Sunday, 7 December 2014

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.
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.


Lola said...

This commute time opportunity cost thingy is exactly why I decided to develop my business in Suffolk where I can commute to work in 15 minutes.

L fairfax said...

On the question of commuting. Why do you think people do uneconomic commutes? E.g. Brighton to London (some suburbs of London are cheaper than Brighton).

Mark Wadsworth said...

L, that's all fine, but you also restrict your customer base.

LF, your guess is as good as mine. People like that baffle me, but it's a free world.

Lola said...


Well, yes - ish. I can also access London in accordance with VT formula since I can maximise 'P' to London rates less a bit. And I can select when I journey to London. What VT didn't have was IT and telephony etc. This enables me to locate somewhere with low rents but access business in an area with high rents, in the sense I don't go there until I have worked out that it will be profitable.

Going back to the formula I had observed this in the structure of Suffolk market towns which are each about 12 miles apart. This being precipitated by the distance it is feasible to drive stock to market in a day and get back, which is about 6 miles each way.

I wonder whether being able to work on the train (IT again) slightly modifies his formula?

Lola said...

LF / MW. Their spouses tell them that's where they are going to live?

Bayard said...

They want to be beside a bit of the sea that isn't the Thames estuary?

Lola said...

B. Or they are getting ready for 'retirement'?

Derek said...

Good stuff. And on a related topic, here's another article, which also points to falling transport costs as the reason that house prices didn't start rising until the late 20th century. Doesn't mention von Thünen but it probably should have.

Logan Boettcher said...

I saw that article also Derek. The title to their conclusion was bleakly hilarious: "Ricardo might have been right."

Well, you don't say. It took this long for a self-evident, prescriptive and immutable LAW of economics (the Law of Rent) to be declared maybe right.

In other news, 2+2=4 might also be right.

Mark Wadsworth said...

D, LB, that is another possible explanation - transport costs are no longer falling.

But I don't think that the cash cost of travelling is that important - what is more important is TIME, and as transport is not getting quicker (more traffic jams etc), the effective cost of travel is going up.

Lola said...

MW Agreed about 'time'. The electrification of the Norwich / London line saw an increase in commuting from stops further away form London - plus an increase in house prices...