Tobacco duty and The Laffer Curve

There was an interesting debate in the comments at VGIF. Here's my adaptation of Pub Curmudgeon's theory on how countries set their tobacco duty rates...

It is clearly impossible for every country to set the duty rate a little bit higher than their neighbours, neither is it possible for every country to set it lower than their neighbours.

Assuming equal size countries, the rate would be the same everywhere (with a lower upper limit for booze than for tobacco). We can then introduce your perfectly valid observation about the ideal rate being lower in small countries and higher in large countries and we lead to some sort of equilibrium.

My caveat would be that it's not 'size of country' that matters as much as 'how easy it is for your citizen's to go abroad' i.e. UK and France are similar size/population, but we Brits are stuck with buying in the UK, the French can go to E, CH, D or Benelux quite easily.
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So let's see whether this stacks up in real life...

The price of a packet of twenty in various European countries is relatively easy to find, e.g. here, plus two missing ones from here. Populations are easy to find e.g. here.

The resulting scatter graph looks like this:The generalisation that big country = high tobacco duty clearly holds for the seven largest countries. In order from left to right these are Romania, Poland, Spain, Italy, UK, France, and Germany, the coefficient of correlation between population and price per packet is quite high at 0.76 (see footnote).

But for the smaller countries with populations under 20 million, there is no correlation whatsoever, and the coefficient of correlation for the whole data set is only 0.13, practically meaningless.
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So let's strip out the 'big seven' and do another chart plotting price per packet against 'how easy it is for a country's citizens to pop over the border to buy cheaper elsewhere' for the remaining countries. The simplest way of measuring 'how easy it is [etc]' is to count the number of land borders a country has with other countries. The resulting chart looks a lot more promising - rather unsurprisingly, the most expensive cigarettes are to be found in countries which have no or only one land border(s) with another country (Iceland, Malta, Ireland, Norway).

The coefficient of correlation for this sub-set is -0.55, not staggeringly high but enough to mean something:Footnote: The 'border' effect also conveniently explains why line for the big seven diverges at the top. Germany is larger than the UK but it has land borders with nine other countries whereas the UK has none (ignoring the border between Northern Ireland and Ireland). The 'border' effect thus has a stronger impact than the size effect and cigarettes are cheaper in Germany than in the UK.
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Finally, we can put the two theories together.

Let's assume that the price per packet is EUR 9, reduced by EUR 1 for each border a country has, plus EUR 1 for every 15 million in the population of that country, and then plot price per packet against the result. The constants 9 and 15 million are arrived at by observation, trial and error* so as to end up with the highest possible coefficient of correlation, which is 0.52. The resulting chart looks like this:* For example, Germany has borders with nine other countries, so the border element of its tobacco duty is EUR 9 minus 9 x EUR 1 = EUR 0. It has a population of 82.2 million, divided by 15 million = a population element of EUR 5.48, EUR 0 + EUR 5.48 = EUR 5.48. The actual price of a packet of cigarettes = EUR 5.16.

At the other extreme, Malta has no land borders, so has a full border element of EUR 9. It has a population of 400,000, divided by 15 million = population element EUR 0.03. EUR 9 + EUR 0.03 = EUR 9.03. The actual price of a packet of cigarettes = EUR 9.

Hungary is somewhere in the middle. It has borders with 7 countries, so the border element is EUR 9 minus 7 x EUR 1 = EUR 2. It has a population of 10 million, divided by 15 million = EUR 0.67. EUR 2 + EUR 0.67 = EUR 2.67. The actual price of a packet of cigarettes = EUR 2.51.