BRUSSELS – When it comes to bilateral trade, gains and losses are distributed asymmetrically between the larger and the smaller economy. In the best of times, that would be bad news for the United Kingdom as it seeks new trade deals with the European Union and others. And these are not the best of times.

Economic theory predicts that erecting new trade barriers hurts both sides. But economic principles also suggest that the larger of the two economies is likely to lose less.

In the case of a tariff, for example, lower demand from the larger economy will tend to push down the prices of the goods that it imports. The smaller economy is unlikely to have enough of an impact on overall demand for the goods it imports, and thus on their prices.

The advantage of the larger economy is even greater when it comes to non-tariff barriers, which often result from differences in regulations and standards among trading countries. In most cases, the smaller country must simply accept the larger one’s rules.

Given this, Brexiteers are wrong to claim that the UK, as a net importer, will be in a strong position in trade negotiations with the EU. What counts is relative size, not net trade flows.

Multiple studies confirm this, concluding that the UK will bear the lion’s share of the costs of Brexit. If the UK and the EU agree to a new trade relationship based on World Trade Organization (WTO) rules, the studies predict, the UK will lose about €110 billion ($119 billion), whereas the EU will lose only about €50 billion. Given that the EU’s economy is about five times larger than that of the UK, this implies that the loss for the UK, as a share of GDP, would be about ten times larger.

If no deal is reached, the same imbalance will emerge, only the costs to the UK will be even larger – a reality that British Prime Minister Theresa May, declaring that the UK will walk away from negotiations that don’t go its way, refuses to recognize. Notwithstanding political rhetoric, a "bad deal” is actually better for the UK than no deal at all.

But the talks with the EU are only the beginning. The UK will also have to negotiate trade deals with other partners, including the world’s two largest economies: the United States and China.

At first glance, the negotiations with the US may seem like nothing to worry about. After all, President Donald Trump has indicated that the UK would be "first in line” for a US trade deal. Moreover, he has praised Brexit, even encouraging other EU member states to follow the UK out of the bloc.

But Trump has also pledged to put "America first” in all deals it makes and actions it takes, particularly regarding trade. This raises doubts about whether Trump will be willing to open US markets in the few areas where the UK can still compete, like the aerospace and automotive industries. Even if he does, he is not likely to do it for free. At the very least, the UK will have to adhere to US standards and regulations.

May knows that, to get a decent deal out of Trump, she has to play his game. So when Trump signed an executive order to bar anyone from seven Muslim-majority countries from entering the US for 90 days, and to close the door to refugees from Syria indefinitely, she avoided any strong statements. By contrast, her EU counterparts, confident in the size and strength of the EU as a trading bloc, were uninhibited in condemning the move.

This highlights a challenge that the Brexiteers did not anticipate. They expected Brexit to occur against the backdrop of the rules-based multilateral trading system. With global trading frameworks like the WTO in place, it seemed that even the worst-case scenario for Britain wasn’t all that bad, and, therefore, that the consequences of leaving the EU would be minor.

But the world has changed considerably since then. Trump’s rise to power was fueled by promises to throw off the fetters of the WTO – indeed, of all international organizations – and to take unilateral decisions based on America’s own interests. Even trade negotiations with the EU seem too multilateral to some of Trump’s cohorts, because they involve 27 member countries.

Without the US on board, the rules-based international system would be far less secure – not least because others might soon follow Trump’s example, choosing bilateral deal making over multilateral cooperation. As the world trading system became less open, everyone would lose, but not equally. The US, China, and the EU (provided it survives) would do far better than smaller economies, like the UK.

It remains to be seen whether the US, with its economic might, can afford Trump’s protectionist approach. But it seems clear that the UK will incur some heavy costs during the Brexit process. If more countries follow Trump’s lead, and the rules-based global system continues to deteriorate, those costs will only grow.

Daniel Gros is Director of the Center for European Policy Studies.