A Dynamic Optimization on Energy Efficiency in Developing Countries

This paper introduces a way for measuring the energy efficiency in economics besides the methods in physics. The linkage among energy efficiency, energy consumption and other macroeconomic variables is demonstrated primarily. Based on the methodology of dynamic optimization, a maximum problem of energy efficiency over time is subjected to the extended Solow growth model and instantaneous investment rate. In this model, energy consumption is set as control variable and investment is regarded as state variable. The analytic solutions can be derived and the diagrammatic analysis provides saddle-point equilibrium. With assigning values to parameters, a numerical simulation is presented; meanwhile the optimal paths of investment and energy consumption can be drawn. The discussion on modelling and implications is organized in the end. The dynamic optimization encourages governments in developing countries to pursue higher energy efficiency as it can reduce energy use without influencing the achievement of steady state in terms of Solow model.