If Jamaica’s inflation rate falls while the rates in other Caribbean countries remain constant, Jamaica’s balance of payments will (all other things being equal) improve. In other words, Jamaica will import less and export more. Of course, the effect will depend upon how much trade Jamaica does with these other countries.
When the inflation rate in Jamaica (or any country) falls relative to the rate in other countries, Jamaica will tend to import less and export more. This is because Jamaica’s products become more competitive with the products from the countries with higher inflation. Imagine that it has cost $100 to produce some good in another country. Now, that country experiences high inflation relative to Jamaica and it costs $110 to produce that same product. That product will not be as capable of competing with Jamaican products because the Jamaican products’ prices will not have increased as much.
For this reason, Jamaica will be able to import less from and export more to other Caribbean countries if its inflation rate drops relative to theirs. This would bring about an improved balance of payments.