This has been something of a controversial topic at times in American history. Most notably, about 100 years ago, a historian named Charles Beard famously argued that the Constitution represented a selfish grab for power by members of the economic elite. Beard argued that the great majority of the Framers of the Constitution were members of the economic elite. He argued that they created various provisions of the Constitution in an attempt to further their own interests.
The main argument for this idea is that the Framers were elites and the Constitution created a governmental system that did help elites to some degree. The new Constitution protected things like the obligations incurred by contracts, making it impossible for the government to pass laws forgiving debts. The Constitution also made it easier (by making the Senate an appointed body, for example) for elites to dominate the government.
That said, it is not clear that the economic elites were trying to execute some sort of malicious takeover of government as this question implies. Instead, it seems more likely that they were trying to set up what they saw as the best form of government. It is for this reason that Beard’s thesis has largely been discredited among historians.
I would argue that the economic elites did set up a government that worked in their favor, but I do not believe that they did so out of self-interest.