What affect, if any does an increase in minimum wage have on wages of those who earn more than the minimum?

legally, it has no affect. Depending on the type of business or industry you are in, and how employee friendly your company is, you may see an increase. But it is not required (unless minimum wage is raised above what you currently make, at which point you would be raised to at leat that).

It's called "salary compression". When lower end starting wages increase without increasing wage scales across the board, it compress the distance between the higher level wage scales so that movement between the scales (i.e. salary ranges/classifications) becomes negligible. The result is that you have trainees or entry level employees starting at or just below the wage paid current employees in the lower level job classifications. (Not a popular trend.)