# Flat tax and safety net - how it looks

A system with a state-funded social safety-net and a flat tax on earnings looks very simple in terms of the relationship between earned income and disposable income (the amount of money left after tax and welfare payments):

It is a straight-line graph, whose gradient represents the flat-tax rate, and which crosses the vertical axis at the level of the social safety-net provision. For instance, the graph above is based on a household with two adults and no children, whose combined social safety-net is £10,000, and whose flat rate of tax on earnings is 43% (i.e. the government takes 43p in every pound). You could substitute your own numbers for the levels of the safety-net and the flat-tax (and you would have to consider how to balance the government's budget correspondingly). This is just by way of example.

In this model, everyone is guaranteed a minimum income necessary to maintain a dignified quality of life, and for every extra pound that is earned, the household income increases accordingly.

Those who remember their basic maths will recognise this graph. It is described algebraically by the formula:

y = ax + b, where

y = Household disposable income (i.e. how much money the household has left to spend after tax and benefits),
a = The balance of the flat rate of tax from 100% (e.g. if the flat-tax is 43%, a = (100 - 43) / 100 = 57%),
x = Primary income (i.e. the main source of the primary earner's income: pay, savings, etc.), and
b = The level of the social safety-net for all members of the household.

### Effective rate of tax

Some might think that this is not progressive, but if we look at what this means in terms of the effective rate of tax, we can see that it is actually highly progressive:

What this shows is that a household receiving a safety-net payment of £10,000 and paying a flat-rate tax of 43% will be receiving more from the government than it is paying in tax until the couple's combined earnings reach around £23,250. Below that, the effective tax-rate tends to negative infinity (the value when earnings are zero, because the negative tax of the £10,000 safety-net is divided by zero earnings). Above that, the effective tax-rate tends towards the nominal tax-rate (43%).

• The average household with earnings of around £25,000 would be paying a small amount of effective tax;
• a modestly comfortable household with earnings of around £40,000 would be paying modest effective tax of around 20% and
• a well-off household with earnings of around £100,000 would be paying a reasonable effective tax of around 33%.

We will show later how this compares with the current system, but suffice to say for now that it is sufficiently similar that it does not have major implications for government budgets. The big gain is in the efficiency of achieving the outcome and reduction of poverty traps and other disincentives.

### Marginal effective rate of tax

We noted previously that two rates of tax are relevant to the effect on households: the effective rate (above) for how well-off the household feels, and the marginal effective rate for the impact of taxation and welfare on incentives to work. Marginal effective rates in the current system are all over the place, sometimes rising above 100% (i.e. the government takes more than you earn extra). Here is how marginal effective rates of tax would look under a flat tax plus social safety-net system:

What this shows is that, however much you are earning, if you earn an extra £100, the government will take £43 of that, leaving you with £57. The marginal effective tax-rate under this system is the same as the nominal rate of the flat tax.

43% is higher than desirable (and remember, this is just for demonstration at this stage - we will get to how the numbers pan out later). For the sake of honest analysis (anyone can play the game of proposing tax-cuts without associated spending cuts, but our aim is to be transparent and conservative), this is intended for comparison with the current system, bloated bureaucracy and all. With cuts in the cost of government, such as should be achievable through the massive reduction of bureaucracy that this system would entail, the headline and marginal rates of tax should be reduced significantly. But even at this high rate, it is a significant improvement on the highly volatile and sometimes punitive current system, with its many poverty traps of high, marginal effective tax-rates. We will come to the comparison on a later page. But the basic point to take from here is that no system can have an average marginal household tax-rate much below that shown without making massive cuts in government spending, and that, for a given level of expenditure, a static marginal rate provides the least disincentive to work along the whole pay-scale.