I can't speak for the Cayman Islands, but have a lot of experience of the Out Islands. Beer, in particular, is very pricey -- $72/case for imported beer is about par for the course; local beer (Kalik or Sands) might be a little less.

Remember that very little grows on these islands, so it is all imported and then slapped with a duty. So, you can expect limited selection and higher prices -- about 50% more than you're used to in the U.S. (the best grocery store I saw in Eleuthera was in Rock Sound). But beer is even more pricey -- that's why we drank rum!

If you found more reasonable prices in the Caymans, it's because their principal "industry" isn't tourism -- it's offshore financial services. So I suspect that imported food is not subject to such a mark-up.