I once tutored a middle schooler for the ISEE–like the SAT, but for admission to private high schools.
“Dearth,” I explained to him one day, “means lack.”
“Dearth can’t mean lack!” He lamented. “Paucity already means lack!”
Good point, but unfortunately it doesn’t work that way.
In other news, the word dearth has a great etymology. You know how “dear” can mean “expensive,” especially in British English or in French (“cher”)? Well, dearth originally meant dear-ness: expensiveness. But because expensiveness often reflects scarcity, dearth evolved to mean scarcity. Per the online etymology dictionary, this word was “originally used of famines, when food was costly because scarce; extended to other situations of scarcity from early 14c.”