Optimal economic growth

The Advanced Systems Analysis (ASA) researchers in 2013 worked on developing new economic growth models capable of generating “green growth” and sustainable development solutions.

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Optimal growth

Neoclassical endogenous economic growth theory is used to model long-term economic growth. It operates using small-scale stylized models in the form of optimal control problems (OCPs), often on the infinite time horizon; the Pontryagin maximum principle (MP) is used to derive a solution.

Long-term economic growth is explained by the dynamics of production factors that evolve due to investments, and by other inputs, of which environmental feedback has become important in recent years.

The environment sets up additional constraints to growth; these were passive in the past when Earth functioned well away from the planetary boundaries. The closer humanity approaches the planetary boundaries, however, the more noticeable the feedback of the environment to human economic activity is becoming. This necessitates new economic growth models capable of generating “green growth” and sustainable development solutions.

ASA has long been an advocate of research on economic growth at IIASA. A monograph was published based on the results of the symposium “Green Growth and Sustainable Development” held at IIASA on 9-10 December 2011 [1]. This collects models developed by IIASA and other research groups which integrate environmental constraints into economic growth models.

For example, scientists considered a dynamic optimization model of investment in resource productivity in which the dematerialization of the economy is an option  [2]. The authors identified a domain of model parameters for which optimal dynamics converge to a steady state, indicating a possibility of sustainable economic growth with exhaustible resources: the return on investment in green technology should exceed the discount factor, whereas the discount factor should stay higher than a growth rate in production factors that is adjusted in inverse proportion to the output elasticity of the resource.

Scientists continued studying the model of resource productivity and suggested a stair-wise suboptimal approximation to an optimal control under the constraints on natural resources [3].

The issue of economic growth and exhaustible resource consumption was studied [4]. The authors considered a model in which a central planner chooses between allocating a resource to production or to R&D, and analyzed this using a specially developed version of the MP. The optimal growth is shown to be unsustainable if the accumulation of knowledge relies on the resource as an input, if the new knowledge is produced with a decreasing return to scale, or if the economy is too small.

An economic growth model was considered under extreme (catastrophic) events affecting production that may trigger stagnation and shrinkage of an economy [5]. The stabilization of growth must rely on two-stage strategic ex ante (before an event) risk reduction and risk transfer options, such as hazard mitigation and catastrophic insurance, as well as on ex post (after an event) borrowing: the coexistence of ex ante and ex post options generates stronger risk aversion. 

By means of an economic growth model with an option of "green" technology, strategies were elaborated for the development of solar energy in Japan [6].

A family-optimization model with endogenous fertility and status seeking was used to consider the effects on economic and demographic growth of land ownership and land reforms [7]. It showed strong incentives for poor farmers to limit their family size and improve the productivity of land. Even though the income effect due to the land reform tends to raise fertility, it is outweighed by a strong enough status effect, thus generating a decrease in population growth.  

European demographic history provides supporting anecdotal evidence for this theoretical result. The greenhouse gas emission policy was studied of regions that use land, labor, and emitting inputs in production and that enhance their productivity by devoting labor to R&D, but with different endowments and technology [8]. The results indicate that if a self-interested central planner allocates emission caps in fixed proportion to past emissions (i.e., grandfathering), then this establishes the Pareto optimum, decreasing emissions and promoting R&D and economic growth. There was also an examination of optimal capital taxation with wage-setting labor unions when the government taxes consumption and subsidizes labor and capital [9]. The optimal labor subsidy was proven to be positive; the optimal capital subsidy was proven to be zero in the absence of the hold-up problem, but positive in its presence.  

Research was also carried out biodiversity management run by a self-interested central planner in an economic union where regions devote labor to R&D [10]. It was found that biodiversity is promoted by sparing ecological habitats from production.If a central planner has no budget, then the political economy leads to Pareto optimum, but if a budget is in place, the Pareto-optimal allocation of labor between production and R&D will be distorted by the subsidy. If this is applied to NATURA 2000 in the European Union, then this suggests that regulatory power is appropriate for the European Commission.


[1] Crespo Cuaresma J, Palokangas T, Tarasyev A (Eds.) (2013). Green Growth and Sustainable Development.Dynamic Modeling and Econometrics in Economics and Finance, Springer-Verlag, Berlin Heildelberg, 14.
[2] Tarasyev A , Zhu B (2013). Optimal proportions in growth trends of resource productivity. In: J.CrespoCuaresma, T.Palokangas, A.Tarasyev (Eds.). Green Growth and Sustainable Development. Dynamic Modeling and Econometrics in Economics and Finance, Springer-Verlag, Berlin Heildelberg, 14, 49–66.
[3] Tarasyev A, Usova A (2013). Algorithms for construction of optimal trajectories based on control approximations in problems on infinite time horizon. Proceedings of the Scientific Conference on Informatics Problems (SPISOK 2013), St. Petersburg, Russia, 346—353.[in Russian].
[4] Aseev SM (2013). On some properties of adjoint variables in relations of the Pontryagin maximum principle for optimal economic growth problems.Proceedings of the Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, 19 (4), 15—24 [In Russian].
[5] Ermoliev Y, Ermolieva T (2013). Economic growth under catastrophes. In: A. Amendola, T. Ermolieva, J. Linnerooth-Bayer, R. Mechler (Eds.). Integrated Catastrophe Risk Modeling: Supporting Policy Processes, Springer, Dordrecht, Netherlands, 103—117.
[6] Watanabe C, Shin J-H (2013). Utmost fear hypothesis explores green technology driven energy for sustainable growth. In: J. Crespo Cuaresma, T. Palokangas, A. Tarasyev (Eds.). Green Growth and Sustainable Development. Dynamic Modeling and Econometrics in Economics and Finance, Springer-Verlag, Berlin Heildelberg, 14, 191-216.
[7] Lehmijoki U, Palokangas T (accepted 2013). Landowning, status and population growth. In: Dynamic Modeling and Econometrics in Econometrics and Finance Series, Springer Verlag, 2014.
[8] Palokangas T (accepted 2013). One-parameter GHG emission policy with R&D-based growth.In: Dynamic Modeling and Econometrics in Econometrics and Finance Series, Springer Verlag, 2014.
[9] Palokangas T (under review). Optimal capital taxation, labor unions, and the hold-up problem. LABOUR: Review of Labour Economics and Industrial Relations, Wiley.
[10] Palokangas T (under review). Biodiversity Management with R&D-based Growth. HECER Discussion Paper No. 368.


IIASA's National Member Organizations of Finland and Russia strongly support IIASA research on economic growth.
ASA’s main collaborators in the field of optimal economic growth include J. Crespo Cuaresma, Research Scholar, POP, IIASA, Austria; S. Kaniovski, Austrian Institute of Economic Research (WIFO), Austria; L. Lambertini, Professor, Department of Economic Sciences, University of Bologna, Italy; U. Lehmijoki, Professor, Department of Economics, Helsinki University, Finland; S. Pickl, Professor, Department of Operations Research, Federal Armed Forces University Munich, Germany; W. Semmler, Professor, The New School for Social Research, USA; and B. Zhu, Professor, Tsinghua University, China.

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Last edited: 21 May 2014


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