I don't know much about higher maths, but I do know some things: the above fraction is quite simply true.
Applied to my favourite topic, shifting taxes from incomes to land values, what it means is this:
X = the required tax take
Make up your own figure, but the total tax receipts from incomes or output in the broader sense (income tax, National Insurance, VAT, corporation tax) are around £340 billion a year (which is only enough to cover about half of total government spending - the rest is made up of an infinite number of other stupid little taxes; other income and receipts; and a MASSIVE GREAT ANNUAL DEFICIT - but we'll deal with that later)
Y = the tax base
A. If we decide to raise that sum of money from incomes and output, then let's guesstimate total wages at £750 billion (30 million workers x £25,000) plus £100 billion corporate profits, we have a tax base of £850 billion, so the required average rate is 40% (which looks 'about right' - the average marginal rate is about 50% if you take into account Working Tax Credits withdrawal, but the personal allowance and the Working Tax Credits themselves reduce the average rate).
So X = £340 billion, Y = £850 billion, X/Y = 40% and 40% times Y = £340 billion.
B. If we decide to raise that sum of money from the rental value of land, we could simply take the total market value of residential and commercial land and buildings, which at current selling prices (as a proxy for rental values) are worth (say) £4,250 billion, which gives us an average rate of 8%, which looks 'about right' to me (but I've done these workings a thousand times). The purists say you shouldn't tax the value of the buildings, but we can deal with this via personal allowances (or a Citizen's Income).
So X = £340 billion, Y = £4,250 billion, X/Y = 8% and 8% x Y = £340 billion.
That's the same amount of money raised from the same people - us. (Again, the fact that the government should be spending a lot less and spending it more wisely is a separate debate).
Clearly, incomes are not distributed the same way as land 'ownership' is. The former is skewed, but that has largely to do with people's inherent differences; the latter is far more skewed, and that has largely to do with the government defending the interests of land 'owners' above all else. To put it crudely, the top ten per cent of earners earn thirty per cent of all profits or wages; the top ten per cent of landowners own seventy per cent of all land (or whatever the figures are).
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The basic formula will always hold, at all times in all situations.
The defenders of privilege (Homeys and Faux Libertarians alike) say that if we were to tax land values instead of taxing incomes and output, that value would be 'destroyed' (so the tax base would be eroded), and that everybody would be scrambling to move to the lowest rated houses, and so the selling prices of these would be pushed up and the selling price of the highest rated houses would fall.
Well, firstly, neither of those things would happen: all that would happen is that lower earners would trade down and higher earners would trade up. But even if they did, so what?
In Year Two, we would simply work out what the new tax base ('Y') is, maybe the total theoretical selling price would fall to £3,400 billion; maybe it would increase to £4,860 billion (scrapping taxes on incomes and output would be an enormous boost to the economy), and plug it back in to the formula.
In the former case, the nominal LVT rate goes up to 10%; in the latter case it falls to 7%. Either way, X (which is the figure we really care about) remains the same, and total tax revenues are £340 billion.
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Footnote: LVT is ultimately on the rental value of land, so when the formula is recalculated, the actual rental value of any house would be taken to be:
[existing tax on that house] + [notional residual rental value, being selling price x 5%]
which would greatly soften the up- or downward swings, it's a slightly circular calculation which would quickly settle down to an equilibrium. Whether you go to the bother of deducting the rental value of the bricks and mortar or just make sure than there is a personal allowance or a Citizen's Income to cover it is just details.
Thursday, 19 May 2011
X/Y times Y = X
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10 comments:
I like your arguments, but LVT seems so transparent. As I read it, LVT would illuminate numerous murky little corners where the rich and powerful lurk.
AK, they won't stay rich and powerful for long once I'm in charge :-)
And then we'll get cracking on slashing the forty per cent of government spending that goes on corporatist subsidies and procurement, the largest single category of govt. spending.
But this post was purely about the maths of it.
1) You are assuming that all property value is a function of current income. It isn't. Some of the value in property is capital, ie saved income. Most expensive properties are bought with capital, not with borrowed money funded from income.
2) 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.
3) When you tax something you get less of it (often you are trying to get less of it - eg cigarette duty). Thus if you tax house prices (or rental values as you call them, but there isn't a great deal of correlation between the two IMO) you are going to get lower house prices, especially if other forms of capital (money, share, bonds etc etc) are not taxed at all. 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. And many will prefer to stay put and spend the extra income on other things anyway, as LVT will depress higher house prices, and they will become less of a desirable 'investment'.
