There's one interesting bit in these otherwise fairly meaningless stat's

From The Daily Mail:

* More tenants ditch city living in favour of living in commuter towns and villages
* Between May and August 2020, 34% of tenants wanted at least one more room
* Upsizing costs more with tenants who do so paying £149 more per month
* LonRes survey also found that space and gardens are in demand among buyers

So 34% of tenants rented a slightly larger home after they moved against 25% in the previous quarter? That's not surprising as more people are working from home now, so they need more space at home, and what they save on season tickets or commute costs they can spend on renting somewhere larger.

Plus, in the grander scheme of things, the stock of rented housing and the number of households renting is fairly stable. For every tenant trading up, there's probably one trading down. As Frank points out in the comments, on closer inspection, it might be trickier than this but we don't have that level of detail.

Tenants living in the South East of England are paying the most and have been the most likely to trade up, with 47 per cent of those moving post-lockdown adding at least one bedroom in their move. On average they are spending an additional £266 per month.

Yes, rents and prices in London are high to reflect the fact that wages are higher there, rents in the rest of the South East were slightly lower - people lived there but commuted into London, so the rents were depressed by commuting costs (Von Thünen's law of rent). Also, London was great for socialising, meetings, concerts and so on, but that has all fallen by the wayside now. Tenants' total rent-plus-commuting costs has probably gone down a bit, on average (assuming two adults commuting).

So far, so blah. Here's the interesting bit:

Renters remaining in the capital are benefiting from renters leaving in their droves for commuter towns and villages. It means, the average London-based tenant looking for more space spent £86 per month less, despite gaining at least one extra bedroom.

We'd expect that to happen, but it's nice to have confirmation of how big the fall is. £86 less for one extra room looks like about one-third less in space-adjusted terms, although HomeLet's August index says that London rents are only down by 2.1% year-on-year. Which I suppose is another interesting bit, how can two sources differ so wildly?

"Why is the "Cost of Living" in Cities so High?"

Spotted by Lola at Mises.org.

Most of the article is the author discussing the correct interpretation of The Gospel according to St Mises, the interesting bit is near the end:

This raises the question, then, of why do workers move to a big city where the rent is so high? As I’ve exhaustively argued above, this isn’t a mere matter of units. Dollars are the same in San Francisco, but most of the prices are higher. Why do people put up with this?

The obvious answer is, “Because wages and salaries tend to be higher.”

... The brief explanation is that the productivity of many types of labor is much higher in urban areas than elsewhere. Historically the development of the big cities in the United States was tied to water transport: New York, Los Angeles, and Houston are still major port cities, while Chicago’s access to the Great Lakes and key rivers played an important role in its growth.

So it wasn’t a coincidence that America’s largest cities developed where they did. However, once people start living in close proximity because of some external factor (such as access to the water), there is a separate effect: Their productivity is amplified in other areas too, simply because of their proximity. The “economic approach to cities” is an entire subfield, so I won’t dwell on it here. Suffice it to say, people don’t spread out uniformly across the land, the way electrons repel each other on the surface of an object to distribute the electric charge uniformly.

Rather, more than half of the people in the world currently live in urban areas or cities, with projections that that figure will rise to two-thirds by 2050. There must be some reason for this attraction. On the consumer side, it might be the ability to eat at the finest restaurants and go to a Broadway show (if we’re talking about Manhattan). On the producer side, it might be because cities offer the highest salaries, and are worth moving to, despite the higher price for an apartment of a certain size.

Yet contrary to Cochrane, these high wages aren’t due to a difference in currency; they are supported by the fact that the productivity of workers is genuinely higher. The worker who is paid $100,000 in San Francisco is producing twice as much for his employer as the worker who is paid $50,000 in Cleveland. This isn’t because the units are different, it’s because the first worker is genuinely more productive.

