Before you spend the money on a pump, check the material. If it is galvanized steel, one sign of corrosion are little 'rust warts' on the outside of the pipe. If the supply lines are in good shape, then the loss over 15 meters shouldn't be the cause.
Just to make sure, is the kitchen at the same elevation as the bathroom? If there is more vertical rise to the kitchen, then that could explain it and you would need to boost the pressure.
If you can isolate the problem to the mixer, it would be better to replace that. If you have good pressure to the other fixtures, boosting the pressure could cause new problems. To test the mixer, make sure to shut off the faucet supply, remove the hose, and test the pressure when it is not going through the faucet. If it is good, then its the faucet.