Brownean motion

There is one big rule in local public finance. Do not use local income taxes to fund city governments. Ed Glaeser helps explain why:

In addition, some cities, like New York and Philadelphia, also have income or wage taxes that generate significant revenues. Typically smaller jurisdictions are not granted the authority to  levy these taxes, and many would not want to anyway, given the fears of repelling businesses and wealthier individuals. Indeed, Haughwout et al. (2004) estimate that the elasticity of earnings in cities with respect to the tax rate is so high that income tax rates quickly become counter-productive for producing revenue. 

...But the property tax also has several key virtues for a locality. First, property is considerably less mobile than income or other forms of wealth. Even the tiniest community, like a business improvement district, can levy a charge based on the amount of real property in the community. That property will not just get up and walk away, while an attempt to have a neighborhood level income tax would surely lead to considerable out-migration by the wealthy. 

...Income taxes, of course, can be far more redistributive than sales taxes and that is one of the reasons for their attraction to many cities. The problem with local income taxes, of course, is that they potentially repel wealthier individuals. That provides one reason why many forms of local redistributive services are actually funded by higher levels of government. 

Bottom line: income taxes are a reasonable way of funding redistribution from rich to poor. Rich people prefer not having to pay them. So, run your big income redistribution programmes at the national level, funded by income taxes, and leave local government to provide local public goods, funded by land or property taxes.

Glaeser and Shleifer also showed that Detroit's Coleman Young and Boston's James Michael Curley's use of high local income taxes encouraged their richer opponents to move outside of their cities' limits, beggaring their cities but helping to ensure their continued re-election.

Here's Auckland mayor Len Brown [ht @MarkHubbard33]:

Making all Aucklanders pay a council income tax may help elderly people in affluent areas who can't afford their rates, mayor Len Brown says.
The current system is "inherently unfair" on people living on fixed incomes and paying high rates because of the value of their properties in areas like Devonport-Takapuna, Brown says.
Introducing an income-related tax for local council services that everyone pays is an option, he says.
Only property owners pay rates but the council is spending money on infrastructure and services for everyone, Brown says.
He believes the only way to mitigate the rates burden as property prices rise is to rethink how local government is funded.
Brown won't express a view on what alternative might work saying he is "quite open minded".
Options could include funding through income tax, GST, user pays charges, or bed taxes from hotel.

A few things worth noting:

1. Everyone in Auckland pays property taxes, though only homeowners and business owners make direct payments to councils. Renters bear some of the burden through their rental payments. Shoppers bear some of the burden through their purchases from local taxed establishments. 
2. An income tax is only feasible if Auckland Council is now large enough that commuting in to Auckland from outside of its rating zone is infeasible, or if the amenities it provides to rich folks are just super-awesome and don't do much for commuters. Otherwise, the richest folks keep their residence just outside of town and maybe have a small commuter apartment in town.
3. Property taxes are a way of taxing wealth rather than income. They're then a nice complement to existing national taxes on income and consumption. The elderly person on a fixed income, sitting on a million-dollar Davenport property, is really really rich, even if she has little income. Getting rid of the only wealth tax we have in favour of more taxes on income does even more to screw up the system. The existing system already has big transfers from less wealthy people on high current income to very wealthy people on low current income: superannuation payments going from young mortgage-holders to old homeowners. Brown is proposing to make this even worse. 
4. Further, a reverse mortgage can solve the problem for many wealthy but low income elderly. 
5. For those for whom the annuity wouldn't be enough, well, is it really worse to have a few wealthy but low-income elderly move to a smaller house or apartment than to wreck your local council's ratings base with an income tax? And you know that Councils can, in some cases, put in a limited property tax abatement scheme for those on lower incomes, right? 

User charges for some Council services can make sense. If Gerry Brownlee hadn't somehow banned Auckland from putting in congestion charging, that would have been a good one for Auckland. But local income taxes are a pretty bad idea.