Far from being wildly profitable and draining the colonies of their wealth like like vampire bats, the European empires weren't particularly profitable overall. (Some particular investors, of course, made large profits, the most notorious being Leopold II of Belgium, who ran the Congo as his own private demesne, killing millions, until a European wide outcry forced him to transfer the Congo to the Belgian state in 1908.) And most of the profits flowed to a small group of already rich Europeans, whose investments were subsidised by government spending on infrastructure, the military, etc, from the taxes of poor and middle class Europeans. Even if the profits from Empire had been spent on eliminating poverty amongst poor Europeans, the profits were a tiny fraction of the amounts required to do such a thing in the countries involved (to say nothing of the poor in the other European countries which did not have extensive 3rd world empires). Europe mostly got rich through domestic industrialisation.

Davis and Huttenback found that the British as a whole did not benefit from the empire in India over a 50 year period. They found that investment in India somewhat outperformed domestic or foreign investments before the mid 1880s, but not after.

Thompson thought that Davis and Huttenbeck had if anything, overestimated the profitability of British investment in India, finding it did not offer superior returns to foreign or domestic investment.

Other researchers have looked at different European countries and their empires, generally finding that percentage return was not greatly higher than other forms of investment.

Mammon and the Pursuit of Empire: The Political Economy of British Imperialism, 1860-1912, Lance Edwin Davis & Robert A. Huttenback, Cambridge University Press 1986

The Empire Strikes Back?: The Impact of Imperialism on Britain from the Mid-nineteenth Century, Andrew Thompson, Pearson 2005