Yes and amen to all that, that's Von Thünen's-Ricardo's law of Rent. The author does not just trot out the Faux Lib argument about lack of supply. Whether he draws the obvious conclusion on what should and what shouldn't be taxed is unknown.

Von Thünen's Law of Rent - it's all about lack of supply... NOT!

In an idle moment, I googled "average disposable income UK regions wages rent", the first relevant result was in This is Money:

The survey compared average city salaries against local rent and other standard monthly outgoings for 30 UK cities, calculating the disposable income of city residents after deducting tax, bills and other necessary general outgoings such as travel and food.

It discovered that the average British person gets to keep £1,083 per month after expenses and tax with the average monthly wage coming in at £2,073, while the average essential outgoings, such as rent, travel and food, total £990...

Despite Londoners' earning the highest wage, they also, unsurprisingly, have the most bills and so feature much lower on the overall list. Their disposable income is £1,095, only £12 above the UK average in the study. Their monthly outgoings of £1,629 are also over £350 more than any other city.

Hull is the city with the lowest outgoings of any city in the UK at just £767 per month. However, residents have a lower monthly wage of £1,816 which means their disposable income is £1,049, below the study’s UK average.

Which is exactly what you'd expect from Von Thünen's law (or even just a basic understanding of human nature). The lowest wage area sets the baseline. In areas with higher wages, the extra wages go into higher rent (other fixed costs are pretty much the same everywhere).

The equilibrium is reached when few people are willing to move because the rent saved is matched by lower wages; or the higher wages are matched by higher rent, which is what we observe in real life.

For sure, there are outliers - the survey mentions Derby with the highest disposable income after rent (£1,456) and Brighton with the lowest (£751). This can't be explained by the basic analysis, but boils down to the fact that Derby is considered boring (no idea if it is, but perceptions matter) and Brighton is considered fun, hip and fashionable, plus has nicer weather and a beach.

To paraphrase W C Fields, "people would rather be dead in Brighton that live in Derby" and they are prepared to pay £700 a month for the pleasure.

Here is their chart which is quite striking (blue dots = wages, red does = rent plus other fixed costs):


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So the next time somebody says that rents are high in London because of "lack of supply", refer them to this.

You do not need to adjust for "lack of supply", all you need to know is average monthly wages in any area. You subtract £1,800 (average wages in lowest wage areas), which gives you location rent. Add on about £400 for cost/value of bricks and mortar and that tells you local average monthly rents.

To estimate house prices in an area, you then divide annual rents by mortgage repayment rates (interest + principal, currently about 3% - 4%).

Killer Arguments Against LVT, Not (461)

Via Labour Land Campaign, an article in Prospect from last year, which, despite the sub-heading, only touches briefly on LVT.

True to form, a drone at Conservative Central Office - who presumably have a member of staff on their online response team tasked with responding to the day's Google search results for 'Land Value Tax' - leaves the following sob story:

I [bought] my house for £100,000. I live in it for 20 years. It is big enough for my family, the transport links are OK for work, schools for the kids are accessible.

Because of things like 'Help To Buy' and ultra low interest rates, house values in my area mean my house is now worth £1m. In the meantime my pay has doubled, but because of inflation I am actually no better off than when I bought the house. A land value tax at say 1% would mean I would have to find an additional £10,000 a year, despite being no richer.

Yes, my house may be 'worth' £1m, but that doesn't mean I actually have £1m, or even an extra £10,000. I would have to sell. I might well not be able to afford anything else local, and have to move jobs, the kids move schools, and all as a distressed seller. This is politically unlikely, and economically crass.

If you want to tax houses on value, start whittling away at the exemption from CGT - but gradually.

A proposal to get rid of the capital gains tax exemption for main residences would meet with the same vitriolic response; and taxing long terms gains rather than imposing an annual service charge is a terrible idea anyway, so let's skip that last bit.

Why do I have zero sympathies with this person? Because that's basically my life story (and typical for millions of Londoners who bought more than 20 years ago, we're nothing special). Just replace '£1 million' with £800,000 (based on recent selling prices of larger and smaller homes on my street). I know how bloody lucky I am.

