Switzerland does not have a minimum wage, and yet the very lowest earners on average make about £40,000 per year, versus £20,000 in the UK - cost of living is also higher, but Switzerland also has much lower levels of taxation, and lower unemployment - ergo, the cost of government is lower (and the state also runs budget surpluses). Competition drives up wages.
All of which is precisely because Switzerland does *not* have a giant government. Businesses can flourish freely.