“If the UK votes to leave the EU, rather than sending £300 million a week to Brussels, we can spend that money on our own priorities including healthcare,” the GO campaign said at the weekend.

This is so wildly untrue as to be a blatant lie. And if it is even half-true, it reveals an awful fact out-ers are hiding – there ain’t no advantageous trade deal post-Brexit.

The House of Commons Library research service (a good source for unbiased facts) published in January an excellent Brexit briefing paper. Here’s the facts on Britain’s EU membership subs.

First, the gross contribution ranges from a forecasted £19.6 billion in 2016 to £20.3 billion in 2020. This is the source of the £20 billion Nigel Farage regularly cites or the £400 million per week (actually £384 million) sometimes quoted. But this misses out Britain’s rebate, famously negotiated by Margaret Thatcher.

The rebate is estimated to be between £4.3 billion in 2016 and £5.5 billion in 2020, bringing down the actual contribution for those years to between £15.3 billion and £14.8 billion, or, on average about £288 million a week, the figure GO was presumably rounding.

But there are also the EU payments we receive – farming subsidies, regional structural aid, etc – totalling between £4.2 billion and £5.1 billion annually and reducing the annual net contribution to between £11.1 billion in 2016 and £9.8 billion in 2020.

This yields the rounded figure of £10 billion per annum fairly cited by Bill in his Scotbuzz article last week, and less than two-thirds of the sum quoted by GO.

But it is most unlikely this figure would be available to spend on the NHS or any of the other things out-ers have spent it on ten times over.

The reason is that the countries which have the closest trade deals with the EU – Norway and Switzerland – have to make contributions to the EU, not into its central budget but to various programmes, for example, the fund set up to improve the economies of recent EU entrants such as Romania and Bulgaria and the Erasmus student exchange programme. Otherwise, the two countries would just be free-riding on the EU’s economic benefits.

Since Norway, as part of the European Economic Area, and Switzerland, the sole remaining member of the slightly more removed European Free Trade Area, have trade deals with the EU which are argued by some out-ers as models which a Britain outside the EU could emulate, what they pay the EU should also be taken into account.

Another Commons Library paper, published in 2013, worked out that on a per capita comparison, Norwegians paid in 2011 about 83 per cent of what the British pay, and the Swiss about 40 per cent.

So it is reasonable to think that a Norwegian-style trade deal would save only £1.7 billion, and a Swiss-style arrangement about £6 billion, from Britain’s EU contributions. And on the debit side, British exporters to the EU would have the costs of trade tariffs (for example, 9.8 per cent on motor vehicles) that Norway and Switzerland bear and would still have to comply with EU regulations.

Depending on badly such tariffs affected the economy, the consequent loss of tax revenues could well be more than any savings from EU contributions. The only way to get the full £10 billion back would be to have a Canada-type free trade deal (which still has tariffs and quotas) which might be negotiated quite quickly, but only if Britain keeps what the out-ers most want rid of – all the existing EU regulation and free movement of labour.

In this modern world, there ain’t no such thing as a free lunch.

Peter Jones is a freelance journalist based in Scotland, working primarily for The Economist and The Times, specialising in business, economics and politics.

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