Both of our kids changed primary schools halfway through because of moving, it was no biggie, at that age, they adjust. They both always went to secondary school using public transport by themselves; if we moved, they wouldn't change schools, they'd just take a different route. Plenty of Londoners spend an hour commuting, you don't change jobs just because you move within London. We moved outwards (white flight) and we took the extra twenty minutes each way each day on the chin.

Like this person, I don't have actually have £800,000, nobody said I did. That is not, and never was, the point.

This person makes clear, that house prices/rental values are a trade-off for convenience (von Thünen's Law of Rent). They don't want to move to a cheaper area, which in London terms means 'further out on the Tube or rail network' because of the extra time/cost spent commuting, sure, why would they? But they claim they don't want to pay the extra £10,000 a year either.

So what will they choose? The inconvenience or paying the £10,000?

We know for a fact that this person is happy to be £10,000 a year worse off as a trade-off for the convenience. How? Because they could sell their 'big enough family home' in Islington (or wherever it is) and buy something that for half that in Barking, or Harlow, or Croydon or somewhere cheaper/less convenient, banking £400,000 tax free cash after SDLT, moving costs and new carpets, which would give them an extra £10,000 a year cash to spend for the rest of their lives.

So the chances are, they'd pay the additional £10,000 (even assuming there weren't corresponding reductions in other taxes which would make most working couples better off). I know that I would, because the alternative is me and Mrs W and both of our kids spending more on travel and wasting an extra X minutes a day each sitting on public transport. We might pay our £8,000 a year through gritted teeth, but we'd pay it.
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Seriously though, what planet are these people on? There are plenty of people outside London/south east who bought homes for £50,000 - £100,000 twenty years ago which only have kept pace with inflation or less.

How much sympathy are they supposed to feel for those with an unearned windfall gain - made at the taxpayers' expense, as the drone admits - equivalent to an average lifetime's earnings who are asked to pay a little bit of extra tax?

Von Thünen's/Ricardo's Law of Rent, part the manieth.

From The Metro:

Jobs website Adzuna compared average advertised salaries with average rental figures across the UK to find the most and least affordable towns and cities for renters to live. In Swindon, workers typically spend 11.5 per cent of their take-home pay on rent, compared with a national average of 22.1 per cent.

Bradford, Hull, Dudley and Durham complete the best-value top five, with workers in these areas typically paying less than 13 per cent of their net wages on rent. At the other end of the spectrum, Londoners typically shell out 41 per cent of their pay on rent while those in Oxford can expect to see it swallow up 39 per cent of their take-home wages...

Andrew Hunter, co-founder of Adzuna, said: ‘Even though workers may be paid a higher monthly salary, their left-over cash is often smaller after paying steep living costs and local property premiums.’

Correct. Why would you expect any other outcome?

They list the areas with the lowest and highest rent-to-income ratios, quite unsurprisingly, these are pretty much in line with the local average wages that people in their twenties and thirties can earn.

Von Thünen's Law of Rent in action...

From The Telegraph:

House price growth at stations on Southern Rail's routes has ground to a halt as strikes by the RMT Union continue to make commuters' lives a misery.

New research by the online estate agency HouseSimple found that properties on the Brighton Mainline, Mainline West and East routes have fallen in value by an average of 0.4pc, losing £1,875 in value in the last three months.

This is not due to a general slump in house prices in the area during a traditional summer lull: in the south-east of England, house prices have risen on average 2.4pc between June and August, according to the Land Registry.

Von T's rings assume constant travelling speed (in the days of horses and carts) so it is only distance that matters; what actually matters is time, cost and hassle, so if a train service is less reliable, that is effectively further away from The Centre.

