutture di convergenza, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 14 (1960), 63–92 (Italian). MR 114201
- A. D. Ioffe and V. M. Tihomirov, Theorie der Extremalaufgaben, VEB Deutscher Verlag der Wissenschaften, Berlin, 1979 (German). Translated from the Russian by Bernd Luderer. MR 527119
- V. L. Levin, Lebesgue decomposition for functionals on the space $L^{\infty }_{X}$ of vector-valued functions, Funkcional. Anal. i Priložen. 8 (1974), no. 4, 48–53 (Russian). MR 0370174 B. Peleg and H. Ryder, On optimal consumption plans in a multisector economy, Rev. Econom. Stud. 39 (1972), 159-169.
- Akira Takayama, Mathematical economics, 2nd ed., Cambridge University Press, Cambridge, 1985. MR 832684
- Martin L. Weitzman, Duality theory for infinite horizon convex models, Management Sci. 19 (1972/73), 783–789. MR 337334, DOI 10.1287/mnsc.19.7.783
- Kôsaku Yosida and Edwin Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46–66. MR 45194, DOI 10.1090/S0002-9947-1952-0045194-X
- Itzhak Zilcha, Characterization by prices of optimal programs under uncertainty, J. Math. Econom. 3 (1976), no. 2, 173–183. MR 421618, DOI 10.1016/0304-4068(76)90026-4 V. Arkin and I. V. Evstigneev, Stochastic models of control and economic dynamics, Academic Press, London, 1987. E. B. Dynkin, Some probability models for a developing economy, Soviet Math. Dokl. 12 (1971), 1422-1425. —, Concave stochastic dynamic programming, Math. USSR-Sb. 16 (1972), 501-515.
- I. V. Evstigneev, Optimal stochastic programs and their stimulating prices, Mathematical models in economics (Proc. Sympos. and Conf. on von Neumann Models, Warsaw, 1972) North-Holland, Amsterdam, 1974, pp. 219–252. MR 0381650
- Roy Radner, Optimal stationary consumption with stochastic production and resources, J. Econom. Theory 6 (1973), no. 1, 68–90. MR 452560, DOI 10.1016/0022-0531(73)90043-4
- M. I. Tacsar, Optimal planning over infinite time interval under random factors, Mathematical models in economics (Proc. Sympos. and Conf. on von Neumann Models, Warsaw, 1972) North-Holland, Amsterdam, 1974, pp. 289–298. MR 0401104
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 227-240
- MSC: Primary 90A16; Secondary 49K27, 49N15, 90A17, 93E20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195728-X
- MathSciNet review: 1195728