Making purple frosting isn't difficult and can be made with the simplest of supplies and using plain white frosting, either homemade or store-bought. Make sure that you add your colors slowly to get exactly the right shade, as it's much easier to darken your frosting than to lighten it.
Take 1/2 cup (or one stick) of room temperature butter and place it an bowl and beat with an electric mixer until fluffy.
Add in 1/2 tsp of vanilla extract with 2 tbsp milk. Beat on high until blended. Add more milk if your frosting is too stiff, one tablespoon at a time.
Place 1 cup of powdered sugar into the mixture and beat until blended. Repeat until all the powdered sugar is combined.
Beat until fluffy and then add 10 drops of red food coloring for every five drops of blue coloring. Add color until you achieve your desired hue.
You may want to consider buying cake decorating icing coloring that comes in a paste. This will provide a rich, deep color without having to add too much food coloring.