Right at the end there's a nice bit of Home-Owner-Ist double counting:

Alex Gosling, chief executive of HouseSimple, said: “House prices along Southern Rail routes haven’t gone into freefall just yet, but these figures do suggest that the ongoing dispute is hurting local property markets.

"It would be a real kick in the teeth if homeowners, who have had to endure the daily misery of train delays, cancellations and strike action, started to see the value of their homes falling because of the RMT and Southern Rail’s inability to reach a deal."

The amount by which rental values (and hence house prices) fall is not in addition to the grief and hassle, it is the market's estimate of the cost of the grief and hassle.

People value their own time at £10 an hour: shock

Pub Curmudgeon emailed in this article from The Daily Mail:

The cost of a home on London's commuter belt rises by £3,000 for every minute the property is closer to the city centre by train, a study has revealed.

A survey of 100,000 house sales recorded around 314 stations on the outskirts of the capital found how prices rise as addresses edge closer to the city. It concluded that for each minute less spent on the train into central London, buyers should expect to pay a further £3,048 to secure the property.

Good research (and splendid interactive map), but it just confirms Von Thünen's Law of Rent:

Let's assume two commuters per home, that's 2 people x 10 trips/week x 46 weeks/year = 920 minutes/year = 15 hours time saved/year. People value their time at about £10/hour and/or are happy to pay £10 extra to save one hour's commuting = £150 a year.

If a couple is prepared to spend an extra £150 a year on rent or mortgage repayments, that means they will be prepared to pay about £3,000 extra to save that one minute per journey.

This is what we refer to as 'location, location, location' or 'community generated land values'. A lot of it is down to simple spatial geometry.
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Which nukes the argument that people would all downsize to reduce their Land Value Tax bills. Quite clearly, if we assume that a home ninety minutes away has a zero 'near London premium', then a home sixty minutes away has a £4,500 annual premium and so on. If the tax on the ninety-minute home is £nil, people will pay £4,500 LVT to live in the sixty minute home and so on.

Let's say there are eight million homes within ninety minutes of London with an average premium of 90 x £150/2, that's a total annual premium/value of £54 billion (plus minus huge margin of error), which is twice as much as the whole of the UK pays in Council Tax.

The tax shift: a very nuanced and circular calculation.

BenJamin and I were discussing this thorny topic in the pub, i.e. if we taxed land/location values instead of earnings/profits, and ignoring the boost to the economy from losing deadweight costs, how much would flow through into higher rents, which enable more taxes to be collected from land/location and enabling taxes on earnings/profits to be reduced yet further..?

We started by writing down what we know:

1. Just about all increases in wages flow through into higher rents. We know this for a fact; London wages are about £8,000 higher than the rest of the UK and rents are also about £8,000 higher. Back in the 1980s when the North Sea oil boom took off, people in Aberdeen were proud to boast that their house prices rose to London levels. That's Ricardo's law of rent #1, which applies on a regional basis.

2. Von Thünen's law of rent, which applies on an sub-regional basis says the same. Rents are the inverse of travel costs, and the bulk of travel costs is hours wasted, and the value people place on their time is "how much money they could earn if they moved closer to where they work and worked longer hours instead of commuting". There are plenty of London-wide statistics that back this up.

3. Effects 1 to 2 are short-term/static things. If only 1 and 2 were true, then by now, 90% of GDP would go into rents and normal living standards would be no higher than at the start of the Industrial Revolution, which is clearly not true.

We also know long-term that people are prepared to spend about one-third of their income on rent (gross or net income? This is unclear). This is a crude average and more relevant is Ricardo's law of rent #2, which says that any rent = net income minus cost of a normal, basic living standard. So if wages drop to or below this level, land/location rent is zero.

4. Also, to counter-act 3, what people consider a normal, basic living standard changes over time, and tends to go up. But whatever happens, rents tend to go up slightly faster than that.

