That Social Housing Myth

Tim W, in The Register on below-market rents in social housing:

Taking rent foregone as just as much a subsidy as cash paid out, my back-of-the-fag-packet numbers are that housing subsidies cost £40 to £60 bn a year (£20-£40 bn in lost rents, a wide range as no one actually publishes the figure that I can find, plus £20 bn HB).

Nope.

1) Firstly, there are published figures for this, see e.g. Professor John Hills, pages 8 and 9 of his summary from 2007:

One estimate of the “economic subsidy” to social housing (the difference between actual rents and those giving an economic return) was that it had reached £6.6 billion across in England as a whole in 2004, slightly higher in real terms than in 1996. Three-fifths of this total went to social tenants in London, the South East and South West. In Northern regions and the Midlands, actual social rents were £10-20 per week below those that would give a comparable return on housing capital values to those in the private sector, but in the East and South East the difference was £40-50, and in London about £70-80.

2) It all depends on what you consider 'the market rent' to be. In very round figures, there are 20 million privately 'owned' homes in the UK, with rents from £100 per week all the way up to £1,000s per week for a couple of million homes in really desirable areas, let's say the average is £300, which is rather more than the median of maybe £150 - £200 per week:
3) Then there are 5 million units of social housing, with average official rents of (say) £50 per week. There are some estates where everybody is unemployed, so the £50 is a 'made up figure', none of the tenants actually pay that, the DWP just remit that amount to the local council who passes it back to the social housing fund. And there's a lot of social housing that could be let out for far more than £50 a week (or is illegally sub-let for for far more than that, depending on the area):
4) In order to arrive at an implied subsidy or discount to market rent of £40 billion a year, you'd have to assume that these could all be let out for £210 per week each (£40 billion divided by 5 million units divided by 50 weeks = £160, plus official rent of £50). Even taking Tim W's lower figure of £20 billion means that these could all be let out for £130 per week, i.e. rather more than the weekly rents of £100 for 'not so nice houses'.

5) Remember that land 'ownership' is a series of local monopolies or a cartel. The prices (rental values) of housing have little or nothing do with the owner's input costs (remembering that interest on loans is not an input cost, it is a cost of ownership), the prices are set entirely by what people are willing and able to pay - it is largely because there are practical or political restrictions on the amount of housing that is available that landlords can make super-profits in most areas.

6) So what would happen if the state scrapped Housing Benefit entirely (the bulk of which is a transfer between government departments, and not a cost to the taxpayer as such) and sold off all available social housing? There is a fixed number of people in the UK, with a fixed amount of money to spend and a fixed amount of housing. So while it is quite true that there are some council flats in Westminster which could be let out for at least £500 per week, this is largely because of the scarcity of flats that are available for working people to rent.

7) If all existing social tenants were booted out and all ex-social housing were let at 'market rates' (i.e. 'as much as the new landlord can get'), the chances are that market rents for those Westminster flats would fall below £500 per week (to £450? to £400?), and the market rents for London flats that had always been privately 'owned' would fall as well (because there'd be far more flats for working people to choose from). And on the council estates where everybody is unemployed, the rents would be +/- nothing, call it £10 or £20 a week, because that is all that people on the dole can afford to pay.

8) To summarise, there's a grey shaded triangle for 'rent foregone' and a white triangle for 'inflated rents'. By and large, the two triangles are the same size, so (bearing in mind that the whole curve would shift down slightly if Housing Benefit were scrapped and all social housing sold off) the overall subsidy of [Grey triangle] - [white triangle] probably nets off to very little indeed, probably far less than Professor John Hills' estimate of £6.6 billion a year.
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9) As a final thought, it seems a tad unfair to me to mention the implied subsidy to the half of social tenants who genuinely do pay below market rents without mentioning the implied subsidy to private land 'ownership' in the UK, which must be in the region of £125 billion a year*, plus/minus a huge margin of error, i.e. [20 million homes] x [market rents £200 per week minus actual cost of production, i.e. bricks and mortar, repairs etc of £75 per week]:
* About a third of this is collected by the banks as mortgage interest, but glossing over that, this means that even if Land Value Tax were introduced as an additional tax rather than a replacement tax (which I do not and have not ever proposed - most existing taxes are very bad taxes indeed and ought to be scrapped anyway), annual revenues would be in the order of £125 billion, plus/minus a huge margin of error.