I don't use, but one of my friends have one at their home. It gets heated very quickly, but I won't say its economical over LPG. It consumes 1800 Watt.. so, it must be expensive over LPG.
With the shortage of LPG, the induction stove is in great demand and the marketing people are telling that it is very cheap and economical over LPG. Isn't it that economical?
I don't own one but I've cooked with a few. I consider them the best of all ovens as they cook trough and through. If you get one, get the best you can afford. The cheap ones don't give you full heating coverage.