Sherman Antitrust Act of 1890 was the first major piece of legislation against monopolies. The goal was to keep things competitive. They were trying to keep prices from rising due to a company or group of companies purposely withholding stock or goods to create an artificially high demand for a product and causing the price to rise.
They needed help in their textile mills.
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To answer your first question, social darwinism is a theory that supports the rich getting richer. Republican party is based around this theory. Since they believe that those who are the fittest get the money, there is no reason to help the poor, because that is their fault. We can also attach to this the theory of mercantilism where everyone get what they truly deserve. On the other hand, social gospel movement is a christian movement that wanted to help the poor based on christian values. This movement applied christian ethics to social problems such as poverty, delinquency, racism, child labor and so on.