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Optimal growth in a two-sector economy facing an expected random shock. (English) Zbl 1308.91109
Proc. Steklov Inst. Math. 276, Suppl. 1, S4-S34 (2012) and Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 2, 271-299 (2011).
This article deals with an optimal growth in the two-sector model with two kind of technologies (“clean” and “dirty”). The growth of each sector is described by the system of linear differential equations. It is assumed that in some random time the parameters of the equation change while the moment of the change has an exponential distribution. The problem of optimizing the social welfare function is stated as the optimal control problem and solved using Pontryagin’s maximum principle. The authors give a characterization of the solutions for all possible cases (relations of the values of parameters). The analysis is performed by the qualitative analysis of differential equations: phase diagrams and checking vector fields generated by the system.

MSC:
91B62 Economic growth models
91B55 Economic dynamics
91B66 Multisectoral models in economics
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90 Applications of optimal control and differential games
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References:
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