How do the theories of John Hobson and Cain & Hopkins relate to the British Empire's involvement in the Scramble for Africa?
All of these scholars are trying to explain why Britain engaged in the "new imperialism" of the Scramble for Africa. They all argue that this imperialism was caused mainly by the economic needs of capitalists.
Hobson makes an argument that is very similar to that of Lenin. He says that industrialization in Britain led to a situation where the factories produced much more than the population (most of whom were poor) could consumer. Because of that, Britain needed to go out and capture new imperial possessions. The surplus goods made by British factories could be sold to the people in those possessions.
Cain and Hopkins' idea is similar, but not exactly the same. They say that it was the financial powers in the City of London who needed the new possessions. The financial sector of the economy needed new places in which to invest to get a better return on their investment.
Both of these arguments hold that the new imperialism was caused by economics, but they disagree on which sectors of the British economy were behind the imperialism.