## Monday, 8 January 2018

### ATCOR and tax incidence

ATCOR is an acronym for "all taxes come out of rent". This means that apart from a poll tax, all other taxes are incident to some degree or another on land rental incomes and thus selling prices. It doesn't mean that every penny of every tax is incident upon land.

To illustrate, consider the simplified example of a hypothetical country called SmallLand.

SmallLand has a population of 1 million. They all rent their immovable property from a landlord called Mr Monopoly. Total incomes are £15bn per year. Due to agglomeration effects there is a linear relation between the size of a locations population and its average income.   Average incomes are lowest in the smallest town (A) Poorville at £10,000 pa rising to £20,000pa in the biggest town (B) StreetsofgoldCity.

Ricardos Law of Rent tell us that Mr Monopoly can extract the difference between the averages. Leaving the average discretionary incomes in SmallLand before taxes are applied at £10,000 pa(C), while Mr Monopoly gets a yearly income of £5bn(D) from land (leaving out income from bricks and mortar)

SmallLand's government needs to raise £5bn a year in taxes. It can do so by either a poll tax, a flat income tax, or a land value tax. The graphs below show how each of the taxes effect the incomes of the population.

To raise £5bn from a poll tax(F), everyone would pay £5000 pounds each, leaving total discretionary incomes at £5bn(E) for all those paying rent. Mr Monopoly's income becomes £5bn -£5000(G)

To raise £5bn from a flat income tax, it would be set a 33.3...%. For that part of incomes at £10,000 pa and under it would raise £3.33..bn(I). As incomes rise over £10,000pa the amount raised goes up in proportion to incomes, totaling £1.66..bn(J). This leaves total discretionary incomes £6.66..bn(h), leaving £6,666.66 for each renter. Mr Monopoly's income falls from £5bn-£1.66...bn, totaling £3.33..bn pa(K).

To raise £5bn from a LVT it would be set at 100%, so that the total income of Mr Monopoly (D) is converted into tax revenue (M). Therefore, in essence, those living in SmallLand who all rent become tax free so their discretionary incomes (L) is the same as (C).  The rent they pay is in effect rebated aback to them as State spending.

In conclusion, the incidence of a LVT and Poll Tax on land are at the opposite ends of the spectrum. Because incomes are dependent upon location, taxes upon output share their incidence between land, labour and capital in proportion to their "progressiveness".

In my example above, a flat 33% income tax is shared 1/3 land to 2/3 incomes. As the UK tax system is only mildly progressive in total, this this probably a good guesstimate of how much revenue a tax shift to LVT would raise.

Assuming no Laffer effect, the required income tax rate in the second scenario would actually be (just over) 27% and Mr Monopoly's net income after tax would be £2.7 billion.

1. People pay rent out of post-tax wages. The excess of national wages over the base line set in Poorville is thus £3.65 billion (down from £5 billion) and that is the max rent that Mr M can charge.

2. The tax base is now £15 bn earned income plus £3.65 rental income = £18.65 bn (you didn't say anywhere that rental income would be exempt so i assume it will be taxable like in most countries).

3. Apply a tax rate of 27% to that = £18.65 bn x 27% = £5 bn.

4. Mr M's gross rental income is £3.65 bn less 27% income tax = £2.7 bn.

5. Of the £5 bn tax raised, Mr M appears to be paying just under £1 bn and the tenants appear to be paying just over £4 bn.

6. In truth, Mr M is paying £2.3 billion and his tenants are paying £2.7 (if you adjust their liabilities for the rent reduction).

7. So even with a low-ish income tax rate of 27%, nearly half of it comes out of rent.

Ben Jamin' said...

Not I didn't include Mr Monopolys rent as taxable income to keep things simple because else its too much for my poor maths skilz to handle :) Thanks for a more realistic model.

Regarding points 6 & 7, I think that just goes to show how our current tax system acts as a coarse grained LVT (opposed to a poll tax). Even more so if there had been £10K tax threshold, as then any income tax acts to collect land rents, albeit one that distorts work incentives.

If half of a flat tax comes out of rents, then flattening a progressive income tax would be even more beneficial for increasing rental incomes and selling prices. No wonder VAT is so popular with some people.

BJ, re 6 and 7, they illustrate your point that some but not all taxes come out of rent - a bit more than you thought but certainly not all of it.

I'm not sure that the tax rate makes much difference, I tried again with a very high tax rate, and again, Mr M ended up paying just under half of it.

The banks and landowners love VAT in particular because they are exempt from it (by and large). VAT is of course just a kind of income tax on the private, productive sector so shifting from VAT to income/corporation tax would in and of itself mean that more tax comes out of rent (because they would have to pay it) I don;t think there is any point being more sophisticated about it than that.

Ben Jamin' said...

@ MW

"I'm not sure that the tax rate makes much difference, I tried again with a very high tax rate, and again, Mr M ended up paying just under half of it."

That's interesting and counter intuitive. Is that just a feature because its a flat tax? I wonder if that would change the tax rate got higher in proportion to incomes? ie more progressive.

BJ, that is an argument in favour of progressive income taxes (I think in political terms we ought to live with it anyway - let's focus our ire on VAT and NIC).

As you said in a later comment, if in Small Land they raise the £5 billion by having a VERY high tax on incomes over £10,000 a year (and rental income), then the amount of rent which Mr M can collect is minimal. But the economy would be buggered...

Physiocrat said...

ATCOR is a corollary of Ricardo's Law of Rent but... there are trends working in opposite directions.

Under an LVT-only tax regime, all existing taxes are absorbed into rents. This grows the tax base. However, vacant land above the margin comes into use. Land previously considered marginal is abandoned and the margin moves upwards ie wages rise. So aggregate rents fall.

Unless there is something I am missing...

1. "vacant land above the margin comes into use"

Agreed.

2. "Land previously considered marginal is abandoned"

Good question.

A.If areas which are currently marginal because of the cliff edge effect of the current tax system, then no, they will become profitable.

B.If people/businesses move from marginal areas to prime areas which have been brought into use under 1, then yes.

In terms of square miles of physical area, I would expect A to vastly outweigh B. It's not just the physical area, it is all the millions of people stranded there, who are just as intelligent or capable as those in the good areas.

It will be interesting to see how this plays out. And when I say "will" I mean "would".

Ben Jamin' said...

@ Phys

1. Surely LVT narrows the tax base?

2. LVT shrinks the margin of production. This increases agglomeration effects, concentrates resources thus demand for proximity to them.

Aggregated land rents measure optimal resource allocation in an economy. Higher the better. This is probably the most important benefit from LVT as it aligns the incentives of the state to get the correct balance of rules and regulations in order to maximise rental returns.

If what you said was true, that would be a legitimate KLN against LVT and would sink it below the waterline IMHO.

BJ, can we stop waffling about "narrow tax base" that's a typical KLN and means nothing.

A. Point is, with no VAT or NIC, marginal areas/people/businesses will become viable/profitable.

B. Central areas/profitable businesses will become even more viable and more intensively used.

Land rents flow from the economy as a whole, if the economy as a whole grows, then so does the 'tax base'.

We don't need to worry about the relative impact of A or B, they work in tandem, and a sensible government would ensure that some of the extra value in central areas is redistributed to less successful areas (which again, is likely to make them more successful).

Ben Jamin' said...

@ MW

I didn't think asking Phys a five worded question constituted waffle :(

But seeing as I'm at it, is not the whole point in broadening the tax base to lessen deadweight losses that happen when we tax output?

This doesn't apply to taxing natural resources. KLN refuted.