X/Y times Y = X (Part 2)

Sobers, commenting on part one:

If you recalculate the LVT rate in year 2 to 10% to get the same amount of income, what will happen? The people at the bottom of the pile will see their gains eroded and many will tip into losses. Those at the top will be even greater losers and thus have even greater incentive to sell their houses thus reducing the price.

The house prices get pushed into a smaller and smaller band in the middle (because most incomes are in that middle band) and thats where the majority of the LVT burden will eventually fall, on the same people tax does now, the masses.

As I explained in the footnote, LVT is a tax on rental values and what Sobers thinks will happen will not happen to any great degree.

Let's boil all UK houses down to two sample houses, one Up North in a low wage area costing (presently) £100,000 (HUN) and one Down South in a high wage area costing (presently) £200,000 (HDS). The main reason for the difference is because the higher net wages bids up the price of HDS (there is a very close correlation between wages and house prices).

So the rental value of HDS is clearly (say) £4,000 a year more than the HUN, which is because net wages are (say) £5,000 higher. And with a marginal tax rate of about fifty per cent, that means the person buying or renting HDS is paying £9,000 more in [rent + tax].

Let's say in Year One, the tax on the house Up North is £8,000 and Down South it's £16,000 and all other taxes are scrapped. What happens if Sobers is right, and the HUN rises in price to £120,000 and HDS falls to £150,000?

Answer: not much.

In Year Two, our required tax take from those two houses 'X' is still £24,000, and the tax base 'Y' is now as follows:

HUN: [selling price x 5%] + [current LVT bill] = £14,000
HDS: [selling price x 5%] + [current LVT bill] = £23,500
Y, total tax base = £37,500 (rental value, not selling prices).

So X/Y now becomes 64% (£24,000 ÷ £37,500)

The tax on HUN is adjusted to £14,000 x 64% = £8,960
The tax on HDS is adjusted to £23,500 x 64% = £15,040.

We see that because it is a circular calculation, in Year Two, despite the large change in relative prices, in absolute terms, the tax on HUN goes up £960 and the tax on HDS goes down £960, and so on every year in ever smaller increments, because people will anticipate the changes

Now, let's also focus on the difference in the total tax bill; if you live in HDS, in Year Two you are paying £6,080 a year more in LVT than the bloke in HUN. Under current rules, you would be paying £9,000 more in [tax + rent], and that balance of £3,000 (in round terms) will still feed into a higher rent receivable by the landlord of HDS, clear of all taxes, which, capitalised at 4%* still means that HDS will be worth £75,000 more than HUN - so it's clear that the difference in price between HDS and HUN would not fall significantly.

* I used 4% for consistency with the example above; you could just as well argue that under current rules, £4,000 rent before tax = £3,000 after tax, and the capitalised amount is £100,000. Therefore under LVT, £3,000 extra rent before tax = £3,000 after tax, so the capitalised amount remains £100,000, and there is no change in the price differential between HUN and HDS.

It's all very simple, really. As a general rule, not much will happen apart from some people trading down and others trading up.
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"People have a natural aversion to paying tax, so while the people losing out will definitely want to downsize to something they can afford, the people below will not want to upsize to somewhere they can't afford."

Simply not true.

Rich people are happy to spend £60,000 on a flash new car, even though the price includes £10,000 VAT. (While I'm on the topic, the total taxes paid by car drivers is over £50 billion a year; twice as much as Council Tax!) Rich people are happy to pay £10,000's a year in rent (or mortgage interest) to live in a flash house. If all people had such an aversion to paying tax or rent or interest, why don't rich people all drive round in battered old VW Beetles, or live in bed sits?