Answer:
The Europeans were willing to engage in imperialism despite the costs because even if imperialism was costly, the economic revenue that it provided was higher than the cost, and when revenue is higher than cost, there is profit. In other words, imperialism was profitable.
Step-by-step explanation:
The reason why imperialism was profitable is that it allowed Europeans to exploit the indigenous peoples of the colonies, and to extract raw materials from them, at the same time that the colonies became markets for the more elaborated goods that were produced in Europe.
This economic system was known as mercantilism (capitalism was also developing at the same time, and would soon take over), and it resulted very profitable for the European Empires of the nineteenth century and early twentieth century.