With the NZ tax system if you reduce the tax rate on the lower bracket, everyone gets a modest tax cut.
The simplest way to selectively give lower income earners a tax breaks is tog ive a tax credit below a certain total income.
You can also transfer the tax burden from the lowest bracket (e.g by 5%) to the higher brackets but that requires a balancing exercise e.g. upper brackets may have to increase by 10%.
A challenge that remains in NZ that looking purely at PAYE there is only a small a minority of taxpayers who make a net, direct contribution to the govt coffers. If you research Fiscal Impact it's a disturbingly unsustainable picture.