There was command-administrative economic system in USSR. Prices were calculated and fixed by administration.
Growth of economic sometimes led to recalculation of prices to lower values.

'волненья' is for 'disturbance/riot/worries' here. It can be act of riot or just feeling of 'political anxiety' in society. Second meaning is implied here. You translation of first line is correct, but I do not remember proper english term right now.

За прекрасное “завтра” державы. = 'because State promised beautiful "tomorrow"'
It's a little bit tricky collocation. 'in exchange for State's beautiful "tomorrow"' literally.