By Sabine Pickenhain (auth.), Jesús Crespo Cuaresma, Tapio Palokangas, Alexander Tarasyev (eds.)
The ebook makes a speciality of the sustainability of monetary progress in a altering setting, below the consequences of worldwide warming, dwindling power assets, and technological switch. It additionally offers motives for major fluctuations in nations’ development premiums. the consequences are derived from ancient facts on monetary development relating to environmental coverage, technological swap, improvement of shipping infrastructure, inhabitants matters, and environmental mortality. The rigorous research of theoretical and utilized elements finds very important coverage implications for optimum funding, optimum timing of abatement actions, and for an optimum balancing of financial development with environmental concerns.
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Additional info for Dynamic Systems, Economic Growth, and the Environment
Basing on these two properties one can obtain the sufficient result for optimality conditions of the Pontryagin maximum principle (see Krasovskii and Tarasyev 2008). 3 Hamiltonian Systems in the Pontryagin Maximum Principle Let us introduce the following notation z(t) = k(t)ψ(t) for the cost of capital. Three optimal control regimes generate three Hamiltonian systems. The Hamiltonian system for the zero control is defined by the following system of differential equations ⎧ ⎨ z˙ = δz − kf (k) , (11) f (k) ⎩ k˙ = −λk, in the domain D1 described by relations D1 = (k, z) : z ≤ k , k > 0, z > 0 .
Thus the following condition is necessary and sufficient for optimality of x ∗ (t) ξ (t, x ∗ (t)) = y (t) − y(t) − 1 ≥ 0. (89) For any c ∈ R the function y(t) = −1 + cet solves the equation y (t) − y(t) − 1 1 = 0. This solution y belongs to the Sobolev space W2,ν −1 ( ) iff c = 0. Finally we determine the function a by (HJ), (t, x ∗ (t)) = a (t) − y(t)x ∗ (t) + (−ξ )(y(t) + 1) = a (t) − e−t = 0 (90) and a(t) = −e−t , a ∈ W11,1 ( ). (91) Summarized we have shown that S(t, ξ ) = a(t) + y(t)(ξ − x ∗ (t)) = −ξ − 2e−t (92) solves the dual problem (Dα )L ∞ .
On Fig. 9 the corresponding curves of optimal growth trajectories are shown in comparison with the real data. One can see that presence of constraints provides qualitatively better results. Sequential Precision of Predictions in Models of Economic Growth 41 Fig. 2 Model Verification Verification of the model is presented by the following procedure. Assume that the proposed approach is applied to a fixed time interval in the given data time series. in the course of time, the data is updated and one can compare the forecast with the new data.
Dynamic Systems, Economic Growth, and the Environment by Sabine Pickenhain (auth.), Jesús Crespo Cuaresma, Tapio Palokangas, Alexander Tarasyev (eds.)