Select the most appropriate option to fill in the blank.

Many developing nations are having a ___________ economy these days.

The correct answer is booming.

Explanation:
In English, specific adjectives collocate naturally with certain nouns to form standard phrases. The term "booming economy" is a well-established collocation that means an economy experiencing rapid growth, expansion, and prosperity.

Let us analyze why the other options are less appropriate:

1. booming: Correct. "Booming" is commonly used to describe a rapidly growing and successful economy or market.
2. boosting: Incorrect. "Boosting" is a transitive verb or participle meaning to raise, increase, or encourage (e.g., "boosting the economy"), but it is not used as an adjective modifying "economy" directly in this context.
3. resounding: Incorrect. "Resounding" usually modifies words like "success", "defeat", or "victory" (meaning unmistakable or emphatic).
4. ringing: Incorrect. "Ringing" typically collocates with terms like "endorsement" or sound-related nouns, not "economy".

Therefore, the complete and grammatically correct sentence is:
"Many developing nations are having a booming economy these days."