Pull 1 to 4 together, and the easiest way to reconcile these countervailing effects is :
Year 1 = income £100 = living costs £80 + £20 on rent.
Year 2, income = £102 = living costs £81 + £21 on rent…
This reaches an upper limit where income = £150 = £100 living costs + £50 on rent, and at that stage the economic/political pressure is to redistribute land wealth a bit (rent caps, social housing, mortgage caps, more construction, selling off social housing or overt redistribution via the tax system etc), so our owner-occupier with income of £150 does not worry about the rental value of £50, he can spend all £150 on living costs and this gets the average down again.

5. If you reduce taxes on earnings/profits, you get more business activity, more employment and more competition, so the unit price of goods you can buy for your net wages goes up. There are three more or less opposite conclusions to be drawn from this:

a) The cost of a normal, basic living standard goes down, so the amount going into rents goes up.

b) Currently, an average family can choose to rent a home with an extra room for £2,000 a year. That means they have to cut other spending by £2,000, so they sacrifice a new car every ten years. If the cost of a new car halves, then the opportunity cost of an extra room doubles. So rents might go down accordingly.

c) People might accept the split between spending on goods and services and on rent and simply consume correspondingly more 'other stuff' leaving spending on rent unchanged. So the basic, minimum living standard goes up in material terms but not in £-s-d.

6. As wealth rises, luxury/status/positional goods become more and more important. Location is the most pristine positional good there is. So if there is more money chasing a fixed supply of land/location, rents and prices go up. The fact that they cost more enhances their signalling power so does not dampen demand. This affects the top of the market more than the bottom, to be fair.

7. As a tie-breaker, we agreed that half the increase in net wages would flow through into higher rents i,e, higher land/location values. This is now a circular calculation:

a) For example, current land/location values are £240 bn a year, of which (say) £80 bn is collected in tax (council tax, business rates, SDLT, IHT, CGT and so on). Total taxes on earnings/profits are £400 bn (income tax, VAT, NIC, corporation tax). So we can collect £240 bn in LVT, an increase of £160 bn and reduce taxes on earnings/profits by £160 bn to £240 bn. That means net wages/profits to be spent on rents are £160 bn higher.

b) So land/location rents increase by half of that = £80 bn. We can then increase LVT by £80 bn and reduce taxes on earnings/profits by another £80 bn from £240 bn to to £160 bn.

c) That means net wages/profits are £60 bn higher and half of that £30 bn goes into higher rents etc…

d) By the time we get to iteration #8, which I did on a spreadsheet rather than boring you with it, LVT receipts would be £400 bn and taxes on earnings and profits would be a modest £80 bn, which means a flat income/corporation tax of (say) 10%.

e) Then we can factor in the loss of deadweight costs. The economy will grow considerably as taxes on earnings/profits are reduced, as a very modest and conservative estimate, by 20% over the transition period = £200 billion a year. Again, let's assume nearly half of that goes into location/land values, giving us the last £80 bn we need to get rid of even a token 10% flat income/corporation tax.

Job done, sorted.

Von Thünen's Law Of Rent, part the manieth.

From City AM:

Professionals working in London are the poorest workers in Britain, despite earning the highest average salary, according to new research from job site CV-Library.

Based on new roles advertised in the third quarter of 2015, CV-Library calculated that the average annual salary in London is £36,905, which is 16.6 per cent greater than the national average of £31,625. However, according to the job site's research, premium costs in the capital “drastically outweigh the slightly higher-than-average salaries meaning Londoners have the least disposable income in the country”.

CV-Library's data shows that employees making an average salary in London are likely to end up with minus £964 each month after paying for basic costs, which include rent for a one-bed flat near the city centre, council tax, a local monthly travel card, basic utility bills and groceries. Professionals making an average salary in Aberdeen are likely to have the most disposable income in the UK, with £1,313 left over each month after basic costs are met.

Obviously they don't run up a deficit of £964 each month, that assumes they rent a one-bed flat near the city centre, they are more likely to be a sharing a flat a bit further out so as to at least break even, but hey. I didn't realise that Aberdeen rents were so much lower, but let's just take that as a given.

