Reasonable? For the price it costs to get from Berlin's city center to the airport, you could easily drive your own car to Hamburg - and probably back.
I really don't understand why it has to be so expensive. For inner city trips the gas costs are a negligible part of the total price, and most drivers are being paid minimum wage. (I've actually heard quite a few taxi drivers complain about minimum wage being introduced because their employers claim that it's too expensive for them and they need to cut costs.)
Either there are too many taxis out there so they need higher prices to be able to pay for the time where they just stand around waiting for customers, or somebody is getting rich.