As the budget comes round again, there are constant cries amongst the chattering classes, about council tax being unfair on poor pensioners in big houses.

Now, these pensioners probably own their houses (if they didn’t, they’d have no option but to move somewhere smaller). So they’re getting the benefits of ownership.

Question: how much does a hard-working person with no assets have to earn to keep up with the poorest pensioner?

OK, we need some working assumptions here. The level of means-tested benefit for pensioners is £114.05 per week (£5947/year) with no tax due, so we’ll take that as the income to compare against. Actually it’s worth quite a lot more, because that figure excludes a range of additional benefits. And since it’s pensioners in bigger houses who are said to be hard done by, let’s put them in an average house worth £200000.

Keeping the equivalent as close as possible, how much does the working person need to keep up? Let’s put the worker in a similar average house. But since the latter owns nothing, he has to rent it at about £800 per month. And he doesn’t get the benefit of house price rises: since the mid-1990s, that is doubling every five years.

So to keep pace (not catch up – he still doesn’t own a house at the end of it and hasn’t closed that £200000 gap), the worker needs to make £200000 in those five years. Plus the £6000 to live on and the £9600 rent each year. We can discount things like council tax because they both pay it (though in fact the pensioner will get a rebate, so in reality the worker needs even more than we’re calculating).

Anyway, that leaves our worker needing to earn £278000 over five years, just to avoid widening the gap. At a constant rate, that’s £55600 per year net. But that comes from taxed income. A quick tax calculation (including the component called “national insurance”, which is compulsory and non-negotiable) reveals that this implies a headline salary of £95155, putting you in the top 1% of earners.

The cost to the employer is even more: there’s an employment tax under the “national insurance” label. At 12.8% on everything over £5058, that adds £11532 to the cost. So just to prevent that wealth gap widening implies a total cost of £106667!

Now if we change our working assumptions a little, and shift from house prices doubling in five years to the long-term average of 7 years, these figures are reduced by £11429 per year (net), 19371 (gross), 21850 (cost). But £75784 is still an extremely high headline salary.

Of course that’s not the whole story, and if you earn £95000 you can get a mortgage to buy that house and enjoy the benefits. But that still leaves the possibility of earning £40000 without ever being rich enough to buy a house. And that leaves you paying tax at the maximum rate, for the benefit of people far richer than you will ever be!

Yet most of the pressure is to kill off all taxes on property, and move to yet more income tax! Moral: if you have old (typically family) wealth, noone questions your right to be rich. But if you work hard you get no help, and no sympathy from the taxman!