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Ongoing climate change most pronounces itself in northern latitudes, including in the Arctic zone of the Russian Federation (AZRF). Climate change is a complex multidirectional process that is characterized by both positive and negative effects on the functioning of territorial economic systems. In this regard, an analysis of the impacts of climate change on economic development is a particularly urgent scientific and practical task that requires comprehensive study. This research was devoted to assessing the probable impacts of climate transformations on the parameters of the economic development of the AZRF regions. The authors created a methodological approach to the assessment of the costs of the effects of climate change for the economy of the AZRF regions, taking into account the average predicted dynamics of surface air temperature and key regional economic specializations, as well as the degree of susceptibility of various industries to the climate change. The energy industry was considered in particular detail since it is the basis for all of the other industries and is the guarantor of life support for the populations that live in the extreme Arctic climate. Calculations have shown that the accumulated economic effects of climate change as a whole for the AZRF economy during the period 2020–2050 will be negative and have been estimated as having a cost of more than RUB 8 trillion (or nearly USD 111 billion in 2020 prices), which would be about 3% of total Russian Arctic GRP in average annual terms. [ABSTRACT FROM AUTHOR]