Why not use a smoothly changing incremental rate? "A steady curve"
First, as it has been clarified that the bracket changes are on incremental income then there are no major discontinuities in the average rate even though there may be in the marginal rate. So one might put the question in reverse: why would you have smoothly changing marginal rates?
There is more interest in the simplifiction and flattening of income tax.
Example: UK margin and average rates of Income Tax & NI
UK taxes on employee income have two components which together comprise the margin rate at which tax is taken. National Insurance was a 'welfare stamp' with an upper income limit, though it has since been used to increase higher rate income tax by 2% without affecting the headline rates that gets most attention
There is also a 'claw back' of the tax free allowance between £100,000 & £125,000 making the peak UK income tax rate be 62%!
There are some difference in tax in Scotland & Wales, so strictly these numbers apply to England and Northern Ireland.
It is pretty bonkers!
But even with all this, when you look at overall amount taken as a % of income ("the average % rate") this is relatively smooth and curved even given the bonkers changes in margin rates.
How would you implement algebraic rates
If you are after smoothly changing average % rates as you can see this is entirely possible with a piecemeal set of marginal rates.
So it is not so clear to me why you would want smoothly changing marginal rates - you can have smoothly changing average rates without them. Further, two particualr problems occur to me:
Any simple formula has all sorts of political and ethical
implications embedded in it that may not correspond to any political
consensus and it would be hard to adjust to reflect any evolution of
public concerns (this might be an advantage from an economists point
of view!) and it would be hard to manage any kind of public debate.
Creating a piecemeal continous margin rate curve (piecewise splines
perhaps!) would add massively to the complexity of the systme with
little clear benefit.
The is also more "plumbing" behind the scenes in the tax system that
may not be obvious at once - rules rounding off, different kinds of
income having different marginal rates, etc that would mean a great
deal of established regulation and system would have to be rebuilt
more the ground up. Again: for what benefit.
What reforms to income tax make sense?
Two current themes in tax reform are:
- Simplification - The US tax code is c. 9,000 pages; the UK's is c. 17,000 and allegedly the longest in the world. This comparesd to say Hong Kong at c. 275 pages. Complexity begats complexity as each change creates new problems, new transitional measures and new anti-avoidance measures.
Guardian - UK has longest tax code in the world
Tax Foundation - length of the US's tax code
- Flattening - the greater the variation in rates the more benefit there is to finding ways of changing the tax status of some income. These schemes will both distort economic decision making, lead to pointless or damaging but tax efficient invesents, lead to far to much money and effort going into developing such schemes, and lead to lots of effort and bureaucracy in an effort to stop such schemes. A simple tax code with single low rate but few exemptions could lead to high compliance, lower collection costs and less damange to the economy.