If the market rate is artificially inflated (minimum hourly wage) then companies will find a way to automate those jobs away. I am sure people will say that this would have happened anyway with certain unskilled labour jobs but you could argue that this only further incentivises them.
I would argue that the UK fast food chains and supermarkets are a good case study to illustrate this. In the UK most of the cashier staff are slowly being removed. Now they normally have 6 - 10 checkouts that are automated and have the customer scan their own items. Tesco (that where I normally go) instead of having 10 checkout staff you can buy 10 machines that are managed by one or two people at most. All the machines in the major supermarkets are using the same vendor for their machines and the software appears to the same for each supermarket but skinned, with the only exception being the german supermarkets.
Similarly at the other end of the scale in the UK. A C# .NET + MVC + JS with some SQL Server experience contract rate is about £350-400 a day. In London because developers expect higher rates (and the higher cost of living pushed the rate up by about £100-200 a day.