Advanced Systems Analysis (ASA) Program researchers develop and study stylized models of endogenous economic growth in which long-term economic growth is generated by such factors as physical and human capital. An extended form of these models also includes feedback with the environment.

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Long-term economic growth not only depends on the dynamics of production factors that evolve based on investment, but also on other inputs, of which environmental feedback is becoming increasingly important. The environment establishes additional constraints to growth, which were passive in the past when the Earth functioned well within the planetary boundaries. However, the closer that humanity approaches the planetary boundaries, the stronger the feedback of the environment becomes to human economic activity. This necessitates the development of new economic growth models capable of generating solutions related to green growth and sustainable development.

ASA has a long tradition of studying models of economic growth and of developing corresponding methods of optimal control. The key methodological tool for finding a solution is the Pontryagin maximum principle on the infinite time horizon. ASA research has focused for many years on the development of models of economic growth. The specific methodological challenge addressed in research published in 2014 is the unboundedness of admissible controls, which may also cause non-convergence of the integral objective function. This is not typical for engineering applications, from which the theory of optimal control originates; thus classical forms of the Pontryagin maximum principle do not cover such cases. Economic applications, on the other hand, quite frequently need to consider unbounded controls (for example, an individual may decide to consume more assets than she possesses, and borrowing in principle can be unlimited). Research by [1][2][3] and [4] introduced so-called weak regularity assumptions covering the case of unbounded controls and derived a new so-called normal-form version of the Pontryagin maximum principle for infinite-horizon optimal control problems, as well as an explicit Cauchy-type formula for the so-called adjoint variables.

Much ASA research effort is dedicated to analyzing particular models of economic growth that address specific drivers, impacts, feedbacks, and so on. In 2014 ASA researchers published works presenting models that addressed issues of governmental policy on regulation of the labor market [5][6] and the land market [7][8]. A simple Ramsey-type economic model was calibrated and extrapolated to the future for Russia in [9][10]. Of particular interest and importance are models in which environmental services, notably natural resources, act as constraints and/or as components of the decision maker’s utility. ASA researchers work on proper inclusion of them into formal models of endogenous economic growth. A review of literature on the topic was presented in [11]. Three papers presented models of economic growth based on input of non-renewable resources in which a central planner aims to improve the resource productivity [12] [13] [14]. This work is being carried out in the framework of the joint Tshinghua University-IIASA project “Optimization of Resource Productivity for Sustainable Economic Development,” funded by the National Natural Science Foundation of China.

References

[1] Aseev SM (2014). On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems. *Proceedings of the Steklov Institute of Mathematics*, 287(Suppl.1):11-21

[2] Aseev SM, Veliov VM (2014a). Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions. *Proceedings of the Steklov Institute of Mathematics*, 20(3):41-57

[3] Aseev SM, Veliov VM (2014b). Needle variations in infinite-horizon optimal control, Variational and Optimal Control Problems on Unbounded Domains. *Contemporary Mathematics*, 619, (eds). G. Wolansky G., Zaslavski A.J., Amer. Math. Soc., Providence, RI, 1–17

[4] Aseev SM, Veliov VM (2014c). Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions. *Research Report 2014-06*, Research Unit ORCOS, Institute of Mathematical Methods in Economics, Vienna University of Technology, Austria

[5] Palokangas T (2014a). Optimal capital taxation, labour unions, and the hold-up problem. *Labour*, 28(4):359-375

[6] Palokangas T (2014b). One-parameter GHG emission policy with R&D-based growth. In: *Dynamic Optimization in Environmental Economics*, E. Moser, W. Semmler, G. Tragler and V.M. Veliov (eds), Heidelberg: Springer Verlag, 111-126

[7] Lehmijoki U, Palokangas T (2014a). Landowning, status and population growth. In: *Dynamic Optimization in Environmental Economics*, E. Moser, W. Semmler, G. Tragler and V.M. Veliov (eds), Heidelberg: Springer Verlag, 315-328

[8] Lehmijoki U, Palokangas T (2014b). Land reforms, status and population growth. IZA Discussion Paper No. 8054

[9] Tarasyev AM, Usova AA, Shmotina YV (2014a). Projection of the Russian economic development in the framework of the optimal control model by investments in fixed assets. *Economy of Region*, 3(2014):265-273

[10] Tarasyev AM, Usova AA, Shmotina YuV (2014b). Prognostic modeling of optimal trends of economic growth. *Proceedings of the XI International Scientific-Applied Conference on Problems on Economic Development in Modern World “Sustainable Development of Russian Regions,”* Ekaterinburg, Ural Federal University, 469-475

[11] Nyambuu U, Palokangas T, Semmler W (2014). Sustainable growth: Modelling, issues and policies. IIASA Interim Report IR-14-019

[12] Tarasyev AM, Usova AA, Russkikh OV, Wang W (2014). Optimal trajectory construction by integration of Hamiltonian dynamics in models of economic growth under resource constraints. *Proceedings of the Institute of Mathematics and Mechanics UrB RAS*, 20(4):258-276 [In Russian, English version to appear]

[13] Tarasyev AM, Usova AA (2014a). Model of development of resource-dependent economy. *Proceedings of the International Conference Dedicated to the 90th Anniversary of N.N. Krasovskii*, Ekaterinburg, Institute of Mathematics and Mechanics UrB RAS – Ural Federal University, 187-188 [In Russian]

[14] Tarasyev AM, Usova AA (2014b). Stepwise approximation in problem of optimization of natural resources productivity. *Proceedings of the 45th International School-Conference “Contemporary Problems in Mathematics” Dedicated to the 75th Anniversary of V.I.Berdyshev*, Institute of Mathematics and Mechanics UrB RAS, 96-99 [In Russian]

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