Economic and mathematical modelling of sustainable extraction of natural resources

Summary To determine the framework to ensure conditions for Ukrainian mining industry`s sustainable development, the methodological principles to determine the level of sustainability and to model the parameters and limits of sustainable development applying the case of coking coal and iron ore mining have been proposed. The method to measure the extractive sector`s level of sustainability, i.e. the sustainability index, which is determined on the basis of the linear and quadratic deviation of production volumes, has been proposed. The method to measure coking coal and iron ore mining level of sustainability has been developed using statistical indicators of relative and accumulated frequencies, which made it possible to obtain absolute indices of sustainability level in kind. It has been recommended to measure the extractive sector`s limit of sustainability finding the extremum of functions that describe the regression relationships between coke and ore production from the extracted raw materials, taking into account export-import flows and their use in metal production. The obtained modelling results provide an opportunity to forecast the optimal volumes of mining as a basis for sustainable development management of the Ukrainian extractive sector.