Solutions for improving resource productivity using optimal control models

Wei Wang describes his YSSP project work in which he explored new economic approaches to include natural resources within the analytical framework.

W. Wang

W. Wang


The limited reserves of natural resources have been a critical constraint for sustainable economic development. Research on resource productivity has been challenged by both economic and environmental studies. There is an urgent need to explore new economic approaches that include natural resources in the analytical framework. The impact of economic structure on economic growth is a new research frontier that could help break the economic system's black box. The aim of this project is to construct a multi-sector economic growth model for the core indicator - resource productivity - to analyze the substitution of capital and technology for non-renewable natural resources and to establish optimal investment strategies for capital goods and for raising resource productivity.


We used optimal control theory combined with an economic growth model to look at the problem. In line with the theory of optimal control and economic growth, we constructed and modified a basic optimal control model to reflect the inter-relationships between different sectors, production factors, and other basic economic variables, as well as their dynamics. The optimal control problem for the investment process is studied within the Pontryagin maximum principle. First we look at the optimal control problem in a one-sector system as a special case. Because of the difficulties in solving high dimensional problems using the Hamiltonian system, we introduce a proportional approach to the solution process to further explore the current model methodology.


Based on the basic model framework for resource productivity in the multi-sector economic system, we look at a one-sector system with capital and natural resources as the main production factors; we obtain the stationary solution of investment for raising resource productivity (R&D investment) and for capital goods. At steady state, the output of the system tends to stability, consumption of non-renewable natural resources tends to be 0, and reserve of non-renewable natural resources also tends to be 0. The investment intensity for raising resource productivity is in direct proportion to rate of technical progress, and inversely proportional to the elasticity of natural resources in the production function. By introducing a proportional approach to solution process, we successfully reduce the dimension of variables and obtain the same investment intensity for raising resource productivity as at steady state.


The stationary optimal solution shows that it is possible to obtain sustainable development by raising productivity and substituting capital and renewable resources for non-renewable resources. The proportional approach provides us with one possible way of dealing with a high dimensional economic optimal control problem that can be applied in further studies.


Tarasyev, A., Zhu, B., Optimal Proportions in Growth Trends of Resource Productivity. 2013. Springer monograph.


Wei Wang, of the Center for Industrial Ecology, Department of Chemical Engineering, Tsinghua University, China, is a citizen of China. He was funded by IIASA's National Member Organization for China, and worked in the Advanced Systems Analysis (ASA) Program during the YSSP.

Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.

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Last edited: 19 August 2015


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