Optimal programs and their price characterization in a multisector growth model with uncertainty
Author:
Nikolaos S. Papageorgiou
Journal:
Proc. Amer. Math. Soc. 122 (1994), 227240
MSC:
Primary 90A16; Secondary 49K27, 49N15, 90A17, 93E20
MathSciNet review:
1195728
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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 is sustained by a system of prices so that the pair is competitive and a strong transversality condition holds. We also show that competitiveness and transversality imply optimality.
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 K. Arrow and M. Kurz, Public investment, the rate of return and optimal fiscal policy, Johns Hopkins Press, Baltimore, 1970.
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 G. Buttazzo, Semicontinuity, relaxation and integral representation in the calculus of variations, Pitman Res. Notes Math. Ser., vol. 207, Longman Sci. Tech., Harlow, 1989. MR 1020296 (91c:49002)
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 J. Diestel and J. Uhl, Vector measures, Math. Surveys Monographs, vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
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 M. Dolcher, Topologie e strutture di convergenza, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1960), 6392. MR 0114201 (22:5026)
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 A. Ioffe and V. Tichomirov, Theory of extremal problems, NorthHolland, Amsterdam, 1979. MR 528295 (80d:49001b)
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 V. Levin, The Lebesgue decomposition for functionals on the vector function space , Functional Anal. Appl. 8 (1974), 314317. MR 0370174 (51:6403)
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 B. Peleg and H. Ryder, On optimal consumption plans in a multisector economy, Rev. Econom. Stud. 39 (1972), 159169.
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 M. L. Weitzman, Duality theory for infinite horizon convex models, Management Sci. 19 (1973), 783789. MR 0337334 (49:2103)
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 K. Yosida and E. Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 4566. MR 0045194 (13:543b)
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 V. Arkin and I. V. Evstigneev, Stochastic models of control and economic dynamics, Academic Press, London, 1987.
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 E. B. Dynkin, Some probability models for a developing economy, Soviet Math. Dokl. 12 (1971), 14221425.
 [16]
 , Concave stochastic dynamic programming, Math. USSRSb. 16 (1972), 501515.
 [17]
 I. V. Evstigneev, Optimal stochastic programs and their stimulating prices, Mathematical Models in Economics (J. Los and M. Los, eds.), NorthHolland, Amsterdam, 1974, pp. 219252. MR 0381650 (52:2541)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919941195728X
PII:
S 00029939(1994)1195728X
Keywords:
Multisector growth model,
feasible program,
discount factor,
free disposability,
intertemporal utility,
support prices,
transversality condition
Article copyright:
© Copyright 1994
American Mathematical Society
