Yes they will fit. In fact, I believe that 225/50/16 is the stock size for a 16 inch wheel.
http://www.miata.net/garage/tirecalc.html
I punched in the sizes and this is what it returned:
"Speedometer reading with non-stick tire is 0.1% too fast.
When your speedo reads 60 mph, you are actually traveling 60.0 mpg."