4) It seems mad to have such a disconnect in taxation between various forms of capital. Lets say I inherit the family home and I sell it for cash. I put it in the bank and get some interest (you remember interest don't you!). Where does that interest come from? The interest someone else has to pay to buy a house on a mortgage in many cases! So how it that different from keeping the family home and renting it out? Both are 'rent seeking' activities - in one case I'm charging for the use of my property, and in the other charging for the use of my capital. But LVT taxes the former massively and the latter not at all. So people will move their wealth as much as possible out of property and into other things, eroding the taxable base. Each year the LVT rate will have to rise to get the same revenue, thus taxing the lower end more and more. Not a recipe for a popular system.
To be a slight pedant, the equation in the title isn't always true - particularly if Y is zero (in which case X/Y is indeterminate) or if either X or Y is infinite (at which point things become more awkward).
But as long as you're dealing with real, non-zero, non-infinite numbers, you're good :-)
Just a quick reply to Sobers:
1) You are assuming that all property value is a function of current income. It isn't. Some of the value in property is capital, ie saved income. Most expensive properties are bought with capital, not with borrowed money funded from income.
I'd argue that while the value inherent in a lot of properties now is capital, the vast majority of that capital is made up of untaxed gains. House prices have risen way in advance of inflation - and the fact that they are rising is being used as an argument that they will keep on rising and are thus a good investment, which means more people paying more and more money for them, driving the prices up even further.
If your house is too expensive for you to pay the LVT on it based on your current wage, you have two options. Sell up and move elsewhere (pocketing any capital gain thus far) or earn more money.
2) 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.
No - because the new tax rate will be 10% of the new, lower values. The total amount raised will still be the same. The average amount paid will be the same - the distribution may change if some houses change price at a different rate to others, but it won't change by a lot.
I can see house prices narrowing a little, but I really don't see little studio flats ever costing anywhere near as much as a mansion in the same area.
(character limit - to be continued)
3) When you tax something you get less of it (often you are trying to get less of it - eg cigarette duty). Thus if you tax house prices (or rental values as you call them, but there isn't a great deal of correlation between the two IMO) you are going to get lower house prices, especially if other forms of capital (money, share, bonds etc etc) are not taxed at all. 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. And many will prefer to stay put and spend the extra income on other things anyway, as LVT will depress higher house prices, and they will become less of a desirable 'investment'.
House prices may well decrease, they will be a less desirable investment. That's not a bad thing...
4) It seems mad to have such a disconnect in taxation between various forms of capital. Lets say I inherit the family home and I sell it for cash. I put it in the bank and get some interest (you remember interest don't you!). Where does that interest come from? The interest someone else has to pay to buy a house on a mortgage in many cases! So how it that different from keeping the family home and renting it out? Both are 'rent seeking' activities - in one case I'm charging for the use of my property, and in the other charging for the use of my capital. But LVT taxes the former massively and the latter not at all. So people will move their wealth as much as possible out of property and into other things, eroding the taxable base. Each year the LVT rate will have to rise to get the same revenue, thus taxing the lower end more and more. Not a recipe for a popular system.
I'm really not sure I understand this. People will move their money out of housing - but the thing is, there's a fixed amount of land around, and someone's got to own it. Worst case scenario, LVT would be equal to the rental value of the land - so even if people release their land and hand it over to the govt, the govt rents it out and makes at least as much as the LVT by doing so. So how can people "get out" of land?
"The people at the bottom of the pile will see their gains eroded and many will tip into losses."
Which is exactly what will happen if interest rates go up. Much the capital "gain" made by people on their houses will disappear as prices fall, and those who bought at the peak of the bubble will be facing capital losses.
RA, thanks for you replies, that's saved me the bother.
On his point 1), it is quite clear that rents or selling prices are very much a function of (local average) incomes; the fact that a lot of people would no longer be able to afford to buy their own homes is a BIG RED WARNING LIGHT.
Conversely, if nobody had to pay income tax or VAT, nearly all of us would be able to afford to RENT the home we currenly live in, which is a good place to start the argument.
I don't get the point of the basic formula .Surely if you divide a figure then multiply by exactly the same amount you will end up with what you started with: you're dividing then multiplying the same thing .Got the same feeling watching Brian Cox dropping a stone on the ground (in some far-flung filmed location): "Gravity, is n't it amazing?" he said eyes popping out of his head.
DBC, yes exactly, of course the formula is blindingly obvious and dull...
But the Homeys and Faux Lib's swear blind that if you raise £x bilion in LVT (or even Council Tax or Business Rates) and cut other taxes by the same amount, then rocks will start falling out of the sky, fear and pestilence will stalk the land etc.
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