"According to economics..."

James James in the comments here:

"According to economics, the burden of commuting is chosen when compensated either on the labour or on the housing market so that individuals’ utility is equalized. However, in a direct test of this strong notion of equilibrium, we find that people with longer commuting time report systematically lower subjective well-being."

There are endless studies by estate agents showing that each extra minute's walk from the nearest Tube or train station in London = £A off the rent or £B off the price of a home; that each extra minute's commute time from London overground stations = £C off the average rent or £D off the price of a home etc.

It's a bit presumptuous of these psychologists to say that all this numbers are "too low". Nearly half of people in London rent and most new arrivals rent; the rental market is very fluid so if people were really so hacked off with commute times, they can move somewhere else in six months' time. We have to assume that £A, £B etc. are roughly correct.

We can reasonably assume that if we have two same aged people with same amount of savings, who both start a new job at the same place in central London with the same pay and working hours will make that difficult trade-off between walking time, train time, ticket cost and rent. This tells us the value in £'s per hour that people place on shorter commute times.

But you can bet a pound to a penny that the psychologists haven't equivalised for all these factors.

So on the whole people with longer commute times will probably be younger people on lower pay with high rents; and those with shorter commute times will be older people with a small or no mortgage who had the luck to buy nearer the centre more than fifteen years ago. So the latter group has shorter commute times, lower effective housing costs and lower travel costs and it's hardly surprising that the former group has a systematically lower sense of well-bring.

(And we also know that plenty of people who move out of London into the Faux Bucolic Rural Idyll end up bitterly regretting it; they just can't survive out in the real world any more, just like zoo-raised animals released into the wild.)

Homey homies (2): The effect of congestion on rental values

The Stigler looked at an article on gentrification a few days ago.

Apart from illustrating that society as a whole creates rental values by imposing/accepting law and order, this bit is a good illustration of von Thünen's theory of rent:

Key to attracting companies and families is Compton's geographical location close to LAX airport, Long Beach port which is the second busiest container port in the US, and near office buildings in downtown Los Angeles.

[Mayor Mrs Aja Brown] said: "In California they're not making any more land. And with the high cost of land, from a business standpoint, being able to move your goods quickly and cheaply makes Compton an attractive place to be.

"And traffic is so horrible here in Los Angeles, and getting worse, that if you want to have a quality of life not on the freeway, you may want to live nearer where you work. I think people are getting to grips with that. I think Compton is a really attractive place for young families."

We can hold some of von Thünen's variables constant; what has changed is

a) The value of being close to the centre of activity has gone up,

b) Hence the amount of traffic has gone up,

c) So although Compton's physical distance from the centre has not changed, travel times/travel costs have changed.

Assuming that the overall attractiveness of the whole area is roughly constant (more people makes the centre more valuable but more traffic pushes rents down again), what happens is that rental values close to the centre increase disproportionately and rental values further out go down slightly.

This is true even if travel times from Compton have gone up in absolute terms; as long as travel times have gone up even more for people commuting from further afield.

(Rhetorical questions: Can any single landowner in Compton claim to have created or earned that extra value and/or can any single landowner in surrounded areas be blamed for the fact that the rental value of his land has fallen?)

Von Thünen's Theory of Rent

Although Ricardo was quite correct, he explained his Theory of Rent in such a clunky fashion (using agricultural land to illustrate the point) that it's easy for the Faux Lib's and Homeys to attack (they are attacking the explanation, not the underlying observation, but there you go, some people easily confuse the two and have no grasp of analogies).

It turns out that the far more relevant explanation is Von Thünen's, as he factors in travel/transport costs, a model which applies much better to a modern, industrial society where the qualities of the land itself are nigh irrelevant and everybody faces the same two basic constraints - local average earnings and commuting times.

(Fraggle worked this out independently for himself, see here and here).

