My minimum rate for most new clients is $40 and it doesn't matter how small it is, I will drop below this but only if it's going to suit me to do so. ie very small and very close to existing clients so no traveling time.
As I have said before when you're not desperate for work increase your quote prices if you don't get as many jobs you can still find you are making as much money but working less hard also remember 5 x $40 lawns verse 4 x $50 lawns of the same size may appear to be the same amount for 20% less effort but it's actually more in your pocket as you also have a drop in expenses