Stock markets around the world are sending a message to Donald Trump: end your trade war with China or face the nightmare scenario of running for a second term in the White House with the economy in serious trouble.

The big falls seen on the world’s major bourses this week are the result of one thing: the growing fear of the impact of the standoff between Washington and Beijing on trade, industrial production and business confidence.

Trump seriously miscalculated if he thought Xi Jinping would quickly cave in to US pressure. On the contrary, Beijing’s hint that it will restrict exports of the rare-earth metals used in advanced electronics suggests it is digging in for a long battle.

US-China trade: what are rare-earth metals, and what's the dispute? Read more

The trigger point for the stock market jitters has been the inversion of the yield curve. Normally, the yield or interest rate on a bond that matures in a few months is lower than that on one that matures in 10 years because the longer the investment the greater the risk of rising inflation.

When the curve is inverted, yields on shorter-dated bonds are higher than those on longer-dated bonds. This is a pretty rare occurrence and only tends to happen when a recession is looming. It has not been lost on investors that an inverted yield curve provided a warning when things were about to go pear-shaped in 2007.

Trump is in a bit of a spot. The boost from last year’s tax cuts is starting to fade at a time when the lagged effects of last year’s increases in interest rates are beginning to be felt. Add to that a protracted trade war and it is easy to envisage a scenario in which the US economy slows fast.

To head off the prospect of fighting for re-election during a recession, Trump needs the Federal Reserve to cut interest rates and he needs to make his peace with China – both sharpish. For the past few months the target for the president’s tweets has tended to be China rather than the Fed’s chairman, Jerome Powell. Expect that pattern to soon be reversed.

Report shows how wrong minimum-wage critics have been

It’s hard to recall these days but there was quite a kerfuffle when Labour first introduced a national minimum wage in 1999. The idea was opposed by the right on the grounds that interfering with the workings of the labour market would cost jobs.

Yet here we are two decades on and it is the stated ambition of Britain’s Conservative chancellor, Philip Hammond, to raise the minimum wage to two-thirds of average earnings. That would eliminate low pay using the definition applied by the Organisation for Economic Cooperation and Development.

A new report from the Resolution Foundation shows just how wrong the critics of the minimum wage have been. Recent above-inflation increases in the minimum wage have left the UK with its smallest proportion of low-paid workers since 1980 but the employment rate is at its highest level since modern records began. What’s more, jobs growth has tended to be strongest among groups – such as those with fewer qualifications – who tend to be on the minimum wage.

The reason is simple. When people on poverty wages get a pay rise they spend every extra pound they get. That boosts demand and leads to more jobs being created.

Can Trainline live up to its pre-float valuation?

It may be a fraction of the pre-float valuation of Uber, but the £1.5bn figure mooted for ticketing app Trainline, which on Wednesday confirmed its intention for a London IPO, has sent some eyebrows even higher. The business has grown from a website purely selling UK rail tickets since the £500m takeover by US private equity investors KKR in 2015: buying up a European competitor, and spreading to theoretically cover 45 countries and coach travel too, via an ever-whizzier app.

But the bulk of its £3.2bn annual ticket sales come in Britain, where passengers are bamboozled by a combination of archaic fare rules, advance bargains and punitive peak prices, and take some risk in simply walking up to buy a ticket. Even so, profits, when posted, have been meagre. And passengers savvy enough to book ahead might prefer competing sites without Trainline’s booking fees.

On the upside, Trainline argues that revenues can only grow: more than 60% of train tickets are still bought offline, and rail should pick up more guilty air travellers as environmental apocalypse creeps nearer. Meanwhile, given the struggles of rail franchise operators Stagecoach and First Group, the political clamour to boot out Arriva from Northern Rail, and the potential threat of Labour renationalisation, investors might well prefer to pin their money on firms simply selling tickets rather than trying to run trains.