Tuesday 9 December 2014

Me and you and the Duke of Buccleuch

Drumlanrig Castle

I've written before about an exponential land tax. Rather often in fact... Here I want to give a clear account of how it would work, with a computer program (in Clojure) so that you can fiddle with it yourself. Thanks to the magic of Gorilla Repl, it's up on the web here for you to play with.

So, the core of the idea is that you pay a small amount on your first hectare of land, a little bit more on your next hectare, a little bit more on your next, and so on. There are two key numbers in this idea: the constant, which is the amount of money you pay on the first hectare, and the exponent, which is the power the number of hectares we've counted so far is raised to to calculate the little bit more. So what you pay in tax is Σ1..n(cn)e, where n is the number of hectares you own.

Expressed as a clojure function, that's:

(defn summed-exponential-series 
  "Sum an exponential series from 1 to limit.
   `constant`: the constant by which integers in the range are multiplied;
   `exponent`: the exponent to which they are raised;
   `limit`: the limit of the range to be summed."
  [constant exponent limit]
  (reduce + (map #(math/expt (* constant %) exponent) (range limit))))

We now need to create a table of sizes of interesting land-holdings as Clojure code (areas in hectares):

(def holding-sizes
  [["Average croft" 5]
   ["Average farm" 101]
   ["Glasgow Airport" 300]
   ["Edinburgh Airport" 400]
   ["Grangemouth Refinery" 700]
   ["Countess of Sutherland" 33000]
   ["Earl of Seafield" 40000]
   ["Captain Alwynn Farquharson" 51800]
   ["Duke of Westminster" 54000]
   ["Duke of Atholl" 58700]
   ["Duke of Buccleuch" 109000]])

and finally a little function to map the first function over the table:

(defn sample-taxes
  "Prints sample taxable amounts for a table of holdings."
  [constant exponent holdings]
  (map #(print (format "\n%s: £ %,.2f" 
                (first %) 
                (summed-exponential-series constant exponent (second %))))

We can now ask, given a constant and an exponent, how much tax each of these holdings would pay.

For example, if we start with a modest £1 of tax on the first hectare, and set an exponent of only 1.05, we get this pattern:

Average croft:£ 10.53
Average farm:£ 6,204.08
Glasgow Airport:£ 58,191.38
Edinburgh Airport:£ 105,040.07
Grangemouth Refinery:£ 331,177.47
Countess of Sutherland:£ 893,688,616.49
Earl of Seafield:£ 1,325,738,877.59
Captain Alwynn Farquharson:£ 2,252,234,219.56
Duke of Westminster:£ 2,452,703,794.50
Duke of Atholl:£ 2,910,359,665.77
Duke of Buccleuch:£ 10,350,620,262.71

So ordinary people would pay trivial amounts; farmers would pay a bit more than I really want them to; the airports and the refinery, amounts which are perfectly affordable to them... and the aristocracy would have either to abandon most of their lands or be bankrupted utterly (yes, that is ten billion pounds the Duke of Buccleuch would owe, each year).

The point of offering you this as code that you can fiddle with is that by changing the constant and the exponent you can change the pattern of charges. The curve isn't quite right here; I feel that the levy on farmers is relatively speaking too high, on the refinery perhaps a little low. Tweaking the constant down and the exponent up changes the picture.

Obviously, an exponential land tax would not generate very much revenue, since most people wouldn't pay very much at all and most of the few who would be assessed for large amounts would have to abandon their land immediately. But the point is not to generate revenue, the point is to redistribute land; and it would do that exceedingly effectively.


moglet73 said...

Great idea, this also gives a real sense of scale re the quantities of land we are considering - often too much of an abstract concept to grasp. Would love to see this as a table for the 500 people who own half of Scotland (or whatever the figure is).

Simon Brooke said...
This comment has been removed by the author.
Simon Brooke said...

Sorry, missed your comment as you posted it. The figures I'm working with - which are about eight years out of date - are as follows (all numbers in hectares)

"Average croft" 5

"Average farm" 101

"Glasgow Airport" 300

"Edinburgh Airport" 400

"Grangemouth Refinery" 700

"Thousand hectares" 1000

"Ten thousand hectares" 10000

"Countess of Sutherland" 33000

"Earl of Seafield" 40000

"Captain Alwynn Farquharson" 51800

"Duke of Westminster" 54000

"Duke of Atholl" 58700

"Duke of Buccleuch" 109000

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