Let’s look at Switzerland, an excellent example in this case:
Switzerland is classified as a capitalist economy, as seen by its high levels of free-market economics, and minimal government involvement.
In Switzerland, there are very low levels of social programs, typically only reserved for the extremely poor— nearly the exact opposite of a welfare state. For example, welfare extends to a fraction of the residents in the country, and governmental healthcare programs are barely subsidized.
As a result, the private sector largely runs Switzerland’s economy, controlling prices, production, and almost everything else.
Residents of Switzerland (both rich and poor) pay very low taxes (compared to command economies).