First of all, on an island everything (or basically everything) is imported (just referring here to island in the Caribbean, most of which are very small and don't have the space for large manufacturing facilities or land suitable for cultivation (most of those islands are mountainous). I lived in Puerto Rico for 6 years. When I left (in 2012), a head of lettuce was over $2.50 and it had a shelf life of about 2 days due to humidity and the transit time. I visited the BVI and paid $10 for a bag of Utz chips. PR also has import duties on cars, which increases the prices up to 50% of what you pay on the mainland.
Second is the cost of utilities. In PR, the power company is a state-run monopoly who runs their generation plants on fuel. There is no incentive to switch to more efficient forms of fuel because all operating losses are passed on to the consumer. My husband and I were only home, using power, from around 7 a.m. to 6 a.m. My electric bills were more than $500/month. I don't about the other islands' situations but I can't imagine it is much cheaper. I know that power per Kw in Hawaii is very expensive, might be slightly more than PR.
Real estate (again, in PR) is relative. I am right outside of DC and housing prices here are insane. You can low housing in PR however it is not necessarily where you want to live.
I can totally understand why someone would want to retire in the Caribbean – beaches and warm weather. However you usually need to have a fairly sizeable income to do that. You also need to think about things like medical facilities, etc. when you are at retirement age.
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