Power Energy Efficiency with Environmental Restrict: View from Shadow Price

This paper proposes a new method to deal with directional technology distance function. We propose a new concept: partial directional distance function, which describe the distance of one element (including inputs, outputs, desirable and undesirable) in their direction given the partial distance of the other elements. Based on this, we present the multi-goals programming problem and its solution arithmetic. Then we present the measure of partial marginal effect and the shadow price of resource/environment to outputs. At last, we apply the methodology to empirical data. It turns out this method is feasible and very useful.