At noon today, the Prime Minister will set-out the government’s strategy for Brexit. Mrs May will no doubt repeat that Brexit means Brexit. But the important question is what will be the UK’s future economic arrangement with the EU? The Prime Minister will try and keep her options open, but the trade-offs involved seem to make a ‘Hard Brexit’ inevitable.

One way to understand the government’s apparent confusion is to see that something valuable must be given-up. Even the wishes of everyone who voted for Brexit cannot be satisfied. A popular way to characterise these policy trade-offs is in terms of an ‘impossible trio’. The origin of these models is Keynes’s uncovered interest parity theorem, but these days they are applied in many different contexts. The idea is that a government can choose two but not all three desirable governance arrangements. Choosing all three is inconsistent.

A decade ago Dani Rodrik proposed a Political Trilemma to describe the international economic system and he has since discussed the EU and Brexit in these terms. I have translated this into a simple diagram (see below) to show the Prime Minister’s policy options on the sides of the triangle. The three desirable governance arrangements are membership to the Single Market, the world’s largest economic market, national sovereignty and the exercise of democratic control. Of course, the Prime Minister would like to find a way of having all three, but in the limit this is impossible.

Being a member of the EU and therefore the Single Market requires sharing some sovereignty. Laws are made by the Council of Ministers in Brussels and the European Parliament in Strasbourg. If there is a conflict between EU law and UK law, then EU law prevails. And all Member States must accept that the EU has exclusive power over some areas of law. In particular the power to negotiate trade agreements and to agree a Common Commercial Policy are both necessary for the EU’s Customs Union. The advantage of sharing some sovereignty is being a member of the largest Single Market in the world.

The sides of the triangle describe the policy options facing the Prime Minister. Membership of the Single Market and democratic politics are entirely consistent if one is prepared to accede significant amounts of national sovereignty and accept the authority of the European institutions. Reasonable people can disagree about how much power ought to be shared and how much reserved for national parliaments – where the compromise should be. But an effective Single Market requires a single rulebook and a single court to enforce the rules. The UK electorate rejected this option in June last year.

An alternative is to become an ‘associate’ member of the Single Market by re-joining the European Economic Area, like Norway and Lichtenstein. But the UK would have to settle for a consultative role in shaping Single Market rules and regulations. It is very difficult to see how this is compatible with exercising democratic politics. We would have to accept laws yet have no formal role in deciding them. A milder version may be to reach a new Customs Union agreement with the EU, but it is difficult to see how handing back trade negotiations is consistent with ‘taking back control’. For either option is it difficult to see how this would be acceptable for the fifth largest economic power in the world.

This leaves only the third option. Giving up our membership to the Single Market. Of course the Prime Minister will no doubt emphasise that the UK will seek fullest possible access to the Single Market. The key will be how much access can be negotiated. Or in other words, what is the shadow price for transferring legal powers back to the UK government. For some it will be a price worth paying, and for others the price will be too high. But anyone who claimed we could transfer all legal powers back and also stay in the Single Market was selling snake oil.