Explanation:

- Option 1: Dadabhai Naoroji

- Dadabhai Naoroji is the correct answer. He wrote 'Poverty and Un-British Rule in India,' a significant work discussing economic exploitation under British rule.

- Option 2: Shashi Tharoor

- An acclaimed author and politician, Shashi Tharoor has written about colonialism, but not this specific book. His book 'Inglorious Empire: What the British Did to India' covers similar themes.

- Option 3: Jairam Ramesh

- Jairam Ramesh is an Indian economist and politician. He has authored several books but isn’t related to 'Poverty and Un-British Rule in India.'

- Option 4: Annie Besant

- Annie Besant was an influential British socialist and supporter of Indian self-rule. Though she wrote about India, she did not author this book.