Caveat 1: The costs of transporting actual consumer goods are relatively low in the grander scheme of things, and the price of consumer goods are pretty much the same all across the country (higher rents in town centres are because a retailer can sell more goods per unit area; not because he can sell for higher prices).

Caveat/modification 2: What really matters is commuting times, and to a lesser degree 'getting the kids to school' and 'getting to the shops' times. Travel time is not the same as distance as the crow flies. Door-to-door is what counts. Hence why sensible retail areas give over at least half their space to car parks. They can't make the land any nearer to their potential visitors, but they can easily shave ten minutes from the door-to-door travel time by having plenty of parking spaces.

Caveat 3: There are lots of other things which explain local differences, such as being near a public park; in the catchment area of a good school and/or being nearer the school; having a nice view; being near the coast - but let's put those to one side for now, that's a simple plus/minus adjustment once we've done the basic workings.
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1. The first constraint is local average wages. If you look at average rental values (in terms of actual rents or selling prices) for whole conurbations/regions, they are closely related to average (net) wages, which is blindingly obvious. If average worker can earn £1,000 a year more by moving from A to B and doing the same job, then average rents in B will be £1,000 higher.

2. Commuting costs make up a huge share of GDP, if you express them in terms of hours x notional cost/value per hour. For example, average commute time 45 minutes and people value their own leisure time at £10 per hour, (or could earn £10 an hour by doing overtime, or they value their leisure time at £8 and commuting costs £2/hour etc), for one person the "cost" is 7.5 hrs/week x 48 weeks/year x £10 = £3,600. There are 30 million workers in the UK, 30 million x £3,600 = £108 billion a year, approaching ten per cent of GDP. Or, people spend one-fifth as much again commuting as working, in which case commuting is a hidden cost of one-fifth of of GDP.

3. So if everybody in the whole conurbation/region was on exactly the same wage, the gradient between the centre and somewhere half an hour (twenty miles?) further out would be £4,800 per hour, capitalised at 4% = £120,000 on the price of an identical sized home/garden. The rental gradient is £80/minute (being £4,800/hour divided by 60 minutes). The price gradient is that amount capitalised at (say) 4% = £2,000/minute.

But... Caveat 4: This assumes that all homes are of the same size.

Clearly this is not true; in the same way as people as people prefer short commute times to long commute times, they also prefer more space to less space. So the price gradient for "an average home" is much flatter. By and large, in a larger town or city, the price of a flat in the centre = the price of a terraced house in the inner suburbs = the price of a semi-detached house in the outer suburbs.

4. So build densities vary. If all homes cost the same but there are 50 flats per acre in the centre and 10 semi-detached houses per acre in the outer suburbs, then the rental value of one acre of the centre is worth five times as much as the rental value of one acre of outer-suburb.

And... Caveat 5: Not everybody earns the same, and each earner has his or her own price gradient. The larger the conurbation, the higher the average salary and the higher the difference between the highest and lowest earners. So in a very large conurbation/city state, the gradient is £80/minute for median earners, £160/minute for higher earners and £500/minute for top earners.

6. So there are three gradients (in fact there are infinite, but this is getting complicated enough), at the centre, the top earners create a gradient of £500/minute and price out the higher earners; the next concentric circle is the higher earners who create a gradient of £160/minute and price out the median earners; once the top earners and higher earners have their homes, the median earners make do with the rest with a price gradient of £80/minute.

7. Or you can start from the margin. Home rental values at the margin are zero, they and climb by £80/minute for a good long while (lots of median earners), then the price curve steepens to £160/minute for a shorter distance (fewer higher earners); then climb by £500/minute at the very centre.

8. Land values per acre are just one measure or all this. You can also look at population density or build density and it is always exactly the same gradient. Look at a long range photo of any major city and the skyscrapers are always in a cluster in the middle; then it's office blocks and blocks of flats, then terraced houses, then semi-detached houses, then industrial estates and then suddenly it's countryside.