New Delhi, Aug. 10 -- A Balenciaga handbag designed to look like a garbage bag sells for Rs.2.7 lakh. A Lamborghini-branded stroller, made in collaboration with premium baby gear maker Cybex costs over Rs.1 lakh. And a life-sized Ferrari F1 show car that cannot actually race, but can cost tens of thousands of euros.

A growing slice of the country's wealthy shoppers is shifting from recognisable logos to objects that are rare, eccentric and sometimes serve little purpose.

Luxury retailers and concierge services say they are seeing a surge in demand for limited-edition and hard-to-source products, with some buyers willing to pay whatever it takes to acquire products unavailable through mainstream channels.

Limited-edition drops from bran...